Η Κβαντική θεωρία είναι ανοικτή σε διαφορετικές ερμηνείες και η παρακάτω εργασία επανεξετάζει κάποια απ’ τα σημεία τριβής. Η συνηθισμένη ερμηνεία της κβαντικής φυσικής δέχεται ότι, ο κβαντικός κόσμος χαρακτηρίζεται από απόλυτη αιτιοκρατία και ότι τα κβαντικά συστήματα υπάρχουν αντικειμενικά μόνο όταν μετρούνται ή παρατηρούνται. Η οντολογική ερμηνεία της κβαντικής θεωρίας του David Bohm, απορρίπτει και τις δύο αυτές υποθέσεις.
Η κβαντική θεωρία θεωρείται γενικά σαν μια απ’ τις πιο επιτυχημένες επιστημονικές θεωρίες που διατυπώθηκαν ποτέ. Αλλά ενώ η μαθηματική περιγραφή του κβαντικού κόσμου επιτρέπει, οι πιθανότητες των πειραματικών αποτελεσμάτων να είναι υπολογίσιμες με υψηλό βαθμό ακρίβειας, δεν υπάρχει ομοφωνία στο τι σημαίνει σε εννοιολογικούς όρους.
Η θεωρία του Bohm ότι τα κβαντικά συμβάντα καθορίζονται εν μέρει από ανεπαίσθητες δυνάμεις, που λειτουργούν σε βαθύτερα επίπεδα της πραγματικότητας, συνδέεται στενά με τη θεωρία του νομπελίστα νευροφυσιολόγου John Eccle ότι, οι διάνοιές μας υπάρχουν έξω από τον υλικό κόσμο και αλληλεπιδρούν με άλλες διάνοιες στο κβαντικό επίπεδο. Τα παραφυσικά φαινόμενα υποδεικνύουν ότι οι διάνοιές μας επικοινωνούν με άλλες και επηρεάζουν μακρινά φυσικά συστήματα με ασυνήθιστους τρόπους. Είτε τέτοια φαινόμενα μπορούν να εξηγηθούν ικανοποιητικά με όρους μη-τοπικότητας και κβαντωμένου κενού είτε περιλαμβάνουν υπερφυσικές δυνάμεις και καταστάσεις της ύλης άγνωστες ακόμα στους επιστήμονες, αποτελεί ακόμα μια ανοικτή ερώτηση η οποία αξίζει επιπλέον πειραματικής μελέτης.
Κβαντική αβεβαιότητα
Σύμφωνα με την αρχή της αβεβαιότητας, η θέση και η ορμή ενός υποατομικού σωματιδίου, δεν μπορούν να υπολογισθούν ταυτόχρονα, με ακρίβεια μεγαλύτερη απ’ αυτή που ορίζει η σταθερά του Plank. Κι αυτό επειδή, σε κάθε μέτρηση, ένα σωματίδιο πρέπει να αλληλεπιδράσει με ένα τουλάχιστον φωτόνιο ή κβάντα ενέργειας, το οποίο δρα και σαν σωματίδιο και σαν κύμα και το επηρεάζει με απρόβλεπτο και ανεξέλεγκτο τρόπο. Μια ακριβή μέτρηση της θέσης ενός ηλεκτρονίου σε τροχιά, μέσω μικροσκοπίου για παράδειγμα, απαιτεί τη χρήση μικρού μήκους κύματος φωτός, με αποτέλεσμα να μεταφέρεται στο ηλεκτρόνιο μια μεγάλη αλλά απρόβλεπτη ορμή. Απ’ την άλλη μεριά, μια ακριβή μέτρηση της ορμής του ηλεκτρονίου, απαιτεί κβάντα φωτός πολύ χαμηλής ορμής (και γι’ αυτό μεγάλου μήκους κύματος), κάτι που οδηγεί σε μεγάλη γωνία περίθλασης στο φακό και κακό προσδιορισμό της θέσης.
Αλλά, σύμφωνα με τη συνηθισμένη ερμηνεία της κβαντικής φυσικής, όχι μόνο μας είναι αδύνατο να υπολογίσουμε ταυτόχρονα τη θέση και την ορμή ενός σωματιδίου με ίδια ακρίβεια, αλλά και ένα σωματίδιο δεν έχει καλά καθορισμένες ιδιότητες όταν δεν αλληλεπιδρά με ένα όργανο μέτρησης. Γι’ αυτό, η αρχή της αβεβαιότητας συνεπάγεται ότι, ένα σωματίδιο δεν μπορεί ποτέ να βρίσκεται σε ακινησία, αλλά υπόκειται σε σταθερές ταλαντώσεις ακόμα κι όταν δεν διεξάγεται κάποια μέτρηση και αυτές οι ταλαντώσεις υποτίθεται ότι δεν έχουν καθόλου αιτία. Με άλλα λόγια, ο κβαντικός κόσμος πιστεύεται ότι χαρακτηρίζεται από πλήρη έλλειψη αιτιοκρατίας, εγγενή ασάφεια και αμείωτη ανομία. Όπως το θέτει ο σύγχρονος φυσικός David Bohm (1984): "υποτίθεται ότι σε κάθε πείραμα, το ακριβές αποτέλεσμα που θα επιτευχθεί, είναι εντελώς αυθαίρετο, με την έννοια ότι δεν έχει σχέση με ο,τιδήποτε άλλο που υπάρχει ή που έχει υπάρξει στον κόσμο."
Ο Bohm θεωρεί ότι, η εγκατάλειψη της αιτιότητας υπήρξε πολύ βιαστική: "είναι αρκετά πιθανό, ενώ η κβαντική θεωρία και μαζί της και η αρχή της απροσδιοριστίας είναι έγκυρες με πολύ βαθμό προσέγγισης σε ένα συγκεκριμένο πεδίο παύουν και οι δύο να είναι έχουν αξία σε νέα πεδία κάτω απ’ αυτό το οποίο η σύγχρονη θεωρία είναι εφαρμόσιμη. Έτσι, το συμπέρασμα ότι δεν υπάρχει βαθύτερο επίπεδο αιτιατά καθορισμένης κίνησης, είναι απλά κυκλική αιτιολόγηση, αφού θα προκύψει μόνο αν υποθέσουμε προκαταβολικά ότι δεν υπάρχει τέτοιο επίπεδο." Παρ’ όλα αυτά, οι περισσότεροι φυσικοί αρκούνται να δεχθούν την υπόθεση του απόλυτα τυχαίου. Θα επιστρέψουμε σ’ αυτό το θέμα αργότερα, σε συνδυασμό με την ελεύθερη βούληση.
Συρρικνώνοντας την κυματοσυνάρτηση
Ένα κβαντικό σύστημα αναπαριστάται μαθηματικά με μια κυματοσυνάρτηση, που προκύπτει απ’ την εξίσωση Schrodinger. Η κυματοσυνάρτηση μπορεί να χρησιμοποιηθεί για να υπολογίσουμε την πιθανότητα να βρεθεί ένα σωματίδιο σε κάποιο σημείο του χώρου. Όταν πραγματοποιείται μια μέτρηση, το σωματίδιο βρίσκεται φυσικά σε μία μόνο θέση, αλλά αν η κυματοσυνάρτηση υποτίθεται ότι παρέχει μια πλήρη και επακριβή περιγραφή της κατάστασης του κβαντικού συστήματος – όπως είναι στην συνηθισμένη ερμηνεία – αυτό θα σήμαινε ότι μεταξύ των μετρήσεων το σωματίδιο διαλύεται σε μια "επαλληλία κυμάτων πιθανοτήτων" και είναι δυναμικά παρόν σε πολλά διαφορετικά μέρη ταυτόχρονα. Τότε, όταν πραγματοποιείται η επόμενη μέτρηση, αυτό το πακέτο κυμάτων υποτίθεται ότι "διαλύεται" ακαριαία, με κάποιο τυχαίο και μυστηριώδη τρόπο, ξανά σε ένα σωματίδιο σε ορισμένο χώρο. Αυτή η ξαφνική και συνεχή "διάλυση" παραβιάζει την εξίσωση Schrodinger και δεν επεξηγείται περαιτέρω στην συνηθισμένη ερμηνεία.
Αφού η συσκευή μέτρησης που υποτίθεται ότι κάνει την κυματοσυνάρτηση ενός σωματιδίου να καταρρεύσει, είναι φτιαγμένη από υποατομικά σωματίδια, φαίνεται ότι η δική της κυματοσυνάρτηση θα έπρεπε να καταρρέει από άλλη συσκευή μέτρησης (η οποία θα μπορούσε να είναι το μάτι και το μυαλό ενός ανθρώπινου παρατηρητή), η οποία με τη σειρά της χρειάζεται να καταρρεύσει από μία ακόμα συσκευή μέτρησης κ.ο.κ., οδηγώντας σε μια άπειρη διαδρομή προς τα πίσω. Στην πραγματικότητα, η κοινώς αποδεκτή ερμηνεία της κβαντικής θεωρίας συνεπάγεται ότι όλα τα μακροσκοπικά αντικείμενα που βλέπουμε γύρω μας υπάρχουν σε μια αντικειμενική, ευκρινή κατάσταση μόνο όταν μετριούνται ή παρατηρούνται. Ο Schrodinger επινόησε μια διάσημη ιδέα-πείραμα για να επιδείξει παράλογες συνέπειες αυτής της ερμηνείας. Μια γάτα τοποθετείται σ’ ένα κουτί που περιέχει μια ραδιενεργή ουσία, έτσι ώστε να υπάρχει πιθανότητα 50-50 ένα άτομο να διασπασθεί σε μία ώρα. Αν ένα άτομο διασπασθεί, προκαλεί την απελευθέρωση ενός δηλητηριώδους αερίου, που σκοτώνει τη γάτα. Μετά από μια ώρα η γάτα υποτίθεται ότι είναι ταυτόχρονα νεκρή και ζωντανή (και καθετί ανάμεσα στα δύο), μέχρι κάποιος να ανοίξει το κουτί και ακαριαία να προκαλέσει την κατάρρευση της κυματοσυνάρτησης του, σε μια νεκρή ή ζωντανή γάτα.
Ποικίλες λύσεις έχουν προταθεί για το "πρόβλημα μέτρησης" που σχετίζεται με την κατάρρευση της κυματοσυνάρτησης. Κάποιοι φυσικοί υποστηρίζουν ότι ο κλασικός κόσμος ή μακρόκοσμος δεν πάσχει από την κβαντική ασάφεια, επειδή μπορεί να αποθηκεύσει πληροφορίες και υπόκειται σ’ ένα "βέλος του χρόνου", ενώ ο κβαντικός κόσμος ή μικρόκοσμος προβάλλεται ως αδύνατος να αποθηκεύσει πληροφορίες και χρονικά ανατρέψιμος (Pagels, 1983). Μια πιο εξωφρενική προσέγγιση, είναι η υπόθεση των πολλαπλών συμπάντων, η οποία ισχυρίζεται ότι το σύμπαν διχάζεται κάθε φορά που εκτελείται μια μέτρηση (ή μια αλληλεπίδραση παρόμοια με μέτρηση), έτσι ώστε όλες οι πιθανότητες που αναπαριστούνται απ’ την κυματοσυνάρτηση (π.χ. μια ζωντανή γάτα και μια νεκρή γάτα) υπάρχουν αντικειμενικά, αλλά σε διαφορετικά σύμπαντα. Η Συνείδηση μας, υποτίθεται ότι διαιρείται σταθερά σε διαφορετικούς εαυτούς, που κατοικούν αυτούς τους πολλαπλασιαζόμενους, μη-επικοινωνούντες κόσμους.
Άλλοι θεωρητικοί υποθέτουν ότι, είναι η Συνείδηση που προκαλεί την κατάρρευση της κυματοσυνάρτησης και έτσι δημιουργεί την πραγματικότητα. Στην άποψη αυτή, ένα υποατομικό σωματίδιο δεν προσλαμβάνει συγκεκριμένες ιδιότητες όταν αλληλεπιδρά με μια συσκευή μέτρησης, αλλά μόνο όταν η ανάγνωση της συσκευής μέτρησης καταγράφεται στο μυαλό ενός παρατηρητή (το οποίο μπορεί φυσικά να συμβεί, πολύ μετά αφού έχει πραγματοποιηθεί η μέτρηση). Σύμφωνα με την πιο ακραία, ανθρωποκεντρική εκδοχή αυτής της θεωρίας, μόνο τα ενσυνείδητα όντα, όπως εμείς, μπορούν να προκαλούν την κατάρρευση μιας κυματοσυνάρτησης. Αυτό σημαίνει ότι, όλο το σύμπαν πρέπει να υπήρχε πρωταρχικά σε λανθάνουσα κατάσταση σε μια υποθετική σφαίρα κβαντικών πιθανοτήτων, μέχρι που ενσυνείδητα όντα εξελίχθηκαν βαθμιαία και προκάλεσαν την κατάρρευση του εαυτού τους και του υπόλοιπου του τμήματος της πραγματικότητάς τους στον υλικό κόσμο και τα αντικείμενα παραμένουν σε μια κατάσταση πραγματικότητας, μόνο όσο παρατηρούνται απ’ τους ανθρώπους (Goswami, 1993). Παρ’ όλα αυτά, άλλοι θεωρητικοί πιστεύουν ότι, μη ενσυνείδητες οντότητες, συμπεριλαμβανομένων γατών και πιθανόν ακόμα και ηλεκτρονίων, μπορούν ίσως να προκαλέσουν την κατάρρευση των κυματοσυναρτήσεων τους (Herbert, 1993).
Η θεωρία της κατάρρευσης της κυματοσυνάρτησης (ή κατάρρευση των ανυσμάτων κατάστασης, όπως αποκαλείται μερικές φορές), εγείρει το ερώτημα, πώς τα "κύματα πιθανότητας" που η κυματοσυνάρτηση θεωρείται ότι αναπαριστά, μπορούν να καταρρεύσουν σε ένα σωματίδιο, αν δεν είναι τίποτα άλλο παρά αφηρημένα μαθηματικά δημιουργήματα. Αφού η ιδέα των πακέτων κυμάτων που απλώνονται και καταρρέουν δεν βασίζεται σε αυστηρά πειραματικά δεδομένα, αλλά μόνο σε ιδιαίτερες ερμηνείες της κυματοειδούς συνάρτησης, αξίζει να ρίξουμε μια ματιά σε μια απ’ τις κύριες εναλλακτικές ερμηνείες, αυτή του David Bohm και των συνεργατών του, που παρέχει μια κατανοητή εκτίμηση του τι μπορεί να συμβαίνει στο κβαντικό επίπεδο.
Η ενυπάρχουσα τάξη
Η οντολογική ερμηνεία της κβαντικής φυσικής του Bohm, απορρίπτει την υπόθεση ότι η κυματοσυνάρτηση δίνει την πιο σωστή περιγραφή της δυνατής πραγματικότητας και έτσι αρνείται την ανάγκη να εισάγει μια άρρωστα-ορισμένη και μη ικανοποιητική έννοια της κατάρρευσης της κυματοσυνάρτησης (και όλων των παραδόξων που την συνοδεύουν). Αντίθετα υποθέτει την πραγματική ύπαρξη των σωματιδίων και των πεδίων: τα σωματίδια έχουν μια περίπλοκη εσωτερική δομή και συντροφεύονται πάντα από ένα κβαντικό κυματικό πεδίο· επηρεάζονται όχι μόνο από κλασικές ηλεκτρομαγνητικές δυνάμεις, αλλά και από μια λεπτότερη δύναμη, το κβαντικό δυναμικό, που ορίζεται απ’ το κβαντικό τους πεδίο, το οποίο υπακούει στην εξίσωση Schrodinger (Bohm & Hiley, 1993, Bohm & Peat, 1989, Hiley & Peat, 1991).
Το κβαντικό δυναμικό μεταφέρει πληροφορίες απ’ όλο το περιβάλλον και παρέχει άμεσες, μη-τοπικές συνδέσεις μεταξύ κβαντικών συστημάτων. Κατευθύνει τα σωματίδια με τον ίδιο τρόπο που κατευθύνουν τα ραδιοφωνικά κύματα ένα πλοίο με αυτόματο πιλότο – όχι με την έντασή τους, αλλά με τη μορφή τους. Είναι εξαιρετικά ευαίσθητο και περίπλοκο, ώστε οι σωματιδιακές τροχιές εμφανίζονται χαοτικές. Αντιστοιχούν σ’ αυτό που ο Bohm ονομάζει ενυπάρχουσα τάξη, η οποία μπορεί να θεωρηθεί, σαν ένας αχανής ωκεανός ενέργειας στον οποίο ο φυσικός ή αναπτυσσόμενος κόσμος είναι ένας απλός κυματισμός. Ο Bohm δείχνει ότι η ύπαρξη μιας δεξαμενής ενέργειας αυτού του είδους αναγνωρίζεται, αλλά της δίνεται μικρή εκτίμηση, απ’ την κοινώς αποδεκτή κβαντική θεωρία, η οποία αξιώνει ένα καθολικό κβαντικό πεδίο – το κβαντικό κενό ή πεδίο μηδενικού σημείου – που αποτελεί τη βάση του υλικού κόσμου. Πολύ λίγα είναι σήμερα γνωστά για το κβαντικό κενό, αλλά η ενεργειακή του πυκνότητα εκτιμάται στο αστρονομικό 10108 J/cm3 (Forward, 1996, σελ. 328-37).
Στην συμπεριφορά της θεωρίας του για το κβαντικό πεδίο, ο Bohm προτείνει ότι, το κβαντικό πεδίο (η ενυπάρχουσα τάξη) υπόκειται στη διαμορφωτική και οργανωτική επιρροή ενός υπερ-κβαντικού δυναμικού, που εκφράζει τη δράση μιας υπερ-ενυπάρχουσας τάξης. Το υπερ-κβαντικό δυναμικό κάνει τα κύματα να συγκλίνουν ή να αποκλίνουν, παράγονταν ένα είδος συμπεριφοράς όμοιας με των σωματιδίων. Οι φαινομενικά διαφορετικές μορφές που βλέπουμε γύρω μας είναι συνεπώς μόνο σχετικά σταθερά και ανεξάρτητα μοτίβα, που δημιουργούνται και υποστηρίζονται από μια ακατάπαυστη και βασική κίνηση τυλίγματος και ξετυλίγματος, με τα σωματίδια να διαλύονται σταθερά σε μια ενυπάρχουσα τάξη και μετά να κρυσταλλοποιούνται ξανά. Αυτή η διαδικασία πραγματοποιείται ακατάπαυστα και με μια εκπληκτική γρηγοράδα και δεν εξαρτάται από κάποια μέτρηση που γίνεται.
Στο μοντέλο του Bohm, ο κβαντικός κόσμος υπάρχει όταν δεν παρατηρείται και μετριέται. Απορρίπτει την θετικιστική άποψη, ότι κάτι που δεν μπορεί να μετρηθεί ή να γίνει γνωστό με ακρίβεια, δεν μπορεί να ειπωθεί ότι υπάρχει. Με άλλα λόγια δεν συγχέει την επιστημολογία με την οντολογία, τον χάρτη με την περιοχή. Για τον Bohm, οι πιθανότητες που υπολογίζονται για την κυματοσυνάρτηση, υποδεικνύουν τις πιθανότητες ενός σωματιδίου να βρίσκεται σε διαφορετικές θέσεις, άσχετα από το αν γίνεται μια μέτρηση, ενώ στην κοινά αποδεκτή ερμηνεία, υποδεικνύουν τις πιθανότητες ενός σωματιδίου να δημιουργείται σε διαφορετικές θέσεις όταν γίνεται μια μέτρηση. Το σύμπαν αυτοπροσδιορίζεται συνεχώς μέσα απ’ τις ακατάπαυστες αλληλεπιδράσεις του – απ’ τις οποίες η μέτρηση είναι μόνο ένα συγκεκριμένο παράδειγμα – και γι’ αυτό δεν μπορούν να προκύπτουν παράλογες καταστάσεις, όπως νεκρο-ζωντανές γάτες.
Έτσι, αν και ο Bohm απορρίπτει την άποψη ότι η ανθρώπινη συνείδηση δημιουργεί τα κβαντικά συστήματα και δεν πιστεύει ότι οι διάνοιές μας έχουν φυσιολογικά σημαντική επίδραση στο αποτέλεσμα μιας μέτρησης (εκτός με την έννοια ότι επιλέγουμε τη διευθέτηση του πειράματος), η ερμηνεία του ανοίγει το δρόμο για τη λειτουργία βαθύτερων, λεπτότερων και περισσότερο νοητικών επιπέδων της πραγματικότητας.
Υποστηρίζει ότι η συνείδηση ριζώνει βαθιά στην ενυπάρχουσα τάξη και γι’ αυτό είναι παρούσα σε κάποιο βαθμό σε όλες τις υλικές μορφές. Προτείνει, ότι ίσως υπάρχει μια άπειρη σειρά από ενυπάρχουσες τάξεις, με την καθεμιά να έχει ταυτόχρονα μια υλική πλευρά και μια συνειδησιακή πλευρά: "καθετί υλικό είναι επίσης και νοητικό και καθετί νοητικό είναι επίσης υλικό, αλλά υπάρχουν ακόμα λεπτότερα επίπεδα ύλης απ’ όσα γνωρίζουμε" (Weber, 1990, σελ. 151). Η έννοια του ενυπάρχοντος πεδίου θα μπορούσε να ειδωθεί σαν μια εκτεταμένη μορφή υλισμού, αλλά, λέει, "θα μπορούσε εξίσου να αποκαλείται ιδεαλισμός, πνεύμα, Συνείδηση. Ο διαχωρισμός των δύο – ύλης και πνεύματος – αποτελεί μία αφαίρεση. Το έδαφος είναι πάντα ένα." (Weber, 1990, σελ. 101)
Νους και ελεύθερη βούληση
human-consciousness Η κβαντική απροσδιοριστία είναι ξεκάθαρα ανοικτή σε ερμηνεία: είτε σημαίνει κρυμμένες (για μας) αιτίες, ή πλήρη απουσία αιτιών. Η θέση πως κάποια γεγονότα "μόλις συμβαίνουν" για κανένα λόγο δεν είναι δυνατό να αποδειχθούν, επειδή η ανικανότητά μας να αναγνωρίσουμε μια αιτία, δεν σημαίνει αναγκαστικά ότι δεν υπάρχει αιτία. Η έννοια της απόλυτης πιθανότητας συνεπάγεται ότι τα κβαντικά συστήματα μπορούν να δράσουν εντελώς αυθόρμητα, εντελώς απομονωμένα και ανεπηρέαστα από καθετί άλλο στο σύμπαν. Η αντίθετη άποψη είναι ότι, όλα τα συστήματα συμμετέχουν συνεχώς σε ένα περίπλοκο δίκτυο αιτιατών αλληλεπιδράσεων και διασυνδέσεων, σε πολλά διαφορετικά επίπεδα. Μεμονωμένα κβαντικά συστήματα συμπεριφέρονται σίγουρα απρόβλεπτα, αλλά παρ’ όλα αυτά αν δεν υπόκεινταν σε κάποιους αιτιατούς παράγοντες, θα ήταν δύσκολο να καταλάβουμε, γιατί η ομαδική τους συμπεριφορά παρουσιάζει στατιστικές κανονικότητες.
Η θέση ότι, καθετί έχει μια αιτία, ή μάλλον πολλές αιτίες, δεν συνεπάγεται απαραίτητα ότι όλα τα γεγονότα, συμπεριλαμβανομένων των πράξεων και των επιλογών μας, είναι αυστηρά προκαθορισμένα από καθαρά φυσικές διαδικασίες – μια άποψη που συχνά αποκαλείται "αυστηρή αιτιοκρατία" (Thornton, 1989). Η έλλειψη αιτιοκρατίας στο κβαντικό επίπεδο, παρέχει ένα άνοιγμα για δημιουργικότητα και ελεύθερη βούληση. Αλλά αν αυτή η έλλειψη αιτιοκρατίας ερμηνεύεται σαν απόλυτη πιθανότητα, θα σήμαινε ότι οι επιλογές και οι δράσεις μας απλά "ξεφυτρώνουν" με εντελώς τυχαίο και αυθαίρετο τρόπο, κατά την οποία περίπτωση μετα βίας θα αποκαλούνταν δικές μας αποφάσεις και έκφραση της δικιάς μας ελεύθερης βούλησης.
Εναλλακτικά, η έλλειψη κβαντικής αιτιοκρατίας θα μπορούσε να ερμηνευθεί σαν αιτιότητα από λεπτότερα, μη-φυσικά επίπεδα, έτσι ώστε οι πράξεις της ελεύθερης βούλησής μας έχουν αιτία – αλλά αυτή των αυτοσυνείδητων διανοιών μας. Απ’ αυτή την προοπτική – που μερικές αποκαλείται "ήπια αιτιοκρατία" – η ελεύθερη βούληση περιλαμβάνει την ενεργή, αυτό-συνείδητη αυτό-αιτιοκρατία.
Σύμφωνα με τον ορθόδοξο επιστημονικό υλισμό, οι διανοητικές καταστάσεις είναι πανομοιότυπες με τις καταστάσεις του εγκεφάλου· οι σκέψεις μας και τα συναισθήματά μας και η αίσθηση του εαυτού μας, γεννιούνται από ηλεκτροχημική δραστηριότητα στον εγκέφαλο. Αυτό θα σήμαινε είτε ότι ένα μέρος του εγκεφάλου ενεργοποιεί ένα άλλο, το οποίο ενεργοποιεί μετά ένα άλλο κ.λπ. ή ότι μια ιδιαίτερη περιοχή του εγκεφάλου ενεργοποιείται αυτόματα, χωρίς κάποια αιτία και είναι δύσκολο να δούμε πώς καθεμία απ’ τις εναλλακτικές λύσεις θα παρείχε μια βάση για ένα συνειδητό εαυτό και μια ελεύθερη βούληση. Ο Francis Crick (1994), για παράδειγμα, που πιστεύει ότι η συνείδηση είναι βασικά ένα πακέτο νεύρων, λέει ότι η κύρια έδρα της ελεύθερης βούλησης είναι πιθανόν μέσα ή κοντά σε ένα κομμάτι του εγκεφαλικού φλοιού γνωστό σαν anterior cingulate sulcus, αλλά υπαινίσσεται ότι η αίσθηση της ελευθερίας μας είναι σε μεγάλο μέρος, αν όχι ολοκληρωτικά, μια παραίσθηση.
Εκείνοι που μειώνουν τη συνείδηση σε ένα υποπροϊόν του εγκεφάλου διαφωνούν για τη σπουδαιότητα των κβαντο-μηχανικών απόψεων των νευρωνικών δικτύων: για παράδειγμα, ο Francis Crick, ο αείμνηστος Roger Sperry (1994), και ο Daniel Dennett (1991), τείνουν να αγνοήσουν την κβαντική φυσική, ενώ ο Stuart Hameroff (1994) πιστεύει ότι η συνείδηση προέρχεται από κβαντική συνοχή στους μικροσωληνίσκους πρωτοπλάσματος μέσα στους νευρώνες του εγκεφάλου. Μερικοί ερευνητές βλέπουν μια σχέση μεταξύ της συνείδησης και του κβαντικού κενού: για παράδειγμα, ο Charles Laughlin (1996) υποστηρίζει ότι οι νευρωνικές δομές που μεσολαβούν για την συνείδηση ίσως να αλληλεπιδρούν μη-τοπικά με το κενό (ή κβαντική θάλασσα), ενώ ο Edgar Mitchell (1996) πιστεύει ότι, τόσο η ύλη όσο και η συνείδηση απορρέουν απ’ το ενεργειακό δυναμικό του κενού.
Ο Νευροεπιστήμονας Sir John Eccles απορρίπτει την υλιστική άποψη σαν "πρόληψη" και υποστηρίζει τη δυαδική διαδραστικότητα: υποστηρίζει ότι υπάρχει ένας ψυχικός κόσμος μαζί με τον υλικό κόσμο, και ότι ο νους μας ή ο εαυτός μας ενεργεί στον εγκέφαλο (ειδικά η συμπληρωματική κινητήρια περιοχή του νευροφλοιού) στο κβαντικό επίπεδο, αυξάνοντας την πιθανότητα της πυροδότησης επιλεγμένων νευρώνων (Eccles, 1994, Giroldini, 1991). Υποστηρίζει ότι ο νους όχι μόνο δεν είναι φυσικός, αλλά απολύτως μη υλικός και μη στερεός. Παρ’ όλα αυτά, αν δεν σχετίζονταν με κάποιο είδος ενέργειας-ουσίας, θα ήταν μια φτωχή αφαίρεση και γι’ αυτό ανήμπορος να ασκήσει οποιαδήποτε επιρροή στο φυσικό κόσμο. Αυτή η αντίρρηση, εφαρμόζεται επίσης σε αυτούς που είναι αντίθετοι στην ελάττωση, οι οποίοι κρατιούνται μακριά από τη λέξη "δυαδικός" και περιγράφουν την ύλη και τη συνείδηση σαν συμπληρωματικές ή δυαδικές όψεις της πραγματικότητας, και ακόμα αρνούνται στη συνείδηση κάθε ενεργητική και πραγματική φύση, υποδηλώνοντας έτσι ότι είναι κατ’ ουσία διαφορετική απ’ την ύλη και στην πράξη μια απλή αφαίρεση.
Μια εναλλακτική τοποθέτηση είναι αυτή που αντηχεί σε πολλές μυστικιστικές και πνευματικές παραδόσεις: αυτή η φυσική ύλη είναι μόνο μια "οκτάβα" σε ένα άπειρο φάσμα ύλης-ενέργειας ή συνείδησης-ουσίας και όπως ο φυσικός κόσμος οργανώνεται και συντονίζεται κατά μεγάλο μέρος από εσωτερικούς κόσμους (αστρικό, νοητικό και πνευματικό), έτσι το φυσικό σώμα ενεργοποιείται και ελέγχεται κατά μεγάλο μέρος από λεπτότερα σώματα ή ενεργειακά πεδία, συμπεριλαμβανομένου ενός αστρικού σώματος-ομοιώματος και ενός νου ή ψυχής (βλ. Purucker, 1973). Σύμφωνα με την άποψη αυτή, η φύση γενικά, και όλες οι οντότητες που την αποτελούν, σχηματίζονται και οργανώνονται κυρίως από μέσα προς τα έξω, από βαθύτερα επίπεδα της δομής τους. Αυτός ο εσωτερικός προσανατολισμός είναι κάποτε αυτόματος και παθητικός, κάνοντας να εμφανίζονται οι αυτόματες σωματικές λειτουργίες μας και η συνήθης και ενστικτώδης συμπεριφορά και τακτικά, οι νομιμοφανείς λειτουργίες της φύσης γενικά, και κάποτε είναι ενεργός και αυτοσυνείδητος, όπως στις σκόπιμες και βουλητικές πράξεις μας. Ένα φυσικό σύστημα που υπόκειται σε τέτοιες λεπτότερες επιρροές δεν δέχεται τόσο επιδράσεις από έξω, όσο κατευθύνεται από μέσα. Εκτός του ότι επηρεάζουν τους εγκεφάλους και τα σώματά μας, οι διάνοιές μας φαίνεται επίσης ότι μπορούν να επηρεάσουν άλλες διάνοιες και σώματα και άλλα φυσικά αντικείμενα σε απόσταση, όπως φαίνεται στα παραφυσικά φαινόμενα.
EPR και ESP
Ήταν ο David Bohm και ένας απ’ τους υποστηρικτές του, ο John Bell απ’ το CERN, που έθεσαν το μεγαλύτερο μέρος του θεωρητικού υπόβαθρου για τα πειράματα ERP που πραγματοποιήθηκαν απ’ τον Alain Aspect το 1982 (το πρώτο πείραμα-σκέψης προτάθηκε απ’ τους Einstein, Podolsky, και Rosen το 1935). Αυτά τα πειράματα έδειξαν ότι, αν δύο κβαντικά συστήματα αλληλεπιδράσουν και κατόπιν διαχωριστούν, η συμπεριφορά τους, συσχετίζεται με ένα τρόπο που δεν μπορεί να εξηγηθεί με όρους σημάτων που ταξιδεύουν ανάμεσά τους με την ταχύτητα του φωτός ή χαμηλότερη.* Αυτό το φαινόμενο είναι γνωστό ως μη τοπικότητα και δέχεται δύο βασικές ερμηνείες: είτε συνεπάγεται άμεση, ακαριαία δράση από απόσταση, ή συνεπάγεται μεταβίβαση σημάτων ταχύτερη του φωτός.
* Τα πειραματικά αποτελέσματα δεν είναι τόσο σαφή όσο παρουσιάζονται προς τα έξω και εφαρμόζονται ρυθμίσεις με μεγάλη ασάφεια δεδομένων.
Αν οι μη-τοπικοί συσχετισμοί είναι απόλυτα ακαριαίοι, θα ήταν ουσιαστικά μη αιτιατοί· αν δύο γεγονότα συμβαίνουν εντελώς ταυτόχρονα, "αιτία" και "αποτέλεσμα" θα ήταν δυσδιάκριτα, και δεν θα μπορούσε να ειπωθεί ότι το ένα απ’ τα γεγονότα προκαλεί το άλλο μέσω μεταφοράς δύναμης ή ενέργειας, επειδή καμιά τέτοια μετάδοση δεν θα μπορούσε να γίνει απείρως γρήγορα. Γι’ αυτό δεν θα μπορούσε να υπάρξει αιτιατός μηχανισμός μετάδοσης που να εξηγείται, και οι όποιες έρευνες θα περιορίζονταν στις συνθήκες που επιτρέπουν να συμβαίνουν γεγονότα συσχέτισης σε διαφορετικά μέρη.
Είναι ενδιαφέρον να παρατηρήσουμε ότι το φως και άλλα είδη ηλεκτρομαγνητισμού θεωρήθηκαν επίσης κάποτε ότι διαδίδονταν ακαριαία, έως ότου τα δεδομένα της παρατήρησης απέδειξαν το διαφορετικό. Είναι αδύνατον να επιβεβαιωθεί η υπόθεση ότι, οι μη-τοπικές συνδέσεις είναι απόλυτα ακαριαίες, καθώς θα χρειάζονταν δύο τέλεια συγχρονισμένες μετρήσεις, οι οποίες θα απαιτούσαν άπειρη ακρίβεια. Παρ’ όλα αυτά, καθώς έδειξαν ο David Bohm και ο Basil Hiley (1993, σελ. 293-4, 347), αυτό θα μπορούσε να είναι πειραματικά πλαστογραφημένο. Επειδή, αν οι μη-τοπικές συνδέσεις δεν διαδίδονται με άπειρες ταχύτητες, αλλά με την ταχύτητα του φωτός ή μεγαλύτερες μέσω ενός "κβαντικού αιθέρα" – ένα υποκβαντικό πεδίο όπου η σύγχρονη κβαντική θεωρία και η θεωρία της σχετικότητας θα κατέρρεαν – τότε οι συσχετίσεις που προβλέπονται απ’ την κβαντική θεωρία θα εξαφανίζονταν, αν οι μετρήσεις γίνονταν σε περιόδους μικρότερες απ’ αυτές που απαιτούνται για τη μετάδοση των κβαντικών συνδέσεων μεταξύ των σωματιδίων. Τέτοια πειράματα είναι πέρα απ’ τις δυνατότητες της παρούσας τεχνολογίας, αλλά ίσως να είναι δυνατά στο μέλλον. Αν υπάρχουν αλληλεπιδράσεις υπεράνω του φωτός, θα ήταν "μη-τοπικές" μόνο με τη λογική του μη-φυσικού.
Η μη-τοπικότητα έχει επικαλεστεί σαν εξήγηση για την τηλεπάθεια και τη διόραση, αν και μερικοί ερευνητές πιστεύουν ότι ίσως να περιλαμβάνει ένα βαθύτερο επίπεδο μη-τοπικότητας ή αυτό που ο Bohm ονομάζει "υπερ – μη-τοπικότητα" (ίσως όμοια με τον "μορφικό συντονισμό" ("morphic resonance") του Sheldrake). Όπως ήδη έχει δειχθεί, αν η μη-τοπικότητα ερμηνεύεται ως ικανότητα ακαριαίας σύνδεσης, θα συνεπάγονταν ότι οι πληροφορίες θα "λαμβάνονταν" σε απόσταση, ακριβώς την ίδια στιγμή που γεννιούνται, δίχως να υφίστανται κάποιο είδος μετάδοσης. Κυρίως, κάποιος θα προσπαθούσε τότε να καταλάβει τις συνθήκες που επιτρέπουν την άμεση εμφάνιση της πληροφορίας.
Η εναλλακτική θέση είναι ότι η πληροφορία – που είναι βασικά ένας τύπος ενέργειας – χρειάζεται πάντα κάποιο χρόνο για να ταξιδέψει από την πηγή σε κάποιο άλλο τόπο, ότι η πληροφορία αποθηκεύεται σε κάποιο παραφυσικό επίπεδο και ότι, μπορούμε να έχουμε πρόσβαση σ’ αυτή την πληροφορία ή να ανταλλάξουμε πληροφορίες με άλλες διάνοιες, αν υπάρχουν οι απαραίτητες συνθήκες της "συμπαθητικού συντονισμού". Όπως και με το EPR, η υπόθεση ότι η τηλεπάθεια είναι απόλυτα ακαριαία είναι αναπόδεικτη, αλλά ίσως θα ήταν δυνατό να επινοήσουμε πειράματα που θα μπορούσαν να το ανασκευάσουν. Επειδή, αν τα φαινόμενα ESP περιλαμβάνουν λεπτότερους τύπους ενέργειας που ταξιδεύει με πεπερασμένες αλλά κάτω του φωτός ταχύτητες διαμέσου υπερφυσικών σφαιρών, ίσως είναι δυνατόν να ανιχνεύσουμε μια καθυστέρηση μεταξύ της μετάδοσης και της λήψης και επίσης κάποια εξασθένιση της επίδρασης από πολύ μακρινές αποστάσεις, αν και ήδη αποτελεί στοιχείο ότι κάθε εξασθένιση πρέπει να δοκιμαστεί πολύ λιγότερο απ’ την ηλεκτρομαγνητική ενέργεια, η οποία υπόκειται στον νόμο του αντίστροφου-τετραγώνου.
Όσο για την πρόγνωση, την τρίτη κατηγορία του ESP, μια πιθανή εξήγηση είναι ότι, περιλαμβάνει άμεση, "μη-τοπική" πρόσβαση στο πραγματικό μέλλον. Εναλλακτικά, ίσως να περιλαμβάνει την διορατική αντίληψη ενός πιθανού μελλοντικού σεναρίου, που ξεκινάει να παίρνει μορφή με βάση τις τωρινές τάσεις και προθέσεις, σε συμφωνία με την παραδοσιακή ιδέα ότι τα επερχόμενα γεγονότα ρίχνουν τη σκιά τους πριν απ’ αυτά. Ο Bohm λέει ότι, τέτοια προσκίαση συμβαίνει "βαθιά στην ενυπάρχουσα τάξη" (Talbot, 1992, σελ. 212) – την οποία κάποιες μυστικιστικές παραδόσεις αποκαλούν αστρικές ή ακασικές σφαίρες.
Ψυχοκίνηση και ο αόρατος κόσμος
Η μικρο-ψυχοκίνηση περιλαμβάνει την επιρροή της συνείδησης στα ατομικά σωματίδια. Σε κάποια πειράματα μικρο-ψυχοκίνησης που διεξήχθησαν από τον Helmut Schmidt, ομάδες αντικειμένων μπορούσαν τυπικά να αλλάξουν τις πιθανότητες των κβαντικών γεγονότων από 50% σε 51% και μερικά άτομα κατάφεραν πάνω από 54% (Broughton, 1991, σελ. 177). Πειράματα στο εργαστήριο PEAR στο Πανεπιστήμιο του Princeton απέφεραν μικρότερες μετακινήσεις ενός δεκάκις χιλιοστού (Jahn & Dunne, 1987). Μερικοί ερευνητές έχουν επικαλεστεί τη θεωρία της κατάρρευσης της κυματοσυνάρτησης εξαιτίας της συνείδησης, για να εξηγήσουν τέτοια αποτελέσματα. Υποστηρίζεται ότι, στην μικρο-ψυχοκίνηση, σε αντίθεση με την κοινή αντίληψη, το παρατηρούμενο αντικείμενο βοηθάει να καθορίσουμε ποιο θα είναι το αποτέλεσμα της κατάρρευσης της κυματοσυνάρτησης, ίσως με κάποιο τύπο της πληροφοριακής διαδικασίας. (Broughton, 1991, σελ. 177-81). Ο Eccles ακολουθεί παρόμοια προσέγγιση για να εξηγήσει πώς οι διάνοιές μας ενεργούν πάνω στους εγκεφάλους μας. Παρ’ όλα αυτά, η έννοια της κατάρρευσης της κυματοειδούς συνάρτησης δεν είναι απαραίτητη για να εξηγήσουμε την αλληλεπίδραση πνεύματος-ύλης. Θα μπορούσε ισοδύναμα να υιοθετήσουμε την άποψη ότι, τα υποατομικά σωματίδια πηγαινοέρχονται συνέχεια μέσα και έξω από την φυσική ύπαρξη και ότι, το αποτέλεσμα της διαδικασίας είναι μετατρέψιμο από τη βούλησή μας – μια φυσική δύναμη.
Η μικρο-ψυχοκίνηση περιλαμβάνει την κίνηση σταθερών, φυσιολογικά αμετακίνητων αντικειμένων με νοητική προσπάθεια. Σχετικά φαινόμενα περιλαμβάνουν την κίνηση poltergeist, τις υλοποιήσεις και αποϋλοποιήσεις, την τηλεμεταφορά και την αιώρηση. Αν και έχει συλλεχθεί απ’ τους ερευνητές εντυπωσιακός όγκος μαρτυριών τέτοιων φαινομένων τα τελευταία 150 χρόνια (Inglis, 1984, 1992· Milton, 1994), η μικρο-ψυχοκίνηση είναι ένα θέμα ταμπού και προκαλεί μικρό ενδιαφέρον, παρ’ όλο το δυναμικό του για να ανατρέψει το σύγχρονο υλιστικό παράδειγμα και να προκαλέσει επανάσταση στην επιστήμη – ή ίσως αυτή να είναι η αιτία. Τέτοια φαινόμενα περιλαμβάνουν καθαρά πολλά περισσότερα από την μεταβολή της πιθανολογικής συμπεριφοράς των ατομικών σωματιδίων και αυτό θα μπορούσε να θεωρηθεί σαν ένδειξη δυνάμεων, καταστάσεων της ύλης και μη-φυσικών ζώντων οντοτήτων, ακόμα άγνωστων στην επιστήμη. Μια ακόμα ένδειξη θα παρείχε διαβεβαίωση ότι αυτά τα πράγματα υπάρχουν· το ότι μέσα στην ενότητα της φύσης που περικλείει τα πάντα, υπάρχει ατέλειωτη ανομοιότητα.
Η πιθανή ύπαρξη λεπτότερων πεδίων που αλληλοδιαπερνούν το φυσικό πεδίο εν πάσει περιπτώσει ανοικτή σε έρευνα (βλ. Tiller, 1993) και αυτό είναι κάτι παραπάνω απ’ ό,τι μπορεί να ειπωθεί για τις υποθετικές πρόσθετες διαστάσεις που απαιτεί η θεωρία των υπερχορδών, οι οποίες λέγεται ότι περιπλέκονται σε μια περιοχή δισεκατομμυριοστού-τρισεκατομμυριοστού του τρισεκατομμυριοστού του εκατοστού και γι’ αυτό είναι εντελώς απλησίαστες ή των υποθετικών "συμπάντων-μωρών" και των "συμπάντων-φυσαλίδων" που απαιτούν κάποιοι κοσμολόγοι, τα οποία λέγεται ότι υπάρχουν σε κάποια εξίσου απροσπέλαστη "διάσταση".
Η υπόθεση των υπερφυσικών κόσμων δεν φαίνεται να ευνοείται από πολλούς ερευνητές. Ο Edgar Mitchell (1996), για παράδειγμα, πιστεύει ότι όλα τα φυσικά φαινόμενα περιλαμβάνουν μη-τοπικό συντονισμό ανάμεσα στον εγκέφαλο και το κβαντωμένο κενό και επακόλουθη πρόσβαση σε ολογραφικές, μη-τοπικές πληροφορίες. Κατά την άποψή του, αυτή η υπόθεση θα μπορούσε να εξηγήσει όχι μόνο την ψυχοκίνηση και το ESP, αλλά επίσης τις εξωσωματικές εμπειρίες και τις εμπειρίες κοντά στο θάνατο, τα οράματα και τα φαντάσματα και στοιχεία που παραθέτονται συνήθως υπέρ της μετενσάρκωσης της ψυχής. Παραδέχεται ότι αυτή θεωρία είναι υποθετική, ανεπιβεβαίωτη και ίσως απαιτεί μια νέα φυσική.
Περαιτέρω πειραματικές μελέτες φαινομένων που σχετίζονται με τη συνείδηση, φυσικών και παραφυσικών, θα επέτρεπαν να δοκιμαστούν με πιθανότητες επιτυχίας τα υπέρ και τα κατά των διάφορων συγκρουόμενων θεωριών. Τέτοιες έρευνες θα μπορούσαν να βαθύνουν τη γνώση μας των λειτουργιών τόσο του κβαντικού κόσμου όσο και των διανοιών μας και της σχέσης ανάμεσά τους και να αποκαλύψουν αν το κβαντικό κενό είναι πραγματικά το κατώτερο σημείο της ύπαρξης ή αν υπάρχουν βαθύτεροι κόσμοι στη φύση που αναμένουν να εξερευνηθούν.
Γραμμένο το 1997 από τον David Pratt και αναδημοσιεύεται από την ιστοσελίδα www.esoterica.gr
Παραπομπές
Bohm, D. (1984). Causality and Chance in Modern Physics. London: Routledge & Kegan Paul. First published in 1957.
Bohm, D. & Hiley, B.J. (1993). The Undivided Universe: An ontological interpretation of quantum theory. London and New York: Routledge.
Bohm, D. & Peat, F.D. (1989). Science, Order & Creativity. London: Routledge.
Broughton, R.S. (1991). Parapsychology: The Controversial Science. New York: Ballantine Books.
Crick, F. (1994). The Astonishing Hypothesis: The Scientific Search for the Soul. London: Simon & Schuster.
Dennett, D.C. (1991). Consciousness Explained. London: Allen Lane/Penguin.
Eccles, J.C. (1994). How the Self Controls Its Brain. Berlin: Springer-Verlag.
Forward, R.L. (1996). Mass Modification Experiment Definition Study, Journal of Scientific Exploration, 10:3, 325.
Giroldini, W. (1991). Eccles’s Model of Mind-Brain Interaction and Psychokinesis: A Preliminary Study, Journal of Scientific Exploration, 5:2, pp. 145-61.
Goswami, A. with Reed, R.E. & Goswami, M. (1993). The Self-Aware Universe: How consciousness creates the material world. New York: Tarcher/Putnam.
Hameroff, S.R. (1994). Quantum coherence in microtubules: A neural basis for emergent consciousness? Journal of Consciousness Studies, 1:1, 91.
Herbert, N. (1993). Elemental Mind: Human Consciousness and the New Physics. New York: Dutton.
Hiley, B.J. & Peat, F.D. (eds.) (1991). Quantum Implications: Essays in honour of David Bohm. London and New York: Routledge.
Inglis, B. (1984). Science and Parascience: A history of the paranormal, 1914-1939. London: Hodder and Stoughton.
Inglis, B. (1992). Natural and Supernatural: A History of the Paranormal from the Earliest Times to 1914. Bridport/Lindfield: Prism/Unity. First published in 1977.
Jahn, R.G. & Dunne, B.J. (1987). Margins of Reality: The Role of Consciousness in the Physical World. New York: Harcourt Brace.
Laughlin, C.D. (1996). Archetypes, Neurognosis and the Quantum Sea. Journal of Scientific Exploration, 10:3, 375.
Milton, R. (1994). Forbidden Science: Suppressed research that could change our lives. London: Fourth Estate.
Mitchell, E. with Williams, D. (1996). The Way of the Explorer: An Apollo Astronaut’s Journey Through the Material and Mystical Worlds. New York: Putnam.
Pagels, H.R. (1983). The Cosmic Code: Quantum Physics as the Language of Nature. New York: Bantam.
Purucker, G. de (1973). The Esoteric Tradition. Pasadena, California: Theosophical University Press. 2nd ed. first published in 1940.
Sheldrake, R. (1989). The Presence of the Past: Morphic Resonance and the Habits of Nature. New York: Vintage.
Sperry, R.W. (1994). Holding Course Amid Shifting Paradigms. In New Metaphysical Foundations of Modern Science, edited by W. Harman with J. Clark. Sausalito, California: Institute of Noetic Sciences.
Talbot, M. (1992). The Holographic Universe. New York: HarperPerennial.
Thornton, M. (1989). Do we have free will? Bristol: Bristol Classical Press.
Tiller, W.A. (1993). What Are Subtle Energies? Journal of Scientific Exploration, 7:3, 293.
Weber, R. (1990). Dialogues with Scientists and Sages: The Search for Unity. London: Arkana.
Κυριακή 26 Δεκεμβρίου 2010
Πέμπτη 23 Δεκεμβρίου 2010
Barclay James Harvest - Galadriel
She comes up with the morning sun
And tells me life has just begun
Oh, what it is to be young
And in the early evening light
She brings me flowers from the sun
Oh what it is to be young
And if you see her you will know
She's like a shadow
Falling softly on the snow
And in the early evening light
She brings me flowers for the night
Oh what it is to be young
And if you see her you will know
She's like a shadow
Falling softly on the snow
And in the early evening light
She brings me flowers for the night
Oh what it is to be young
Κυριακή 19 Δεκεμβρίου 2010
Γιασμίνα Ρεζά Το έργο της ζωής της
Μιλήσατε για πεπρωμένο και για συμπτώσεις. Τι σχέση υπάρχει κατά τη γνώμη σας ανάμεσα στις δύο αυτές έννοιες;
«Πρόκειται για έναν αρκετά λεπτό συνδυασμό, η σημασία του οποίου πάνω στο καθετί που μας συμβαίνει είναι δύσκολο να μετρηθεί. Πιστεύω ότι το πεπρωμένο αποτελείται από μια σειρά τυχαίων γεγονότων, από μία σειρά συμπτώσεων που καθοδηγούνται, όμως, από τον χαρακτήρα και την προσωπικότητά μας. Οσο για το ζήτημα του προκαθορισμένου στη ζωή, πιστεύω ότι τα άστρα μπορεί να δίνουν κάποιες κατευθύνσεις, αλλά δεν προκαθορίζουν τη ζωή μας. Η ζωή μας μπορεί να επηρεάζεται από μια διαδοχή συγκυριών που σου δείχνουν έναν δρόμο, αλλά η προσωπικότητά μας είναι στην ουσία εκείνη που καθοδηγεί και επικυρώνει ό,τι μας συμβαίνει. Αν, για παράδειγμα, δεν είχα περιμένει μερικά χρόνια χρόνια προτού ανεβάσω το “Συζητήσεις μετά από μια κηδεία”, έχοντας απορρίψει τέσσερις ή πέντε σοβαρές προτάσεις, τα πράγματα θα είχαν εξελιχθεί διαφορετικά. Οπότε, θεωρώ ότι μάλλον εγώ επηρέασα τις καταστάσεις, παρά η τύχη».
Ενα από τα βασικά στοιχεία της δραματουργίας σας είναι η εστίαση σε μια ασήμαντη λεπτομέρεια της καθημερινότητας, σε μια ρωγμή που καταβροχθίζει την πραγματικότητα και πλημμυρίζει όλη τη σκηνή.
«Μου αρέσει να πηγαίνω από το πιο μικρό στο πιο μεγάλο, διότι πιστεύω ότι η μεταφυσική του ανθρώπου δεν κρύβεται στις μεγάλες ηρωικές στιγμές. Η απόγνωση του ανθρώπου και τα μυστικά του κρύβονται στις αόρατες λεπτομέρειες, σε αυτές τις μόνιμες και ανεπαίσθητες χαραμάδες της καθημερινότητας. Μόνο ο συγγραφέας, και ίσως ο ψυχαναλυτής, μπορεί να τα φέρει όλα αυτά στο φως – σίγουρα όχι οι εφημερίδες. Είναι ο ρόλος του συγγραφέα – τουλάχιστον θεωρώ ότι είναι ο δικός μου ρόλος – να φωτίζει τη μικροσκοπική ρωγμή που γίνεται τεράστια, αν κάποιος βάλει επάνω της το δάχτυλό του. Είναι σαν μια μικρή τρύπα σε ένα πουλόβερ. Αν τραβήξεις την κλωστή, διαλύεται. Οπως ξέρετε, η τέχνη μπορεί να δημιουργήσει παράλληλους κόσμους που μερικές φορές είναι πιο ισχυροί από την πραγματικότητα. Η πραγματικότητα μπορεί κάποτε να είναι βαρετή, διότι είναι φορτωμένη με τόσο πολλές λεπτομέρειες, που το μάτι δεν μπορεί να ξεχωρίσει τι είναι χρήσιμο και τι όχι. Ο καλλιτέχνης, όμως, απομονώνει κάτι που υπάρχει στην ατμόσφαιρα και δεν μπορεί να το συλλάβει το κοινό μάτι. Αυτό είναι το βασικό στοιχείο της τέχνης. Και η λογοτεχνία είναι κάτι ακόμη πιο ξεχωριστό, διότι ωθείται από την ανάγκη να πλάθει φανταστικά πρόσωπα και παράλληλες ζωές, σαν να μην αρκούν οι υπάρχουσες. Η ανάγκη αυτή είναι κάτι ανεξήγητο».
Αυτό που συνδέει και ταυτόχρονα διαχωρίζει την αισθητή πραγματικότητα από τη φανταστική είναι η διάσταση του χρόνου;
«Ακριβώς. Οι ιστορίες μυθοπλασίας δεν είναι εξ ορισμού πιο ενδιαφέρουσες από τις ιστορίες της καθημερινής ζωής. Αυτό που τις καθιστά πιο ενδιαφέρουσες είναι ότι εγγράφουν τον άνθρωπο σε μια διαφορετική χρονικότητα. Για παράδειγμα, το έργο μου “Ο Θεός της σφαγής” είναι γραμμένο σε πραγματικό χρόνο, πράγμα σπάνιο στο θέατρο, όπου υπάρχουν πάντα παύσεις μέσα από τις οποίες περνάμε από τη μία πράξη στην άλλη, από τη μία ημέρα στην άλλη. Στο έργο αυτό, όμως, η ενότητα τόπου, χρόνου και δράσης είναι απόλυτη. Ολα συμβαίνουν μέσα σε μιάμιση ώρα, χωρίς κενά, χωρίς “πέντε λεπτά αργότερα”, για να προσδώσουν στην κατάσταση αμεσότητα και ακρίβεια. Στην πραγματικότητα, όμως, πρόκειται για μια μέγιστη χρονική συμπύκνωση.
Στην πραγματική ζωή, τα πράγματα δεν θα μπορούσαν ποτέ να εκτυλιχθούν έτσι μέσα σε ένα τόσο μικρό χρονικό διάστημα, ανάμεσα σε δύο γονείς που συναντιούνται, επειδή ο γιος του ενός έσπασε το δόντι του γιου του άλλου, και οι οποίοι στην αρχή μιλάνε πολύ ευγενικά και πολιτισμένα για να καταλήξουν σε... σφαγή. Το έργο αυτό είχε παντού τεράστια επιτυχία, ακριβώς επειδή δείχνει καταστάσεις και ανθρώπους απόλυτα αναγνωρίσιμους, αλλά σε χρόνο αλληγορικό. Και αυτό πιστεύω ότι είναι το μεγάλο στοίχημα της μυθοπλασίας. Η μεγάλη δυστυχία του ανθρώπου είναι η αδυναμία του να κυριαρχήσει στον χρόνο. Πόσες φορές δεν σκεφτόμαστε ότι θέλουμε να τον σταματήσουμε ή να τον επιταχύνουμε, αλλά είμαστε εντελώς ανήμποροι να κάνουμε οτιδήποτε; Στην περιπέτεια αυτή είμαστε εντελώς άοπλοι και ανίσχυροι. Οταν, λοιπόν, πλάθουμε ένα πρόσωπο, είναι σαν να ασκούμε εξουσία στον χρόνο, με απώτερο σκοπό να συλλάβουμε και να αποκρυσταλλώσουμε το παρόν, το οποίο στην πραγματική ζωή είναι αδύνατον να βιωθεί, αφού τη στιγμή που το ζούμε ήδη ανήκει στο παρελθόν».
Αυτή η αδυναμία του ανθρώπου εξηγεί την ανάγκη του για την τέχνη και την ανωτερότητα του καλλιτέχνη σε σχέση με την πραγματικότητα;
«Οχι, δεν πιστεύω καθόλου στην ανωτερότητά του. Συχνά, μάλιστα, οι καλλιτέχνες έχουν λιγότερη ευαισθησία από τους άλλους ανθρώπους. Απλώς έχουν την ικανότητα να εκφράζονται μέσα από την τέχνη, επειδή έτσι είναι ο χαρακτήρας τους και επειδή δεν μπορούν να κάνουν διαφορετικά. Αυτό που έχουν μέσα τους πρέπει να βγει, να εκφραστεί, να υπάρξει. Αυτή είναι η μεγάλη διαφορά. Αυτό όμως δεν σημαίνει ότι υποφέρουν λιγότερο. Δεν σημαίνει ότι είναι πιο έξυπνοι, πιο διορατικοί ή ότι ξέρουν να ζουν καλύτερα. Θυμάμαι, όταν είχα γράψει την “Τέχνη”, όλοι μου έλεγαν: “Πρέπει να γνωρίζετε τους άνδρες πολύ καλά για να περιγράψετε την ανδρική ψυχολογία με τόση ακρίβεια”. Μα, το αν γνωρίζω τους άνδρες καλά ή όχι δεν έχει καμία σημασία! Είναι απλώς ζήτημα ακοής. Τους ακούω και τους αναπλάθω. Το θεωρώ αστείο να ζητάει κανείς από έναν καλλιτέχνη να διατυπώσει την άποψή του για ένα ζήτημα. Γιατί θα έπρεπε ο καλλιτέχνης να έχει άποψη;».
Δεν είναι δυνατόν να μην έχει κάποια άποψη...
«Σίγουρα, αλλά δεν καταλαβαίνω γιατί ζητάμε από τους καλλιτέχνες να είναι διορατικοί όσον αφορά την πολιτική, την κοινωνία ή οποιοδήποτε άλλο θέμα. Τους ζητάμε να μας δώσουν κλειδιά για τον τρόπο λειτουργίας της ζωής, να έχουν έναν τρόπο σκέψης ανώτερο του μέσου όρου, να γνωρίζουν τα πράγματα καλύτερα. Οχι! Δεν είμαστε πιο διορατικοί. Εγώ τουλάχιστον δεν είμαι. Και, κατά τη γνώμη μου, κανένας συγγραφέας δεν είναι. Ο συγγραφέας είναι απλώς πιο “πορώδης”. Ξέρει να διηγείται, ξέρει να περιγράφει. Αυτός είναι ο τρόπος με τον οποίο λειτουργεί. Δεν σημαίνει, όμως, ότι είναι και σοφός. Οι μεγάλοι συγγραφείς μπορούν να καταγράψουν και να αποδώσουν τη σοφία, αλλά και την κακή πίστη, την αδικία ή την τρέλα του ανθρώπου. Μπορούν να δώσουν φωνή σε έναν τρελό, σε έναν δολοφόνο, σε έναν άνθρωπο εντελώς ανόητο ή σε μια μεγαλοφυΐα, αλλά αυτό δεν σημαίνει ότι είμαστε κάτι από όλα αυτά! Μπορούμε να γίνουμε κάτι από όλα αυτά στιγμιαία και μέσα στο συγκεκριμένο πλαίσιο αυτού που κάνουμε. Αυτό, όμως, δεν μας καθιστά παντογνώστες. Δείχνουμε απλώς αυτά που εντοπίσαμε. Ξέρουμε ότι υπάρχουν. Και έπειτα έχουμε την αίσθηση του ρυθμού. Είμαστε καλοί μουσικοί. Καλοί μουσικοί της ζωής».
Ποια είναι τα έργα σε παγκόσμιο επίπεδο που αποτέλεσαν αποκαλύψεις για σας;
«Πρώτα απ’ όλα θα έλεγα τον “Ντον Τζιοβάνι” του Μότσαρτ. Το λιμπρέτο του Ντα Πόντε (σ.σ.: λιμπρετίστας του Μότσαρτ) είναι πραγματικά μεγαλοφυές, πολύ ανώτερο για μένα από το κείμενο του Μολιέρου ή του Τίρσο ντε Μολίνα πάνω στο ίδιο θέμα. Νομίζω ότι ο Ντα Πόντε συνέλαβε το νόημα του μύθου καλύτερα από κάθε άλλον. Επιπλέον, πέτυχε να συνδυάσει με τρόπο εκπληκτικό το τραγικό με το κωμικό στοιχείο. Πρόκειται για συνδυασμό που μόνο οι πολύ μεγάλοι δραματουργοί μπορούν να πετύχουν, όπως ο Σαίξπηρ ή ο Τσέχοφ. Και έπειτα, μουσικά, με τον “Ντον Τζιοβάνι” ο Μότσαρτ δημιουργεί ένα από τα πιο δυνατά έργα του παγκόσμιου ρεπερτορίου, το αριστούργημα των αριστουργημάτων. Από λογοτεχνία, θα έλεγα τον “Μάκβεθ” του Σαίξπηρ για τους ίδιους λόγους. Πιστεύω ότι η τραγωδία εμπλουτίζεται όταν συνδυάζεται με την κωμωδία, διότι η ίδια η ζωή δεν είναι ποτέ μόνο το ένα ή μόνο το άλλο. Στα αισθητικά σοκ, θα κατέτασσα επίσης τον Τσέχοφ και τον Μπόρχες. Μιλώντας για τον Μπόρχες, το μυαλό μου πηγαίνει σε έναν ποιητή, συμπατριώτη σας, που αγαπώ ιδιαίτερα, τον Κωνσταντίνο Καβάφη. Τον θαυμάζω για πολλούς λόγους, αλλά ιδιαίτερα για τον τρόπο με τον οποίο ενσωματώνει στην ποίησή του την Ιστορία στη μυθική της διάσταση. Καταφέρνει μυστηριωδώς και με μέγιστη συγκινησιακή δύναμη να συνδυάσει το μεγαλείο του μύθου με τη σύγχρονη ευαισθησία του ήρωα. Θεμέλιο, επίσης, του ανθρώπινου πνεύματος θεωρώ τη μεγαλοφυΐα του Σοφοκλή. Για παρόμοιους λόγους με τον Καβάφη. Και οι δύο τοποθετούν τον άνθρωπο μέσα στην τραγική ελευθερία του, πάντα όμως κάτω από τον ουρανό τον θεών. Εγώ δεν θα μπορούσα – ή δεν θα τολμούσα – να χρησιμοποιήσω τον μύθο στα δικά μου έργα. Ο μύθος, όμως, απροσπέλαστος και θελκτικός, υπεισέρχεται χωρίς να το ξέρουμε στις αποφάσεις του συγγραφέα».
Ο μύθος είναι εξάλλου μια πόρτα προς το «αλλού», που φαίνεται να είναι το αντικείμενο της αναζήτησής σας σε καθένα από τα έργα σας. Πρόκειται για την αναζήτηση μιας ουτοπίας;
«Είναι θαυμάσια η ρίζα της λέξης “ουτοπία”. Ναι, με τη γραφή αναζητώ μια άπιαστη αλήθεια που ίσως δεν υπάρχει. Και αυτό είναι ιδιαίτερα ενδιαφέρον για μένα, διότι ποτέ δεν επεδίωξα να γίνω συγγραφέας. Το ξέρω ότι μια μέρα θα πεθάνω, όπως όλοι μας, και αν το έργο μου μείνει έστω και για λίγο, θα είμαι ευχαριστημένη που τα παιδιά μου θα είναι περήφανα για τη μητέρα τους. Για τα υπόλοιπα αδιαφορώ πραγματικά. Ετσι κι αλλιώς, δεν θα υπάρχω. Το να μείνει το έργο μου, όπως το έργο του Σαίξπηρ ή του Τσέχοφ, είναι μια σκέψη που δεν μου περνάει καν από το μυαλό. Δεν έγραψα για να αφήσω ίχνη. Πότε δεν σκέφτηκα ότι αυτό που έκανα θα ήταν ενδιαφέρον για τους μεταγενέστερους. Η γραφή ήταν για μένα ένα κάλεσμα βοήθειας, μια κραυγή: “Με ακούει κανείς;”. Εδώ και τώρα, όμως, όχι σε μια άλλη ζωή. Αλλά κανείς δεν είναι εκεί για να μας ακούσει ή, ακόμη και αν μας ακούει, δεν θα το μάθουμε ποτέ. Μέσα από το γράψιμο αναζητάμε κάτι μυστηριώδες, κάτι που θέλουμε να συμβεί, αλλά δεν συμβαίνει. Αλλά δεν πειράζει. Εμείς συνεχίζουμε, όπως όταν περπατάμε σε ένα μονοπάτι και πιστεύουμε ότι σίγουρα θα υπάρχει κάτι πέρα από τον ορίζοντα...».
Αυτό το κάτι έχει σχέση με το θείο;
«Δεν πιστεύω σε μια ανώτερη ύπαρξη ή σε μια ζωή πέρα από τον άνθρωπο. Αλλά ταυτόχρονα δεν καταφέρνω να μην το πιστεύω. Δεν πιστεύω ότι υπάρχει κάτι ανώτερο από εμάς που μας κατευθύνει, αλλά ταυτόχρονα δεν μπορεί να χωρέσει το μυαλό μου ότι δεν υπάρχει τίποτε. Είναι τόσο πολύπλοκο! Εχω πολλές αμφιβολίες και ερωτήματα επάνω στο θέμα, αλλά πάντα το λαμβάνω υπόψη. Ο,τι κάνω το κάνω σαν να υπήρχε μια ανώτερη δύναμη. Και αυτό που μου αρέσει σε ένα έργο είναι όταν υπάρχει αυτή η άλλη διάσταση, όπως στον “Ντον Τζιοβάνι” ή σε τόσα άλλα μουσικά ή ποιητικά έργα. Και ξεχωρίζω τη μουσική και την ποίηση από τις άλλες τέχνες, διότι είναι οι κατ’ εξοχήν μορφές καλλιτεχνικής έκφρασης που μας φέρνουν πιο κοντά σε μια δυνατή υπερβατικότητα. Αντίθετα, οι άνθρωποι ή τα έργα που την ακυρώνουν δεν με ενδιαφέρουν ιδιαίτερα».
Η ιδέα της υπερβατικότητας καθιστά δυνατή την καλλιτεχνική δημιουργία και ταυτόχρονα δίνει στον άνθρωπο την πνοή και την ώθηση να ξεπεράσει την ανθρώπινη φύση του...
«Ακριβώς. Αν το καλοσκεφτούμε, θέλουμε να βελτιωνόμαστε συνεχώς και να ξεπερνάμε τον εαυτό μας. Η ιδέα τού ''ψηλότερα'' μας γοητεύει, πόσω μάλλον όταν ξέρουμε ότι δεν υπάρχουν όρια. Τι υπάρχει πιο ψηλά; Δεν το ξέρουμε. Στους μεγάλους μύθους, εξάλλου, η ιδέα του Θεού ή των θεών, του πεπρωμένου, της μοίρας, της ανάγκης, όλων αυτών των ανώτερων αρχών, είναι ουσιαστική και θεμελιώδης. Ολόκληρος ο πολιτισμός μας έχει βασιστεί σε αυτές τις αρχές. Αυτό σημαίνει ότι, παρ’ όλες τις αμφιβολίες μας, έχουμε ενσωματώσει στον τρόπο της ζωής και της σκέψης μας την ιδέα της ύπαρξης μιας ανώτερης ουσίας. Πιστεύω ότι πάντα ο άνθρωπος θα είναι μοιρασμένος ανάμεσα στην πραγματικότητα και στις επιθυμίες του, ανάμεσα στο ορατό και στο αόρατο, στο εδώ και το αλλού. Και το “ανάμεσα”, είναι ίσως ο μοναδικός τόπος, ο ου-τόπος της ελευθερίας. Το να βρίσκεται κανείς στον τόπο αυτό, σε μια λεπτή ισορροπία, κάνει τη ζωή πιο ανάλαφρη και τελικά λιγότερο οδυνηρή».
* Το έργο της Γιασμίνα Ρεζά «Ο Θεός της σφαγής» ανεβαίνει αυτήν τη θεατρική σεζόν και στην Αθήνα, στο Θέατρο Κάτια Δανδουλάκη, σε σκηνοθεσία Σταμάτη Φασουλή, ενώ το έργο της «Art» κάνει πρεμιέρα στην Κεντρική Σκηνή του θεάτρου «Βαφείο - Λάκης Καραλής» στις 20 Δεκεμβρίου. Η βιογραφία του Νικολά Σαρκοζί «Αυγή, βράδυ ή νύχτα» με την υπογραφή της Ρεζά μόλις κυκλοφόρησε από τις εκδόσεις Εστία, ενώ από τις εκδόσεις Ψυχογιός κυκλοφορεί και το βιβλίο της «Λόγια που δεν είπαμε ποτέ».
Δημοσιεύθηκε στο BHMagazino, τεύχος 530, σελ. 28-33, 12/12/2010.
Διαβάστε περισσότερα: http://www.tovima.gr/default.asp?pid=2&ct=152&artId=373432&dt=16/12/2010#ixzz18ZelEUcI
«Πρόκειται για έναν αρκετά λεπτό συνδυασμό, η σημασία του οποίου πάνω στο καθετί που μας συμβαίνει είναι δύσκολο να μετρηθεί. Πιστεύω ότι το πεπρωμένο αποτελείται από μια σειρά τυχαίων γεγονότων, από μία σειρά συμπτώσεων που καθοδηγούνται, όμως, από τον χαρακτήρα και την προσωπικότητά μας. Οσο για το ζήτημα του προκαθορισμένου στη ζωή, πιστεύω ότι τα άστρα μπορεί να δίνουν κάποιες κατευθύνσεις, αλλά δεν προκαθορίζουν τη ζωή μας. Η ζωή μας μπορεί να επηρεάζεται από μια διαδοχή συγκυριών που σου δείχνουν έναν δρόμο, αλλά η προσωπικότητά μας είναι στην ουσία εκείνη που καθοδηγεί και επικυρώνει ό,τι μας συμβαίνει. Αν, για παράδειγμα, δεν είχα περιμένει μερικά χρόνια χρόνια προτού ανεβάσω το “Συζητήσεις μετά από μια κηδεία”, έχοντας απορρίψει τέσσερις ή πέντε σοβαρές προτάσεις, τα πράγματα θα είχαν εξελιχθεί διαφορετικά. Οπότε, θεωρώ ότι μάλλον εγώ επηρέασα τις καταστάσεις, παρά η τύχη».
Ενα από τα βασικά στοιχεία της δραματουργίας σας είναι η εστίαση σε μια ασήμαντη λεπτομέρεια της καθημερινότητας, σε μια ρωγμή που καταβροχθίζει την πραγματικότητα και πλημμυρίζει όλη τη σκηνή.
«Μου αρέσει να πηγαίνω από το πιο μικρό στο πιο μεγάλο, διότι πιστεύω ότι η μεταφυσική του ανθρώπου δεν κρύβεται στις μεγάλες ηρωικές στιγμές. Η απόγνωση του ανθρώπου και τα μυστικά του κρύβονται στις αόρατες λεπτομέρειες, σε αυτές τις μόνιμες και ανεπαίσθητες χαραμάδες της καθημερινότητας. Μόνο ο συγγραφέας, και ίσως ο ψυχαναλυτής, μπορεί να τα φέρει όλα αυτά στο φως – σίγουρα όχι οι εφημερίδες. Είναι ο ρόλος του συγγραφέα – τουλάχιστον θεωρώ ότι είναι ο δικός μου ρόλος – να φωτίζει τη μικροσκοπική ρωγμή που γίνεται τεράστια, αν κάποιος βάλει επάνω της το δάχτυλό του. Είναι σαν μια μικρή τρύπα σε ένα πουλόβερ. Αν τραβήξεις την κλωστή, διαλύεται. Οπως ξέρετε, η τέχνη μπορεί να δημιουργήσει παράλληλους κόσμους που μερικές φορές είναι πιο ισχυροί από την πραγματικότητα. Η πραγματικότητα μπορεί κάποτε να είναι βαρετή, διότι είναι φορτωμένη με τόσο πολλές λεπτομέρειες, που το μάτι δεν μπορεί να ξεχωρίσει τι είναι χρήσιμο και τι όχι. Ο καλλιτέχνης, όμως, απομονώνει κάτι που υπάρχει στην ατμόσφαιρα και δεν μπορεί να το συλλάβει το κοινό μάτι. Αυτό είναι το βασικό στοιχείο της τέχνης. Και η λογοτεχνία είναι κάτι ακόμη πιο ξεχωριστό, διότι ωθείται από την ανάγκη να πλάθει φανταστικά πρόσωπα και παράλληλες ζωές, σαν να μην αρκούν οι υπάρχουσες. Η ανάγκη αυτή είναι κάτι ανεξήγητο».
Αυτό που συνδέει και ταυτόχρονα διαχωρίζει την αισθητή πραγματικότητα από τη φανταστική είναι η διάσταση του χρόνου;
«Ακριβώς. Οι ιστορίες μυθοπλασίας δεν είναι εξ ορισμού πιο ενδιαφέρουσες από τις ιστορίες της καθημερινής ζωής. Αυτό που τις καθιστά πιο ενδιαφέρουσες είναι ότι εγγράφουν τον άνθρωπο σε μια διαφορετική χρονικότητα. Για παράδειγμα, το έργο μου “Ο Θεός της σφαγής” είναι γραμμένο σε πραγματικό χρόνο, πράγμα σπάνιο στο θέατρο, όπου υπάρχουν πάντα παύσεις μέσα από τις οποίες περνάμε από τη μία πράξη στην άλλη, από τη μία ημέρα στην άλλη. Στο έργο αυτό, όμως, η ενότητα τόπου, χρόνου και δράσης είναι απόλυτη. Ολα συμβαίνουν μέσα σε μιάμιση ώρα, χωρίς κενά, χωρίς “πέντε λεπτά αργότερα”, για να προσδώσουν στην κατάσταση αμεσότητα και ακρίβεια. Στην πραγματικότητα, όμως, πρόκειται για μια μέγιστη χρονική συμπύκνωση.
Στην πραγματική ζωή, τα πράγματα δεν θα μπορούσαν ποτέ να εκτυλιχθούν έτσι μέσα σε ένα τόσο μικρό χρονικό διάστημα, ανάμεσα σε δύο γονείς που συναντιούνται, επειδή ο γιος του ενός έσπασε το δόντι του γιου του άλλου, και οι οποίοι στην αρχή μιλάνε πολύ ευγενικά και πολιτισμένα για να καταλήξουν σε... σφαγή. Το έργο αυτό είχε παντού τεράστια επιτυχία, ακριβώς επειδή δείχνει καταστάσεις και ανθρώπους απόλυτα αναγνωρίσιμους, αλλά σε χρόνο αλληγορικό. Και αυτό πιστεύω ότι είναι το μεγάλο στοίχημα της μυθοπλασίας. Η μεγάλη δυστυχία του ανθρώπου είναι η αδυναμία του να κυριαρχήσει στον χρόνο. Πόσες φορές δεν σκεφτόμαστε ότι θέλουμε να τον σταματήσουμε ή να τον επιταχύνουμε, αλλά είμαστε εντελώς ανήμποροι να κάνουμε οτιδήποτε; Στην περιπέτεια αυτή είμαστε εντελώς άοπλοι και ανίσχυροι. Οταν, λοιπόν, πλάθουμε ένα πρόσωπο, είναι σαν να ασκούμε εξουσία στον χρόνο, με απώτερο σκοπό να συλλάβουμε και να αποκρυσταλλώσουμε το παρόν, το οποίο στην πραγματική ζωή είναι αδύνατον να βιωθεί, αφού τη στιγμή που το ζούμε ήδη ανήκει στο παρελθόν».
Αυτή η αδυναμία του ανθρώπου εξηγεί την ανάγκη του για την τέχνη και την ανωτερότητα του καλλιτέχνη σε σχέση με την πραγματικότητα;
«Οχι, δεν πιστεύω καθόλου στην ανωτερότητά του. Συχνά, μάλιστα, οι καλλιτέχνες έχουν λιγότερη ευαισθησία από τους άλλους ανθρώπους. Απλώς έχουν την ικανότητα να εκφράζονται μέσα από την τέχνη, επειδή έτσι είναι ο χαρακτήρας τους και επειδή δεν μπορούν να κάνουν διαφορετικά. Αυτό που έχουν μέσα τους πρέπει να βγει, να εκφραστεί, να υπάρξει. Αυτή είναι η μεγάλη διαφορά. Αυτό όμως δεν σημαίνει ότι υποφέρουν λιγότερο. Δεν σημαίνει ότι είναι πιο έξυπνοι, πιο διορατικοί ή ότι ξέρουν να ζουν καλύτερα. Θυμάμαι, όταν είχα γράψει την “Τέχνη”, όλοι μου έλεγαν: “Πρέπει να γνωρίζετε τους άνδρες πολύ καλά για να περιγράψετε την ανδρική ψυχολογία με τόση ακρίβεια”. Μα, το αν γνωρίζω τους άνδρες καλά ή όχι δεν έχει καμία σημασία! Είναι απλώς ζήτημα ακοής. Τους ακούω και τους αναπλάθω. Το θεωρώ αστείο να ζητάει κανείς από έναν καλλιτέχνη να διατυπώσει την άποψή του για ένα ζήτημα. Γιατί θα έπρεπε ο καλλιτέχνης να έχει άποψη;».
Δεν είναι δυνατόν να μην έχει κάποια άποψη...
«Σίγουρα, αλλά δεν καταλαβαίνω γιατί ζητάμε από τους καλλιτέχνες να είναι διορατικοί όσον αφορά την πολιτική, την κοινωνία ή οποιοδήποτε άλλο θέμα. Τους ζητάμε να μας δώσουν κλειδιά για τον τρόπο λειτουργίας της ζωής, να έχουν έναν τρόπο σκέψης ανώτερο του μέσου όρου, να γνωρίζουν τα πράγματα καλύτερα. Οχι! Δεν είμαστε πιο διορατικοί. Εγώ τουλάχιστον δεν είμαι. Και, κατά τη γνώμη μου, κανένας συγγραφέας δεν είναι. Ο συγγραφέας είναι απλώς πιο “πορώδης”. Ξέρει να διηγείται, ξέρει να περιγράφει. Αυτός είναι ο τρόπος με τον οποίο λειτουργεί. Δεν σημαίνει, όμως, ότι είναι και σοφός. Οι μεγάλοι συγγραφείς μπορούν να καταγράψουν και να αποδώσουν τη σοφία, αλλά και την κακή πίστη, την αδικία ή την τρέλα του ανθρώπου. Μπορούν να δώσουν φωνή σε έναν τρελό, σε έναν δολοφόνο, σε έναν άνθρωπο εντελώς ανόητο ή σε μια μεγαλοφυΐα, αλλά αυτό δεν σημαίνει ότι είμαστε κάτι από όλα αυτά! Μπορούμε να γίνουμε κάτι από όλα αυτά στιγμιαία και μέσα στο συγκεκριμένο πλαίσιο αυτού που κάνουμε. Αυτό, όμως, δεν μας καθιστά παντογνώστες. Δείχνουμε απλώς αυτά που εντοπίσαμε. Ξέρουμε ότι υπάρχουν. Και έπειτα έχουμε την αίσθηση του ρυθμού. Είμαστε καλοί μουσικοί. Καλοί μουσικοί της ζωής».
Ποια είναι τα έργα σε παγκόσμιο επίπεδο που αποτέλεσαν αποκαλύψεις για σας;
«Πρώτα απ’ όλα θα έλεγα τον “Ντον Τζιοβάνι” του Μότσαρτ. Το λιμπρέτο του Ντα Πόντε (σ.σ.: λιμπρετίστας του Μότσαρτ) είναι πραγματικά μεγαλοφυές, πολύ ανώτερο για μένα από το κείμενο του Μολιέρου ή του Τίρσο ντε Μολίνα πάνω στο ίδιο θέμα. Νομίζω ότι ο Ντα Πόντε συνέλαβε το νόημα του μύθου καλύτερα από κάθε άλλον. Επιπλέον, πέτυχε να συνδυάσει με τρόπο εκπληκτικό το τραγικό με το κωμικό στοιχείο. Πρόκειται για συνδυασμό που μόνο οι πολύ μεγάλοι δραματουργοί μπορούν να πετύχουν, όπως ο Σαίξπηρ ή ο Τσέχοφ. Και έπειτα, μουσικά, με τον “Ντον Τζιοβάνι” ο Μότσαρτ δημιουργεί ένα από τα πιο δυνατά έργα του παγκόσμιου ρεπερτορίου, το αριστούργημα των αριστουργημάτων. Από λογοτεχνία, θα έλεγα τον “Μάκβεθ” του Σαίξπηρ για τους ίδιους λόγους. Πιστεύω ότι η τραγωδία εμπλουτίζεται όταν συνδυάζεται με την κωμωδία, διότι η ίδια η ζωή δεν είναι ποτέ μόνο το ένα ή μόνο το άλλο. Στα αισθητικά σοκ, θα κατέτασσα επίσης τον Τσέχοφ και τον Μπόρχες. Μιλώντας για τον Μπόρχες, το μυαλό μου πηγαίνει σε έναν ποιητή, συμπατριώτη σας, που αγαπώ ιδιαίτερα, τον Κωνσταντίνο Καβάφη. Τον θαυμάζω για πολλούς λόγους, αλλά ιδιαίτερα για τον τρόπο με τον οποίο ενσωματώνει στην ποίησή του την Ιστορία στη μυθική της διάσταση. Καταφέρνει μυστηριωδώς και με μέγιστη συγκινησιακή δύναμη να συνδυάσει το μεγαλείο του μύθου με τη σύγχρονη ευαισθησία του ήρωα. Θεμέλιο, επίσης, του ανθρώπινου πνεύματος θεωρώ τη μεγαλοφυΐα του Σοφοκλή. Για παρόμοιους λόγους με τον Καβάφη. Και οι δύο τοποθετούν τον άνθρωπο μέσα στην τραγική ελευθερία του, πάντα όμως κάτω από τον ουρανό τον θεών. Εγώ δεν θα μπορούσα – ή δεν θα τολμούσα – να χρησιμοποιήσω τον μύθο στα δικά μου έργα. Ο μύθος, όμως, απροσπέλαστος και θελκτικός, υπεισέρχεται χωρίς να το ξέρουμε στις αποφάσεις του συγγραφέα».
Ο μύθος είναι εξάλλου μια πόρτα προς το «αλλού», που φαίνεται να είναι το αντικείμενο της αναζήτησής σας σε καθένα από τα έργα σας. Πρόκειται για την αναζήτηση μιας ουτοπίας;
«Είναι θαυμάσια η ρίζα της λέξης “ουτοπία”. Ναι, με τη γραφή αναζητώ μια άπιαστη αλήθεια που ίσως δεν υπάρχει. Και αυτό είναι ιδιαίτερα ενδιαφέρον για μένα, διότι ποτέ δεν επεδίωξα να γίνω συγγραφέας. Το ξέρω ότι μια μέρα θα πεθάνω, όπως όλοι μας, και αν το έργο μου μείνει έστω και για λίγο, θα είμαι ευχαριστημένη που τα παιδιά μου θα είναι περήφανα για τη μητέρα τους. Για τα υπόλοιπα αδιαφορώ πραγματικά. Ετσι κι αλλιώς, δεν θα υπάρχω. Το να μείνει το έργο μου, όπως το έργο του Σαίξπηρ ή του Τσέχοφ, είναι μια σκέψη που δεν μου περνάει καν από το μυαλό. Δεν έγραψα για να αφήσω ίχνη. Πότε δεν σκέφτηκα ότι αυτό που έκανα θα ήταν ενδιαφέρον για τους μεταγενέστερους. Η γραφή ήταν για μένα ένα κάλεσμα βοήθειας, μια κραυγή: “Με ακούει κανείς;”. Εδώ και τώρα, όμως, όχι σε μια άλλη ζωή. Αλλά κανείς δεν είναι εκεί για να μας ακούσει ή, ακόμη και αν μας ακούει, δεν θα το μάθουμε ποτέ. Μέσα από το γράψιμο αναζητάμε κάτι μυστηριώδες, κάτι που θέλουμε να συμβεί, αλλά δεν συμβαίνει. Αλλά δεν πειράζει. Εμείς συνεχίζουμε, όπως όταν περπατάμε σε ένα μονοπάτι και πιστεύουμε ότι σίγουρα θα υπάρχει κάτι πέρα από τον ορίζοντα...».
Αυτό το κάτι έχει σχέση με το θείο;
«Δεν πιστεύω σε μια ανώτερη ύπαρξη ή σε μια ζωή πέρα από τον άνθρωπο. Αλλά ταυτόχρονα δεν καταφέρνω να μην το πιστεύω. Δεν πιστεύω ότι υπάρχει κάτι ανώτερο από εμάς που μας κατευθύνει, αλλά ταυτόχρονα δεν μπορεί να χωρέσει το μυαλό μου ότι δεν υπάρχει τίποτε. Είναι τόσο πολύπλοκο! Εχω πολλές αμφιβολίες και ερωτήματα επάνω στο θέμα, αλλά πάντα το λαμβάνω υπόψη. Ο,τι κάνω το κάνω σαν να υπήρχε μια ανώτερη δύναμη. Και αυτό που μου αρέσει σε ένα έργο είναι όταν υπάρχει αυτή η άλλη διάσταση, όπως στον “Ντον Τζιοβάνι” ή σε τόσα άλλα μουσικά ή ποιητικά έργα. Και ξεχωρίζω τη μουσική και την ποίηση από τις άλλες τέχνες, διότι είναι οι κατ’ εξοχήν μορφές καλλιτεχνικής έκφρασης που μας φέρνουν πιο κοντά σε μια δυνατή υπερβατικότητα. Αντίθετα, οι άνθρωποι ή τα έργα που την ακυρώνουν δεν με ενδιαφέρουν ιδιαίτερα».
Η ιδέα της υπερβατικότητας καθιστά δυνατή την καλλιτεχνική δημιουργία και ταυτόχρονα δίνει στον άνθρωπο την πνοή και την ώθηση να ξεπεράσει την ανθρώπινη φύση του...
«Ακριβώς. Αν το καλοσκεφτούμε, θέλουμε να βελτιωνόμαστε συνεχώς και να ξεπερνάμε τον εαυτό μας. Η ιδέα τού ''ψηλότερα'' μας γοητεύει, πόσω μάλλον όταν ξέρουμε ότι δεν υπάρχουν όρια. Τι υπάρχει πιο ψηλά; Δεν το ξέρουμε. Στους μεγάλους μύθους, εξάλλου, η ιδέα του Θεού ή των θεών, του πεπρωμένου, της μοίρας, της ανάγκης, όλων αυτών των ανώτερων αρχών, είναι ουσιαστική και θεμελιώδης. Ολόκληρος ο πολιτισμός μας έχει βασιστεί σε αυτές τις αρχές. Αυτό σημαίνει ότι, παρ’ όλες τις αμφιβολίες μας, έχουμε ενσωματώσει στον τρόπο της ζωής και της σκέψης μας την ιδέα της ύπαρξης μιας ανώτερης ουσίας. Πιστεύω ότι πάντα ο άνθρωπος θα είναι μοιρασμένος ανάμεσα στην πραγματικότητα και στις επιθυμίες του, ανάμεσα στο ορατό και στο αόρατο, στο εδώ και το αλλού. Και το “ανάμεσα”, είναι ίσως ο μοναδικός τόπος, ο ου-τόπος της ελευθερίας. Το να βρίσκεται κανείς στον τόπο αυτό, σε μια λεπτή ισορροπία, κάνει τη ζωή πιο ανάλαφρη και τελικά λιγότερο οδυνηρή».
* Το έργο της Γιασμίνα Ρεζά «Ο Θεός της σφαγής» ανεβαίνει αυτήν τη θεατρική σεζόν και στην Αθήνα, στο Θέατρο Κάτια Δανδουλάκη, σε σκηνοθεσία Σταμάτη Φασουλή, ενώ το έργο της «Art» κάνει πρεμιέρα στην Κεντρική Σκηνή του θεάτρου «Βαφείο - Λάκης Καραλής» στις 20 Δεκεμβρίου. Η βιογραφία του Νικολά Σαρκοζί «Αυγή, βράδυ ή νύχτα» με την υπογραφή της Ρεζά μόλις κυκλοφόρησε από τις εκδόσεις Εστία, ενώ από τις εκδόσεις Ψυχογιός κυκλοφορεί και το βιβλίο της «Λόγια που δεν είπαμε ποτέ».
Δημοσιεύθηκε στο BHMagazino, τεύχος 530, σελ. 28-33, 12/12/2010.
Διαβάστε περισσότερα: http://www.tovima.gr/default.asp?pid=2&ct=152&artId=373432&dt=16/12/2010#ixzz18ZelEUcI
Παρασκευή 17 Δεκεμβρίου 2010
You only live once: our flawed understanding of risk helps drive financial market instability
Imperial College London News Release
For immediate release
Friday 17 December 2010
Our flawed understanding of how decisions in the present restrict our options in the future means that we may underestimate the risk associated with investment decisions, according to new research by Dr Ole Peters from Imperial College London. The research, published today in the journal Quantitative Finance, suggests how policy makers might reshape financial risk controls to reduce market instability and the risk of market collapse.
Investors know that there are myriad possibilities for how a financial market might develop. Before making an investment, they try to capture these possibilities in a single number to represent likely market performance. They can do this in one of two ways: 'ensemble averaging,' which runs possible scenarios in parallel, or ‘time averaging,’ which runs scenarios in sequence.
The ensemble average is the most commonly used approach. It is based on imagining multiple scenarios that all begin from the same starting conditions, and then averaging their outcomes. The alternative, time averaging, imagines all possible scenarios playing out over time.
As we live on a timeline, previous decisions cannot be undone as time passes. Any new decision constrains our choices when making subsequent ones. Time averaging provides the more accurate prediction for the real world outcome of an investment decision.
Today's study shows that, in the investment world, the differences in the results from these two approaches are critical: time averaging inherently incorporates a measure of risk, but ensemble averaging does not.
This means that ensemble averaging consistently undervalues risk by underestimating the effects of time on investments and overestimating the degree of choice that investors have. It also encourages excessive leveraging of investments, which itself accentuates fluctuations in the market, increases market volatility, and imparts a negative drift in the market that helps drive investors into negative equity.
"In the investment world, ensemble and time averages give different results, with ensemble averages systemically ignoring the effects of fluctuations," said Dr Ole Peters, author of the study from the Department of Mathematics and Grantham Institute for Climate Change at Imperial College London. “If investors routinely used time averages, it would help to avoid scenarios such as the excessive leveraging of investments that contributes to market instability and the likelihood of market collapse."
The recent financial crisis clearly shows the effects of excessive leveraging used both between banks, and between banks and their borrowers. Investors using time averaging to calculate risk would require a good reason to exceed a leverage factor of 1. Leverage factors of 40-60, as used by some banks before the crisis, would ring alarm bells. Thus, time averaging could provide policy makers and regulators with an indication of the kind of ratios that we should expect in a healthy, robust investment market.
"Too often, investors behave as if they had access to different scenarios playing out in parallel universes whose outcomes they combine and average," explained Dr Peters. "This misleadingly encourages them to think they have more choice and face less risk than is actually the case. In reality, we are stuck in one universe and, as a consequence, time has a bigger effect on investment risk than we imagine."
"Finding more accurate ways to predict and manage risk will improve the way we prepare for and respond to extreme events, and will help our consideration of future risks due to a changing climate," said Professor Sir Brian Hoskins, Director of the Grantham Institute for Climate Change at Imperial College London. "In the wake of the financial crisis we are all aware of the fragility of the investment markets. This new research helps us understand why excessive risk-taking happens, how it destabilises the markets, and how regulators might better monitor and manage markets in the future".
For immediate release
Friday 17 December 2010
Our flawed understanding of how decisions in the present restrict our options in the future means that we may underestimate the risk associated with investment decisions, according to new research by Dr Ole Peters from Imperial College London. The research, published today in the journal Quantitative Finance, suggests how policy makers might reshape financial risk controls to reduce market instability and the risk of market collapse.
Investors know that there are myriad possibilities for how a financial market might develop. Before making an investment, they try to capture these possibilities in a single number to represent likely market performance. They can do this in one of two ways: 'ensemble averaging,' which runs possible scenarios in parallel, or ‘time averaging,’ which runs scenarios in sequence.
The ensemble average is the most commonly used approach. It is based on imagining multiple scenarios that all begin from the same starting conditions, and then averaging their outcomes. The alternative, time averaging, imagines all possible scenarios playing out over time.
As we live on a timeline, previous decisions cannot be undone as time passes. Any new decision constrains our choices when making subsequent ones. Time averaging provides the more accurate prediction for the real world outcome of an investment decision.
Today's study shows that, in the investment world, the differences in the results from these two approaches are critical: time averaging inherently incorporates a measure of risk, but ensemble averaging does not.
This means that ensemble averaging consistently undervalues risk by underestimating the effects of time on investments and overestimating the degree of choice that investors have. It also encourages excessive leveraging of investments, which itself accentuates fluctuations in the market, increases market volatility, and imparts a negative drift in the market that helps drive investors into negative equity.
"In the investment world, ensemble and time averages give different results, with ensemble averages systemically ignoring the effects of fluctuations," said Dr Ole Peters, author of the study from the Department of Mathematics and Grantham Institute for Climate Change at Imperial College London. “If investors routinely used time averages, it would help to avoid scenarios such as the excessive leveraging of investments that contributes to market instability and the likelihood of market collapse."
The recent financial crisis clearly shows the effects of excessive leveraging used both between banks, and between banks and their borrowers. Investors using time averaging to calculate risk would require a good reason to exceed a leverage factor of 1. Leverage factors of 40-60, as used by some banks before the crisis, would ring alarm bells. Thus, time averaging could provide policy makers and regulators with an indication of the kind of ratios that we should expect in a healthy, robust investment market.
"Too often, investors behave as if they had access to different scenarios playing out in parallel universes whose outcomes they combine and average," explained Dr Peters. "This misleadingly encourages them to think they have more choice and face less risk than is actually the case. In reality, we are stuck in one universe and, as a consequence, time has a bigger effect on investment risk than we imagine."
"Finding more accurate ways to predict and manage risk will improve the way we prepare for and respond to extreme events, and will help our consideration of future risks due to a changing climate," said Professor Sir Brian Hoskins, Director of the Grantham Institute for Climate Change at Imperial College London. "In the wake of the financial crisis we are all aware of the fragility of the investment markets. This new research helps us understand why excessive risk-taking happens, how it destabilises the markets, and how regulators might better monitor and manage markets in the future".
Πέμπτη 16 Δεκεμβρίου 2010
What is Vedanta?
http://avastu0.blogspot.com/p/what-is-vedanta.html
Vedanta is a "nondual" tradition from Hinduism. It is similar in many ways to other nondual traditions like Zen or Dzogchen Buddhism, Taoism, Christian Mysticism (Gnosticism) and Sufism from Islam. Advaita is a "sect" or branch of Vedanta which says that there is a singularity of reality, a "Oneness" or one essence underlying all that appears to be.
Advaita means - not-two. This is not a path, not a practice. Advaita is a direct description of reality as it is.
Vedanta means - the end of the Vedas - the end of all knowledge - unlearning - not-knowing. Through investigation into the nature of Reality, called "self-knowledge" - the seeker comes to the realization of the nondual nature of Reality.
Advaita Vedanta does not seek to impart a new set of beliefs, but to rip the rug out from under all beliefs, all assumptions, including the assumption that there is an individual entity or person who exists, who was born and will later die.
In the direct recognition of Reality as it is, the seeker falls away as the root or foundation of all false translations.
Paradox
The "seeker" and "realization" cannot co-exist. As a seeker, taking yourself to be an individual "part" of the Universe, you have set up a lose-lose situation. A seeker can never find Oneness, because it is the very idea of a seeker which automatically excludes Oneness as a possibility. It is the concept of a person which is, by definition, the core limitation.
So asking what can I, as the seeker, do to realize Oneness, is futile. It will always be futile. The "seeker" and Oneness are mutually exclusive, we might say. It is only when the very root concept of the individual, the seeker, the person, is questioned, that the opportunity for Oneness or realization can come.
The Subject-"I"
Vedanta asks nothing of the seeker but to inquire into the sense of "I", the subject, Atma it is called. Is the world "I"? What is the world made of? How does it appear to you? It comes as sensory input, objective experience. Yet isn't this the same with the body? Is the body "I"? What about thoughts? Are thoughts "I"?
No. The body is not the subject, as it appears TO the subject-"I". Thoughts are not the subject - thoughts appear to the subject-"I". Any feeling, memory, emotion, sensation, perception, concept, idea - all are objective content to the subject-"I" which you are.
So what IS that subject-"I"? Any sensation is not it. Any perception is not it. Therefore that subject-"I" is without form, not objectifiable in any experience. Yet it is ever there - undeniably. You are ever there for any and all experiences. That subject-"I" is not, in fact, a body or a thought. It is the noticing of the body, thoughts and world.
Is it not true?
Therefore that subject-"I" is pure, without the first attribute, no shape, size, color - no dimension in space or time. What you truly are, in actual experience, is not something which has any objective content, yet it is the most intimate aspect of all experience.
Another word for the "subject" is knowing.
The Dissolution of the Seeker
The goal or aim of spirituality as seen in Vedanta is not the attainment of enlightenment for the seeker. It is the freedom FROM the seeker. That Oneness or one essence is actually what you are - only you have bound yourself to the idea of a limited being. In questioning this idea, you come to know yourself as you are - the whole, the totality, no longer imagining yourself as limited. This is the only goal.
Yet as you are already that totality, this limitation or bondage is only conceptual - the so-called veil or "maya" is only made of concepts. There is no actual separation or limitation in that one essence, even as it appears to be everything.
Therefore enlightenment is simply the recognition that you already are that one essence, and never were bound at all. You are only being as you already are. Free, perfect and whole.
A Metaphor
The gold Chain is suffering - it is seeking Peace and Happiness - it seeks to know what it is, truly.
It meditates - hoping for some vision or special experience of Gold. it's essence. It visits the Guru, asking for guidance to know what it is.
At first it formulates many ideas about Gold, what it must be like, feel like. It desperately seeks to know it's essence of this Oneness called "Gold".
Yet at every turn comes frustration. No vision or experience comes, or if they do come they always pass. No lasting realization of Gold has come.
The Guru says "what you are IS Gold - you cannot SEEK it for you ARE it." The chain is baffled by this paradox and glosses over this wisdom, seeking out Guru after Guru. book after book.
At some point the chain has exhausted all avenues, burned through all concepts about Gold. Gold cannot be found no matter what attempts are made. No concept brings the Peace and Happiness being sought after. The chain is lost without a foothold, Gold is nowhere in sight.
Yet the Guru only smiles. For in reality there never was a chain outside of a form of Gold itself. It was never chain seeking. Chain was a shape of Gold, a manifestation of Gold itself. Chain's only existence was in a concept - the reality always WAS Gold itself. Chain could not find Gold after all.
It was not chain which realized it was Gold. It was Gold which realized it was never "chain".
Right now, you are the totality itself, the one essence - you have taken yourself to be a limited entity, like the chain. As that entity you feel limited and need to seek the totality. Yet that entity you take yourself to be is only a name, only a form, only a manifestation of that One Essence.
Therefore this "I" can never find anything. "I" can never find that essence. It is that essence which realizes it never was that limited "I".
Vedanta is a "nondual" tradition from Hinduism. It is similar in many ways to other nondual traditions like Zen or Dzogchen Buddhism, Taoism, Christian Mysticism (Gnosticism) and Sufism from Islam. Advaita is a "sect" or branch of Vedanta which says that there is a singularity of reality, a "Oneness" or one essence underlying all that appears to be.
Advaita means - not-two. This is not a path, not a practice. Advaita is a direct description of reality as it is.
Vedanta means - the end of the Vedas - the end of all knowledge - unlearning - not-knowing. Through investigation into the nature of Reality, called "self-knowledge" - the seeker comes to the realization of the nondual nature of Reality.
Advaita Vedanta does not seek to impart a new set of beliefs, but to rip the rug out from under all beliefs, all assumptions, including the assumption that there is an individual entity or person who exists, who was born and will later die.
In the direct recognition of Reality as it is, the seeker falls away as the root or foundation of all false translations.
Paradox
The "seeker" and "realization" cannot co-exist. As a seeker, taking yourself to be an individual "part" of the Universe, you have set up a lose-lose situation. A seeker can never find Oneness, because it is the very idea of a seeker which automatically excludes Oneness as a possibility. It is the concept of a person which is, by definition, the core limitation.
So asking what can I, as the seeker, do to realize Oneness, is futile. It will always be futile. The "seeker" and Oneness are mutually exclusive, we might say. It is only when the very root concept of the individual, the seeker, the person, is questioned, that the opportunity for Oneness or realization can come.
The Subject-"I"
Vedanta asks nothing of the seeker but to inquire into the sense of "I", the subject, Atma it is called. Is the world "I"? What is the world made of? How does it appear to you? It comes as sensory input, objective experience. Yet isn't this the same with the body? Is the body "I"? What about thoughts? Are thoughts "I"?
No. The body is not the subject, as it appears TO the subject-"I". Thoughts are not the subject - thoughts appear to the subject-"I". Any feeling, memory, emotion, sensation, perception, concept, idea - all are objective content to the subject-"I" which you are.
So what IS that subject-"I"? Any sensation is not it. Any perception is not it. Therefore that subject-"I" is without form, not objectifiable in any experience. Yet it is ever there - undeniably. You are ever there for any and all experiences. That subject-"I" is not, in fact, a body or a thought. It is the noticing of the body, thoughts and world.
Is it not true?
Therefore that subject-"I" is pure, without the first attribute, no shape, size, color - no dimension in space or time. What you truly are, in actual experience, is not something which has any objective content, yet it is the most intimate aspect of all experience.
Another word for the "subject" is knowing.
The Dissolution of the Seeker
The goal or aim of spirituality as seen in Vedanta is not the attainment of enlightenment for the seeker. It is the freedom FROM the seeker. That Oneness or one essence is actually what you are - only you have bound yourself to the idea of a limited being. In questioning this idea, you come to know yourself as you are - the whole, the totality, no longer imagining yourself as limited. This is the only goal.
Yet as you are already that totality, this limitation or bondage is only conceptual - the so-called veil or "maya" is only made of concepts. There is no actual separation or limitation in that one essence, even as it appears to be everything.
Therefore enlightenment is simply the recognition that you already are that one essence, and never were bound at all. You are only being as you already are. Free, perfect and whole.
A Metaphor
The gold Chain is suffering - it is seeking Peace and Happiness - it seeks to know what it is, truly.
It meditates - hoping for some vision or special experience of Gold. it's essence. It visits the Guru, asking for guidance to know what it is.
At first it formulates many ideas about Gold, what it must be like, feel like. It desperately seeks to know it's essence of this Oneness called "Gold".
Yet at every turn comes frustration. No vision or experience comes, or if they do come they always pass. No lasting realization of Gold has come.
The Guru says "what you are IS Gold - you cannot SEEK it for you ARE it." The chain is baffled by this paradox and glosses over this wisdom, seeking out Guru after Guru. book after book.
At some point the chain has exhausted all avenues, burned through all concepts about Gold. Gold cannot be found no matter what attempts are made. No concept brings the Peace and Happiness being sought after. The chain is lost without a foothold, Gold is nowhere in sight.
Yet the Guru only smiles. For in reality there never was a chain outside of a form of Gold itself. It was never chain seeking. Chain was a shape of Gold, a manifestation of Gold itself. Chain's only existence was in a concept - the reality always WAS Gold itself. Chain could not find Gold after all.
It was not chain which realized it was Gold. It was Gold which realized it was never "chain".
Right now, you are the totality itself, the one essence - you have taken yourself to be a limited entity, like the chain. As that entity you feel limited and need to seek the totality. Yet that entity you take yourself to be is only a name, only a form, only a manifestation of that One Essence.
Therefore this "I" can never find anything. "I" can never find that essence. It is that essence which realizes it never was that limited "I".
Where unconscious memories form
A small area deep in the brain called the perirhinal cortex is critical for forming unconscious conceptual memories, researchers at the UC Davis Center for Mind and Brain have found.
The perirhinal cortex was thought to be involved, like the neighboring hippocampus, in "declarative" or conscious memories, but the new results show that the picture is more complex, said lead author Wei-chun Wang, a graduate student at UC Davis.
The results were published Dec. 9 in the journal Neuron.
We're all familiar with memories that rise from the unconscious mind. Imagine looking at a beach scene, said Wang. A little later, someone mentions surfing, and the beach scene pops back into your head.
Declarative memories, in contrast, are those where we recall being on that beach and watching that surf competition: "I remember being there."
Damage to a structure called the hippocampus affects such declarative "I remember" memories, but not conceptual memories, Wang said. Neuroscientists had previously thought the same was true for the perirhinal cortex, which is located immediately next to the hippocampus.
Wang and colleagues carried out memory tests on people diagnosed with amnesia, who had known damage to the perirhinal cortex or other brain areas. They also carried out functional magnetic resonance imaging (fMRI) scans of healthy volunteers while they performed memory tests.
In a typical test, they gave the subjects a long list of words, such as chair, table or spoon, and asked them to think about how pleasant they were.
Later, they asked the subjects to think up words in different categories, such as "furniture."
Amnesiacs with damage to the perirhinal cortex performed poorly on the tests, while the same brain area lit up in fMRI scans of the healthy control subjects.
The study helps us understand how memories are assembled in the brain and how different types of brain damage might impair memory, Wang said. For example, Alzheimer's disease often attacks the hippocampus and perirhinal cortex before other brain areas.
###
Co-authors on the study are Andy Yonelinas, professor of psychology and at the Center for Mind and Brain; Charan Ranganath, professor at the Center for Neuroscience; former UC Davis graduate student Michele Lazzara, now project coordinator at the University of Illinois at Chicago; and Robert Knight, professor of psychology at UC Berkeley.
The work was funded by the National Institutes of Health.
The perirhinal cortex was thought to be involved, like the neighboring hippocampus, in "declarative" or conscious memories, but the new results show that the picture is more complex, said lead author Wei-chun Wang, a graduate student at UC Davis.
The results were published Dec. 9 in the journal Neuron.
We're all familiar with memories that rise from the unconscious mind. Imagine looking at a beach scene, said Wang. A little later, someone mentions surfing, and the beach scene pops back into your head.
Declarative memories, in contrast, are those where we recall being on that beach and watching that surf competition: "I remember being there."
Damage to a structure called the hippocampus affects such declarative "I remember" memories, but not conceptual memories, Wang said. Neuroscientists had previously thought the same was true for the perirhinal cortex, which is located immediately next to the hippocampus.
Wang and colleagues carried out memory tests on people diagnosed with amnesia, who had known damage to the perirhinal cortex or other brain areas. They also carried out functional magnetic resonance imaging (fMRI) scans of healthy volunteers while they performed memory tests.
In a typical test, they gave the subjects a long list of words, such as chair, table or spoon, and asked them to think about how pleasant they were.
Later, they asked the subjects to think up words in different categories, such as "furniture."
Amnesiacs with damage to the perirhinal cortex performed poorly on the tests, while the same brain area lit up in fMRI scans of the healthy control subjects.
The study helps us understand how memories are assembled in the brain and how different types of brain damage might impair memory, Wang said. For example, Alzheimer's disease often attacks the hippocampus and perirhinal cortex before other brain areas.
###
Co-authors on the study are Andy Yonelinas, professor of psychology and at the Center for Mind and Brain; Charan Ranganath, professor at the Center for Neuroscience; former UC Davis graduate student Michele Lazzara, now project coordinator at the University of Illinois at Chicago; and Robert Knight, professor of psychology at UC Berkeley.
The work was funded by the National Institutes of Health.
Παρασκευή 10 Δεκεμβρίου 2010
What Zen meditators don't think about won't hurt them
New University of Montreal study shows how meditators don't ponder pain
This release is available in French.
Montreal, December 8, 2010 – Zen meditation has many health benefits, including a reduced sensitivity to pain. According to new research from the Université de Montréal, meditators do feel pain but they simply don't dwell on it as much. These findings, published in the month's issue of Pain, may have implications for chronic pain sufferers, such as those with arthritis, back pain or cancer.
"Our previous research found that Zen meditators have lower pain sensitivity. The aim of the current study was to determine how they are achieving this," says senior author Pierre Rainville, researcher at the Université de Montréal and the Institut universitaire de gériatrie de Montréal. "Using functional magnetic resonance imaging, we demonstrated that although the meditators were aware of the pain, this sensation wasn't processed in the part of their brains responsible for appraisal, reasoning or memory formation. We think that they feel the sensations, but cut the process short, refraining from interpretation or labelling of the stimuli as painful."
Training the brain
Rainville and his colleagues compared the response of 13 Zen meditators to 13 non-meditators to a painful heat stimulus. Pain perception was measured and compared with functional MRI data. The most experienced Zen practitioners showed lower pain responses and decreased activity in the brain areas responsible for cognition, emotion and memory (the prefrontal cortex, amygdala and hippocampus). In addition, there was a decrease in the communication between a part of the brain that senses the pain and the prefrontal cortex.
"Our findings lead to new insights into mind/brain function," says first author, Joshua Grant, a doctoral student at the Université de Montréal. "These results challenge current concepts of mental control, which is thought to be achieved by increasing cognitive activity or effort. Instead, we suggest it is possible to self-regulate in a more passive manner, by 'turning off' certain areas of the brain, which in this case are normally involved in processing pain."
"The results suggest that Zen meditators may have a training-related ability to disengage some higher-order brain processes, while still experiencing the stimulus," says Rainville. "Such an ability could have widespread and profound implications for pain and emotion regulation and cognitive control. This behaviour is consistent with the mindset of Zen and with the notion of mindfulness."
###
About the Study:
"A non-elaborative mental stance and decoupling of executive and pain-related cortices predicts low pain sensitivity in Zen meditators" was authored by Joshua A. Grant, Jérôme Courtemanche and Pierre Rainville from the Université de Montréal
Partners in research:
This study was funded by a grant from the Mind and Life Institute with support for Joshua Grant provided by the Canadian Institutes of Health Research.
This release is available in French.
Montreal, December 8, 2010 – Zen meditation has many health benefits, including a reduced sensitivity to pain. According to new research from the Université de Montréal, meditators do feel pain but they simply don't dwell on it as much. These findings, published in the month's issue of Pain, may have implications for chronic pain sufferers, such as those with arthritis, back pain or cancer.
"Our previous research found that Zen meditators have lower pain sensitivity. The aim of the current study was to determine how they are achieving this," says senior author Pierre Rainville, researcher at the Université de Montréal and the Institut universitaire de gériatrie de Montréal. "Using functional magnetic resonance imaging, we demonstrated that although the meditators were aware of the pain, this sensation wasn't processed in the part of their brains responsible for appraisal, reasoning or memory formation. We think that they feel the sensations, but cut the process short, refraining from interpretation or labelling of the stimuli as painful."
Training the brain
Rainville and his colleagues compared the response of 13 Zen meditators to 13 non-meditators to a painful heat stimulus. Pain perception was measured and compared with functional MRI data. The most experienced Zen practitioners showed lower pain responses and decreased activity in the brain areas responsible for cognition, emotion and memory (the prefrontal cortex, amygdala and hippocampus). In addition, there was a decrease in the communication between a part of the brain that senses the pain and the prefrontal cortex.
"Our findings lead to new insights into mind/brain function," says first author, Joshua Grant, a doctoral student at the Université de Montréal. "These results challenge current concepts of mental control, which is thought to be achieved by increasing cognitive activity or effort. Instead, we suggest it is possible to self-regulate in a more passive manner, by 'turning off' certain areas of the brain, which in this case are normally involved in processing pain."
"The results suggest that Zen meditators may have a training-related ability to disengage some higher-order brain processes, while still experiencing the stimulus," says Rainville. "Such an ability could have widespread and profound implications for pain and emotion regulation and cognitive control. This behaviour is consistent with the mindset of Zen and with the notion of mindfulness."
###
About the Study:
"A non-elaborative mental stance and decoupling of executive and pain-related cortices predicts low pain sensitivity in Zen meditators" was authored by Joshua A. Grant, Jérôme Courtemanche and Pierre Rainville from the Université de Montréal
Partners in research:
This study was funded by a grant from the Mind and Life Institute with support for Joshua Grant provided by the Canadian Institutes of Health Research.
IBMT meditation found to boost brain connectivity
11 hours of meditation training leads to positive changes based on brain imaging at the University of Oregon
Just 11 hours of learning a meditation technique induces positive structural changes in brain connectivity by boosting efficiency in a part of the brain that helps a person regulate behavior in accordance with their goals, researchers report.
The technique -- integrative body-mind training (IBMT) -- has been the focus of intense scrutiny by a team of Chinese researchers led by Yi-Yuan Tang of Dalian University of Technology in collaboration with University of Oregon psychologist Michael I. Posner.
IBMT was adapted from traditional Chinese medicine in the 1990s in China, where it is practiced by thousands of people. It is now being taught to undergraduates involved in research on the method at the University of Oregon.
The new research -- published online the week of Aug. 16-21 ahead of regular publication in the Proceedings of the National Academy of Sciences -- involved 45 UO students (28 males and 17 females); 22 subjects received IBMT while 23 participants were in a control group that received the same amount of relaxation training. The experiments involved the use of brain-imaging equipment in the UO's Robert and Beverly Lewis Center for Neuroimaging.
A type of magnetic resonance called diffusion tensor imaging allowed researchers to examine fibers connecting brain regions before and after training. The changes were strongest in connections involving the anterior cingulate, a brain area related to the ability to regulate emotions and behavior. The changes were observed only in those who practiced meditation and not in the control group. The changes in connectivity began after six hours of training and became clear by 11 hours of practice. The researchers said it is possible the changes resulted from a reorganization of white-matter tracts or by an increase of myelin that surrounds the connections.
"The importance of our findings relates to the ability to make structural changes in a brain network related to self regulation," said Posner, who last fall received a National Medal of Science. "The pathway that has the largest change due to IBMT is one that previously was shown to relate to individual differences in the person's ability to regulate conflict."
In 2007 in PNAS, Tang, a visiting scholar at the UO, and Posner documented that doing IBMT for five days prior to a mental math test led to low levels of the stress hormone cortisol among Chinese students. The experimental group also showed lower levels of anxiety, depression, anger and fatigue than students in a relaxation control group.
In 2009 in PNAS, Tang and Chinese colleagues, with assistance from Posner and UO psychology professor Mary K. Rothbart, found that IBMT subjects in China had increased blood flow in the right anterior cingulate cortex after receiving training for 20 minutes a day over five days. Compared with the relaxation group, IBMT subjects also had lower heart rates and skin conductance responses, increased belly breathing amplitude and decreased chest respiration rates.
The latter findings suggested the possibility that additional training might trigger structural changes in the brain, leading to the new research, Tang and Posner said. The researchers currently are extending their evaluation to determine if longer exposure to IBMT will produce positive changes in the size of the anterior cingulate.
Deficits in activation of the anterior cingulate cortex have been associated with attention deficit disorder, dementia, depression, schizophrenia and many other disorders. "We believe this new finding is of interest to the fields of education, health and neuroscience, as well as for the general public," Tang said.
In their conclusion, the researchers wrote that the new findings suggest a use of IBMT as a vehicle for understanding how training influences brain plasticity.
IBMT is not yet available in the United States beyond the research being done at the UO. The practice avoids struggles to control thought, relying instead on a state of restful alertness, allowing for a high degree of body-mind awareness while receiving instructions from a coach, who provides breath-adjustment guidance and mental imagery and other techniques while soothing music plays in the background. Thought control is achieved gradually through posture, relaxation, body-mind harmony and balanced breathing. A good coach is critical, Tang said.
###
Co-authors with Tang and Posner on the new PNAS paper were Qilin Lu of the Dalian University of Technology and Xiujuan Geng, Elliot A. Stein and Yihong Yang, all of the National Institute on Drug Abuse-Intramural Research Program in Baltimore, Md.
The James S. Bower Foundation based in Santa Barbara, Calif., John Templeton Foundation in West Conshohocken, PA, National Natural Science Foundation of China and U.S. National Institute on Drug Abuse-Intramural Research Program supported the research.
About the University of Oregon
The University of Oregon is a world-class teaching and research institution and Oregon's flagship public university. The UO is a member of the Association of American Universities (AAU), an organization made up of the 63 leading public and private research institutions in the United States and Canada. The UO is one of only two AAU members in the Pacific Northwest.
Sources: Yi-Yuan Tang, professor of neuroinformatics (Dalian University of Technology, China) and visiting scholar (University of Oregon), yiyuan@uoregon.edu; and Michael I. Posner, UO professor emeritus of psychology, 541-346-4939 begin_of_the_skype_highlighting 541-346-4939 end_of_the_skype_highlighting, mposner@uoregon.edu
Links:
Posner Web page: http://www.neuro.uoregon.edu/ionmain/htdocs/faculty/posner.html
Yi-Yuan Tang site on IBMT: http://www.yi-yuan.net/english/tyy.asp
Dalian University of Technology (English version): http://www.dlut.edu.cn/en/
National Institute on Drug Abuse-Intramural Research Program: http://irp.drugabuse.gov/
James S. Bower Foundation: http://www.jsbowerfoundation.org/
John Templeton Foundation: http://www.templeton.org/
Just 11 hours of learning a meditation technique induces positive structural changes in brain connectivity by boosting efficiency in a part of the brain that helps a person regulate behavior in accordance with their goals, researchers report.
The technique -- integrative body-mind training (IBMT) -- has been the focus of intense scrutiny by a team of Chinese researchers led by Yi-Yuan Tang of Dalian University of Technology in collaboration with University of Oregon psychologist Michael I. Posner.
IBMT was adapted from traditional Chinese medicine in the 1990s in China, where it is practiced by thousands of people. It is now being taught to undergraduates involved in research on the method at the University of Oregon.
The new research -- published online the week of Aug. 16-21 ahead of regular publication in the Proceedings of the National Academy of Sciences -- involved 45 UO students (28 males and 17 females); 22 subjects received IBMT while 23 participants were in a control group that received the same amount of relaxation training. The experiments involved the use of brain-imaging equipment in the UO's Robert and Beverly Lewis Center for Neuroimaging.
A type of magnetic resonance called diffusion tensor imaging allowed researchers to examine fibers connecting brain regions before and after training. The changes were strongest in connections involving the anterior cingulate, a brain area related to the ability to regulate emotions and behavior. The changes were observed only in those who practiced meditation and not in the control group. The changes in connectivity began after six hours of training and became clear by 11 hours of practice. The researchers said it is possible the changes resulted from a reorganization of white-matter tracts or by an increase of myelin that surrounds the connections.
"The importance of our findings relates to the ability to make structural changes in a brain network related to self regulation," said Posner, who last fall received a National Medal of Science. "The pathway that has the largest change due to IBMT is one that previously was shown to relate to individual differences in the person's ability to regulate conflict."
In 2007 in PNAS, Tang, a visiting scholar at the UO, and Posner documented that doing IBMT for five days prior to a mental math test led to low levels of the stress hormone cortisol among Chinese students. The experimental group also showed lower levels of anxiety, depression, anger and fatigue than students in a relaxation control group.
In 2009 in PNAS, Tang and Chinese colleagues, with assistance from Posner and UO psychology professor Mary K. Rothbart, found that IBMT subjects in China had increased blood flow in the right anterior cingulate cortex after receiving training for 20 minutes a day over five days. Compared with the relaxation group, IBMT subjects also had lower heart rates and skin conductance responses, increased belly breathing amplitude and decreased chest respiration rates.
The latter findings suggested the possibility that additional training might trigger structural changes in the brain, leading to the new research, Tang and Posner said. The researchers currently are extending their evaluation to determine if longer exposure to IBMT will produce positive changes in the size of the anterior cingulate.
Deficits in activation of the anterior cingulate cortex have been associated with attention deficit disorder, dementia, depression, schizophrenia and many other disorders. "We believe this new finding is of interest to the fields of education, health and neuroscience, as well as for the general public," Tang said.
In their conclusion, the researchers wrote that the new findings suggest a use of IBMT as a vehicle for understanding how training influences brain plasticity.
IBMT is not yet available in the United States beyond the research being done at the UO. The practice avoids struggles to control thought, relying instead on a state of restful alertness, allowing for a high degree of body-mind awareness while receiving instructions from a coach, who provides breath-adjustment guidance and mental imagery and other techniques while soothing music plays in the background. Thought control is achieved gradually through posture, relaxation, body-mind harmony and balanced breathing. A good coach is critical, Tang said.
###
Co-authors with Tang and Posner on the new PNAS paper were Qilin Lu of the Dalian University of Technology and Xiujuan Geng, Elliot A. Stein and Yihong Yang, all of the National Institute on Drug Abuse-Intramural Research Program in Baltimore, Md.
The James S. Bower Foundation based in Santa Barbara, Calif., John Templeton Foundation in West Conshohocken, PA, National Natural Science Foundation of China and U.S. National Institute on Drug Abuse-Intramural Research Program supported the research.
About the University of Oregon
The University of Oregon is a world-class teaching and research institution and Oregon's flagship public university. The UO is a member of the Association of American Universities (AAU), an organization made up of the 63 leading public and private research institutions in the United States and Canada. The UO is one of only two AAU members in the Pacific Northwest.
Sources: Yi-Yuan Tang, professor of neuroinformatics (Dalian University of Technology, China) and visiting scholar (University of Oregon), yiyuan@uoregon.edu; and Michael I. Posner, UO professor emeritus of psychology, 541-346-4939 begin_of_the_skype_highlighting 541-346-4939 end_of_the_skype_highlighting, mposner@uoregon.edu
Links:
Posner Web page: http://www.neuro.uoregon.edu/ionmain/htdocs/faculty/posner.html
Yi-Yuan Tang site on IBMT: http://www.yi-yuan.net/english/tyy.asp
Dalian University of Technology (English version): http://www.dlut.edu.cn/en/
National Institute on Drug Abuse-Intramural Research Program: http://irp.drugabuse.gov/
James S. Bower Foundation: http://www.jsbowerfoundation.org/
John Templeton Foundation: http://www.templeton.org/
Τετάρτη 8 Δεκεμβρίου 2010
Δευτέρα 6 Δεκεμβρίου 2010
Seeing the world differently
Seeing the world differently
How the brain's architecture makes our view of the world unique
IMAGE: The Ebbinghaus illusion. Most people will see the first circle as smaller than the second one Researchers found a strong link between the surface area of the primary visual cortex...
Click here for more information.
Wellcome Trust scientists have shown for the first time that exactly how we see our environment depends on the size of the visual part of our brain.
We are all familiar with the idea that our thoughts and emotions differ from one person to another, but most people assume that how we perceive the visual world is usually very similar from person to person. However, the primary visual cortex – the area at the back of the brain responsible for processing what we see in the world around us – is known to differ in size by up to three times from one individual to the next.
Now, researchers at the Wellcome Trust Centre for Neuroimaging at UCL (University College London) have shown for the first time that the size of this area affects how we perceive our environment. Their study is published online today in the journal Nature Neuroscience.
Dr D Samuel Schwarzkopf, Chen Song and Professor Geraint Rees showed a series of optical illusions to thirty healthy volunteers. These included the Ebbinghaus illusion, a well-known illusion in which two circles of the same size are each surrounded by circular 'petals'; one of the circles is surrounded by larger petals, the other by smaller petals. Most people will see the first circle as smaller than the second one
In a second optical illusion, the Ponzo illusion, the volunteers were shown two identically sized circles superimposed onto the image of a tunnel. In this illusion, the circle placed further back in the tunnel appears larger than that placed near the front.
By adapting these illusions, the researchers were able to show that individual volunteers saw the illusions differently. For example, some people saw a big (although illusory) difference in size between the two circles, but others barely saw any difference in apparent size.
Using functional magnetic resonance imaging (fMRI), the researchers were also able to measure the surface area of the primary visual cortex in each volunteer. They found a great deal of variability in the size of this area. Surprisingly, there was a strong link between its size and the extent to which volunteers perceived the size illusion – the smaller the area, the more pronounced the visual illusion.
"Our work is the first to show that the size of part of a person's brain can predict how they perceive their visual environment," explains Dr Schwarzkopf.
"Optical illusions mystify and inspire our imagination, but in truth they show us that how we see the world is not necessarily physically accurate, but rather depends a lot on our brains. Illusions such as the ones we used influence how big something looks; that is, they can trick us into believing that two identical objects have different sizes.
"We have shown that precisely how big something appears to you depends on the size of a brain area that is necessary for vision. How much your brain tricks you depends on how much 'real estate' your brain has put aside for visual processing.
How the brain's architecture makes our view of the world unique
IMAGE: The Ebbinghaus illusion. Most people will see the first circle as smaller than the second one Researchers found a strong link between the surface area of the primary visual cortex...
Click here for more information.
Wellcome Trust scientists have shown for the first time that exactly how we see our environment depends on the size of the visual part of our brain.
We are all familiar with the idea that our thoughts and emotions differ from one person to another, but most people assume that how we perceive the visual world is usually very similar from person to person. However, the primary visual cortex – the area at the back of the brain responsible for processing what we see in the world around us – is known to differ in size by up to three times from one individual to the next.
Now, researchers at the Wellcome Trust Centre for Neuroimaging at UCL (University College London) have shown for the first time that the size of this area affects how we perceive our environment. Their study is published online today in the journal Nature Neuroscience.
Dr D Samuel Schwarzkopf, Chen Song and Professor Geraint Rees showed a series of optical illusions to thirty healthy volunteers. These included the Ebbinghaus illusion, a well-known illusion in which two circles of the same size are each surrounded by circular 'petals'; one of the circles is surrounded by larger petals, the other by smaller petals. Most people will see the first circle as smaller than the second one
In a second optical illusion, the Ponzo illusion, the volunteers were shown two identically sized circles superimposed onto the image of a tunnel. In this illusion, the circle placed further back in the tunnel appears larger than that placed near the front.
By adapting these illusions, the researchers were able to show that individual volunteers saw the illusions differently. For example, some people saw a big (although illusory) difference in size between the two circles, but others barely saw any difference in apparent size.
Using functional magnetic resonance imaging (fMRI), the researchers were also able to measure the surface area of the primary visual cortex in each volunteer. They found a great deal of variability in the size of this area. Surprisingly, there was a strong link between its size and the extent to which volunteers perceived the size illusion – the smaller the area, the more pronounced the visual illusion.
"Our work is the first to show that the size of part of a person's brain can predict how they perceive their visual environment," explains Dr Schwarzkopf.
"Optical illusions mystify and inspire our imagination, but in truth they show us that how we see the world is not necessarily physically accurate, but rather depends a lot on our brains. Illusions such as the ones we used influence how big something looks; that is, they can trick us into believing that two identical objects have different sizes.
"We have shown that precisely how big something appears to you depends on the size of a brain area that is necessary for vision. How much your brain tricks you depends on how much 'real estate' your brain has put aside for visual processing.
Κυριακή 5 Δεκεμβρίου 2010
Intuition
When you struggle with a field of inquiry for a long long time and you eventually master and incorporate not only its formalism but its content, you can make use of it to build things one level higher.
Intuition is a merging of the understander with the understood. It is the deepest kind of knowledge.
Intuition is a merging of the understander with the understood. It is the deepest kind of knowledge.
METAPHORS, MODELS & THEORIES By Emanuel Derman
By Emanuel Derman
Theories deal with the world on its own terms, absolutely. Models are metaphors, relative descriptions of the object of their attention that compare it to something similar already better understood via theories. Models are reductions in dimensionality that always simplify and sweep dirt under the rug. Theories tell you what something is. Models tell you merely what something is partially like.
Introduction
Writing in the New York Times ("They Tried To Outsmart Wall Street" March 9, 2009) , Denis Overbye observed:
Dr. Derman, who spent 17 years at Goldman Sachs, and became managing director, was a forerunner of the many physicists and other scientists who have flooded Wall Street in recent years, moving from a world in which a discrepancy of a few percentage points in a measurement can mean a Nobel Prize or unending mockery to a world in which a few percent one way can land you in jail and a few percent the other way can win you your own private Caribbean island.
They are known as "quants" because they do quantitative finance. Seduced by a vision of mathematical elegance underlying some of the messiest of human activities, they apply skills they once hoped to use to untangle string theory or the nervous system to making money.
Derman, Overbye noted, "fell in love with a corner of finance that dealt with stock options."
"Options theory is kind of deep in some way. It was very elegant; it had the quality of physics" Derman told him.
— JB
EMANUEL DERMAN is physicist and a former managing director and head of the Quantitative Strategies group at Goldman, Sachs & Co., is a professor in Columbia University's Industrial Engineering and Operations Research Department, as well as a partner at Prisma Capital Partners. He is the author of My Life As A Quant.
Emanuel Derman's Edge Bio Page
PERMALINK
METAPHORS, MODELS & THEORIES
Summary
Theories deal with the world on its own terms, absolutely. Models are metaphors, relative descriptions of the object of their attention that compare it to something similar already better understood via theories. Models are reductions in dimensionality that always simplify and sweep dirt under the rug. Theories tell you what something is. Models tell you merely what something is partially like.
_____
1. METAPHORS
Sleep is the interest we have to pay on the capital which is called in at death; and the higher the rate of interest and the more regularly it is paid, the further the date of redemption is postponed.
So wrote Arthur Schopenhauer, comparing life to finance in a universe that must keep its books balanced. At birth you receive a loan – consciousness and light borrowed from the void, leaving an absence in the emptiness. Nightly, by yielding temporarily to the darkness of sleep, you restore some of the emptiness and keep the absence from growing limitlessly. Finally you must pay back the principal, make the void complete again, and return the life originally lent you.
By focusing on the common periodic nature of both sleep and interest payments, Schopenhauer extends the metaphor of a loan to life itself. The principal is life and consciousness, and death is the final repayment. Along the way, sleep is the periodic little death that keeps the borrower solvent.
Good metaphors are expansive; they compare something we don’t understand (sleep), to something we think we do (finance). They let you see in a new light both the object of interest and the substrate you rest it on, and enlighten upwards and downwards.
The common basis of Schopenhauer’s metaphoric extension is periodicity. Taking an analogy based on matching regularities and then extending it into distant regions is a time-honored trick of mathematicians. You can see it at work in the extension of the definition of the factorial function .
Using the exclamation point is traditional but clumsy. Since is a function of , it’s more elegant to express it via the function defined by , which satisfies the recursive property . You can regard this property as almost a definition of the factorial function. If you define , then for all integers greater than 1 can be found from the recursive definition.
The definition works only for positive integers n. The definition seems more malleable. Why shouldn’t there be some function that satisfies the relation where x is not necessarily a positive integer? Why shouldn’t the factorial function exist both for and, say, ?
The Swiss mathematician Leonhard Euler discovered (invented?) the gamma function that does indeed satisfy for all . For integer values of x, it agrees with the traditional factorial function. For non-integer or even complex values of x, serves as a smooth extrapolation or interpolation of the factorial from integer to non-integer arguments. It’s smooth because it coincides with the factorial function for positive integer arguments, but maintains the crucial recursive property for non-integers. Mathematicians call this kind of extension called analytic continuation.
The gamma function is a metaphorical extension of the factorial, in which one property, its recursion, becomes its most important feature and serves as the basis for extending it. It’s a bit like calling an automobile a horseless carriage, preserving the essence of carrying and removing the unnecessary horsefulness, or like calling a railroad ferrovia in Italian or Eisenbahn in German, focusing on the fact that it’s still a road, but one made instead of iron. Analytic continuation is a method of modeling a function. But whereas most models are restrictive – a model train is less than a real train – in mathematics, a new model can be something greater rather than diminished. That’s because mathematics deals entirely with its own world, and everything you do extends it rather than confines it.
Most of the words we use to describe our feelings are metaphors or models. To say you are elated is to say you feel as though have been lifted to a high place. But why is there something good about height? Because in the gravitational field of the earth all non-floating animals recognize the physical struggle necessary to rise, and experience wonder when they see the world spread out beneath them. Being elated is feeling as if you’d overcome gravity. People dream of flying.
Conversely, we speak of feeling depressed, as though we’d been pushed down to a low place. Things are looking up, we say, looking brighter, or less dark. These are metaphors too, derived from our physical senses. Metaphors nest, recursively. When we say the economy is depressed we are comparing the economy’s spirits (another metaphor) to the spirits of a person who feels as though he or she were pulled down by gravity.
Language is a tower of metaphors, each “higher” one resting on older ones “below”. Not every word can be a metaphor or else language would be meaningless. At the base of the tower are words like push and down, two of the non-metaphorical word-concepts on which the tower rests. Push and down are understood by us viscerally, because we are wetware, collections of chemicals rather than silicon or computer code, that experience the world through the sensations that chemicals are capable of. You cannot have lived without knowing what it is to have struggled against gravity and responded to light and warmth, and hence to know that down and dark are bad and up and light are good.
Had life arisen in outer space, free of gravity and light, there would be no perceptible down or up, and hence no possibility of depression or elation. You could be disheartened perhaps, but not depressed. You could feel full or empty, but not light or heavy, bright or dark. And you couldn’t take a dim view of your surroundings.
2. MODELS
We use the word model in many contexts. A model airplane is a scaled-down version of an actual plane, similar in some respects, but not all. The four-year-old’s plastic plane, the twelve-year-old’s radio-controlled glider and the aeronautical engineer’s wind-tunnel airplane are all model airplanes, though they differ from each other. The similarities to the real thing are important, but different users require different similarities.
What do we mean when we call some construct a model?
The Model T is a version of a Ford, one of a class of things belonging to the Ford category. Model T is an instance, less general, not everything a Ford might be.
A fashion model can be an actual person used to display clothing or cosmetics. It’s not everything a person might be. When you’re a model, only parts of you are important. A person is complete, the real thing.
An artist’s model is a proxy for the real thing. A mannequin is a proxy for a proxy. (The work of art that uses the proxy becomes a real thing again.)
A computer model of the weather tries to predict the weather in the future from the weather today. “Weather” is an abstraction for a collection of an indefinite number of qualities and quantities and the way they vary over the short term, among them temperature, pressure, humidity, wind speed. A weather model’s equations focus on a limited number of features of a limitlessly complex system. Even with the right equation, there is always the danger that one has omitted something ostensibly negligible but whose tail effects over long times are crucially important.
An economic model aims to do for the economy what the weather model does for the weather. It too embodies a set of equations that attempts to represent the behavior of the people and institutions interacting in an economy. But just as the notion of weather is more abstract than the notion of an airplane, so the concept of an economy is even more diffuse. Money, supply, demand and utility, just a few of the many variables in an economic model, are much harder to define (let alone quantify) than temperature and pressure. A “market” and an “economy” are even more clearly a construct of the mind. When you model the economy you are modeling abstractions.
Hayek pointed out that in the physical sciences the macroscopic concepts (gases, pressure, etc.) are concrete and the microscopic one (atoms and molecules) abstractions. But in economics, he argues, individuals are concrete and the “economy” is the abstraction.
The Black-Scholes Model tells you how to estimate the value of an option in terms of its underlying risk. It’s a recipe, an engineering model, a Sol LeWitt painting that contains instructions for how to create a work of art. Just as a weather model makes assumptions about how fluids flow and how heat undergoes convection, just as a souffle recipe makes assumptions about what happens when you whip egg whites, so the Black-Scholes model makes assumptions about how stock prices fluctuate up and/or down. But our assumptions about the behavior of stock markets are much less believable than our assumptions about how egg whites turn fluffy. Fluids and egg protein don’t care what people think about them; markets and stock prices do. Like a weather model (but even more so), Black-Scholes is a limited, ingeniously clever mental model of a complex system, a small box that tries to imitate the actual world outside.
The Standard Model, for which Sheldon Glashow, Abdus Salam and Steven Weinberg received the 1979 Nobel prize in physics, is a unified description of the smallest elementary particles (quarks and leptons) and the forces between them. The description incorporates into one coherent framework Maxwell’s 19th century theory of electromagnetism, the 1928 Dirac theory of the electron and Fermi’s 1934 theory of beta decay in which all of these apparently disparate forces are only superficially different aspects of a single more general force. The standard model is not really a “model” at all, but rather a description, and hence a theory.
A theory, as I will argue below, attempts to provide an accurate description of the nature of things, unifying the outward with the inward, not just saving the appearances but identifying their essence. A model arises out of conscious analogy. A theory arises out of a deep intuitive identification of the inner and the outer.
3. WHY IS A MODEL A MODEL?
A model airplane, however complex, is simple when compared to the real thing.
There is a gap between the model and the object of its focus. The model is not the object, though we may wish it were.
A model is a metaphor of limited applicability, not the thing itself. Calling a computer an electronic brain once cast light on the function of computers. Nevertheless, a computer is not an electronic brain. Calling the brain a computer is a model too. In tackling the mysterious world via models we do our best to explain the thus-far incomprehensible by describing it in terms of the things we already partially comprehend. Models, like metaphors, take the properties of something rich and project them onto something strange.
A model focuses on parts rather than the whole. It is a caricature which overemphasizes some features at the expense of others.
A model is a fetish in which the importance of one key part of the object of interest is obsessively exaggerated until it comes to represent the object’s quintessence, a shoe or corset standing in for a woman. (Is that perhaps why most modelers are male?). But the shoe or corset isn’t the woman, just the most important part of the woman for this model user.
The most valuable knowledge is unconscious. Until you can do something without thinking, you can’t move farther up the hierarchy of metaphors of description in language or science. In Zen in the Art of Archery, Eugen Herrigel recounts the struggle to make mental knowledge visceral. Thinking for yourself is hard work. Models provide ways of letting other people do the thinking for you. With Feynman diagrams, almost anyone can calculate elementary particle cross sections mechanically.
In physics or finance, the first major struggle is to gain some intuition about how to proceed; the second struggle is to transform that intuition into something more formulaic, a set of rules anyone can follow, rules that no longer require the original insight itself. One person’s breakthrough becomes everybody’s possession.
The world is multi-dimensional. Models allow us to project the object into a smaller space and then extrapolate or interpolate within it. At some point the extrapolation will break down. What’s amazing is how well it sometimes works, especially in the physical sciences.
But extrapolation based on limited information is dangerous; extrapolation depends on a model, not a fact. Estrogen supplements cause their own problems, and margarine only seemed better than butter.
When unconsciously used models result in paradoxes or conflicts, it becomes necessary to expose and then examine unconscious assumptions. This is what Einstein did with the concept of simultaneity, what Lee and Yang did with parity invariance.
4. WHY IS A THEORY A THEORY?
Models are analogies, and always describe something relative to something else. Theories, in contrast, are the real thing. They don’t compare; they describe the essence, without reference. Every fact, as Goethe wrote, is a theory.
In that sense, a theory is the ultimate non-metaphor.
Moses, tending the flock of his father-in-law Jethro near the mountain of Horeb, saw a burning bush whose flame would not consume it. God, from within the bush, declared himself to Moses and commanded him to deliver the Israelites from Pharaoh.
Whom shall I tell them sent me? asks Moses.
Tell them: I am that which I am, said the voice.
God is riffing on his true name: the Hebrew word for I will be is EHYH. Its root is HVH, the last three letters of God’s name. HVH means being, and is also the name of the present tense in Hebrew grammar. YHVH (Yahweh or Jehovah) is the irreducible substance, the ultimate non-metaphor too, the bottom-level primitive out of which everything else is constructed. Hence, no graven images, no models, are possible. You can’t ask ‘Why?’ about YHVH; you can ask only ‘How?’.
Theories tell you what something is. Models tell you only what something is more or less like. Unless you constantly remember that, therein lies their danger.
My favorite theory is Dirac’s 1928 theory of the electron, still correct today. He sought an equation that satisfied both quantum mechanics and special relativity. The one he found had four solutions. Two of them described the electron that physicists already knew about, a particle with negative charge and two spin states. But Dirac’s equation had two additional solutions, similar to the ones he’d already found, but with incomprehensibly negative energy. The positive-energy solutions described the electron so well that Dirac felt obliged to make sense of the negative-energy ones too.
Dirac postulated that the void, the medium that we call empty space, what physicists call the vacuum, is in fact filled to its rim with negative-energy electrons, and they constitute an infinite sea. This metaphorical Dirac sea is the vacuum we inhabit, and, accustomed to it, we don’t notice the infinite number of negative charges surrounding us. (We smell only pollutants, not air itself.) If this is true, argued Dirac, then when you shoot light into the vacuum and eject a negative energy electron, a hole is left behind. This absence of an electron and its negative charge behaves exactly like an electron with positive charge. Anderson discovered this so-called positron in 1932, and astounded all the physicists uncomfortable with what had been a metaphorical stretch. Just as life is a temporary hole in the darkness, so here too absence becomes a presence.
Dirac’s equation transcended its metaphor and became a theory of reality. A brain may be like a computer, an atom may be like a miniature solar system, but an electron is the Dirac equation. Dirac’s theory of the electron stands on its own two feet, beyond metaphor, the thing itself. Like God in the burning bush identifying himself to Moses, the theory of the electron pronounces, “I am that which I am.”
Theories are deep and inexplicable, difficult to find; they require verification; they are right when they are right. Models are shallow and somewhat easier to invent; they require explanation. We need models as well as theories.
5. SPINOZA'S THEORY OF THE AFFECTS
Spinoza approached what he called the affects, human emotions, in the same way that Euclid approached triangles and squares, aiming to understand their inter-relations by means of principles, logic and deduction. Spinoza’s avowed aim was to find a method to escape the violent sway emotions inflict on human beings caught in their grip.
The Primitives
Spinoza’s primitives are pain, pleasure and desire. Every adult with a human body knows by direct experience what these feelings are, though Spinoza, following Euclid’s definitions of points and lines, makes an attempt to define them.
Desire, he writes, is appetite conscious of itself.
Its cohorts are two more primitives: pleasure and pain.
Though he defines them, as is the case with Euclid’s points and lines, we can recognize neither pain nor pleasure from their verbal definitions; we need to have experienced them directly and had them named. They lie beneath all the other affects and can conveniently be thought of as closer to organic conditions than psychic ones.
Spinoza distinguishes finely between local and global sensations. “Pleasure and pain,” he writes, “Are ascribed to a man when one part of him is affected more than the rest, whereas cheerfulness and melancholy are ascribed to him when all are equally affected.” Suffering, therefore, is localized pain, while melancholy is globalized pain.
His definitions of good and bad are utilitarian at the individual level. “By good I here mean every kind of pleasure, and all that conduces thereto, especially that which satisfies our longings, whatsoever they may be. By evil, I mean every kind of pain, especially that which frustrates our longings.” Good is that which brings pleasure and bad is that which brings pain.
The Derivatives
The primitives are the most fundamental affects, and the more complex emotions bear a more indirect link to the three just named. Just as financial stock options are derivatives that depend on the underlying stock price, so more complex human emotions derive their force from their relation to the three underlying sensations of pain, pleasure and desire. Spinoza elaborates:
Love is pleasure associated with an external object.
Hate is pain associated with an external object.
Hope is the expectation of future pleasure when the outcome is uncertain and doubtful.
Joy is the pleasure we experience when that doubtful expectation is fulfilled.
Disappointment is the pain of unfulfilled pleasure.
Pity is pain accompanied by the idea of evil which has befallen someone else whom we conceive to be like ourselves.
More complex emotions, like exotic financial derivatives, depend on two underlying primitives.
Envy is pain at another's pleasure, like a convertible bond whose value depends on stock prices and interest rates.
Conversely, though Spinoza doesn’t name it, Schadenfreude is pleasure at another’s pain.
Cruelty involves all three primitives: Spinoza defines it as the desire to inflict pain on someone we love or pity.
Financially speaking, Cruelty is a convertible bond whose value depends on the stock price of the underlying stock, riskless interest rates and credit spreads.
Spinoza adds to his system three additional primitives that are meta-emotions. The first is Vacillation, the state of oscillation between two emotions. Thus Jealousy, he explains, is the vacillation between hate and envy towards an object of love in the presence of a rival for it. Jealousy is a derivative of envy, and envy is a derivative of pleasure and pain. If we follow the links far enough, we end up always at pain, pleasure and desire.
The second addition is Wonder. Wonder is what we experience when confronted by something that fills the mind to the exclusion of all else, something unrelated to anything else. Wonder is what we experience in the presence of Yahweh in the burning bush, who is what he is, and bears no relation to anything else.
Spinoza’s final primitive is Contempt, the feeling we have when we contemplate something that most forcibly reminds us of all the qualities it lacks. An absence becomes a nameable presence.
I call what Spinoza created a theory rather than a model. He doesn’t make analogies; he doesn’t attempt to explain how humans behave by comparing them to some other system we already understand. He begins with observations about human beings, obtained through experience, introspection and intuition. He produced a theory accessible to everyone because it analyzes everyday human experiences.
The figure below illustrates the dependency of all the emotions on Desire, Pleasure and Pain.
double click to enlarge
6. Intuition
It takes intuition to discover theories. Intuition may sound casual but it results from intimate knowledge acquired by careful observation and painstaking effort. John Maynard Keynes wrote a speech for the Newton tercentary in which he commented on Newton’s qualities:
Newton came to be thought of as the first and greatest of the modern age of scientists, a rationalist, one who taught us to think on the lines of cold and untinctured reason. I do not see him in this light. Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago …
I believe that the clue to his mind is to be found in his unusual powers of continuous concentrated introspection … His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen straight through it. I fancy his pre-eminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted. Anyone who has ever attempted pure scientific or philosophical thought knows how one can hold a problem momentarily in one's mind and apply all one's powers of concentration to piercing through it, and how it will dissolve and escape and you find that what you are surveying is a blank. I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret. Then being a supreme mathematical technician he could dress it up, how you will, for purposes of exposition, but it was his intuition which was pre-eminently extraordinary - 'so happy in his conjectures', said De Morgan, 'as to seem to know more than he could possibly have any means of proving'.
This perception – that his insight arose independent of his proof – was also James Clerk Maxwell’s opinion about André-Marie Ampère, who, in 1820, discovered the connection between electricity and magnetism. Referring to Ampère as the “Newton of electricity”, Maxwell, who extended Ampère’s discoveries into Maxwell’s equations and found that they described light, wrote:
“We can scarcely believe that Ampere really discovered the law of action by means of the experiments which he describes. We are led to suspect, what, indeed, he tells us himself, that he discovered the law by some process which he has not shown us, and that when he had afterwards built up a perfect demonstration, he removed all traces of the scaffolding by which he had built it.”
When you struggle with a field of inquiry for a long long time and you eventually master and incorporate not only its formalism but its content, you can make use of it to build things one level higher.
Intuition is a merging of the understander with the understood. It is the deepest kind of knowledge.
7. Models in Finance
There are no genuine theories in finance. Financial models are always models of comparison, of relative value. They are metaphors. The efficient market model assumes stock prices behave like smoke diffusing through a room. These are comparisons that have some reasonableness, but they’re not even remotely fact. Newton’s laws and Maxwell’s equations are. There is almost no gap between the object and their description. You can say that stock prices behave like smoke. You cannot say that light behaves like Maxwell’s equations. Light is Maxwell’s equations.
All concepts, perhaps all things, are mental. But there are no genuine theories in finance because finance is concerned with value, an even more subjective concept than heat or pressure. Furthermore, it is very difficult to find the scientific laws or even regularities governing the behavior of economies: there are very few isolated economic machines, and so one cannot carry out the repeated experiments that science requires. History is important in economics. Credit markets tomorrow won't behave like credit markets last year because we have learned what happened last year, and cannot get back to the initial conditions of a year ago. Human beings and societies learn; physical systems by and large don't.
For an experiment to be approximately repeatable, history has to be unimportant. That requires that the system couple very weakly to the rest of the universe. A coin flip can be repeated ad infinitum under almost the same conditions, because external conditions affect its outcome hardly at all. That’s not the case in finance.
What is the point of a model in finance?
It takes only a little experience to see that it’s not the same as the point of a model in physics or chemistry. Mostly, the point of a model is not prediction or divination. Here’s a simple but prototypical financial model that has most of the characteristics of more sophisticated models.
How do you estimate the price of a seven-room apartment on Park Ave. if someone tells you the market price of a typical two-room apartment in Battery Park City? Most likely, you figure out the price per square foot of the two-room apartment. Then you multiply by the square footage of the Park Ave. apartment. Finally you make some rule-of-thumb higher-order corrections for location, park views, light, facilities and so on. You might develop a model for those too.
The model’s critical parameter is the implied price per square foot. You calibrate the model to Battery Park City. Then you use it to interpolate or extrapolate to Park Ave. The price per square foot is implied from the market price of the Battery Park City apartments; it’s not the realized construction price per square foot because there are other variables – exposure, quality of construction, neighborhood – that are subsumed into that one implied number.
Calibration is dangerous; it’s always the fitting a wrong model to the only world we know, and then using it to extrapolate or interpolate. The closer your model to the behavior of the world, the less dangerous your extrapolation.
The Aim of Financial Models
The way property markets use implied price per square foot illustrates the functions of financial models more generally.
Models are used to rank securities by value.
Apartments have manifold features. Implied price per square foot can be used to rank and compare many similar but not identical apartments. It provides a simple one-dimensional scale on which to begin ranking apartments by value. The single number given by implied price per square foot doesn’t truly reflect the value of the apartment; it provides a starting point after which more qualitative factors must be taken into account.
Models are used to interpolate from liquid prices to illiquid ones
In finance, models are used less for divination than in order to interpolate or extrapolate from the known prices of liquid securities to the values of illiquid securities at the current time – in the example above from the Battery Park City price to the Park Ave. value. The Black-Scholes model proceeds from a known stock price and a riskless bond price to the unknown price of a hybrid, an option, similar to the way one estimates the value of fruit salad from its constituent fruits.
No model is correct – a model is not a theory – but models can provide immensely helpful ways of initial estimates of value.
Models transform intuitive linear quantities into nonlinear dollar values
In finance a model is also a means of translating acquired intuition into dollar values. The apartment-value model transforms price per square foot into the value of the apartment. It’s easier to begin with an estimate of price per square foot because that quantity captures so much of the variability of apartment prices. Similarly, it’s easier to convert one’s intuition about future volatility into current options prices than it is to guess at the appropriate prices themselves.
8. THE ONE LAW OF FINANCE
Research papers in quantitative finance look superficially like those in natural science, but the similarity is deceptive. There are no deep laws or theories in finance that can be expressed in mathematics.
The one law you can rely on in finance is the law of one price, which roughly put, dictates: “If you want to know the value of a financial security, use the known price of another security that’s as similar to it as possible.”
The wonderful thing about this law – it’s valuation by analogy – when compared with almost everything else in economics, is that it dispenses with utility functions, the unobservable hidden variable whose ghostly presence permeates most of faux-quantitative economic theory.
The law of one price is not a law of nature. It’s a general reflection on the practices of human beings, who, when they have enough time and enough information, will grab a bargain when they see one. The law usually holds in the long run, in well-oiled markets with enough savvy participants, but there are always short- or even longer-term exceptions that persist.
How do you use the law of one price to determine value? If you want to estimate the unknown value of a target security, you must find some other replicating portfolio, a collection of more liquid securities that, collectively, is similar to, i.e. has the same future payoffs as the target, no matter how the future turns out. The target’s value is then simply that value of the replicating portfolio.
Where do models enter? It takes a model to demonstrate similarity, to show that the target and the replicating portfolio have identical future payoffs under all circumstances. To demonstrate the identity of future payoffs, you must (1) specify what you mean by “all circumstances,” for each security, and (2) you must find a strategy for creating a replicating portfolio that, in each future scenario or eventuality, will have payoffs identical to those of the target. That’s what the Black-Scholes options model does – it tells you precisely how to replicate an option out of stocks and bonds, under certain assumptions. It’s like a recipe that tells you how to make fruit salad – an option – out of fruit, the stocks and bonds. And, ingeniously used, it tells you how to do the inverse – to figure out the value of one type of fruit given the price of other fruits and fruit salad.
Most of the mathematical complexity in finance involves the description of the range of future behavior of each security’s price. Trying to specify all circumstances always reminds me of the 1967 movie Bedazzled, starring Peter Cook and Dudley Moore. In this retelling of the German legend of Faust, Dudley Moore plays a short-order cook at a Wimpy’s chain restaurant in London who sells his soul to the devil in exchange for seven chances to specify the circumstances under which he can achieve his romantic aims with the Wimpy’s waitress he desires. Each time that the devil asks him to specify the romantic scenarios under which he believes he will succeed, he cannot get them quite specific enough. He says he wants to be alone with the waitress in a beautiful place where they are both in love with each other. He gets what he wants—with a snap of the devil’s fingers, he and his beloved are instantly transported to a country estate where he is a guest of the owner, her husband, whom her principles will not allow her to betray. In the final episode, he wishes for them to be alone together and in love with each other in a quiet place where no one will bother them. He gets his wish: The devil makes them both nuns in a convent where everyone has taken a vow of silence. This difficulty is the same difficulty we have when specifying future scenarios in financial models—like the devil, markets always eventually outwit us. Even if markets are not strictly random, their vagaries are too rich to capture in a few sentences or equations.
So die the dreams of financial theories. Only imperfect models remain.
9. THE RIGHT WAY TO USE MODELS
Given that finance’s best tools are shaky models, the best strategy is to use models as little as possible, and to replicate making as little assumptions as you can. Here are some other rules I’ve found to be useful as a practitioner.
Avoid too much axiomatization
Axiomatization is for mathematics. Finance is about the real world. Every financial axiom is pretty much wrong; the practical question is: how wrong, and can you still make use of it?
Good Models are Vulgar in a Sophisticated Way
In physics it pays to drop down deep, several levels below what you can observe (think of Newton, Maxwell, Dirac), formulate an elegant principle, and then rise back to the surface to work out the observable consequences. In financial valuation, which lacks deep scientific principles, it’s better to stay shallow and use models that have as direct as possible a path between observation of similarity and its consequences.
Markets are by definition vulgar, and correspondingly the most useful models are wisely vulgar too, using variables that the crowd uses, like price per square foot, to describe the phenomena they observe. Build vulgar models in a sophisticated way.
Of course, over time crowds and markets get smarter and the definition of vulgarity changes to encompass increasingly sophisticated concepts.
Sweep Dirt Under The Rug, But Let Users Know About It
One should be very humble in applying mathematics to markets, and be extremely wary of ambitious theories, which are, when you face facts, trying to model human behavior.
Whenever we make a model of something involving human beings, we are trying to force the ugly stepsister's foot into Cinderella's pretty glass slipper. It doesn't fit without cutting off some essential parts. Models inevitably mask as well as expose risk. You must start with models and then overlay them with common sense and experience.
The world of markets doesn’t exactly match the ideal circumstances a model assumes, but a robust model allows a savvy user to qualitatively adjust for those mismatches. A user should should know what has been assumed when he uses the model, and he should know exactly what has been swept out of view.
Think of Models as Gedanken Experiments
It’s impossible to make a correct financial model. Therefore, I like to think of financial models as gedanken experiments, like those Einstein carried out when he pictured himself surfing a light wave or Schrodinger when he pictured a macroscopic cat subject to quantum effects.
I believe that’s the right way to use mathematical models in finance, and the way experienced practitioners do use them. Models are only models, not the thing in itself. So, we can’t expect them to be truly right. Models are better regarded as a collection of parallel thought universes you can explore. Each universe should be consistent, but the actual financial and human world, unlike the world of matter, is going to be infinitely more complex than any model you make of it. You are always trying to shoe-horn the real world into one of the models to see how useful an approximation that is.
Beware of Idolatry
The greatest conceptual danger is idolatry, imagining that someone can write down a theory that encapsulates human behavior and relieves you of the difficulty of constant thinking. A model may be entrancing but no matter how hard you try, you will not be able to breath true life into it. To confuse the model with a theory is to embrace a future disaster driven by the belief that humans obey mathematical rules.
Financial modelers must therefore compromise, must firmly decide what small part of the financial world is of greatest current interest, decide on its key features, and make a mock-up of only those. A model cannot include everything. If you are interested in everything you are interested in too much. A successful financial model must have limited scope; you must work with simple analogies; in the end, you are trying to rank complex objects by projecting them onto a low-dimensional scale.
In physics there may one day be a Theory of Everything; in finance and the social sciences, you have to work hard to have a usable Model of Anything.
A
Theories deal with the world on its own terms, absolutely. Models are metaphors, relative descriptions of the object of their attention that compare it to something similar already better understood via theories. Models are reductions in dimensionality that always simplify and sweep dirt under the rug. Theories tell you what something is. Models tell you merely what something is partially like.
Introduction
Writing in the New York Times ("They Tried To Outsmart Wall Street" March 9, 2009) , Denis Overbye observed:
Dr. Derman, who spent 17 years at Goldman Sachs, and became managing director, was a forerunner of the many physicists and other scientists who have flooded Wall Street in recent years, moving from a world in which a discrepancy of a few percentage points in a measurement can mean a Nobel Prize or unending mockery to a world in which a few percent one way can land you in jail and a few percent the other way can win you your own private Caribbean island.
They are known as "quants" because they do quantitative finance. Seduced by a vision of mathematical elegance underlying some of the messiest of human activities, they apply skills they once hoped to use to untangle string theory or the nervous system to making money.
Derman, Overbye noted, "fell in love with a corner of finance that dealt with stock options."
"Options theory is kind of deep in some way. It was very elegant; it had the quality of physics" Derman told him.
— JB
EMANUEL DERMAN is physicist and a former managing director and head of the Quantitative Strategies group at Goldman, Sachs & Co., is a professor in Columbia University's Industrial Engineering and Operations Research Department, as well as a partner at Prisma Capital Partners. He is the author of My Life As A Quant.
Emanuel Derman's Edge Bio Page
PERMALINK
METAPHORS, MODELS & THEORIES
Summary
Theories deal with the world on its own terms, absolutely. Models are metaphors, relative descriptions of the object of their attention that compare it to something similar already better understood via theories. Models are reductions in dimensionality that always simplify and sweep dirt under the rug. Theories tell you what something is. Models tell you merely what something is partially like.
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1. METAPHORS
Sleep is the interest we have to pay on the capital which is called in at death; and the higher the rate of interest and the more regularly it is paid, the further the date of redemption is postponed.
So wrote Arthur Schopenhauer, comparing life to finance in a universe that must keep its books balanced. At birth you receive a loan – consciousness and light borrowed from the void, leaving an absence in the emptiness. Nightly, by yielding temporarily to the darkness of sleep, you restore some of the emptiness and keep the absence from growing limitlessly. Finally you must pay back the principal, make the void complete again, and return the life originally lent you.
By focusing on the common periodic nature of both sleep and interest payments, Schopenhauer extends the metaphor of a loan to life itself. The principal is life and consciousness, and death is the final repayment. Along the way, sleep is the periodic little death that keeps the borrower solvent.
Good metaphors are expansive; they compare something we don’t understand (sleep), to something we think we do (finance). They let you see in a new light both the object of interest and the substrate you rest it on, and enlighten upwards and downwards.
The common basis of Schopenhauer’s metaphoric extension is periodicity. Taking an analogy based on matching regularities and then extending it into distant regions is a time-honored trick of mathematicians. You can see it at work in the extension of the definition of the factorial function .
Using the exclamation point is traditional but clumsy. Since is a function of , it’s more elegant to express it via the function defined by , which satisfies the recursive property . You can regard this property as almost a definition of the factorial function. If you define , then for all integers greater than 1 can be found from the recursive definition.
The definition works only for positive integers n. The definition seems more malleable. Why shouldn’t there be some function that satisfies the relation where x is not necessarily a positive integer? Why shouldn’t the factorial function exist both for and, say, ?
The Swiss mathematician Leonhard Euler discovered (invented?) the gamma function that does indeed satisfy for all . For integer values of x, it agrees with the traditional factorial function. For non-integer or even complex values of x, serves as a smooth extrapolation or interpolation of the factorial from integer to non-integer arguments. It’s smooth because it coincides with the factorial function for positive integer arguments, but maintains the crucial recursive property for non-integers. Mathematicians call this kind of extension called analytic continuation.
The gamma function is a metaphorical extension of the factorial, in which one property, its recursion, becomes its most important feature and serves as the basis for extending it. It’s a bit like calling an automobile a horseless carriage, preserving the essence of carrying and removing the unnecessary horsefulness, or like calling a railroad ferrovia in Italian or Eisenbahn in German, focusing on the fact that it’s still a road, but one made instead of iron. Analytic continuation is a method of modeling a function. But whereas most models are restrictive – a model train is less than a real train – in mathematics, a new model can be something greater rather than diminished. That’s because mathematics deals entirely with its own world, and everything you do extends it rather than confines it.
Most of the words we use to describe our feelings are metaphors or models. To say you are elated is to say you feel as though have been lifted to a high place. But why is there something good about height? Because in the gravitational field of the earth all non-floating animals recognize the physical struggle necessary to rise, and experience wonder when they see the world spread out beneath them. Being elated is feeling as if you’d overcome gravity. People dream of flying.
Conversely, we speak of feeling depressed, as though we’d been pushed down to a low place. Things are looking up, we say, looking brighter, or less dark. These are metaphors too, derived from our physical senses. Metaphors nest, recursively. When we say the economy is depressed we are comparing the economy’s spirits (another metaphor) to the spirits of a person who feels as though he or she were pulled down by gravity.
Language is a tower of metaphors, each “higher” one resting on older ones “below”. Not every word can be a metaphor or else language would be meaningless. At the base of the tower are words like push and down, two of the non-metaphorical word-concepts on which the tower rests. Push and down are understood by us viscerally, because we are wetware, collections of chemicals rather than silicon or computer code, that experience the world through the sensations that chemicals are capable of. You cannot have lived without knowing what it is to have struggled against gravity and responded to light and warmth, and hence to know that down and dark are bad and up and light are good.
Had life arisen in outer space, free of gravity and light, there would be no perceptible down or up, and hence no possibility of depression or elation. You could be disheartened perhaps, but not depressed. You could feel full or empty, but not light or heavy, bright or dark. And you couldn’t take a dim view of your surroundings.
2. MODELS
We use the word model in many contexts. A model airplane is a scaled-down version of an actual plane, similar in some respects, but not all. The four-year-old’s plastic plane, the twelve-year-old’s radio-controlled glider and the aeronautical engineer’s wind-tunnel airplane are all model airplanes, though they differ from each other. The similarities to the real thing are important, but different users require different similarities.
What do we mean when we call some construct a model?
The Model T is a version of a Ford, one of a class of things belonging to the Ford category. Model T is an instance, less general, not everything a Ford might be.
A fashion model can be an actual person used to display clothing or cosmetics. It’s not everything a person might be. When you’re a model, only parts of you are important. A person is complete, the real thing.
An artist’s model is a proxy for the real thing. A mannequin is a proxy for a proxy. (The work of art that uses the proxy becomes a real thing again.)
A computer model of the weather tries to predict the weather in the future from the weather today. “Weather” is an abstraction for a collection of an indefinite number of qualities and quantities and the way they vary over the short term, among them temperature, pressure, humidity, wind speed. A weather model’s equations focus on a limited number of features of a limitlessly complex system. Even with the right equation, there is always the danger that one has omitted something ostensibly negligible but whose tail effects over long times are crucially important.
An economic model aims to do for the economy what the weather model does for the weather. It too embodies a set of equations that attempts to represent the behavior of the people and institutions interacting in an economy. But just as the notion of weather is more abstract than the notion of an airplane, so the concept of an economy is even more diffuse. Money, supply, demand and utility, just a few of the many variables in an economic model, are much harder to define (let alone quantify) than temperature and pressure. A “market” and an “economy” are even more clearly a construct of the mind. When you model the economy you are modeling abstractions.
Hayek pointed out that in the physical sciences the macroscopic concepts (gases, pressure, etc.) are concrete and the microscopic one (atoms and molecules) abstractions. But in economics, he argues, individuals are concrete and the “economy” is the abstraction.
The Black-Scholes Model tells you how to estimate the value of an option in terms of its underlying risk. It’s a recipe, an engineering model, a Sol LeWitt painting that contains instructions for how to create a work of art. Just as a weather model makes assumptions about how fluids flow and how heat undergoes convection, just as a souffle recipe makes assumptions about what happens when you whip egg whites, so the Black-Scholes model makes assumptions about how stock prices fluctuate up and/or down. But our assumptions about the behavior of stock markets are much less believable than our assumptions about how egg whites turn fluffy. Fluids and egg protein don’t care what people think about them; markets and stock prices do. Like a weather model (but even more so), Black-Scholes is a limited, ingeniously clever mental model of a complex system, a small box that tries to imitate the actual world outside.
The Standard Model, for which Sheldon Glashow, Abdus Salam and Steven Weinberg received the 1979 Nobel prize in physics, is a unified description of the smallest elementary particles (quarks and leptons) and the forces between them. The description incorporates into one coherent framework Maxwell’s 19th century theory of electromagnetism, the 1928 Dirac theory of the electron and Fermi’s 1934 theory of beta decay in which all of these apparently disparate forces are only superficially different aspects of a single more general force. The standard model is not really a “model” at all, but rather a description, and hence a theory.
A theory, as I will argue below, attempts to provide an accurate description of the nature of things, unifying the outward with the inward, not just saving the appearances but identifying their essence. A model arises out of conscious analogy. A theory arises out of a deep intuitive identification of the inner and the outer.
3. WHY IS A MODEL A MODEL?
A model airplane, however complex, is simple when compared to the real thing.
There is a gap between the model and the object of its focus. The model is not the object, though we may wish it were.
A model is a metaphor of limited applicability, not the thing itself. Calling a computer an electronic brain once cast light on the function of computers. Nevertheless, a computer is not an electronic brain. Calling the brain a computer is a model too. In tackling the mysterious world via models we do our best to explain the thus-far incomprehensible by describing it in terms of the things we already partially comprehend. Models, like metaphors, take the properties of something rich and project them onto something strange.
A model focuses on parts rather than the whole. It is a caricature which overemphasizes some features at the expense of others.
A model is a fetish in which the importance of one key part of the object of interest is obsessively exaggerated until it comes to represent the object’s quintessence, a shoe or corset standing in for a woman. (Is that perhaps why most modelers are male?). But the shoe or corset isn’t the woman, just the most important part of the woman for this model user.
The most valuable knowledge is unconscious. Until you can do something without thinking, you can’t move farther up the hierarchy of metaphors of description in language or science. In Zen in the Art of Archery, Eugen Herrigel recounts the struggle to make mental knowledge visceral. Thinking for yourself is hard work. Models provide ways of letting other people do the thinking for you. With Feynman diagrams, almost anyone can calculate elementary particle cross sections mechanically.
In physics or finance, the first major struggle is to gain some intuition about how to proceed; the second struggle is to transform that intuition into something more formulaic, a set of rules anyone can follow, rules that no longer require the original insight itself. One person’s breakthrough becomes everybody’s possession.
The world is multi-dimensional. Models allow us to project the object into a smaller space and then extrapolate or interpolate within it. At some point the extrapolation will break down. What’s amazing is how well it sometimes works, especially in the physical sciences.
But extrapolation based on limited information is dangerous; extrapolation depends on a model, not a fact. Estrogen supplements cause their own problems, and margarine only seemed better than butter.
When unconsciously used models result in paradoxes or conflicts, it becomes necessary to expose and then examine unconscious assumptions. This is what Einstein did with the concept of simultaneity, what Lee and Yang did with parity invariance.
4. WHY IS A THEORY A THEORY?
Models are analogies, and always describe something relative to something else. Theories, in contrast, are the real thing. They don’t compare; they describe the essence, without reference. Every fact, as Goethe wrote, is a theory.
In that sense, a theory is the ultimate non-metaphor.
Moses, tending the flock of his father-in-law Jethro near the mountain of Horeb, saw a burning bush whose flame would not consume it. God, from within the bush, declared himself to Moses and commanded him to deliver the Israelites from Pharaoh.
Whom shall I tell them sent me? asks Moses.
Tell them: I am that which I am, said the voice.
God is riffing on his true name: the Hebrew word for I will be is EHYH. Its root is HVH, the last three letters of God’s name. HVH means being, and is also the name of the present tense in Hebrew grammar. YHVH (Yahweh or Jehovah) is the irreducible substance, the ultimate non-metaphor too, the bottom-level primitive out of which everything else is constructed. Hence, no graven images, no models, are possible. You can’t ask ‘Why?’ about YHVH; you can ask only ‘How?’.
Theories tell you what something is. Models tell you only what something is more or less like. Unless you constantly remember that, therein lies their danger.
My favorite theory is Dirac’s 1928 theory of the electron, still correct today. He sought an equation that satisfied both quantum mechanics and special relativity. The one he found had four solutions. Two of them described the electron that physicists already knew about, a particle with negative charge and two spin states. But Dirac’s equation had two additional solutions, similar to the ones he’d already found, but with incomprehensibly negative energy. The positive-energy solutions described the electron so well that Dirac felt obliged to make sense of the negative-energy ones too.
Dirac postulated that the void, the medium that we call empty space, what physicists call the vacuum, is in fact filled to its rim with negative-energy electrons, and they constitute an infinite sea. This metaphorical Dirac sea is the vacuum we inhabit, and, accustomed to it, we don’t notice the infinite number of negative charges surrounding us. (We smell only pollutants, not air itself.) If this is true, argued Dirac, then when you shoot light into the vacuum and eject a negative energy electron, a hole is left behind. This absence of an electron and its negative charge behaves exactly like an electron with positive charge. Anderson discovered this so-called positron in 1932, and astounded all the physicists uncomfortable with what had been a metaphorical stretch. Just as life is a temporary hole in the darkness, so here too absence becomes a presence.
Dirac’s equation transcended its metaphor and became a theory of reality. A brain may be like a computer, an atom may be like a miniature solar system, but an electron is the Dirac equation. Dirac’s theory of the electron stands on its own two feet, beyond metaphor, the thing itself. Like God in the burning bush identifying himself to Moses, the theory of the electron pronounces, “I am that which I am.”
Theories are deep and inexplicable, difficult to find; they require verification; they are right when they are right. Models are shallow and somewhat easier to invent; they require explanation. We need models as well as theories.
5. SPINOZA'S THEORY OF THE AFFECTS
Spinoza approached what he called the affects, human emotions, in the same way that Euclid approached triangles and squares, aiming to understand their inter-relations by means of principles, logic and deduction. Spinoza’s avowed aim was to find a method to escape the violent sway emotions inflict on human beings caught in their grip.
The Primitives
Spinoza’s primitives are pain, pleasure and desire. Every adult with a human body knows by direct experience what these feelings are, though Spinoza, following Euclid’s definitions of points and lines, makes an attempt to define them.
Desire, he writes, is appetite conscious of itself.
Its cohorts are two more primitives: pleasure and pain.
Though he defines them, as is the case with Euclid’s points and lines, we can recognize neither pain nor pleasure from their verbal definitions; we need to have experienced them directly and had them named. They lie beneath all the other affects and can conveniently be thought of as closer to organic conditions than psychic ones.
Spinoza distinguishes finely between local and global sensations. “Pleasure and pain,” he writes, “Are ascribed to a man when one part of him is affected more than the rest, whereas cheerfulness and melancholy are ascribed to him when all are equally affected.” Suffering, therefore, is localized pain, while melancholy is globalized pain.
His definitions of good and bad are utilitarian at the individual level. “By good I here mean every kind of pleasure, and all that conduces thereto, especially that which satisfies our longings, whatsoever they may be. By evil, I mean every kind of pain, especially that which frustrates our longings.” Good is that which brings pleasure and bad is that which brings pain.
The Derivatives
The primitives are the most fundamental affects, and the more complex emotions bear a more indirect link to the three just named. Just as financial stock options are derivatives that depend on the underlying stock price, so more complex human emotions derive their force from their relation to the three underlying sensations of pain, pleasure and desire. Spinoza elaborates:
Love is pleasure associated with an external object.
Hate is pain associated with an external object.
Hope is the expectation of future pleasure when the outcome is uncertain and doubtful.
Joy is the pleasure we experience when that doubtful expectation is fulfilled.
Disappointment is the pain of unfulfilled pleasure.
Pity is pain accompanied by the idea of evil which has befallen someone else whom we conceive to be like ourselves.
More complex emotions, like exotic financial derivatives, depend on two underlying primitives.
Envy is pain at another's pleasure, like a convertible bond whose value depends on stock prices and interest rates.
Conversely, though Spinoza doesn’t name it, Schadenfreude is pleasure at another’s pain.
Cruelty involves all three primitives: Spinoza defines it as the desire to inflict pain on someone we love or pity.
Financially speaking, Cruelty is a convertible bond whose value depends on the stock price of the underlying stock, riskless interest rates and credit spreads.
Spinoza adds to his system three additional primitives that are meta-emotions. The first is Vacillation, the state of oscillation between two emotions. Thus Jealousy, he explains, is the vacillation between hate and envy towards an object of love in the presence of a rival for it. Jealousy is a derivative of envy, and envy is a derivative of pleasure and pain. If we follow the links far enough, we end up always at pain, pleasure and desire.
The second addition is Wonder. Wonder is what we experience when confronted by something that fills the mind to the exclusion of all else, something unrelated to anything else. Wonder is what we experience in the presence of Yahweh in the burning bush, who is what he is, and bears no relation to anything else.
Spinoza’s final primitive is Contempt, the feeling we have when we contemplate something that most forcibly reminds us of all the qualities it lacks. An absence becomes a nameable presence.
I call what Spinoza created a theory rather than a model. He doesn’t make analogies; he doesn’t attempt to explain how humans behave by comparing them to some other system we already understand. He begins with observations about human beings, obtained through experience, introspection and intuition. He produced a theory accessible to everyone because it analyzes everyday human experiences.
The figure below illustrates the dependency of all the emotions on Desire, Pleasure and Pain.
double click to enlarge
6. Intuition
It takes intuition to discover theories. Intuition may sound casual but it results from intimate knowledge acquired by careful observation and painstaking effort. John Maynard Keynes wrote a speech for the Newton tercentary in which he commented on Newton’s qualities:
Newton came to be thought of as the first and greatest of the modern age of scientists, a rationalist, one who taught us to think on the lines of cold and untinctured reason. I do not see him in this light. Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago …
I believe that the clue to his mind is to be found in his unusual powers of continuous concentrated introspection … His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen straight through it. I fancy his pre-eminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted. Anyone who has ever attempted pure scientific or philosophical thought knows how one can hold a problem momentarily in one's mind and apply all one's powers of concentration to piercing through it, and how it will dissolve and escape and you find that what you are surveying is a blank. I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret. Then being a supreme mathematical technician he could dress it up, how you will, for purposes of exposition, but it was his intuition which was pre-eminently extraordinary - 'so happy in his conjectures', said De Morgan, 'as to seem to know more than he could possibly have any means of proving'.
This perception – that his insight arose independent of his proof – was also James Clerk Maxwell’s opinion about André-Marie Ampère, who, in 1820, discovered the connection between electricity and magnetism. Referring to Ampère as the “Newton of electricity”, Maxwell, who extended Ampère’s discoveries into Maxwell’s equations and found that they described light, wrote:
“We can scarcely believe that Ampere really discovered the law of action by means of the experiments which he describes. We are led to suspect, what, indeed, he tells us himself, that he discovered the law by some process which he has not shown us, and that when he had afterwards built up a perfect demonstration, he removed all traces of the scaffolding by which he had built it.”
When you struggle with a field of inquiry for a long long time and you eventually master and incorporate not only its formalism but its content, you can make use of it to build things one level higher.
Intuition is a merging of the understander with the understood. It is the deepest kind of knowledge.
7. Models in Finance
There are no genuine theories in finance. Financial models are always models of comparison, of relative value. They are metaphors. The efficient market model assumes stock prices behave like smoke diffusing through a room. These are comparisons that have some reasonableness, but they’re not even remotely fact. Newton’s laws and Maxwell’s equations are. There is almost no gap between the object and their description. You can say that stock prices behave like smoke. You cannot say that light behaves like Maxwell’s equations. Light is Maxwell’s equations.
All concepts, perhaps all things, are mental. But there are no genuine theories in finance because finance is concerned with value, an even more subjective concept than heat or pressure. Furthermore, it is very difficult to find the scientific laws or even regularities governing the behavior of economies: there are very few isolated economic machines, and so one cannot carry out the repeated experiments that science requires. History is important in economics. Credit markets tomorrow won't behave like credit markets last year because we have learned what happened last year, and cannot get back to the initial conditions of a year ago. Human beings and societies learn; physical systems by and large don't.
For an experiment to be approximately repeatable, history has to be unimportant. That requires that the system couple very weakly to the rest of the universe. A coin flip can be repeated ad infinitum under almost the same conditions, because external conditions affect its outcome hardly at all. That’s not the case in finance.
What is the point of a model in finance?
It takes only a little experience to see that it’s not the same as the point of a model in physics or chemistry. Mostly, the point of a model is not prediction or divination. Here’s a simple but prototypical financial model that has most of the characteristics of more sophisticated models.
How do you estimate the price of a seven-room apartment on Park Ave. if someone tells you the market price of a typical two-room apartment in Battery Park City? Most likely, you figure out the price per square foot of the two-room apartment. Then you multiply by the square footage of the Park Ave. apartment. Finally you make some rule-of-thumb higher-order corrections for location, park views, light, facilities and so on. You might develop a model for those too.
The model’s critical parameter is the implied price per square foot. You calibrate the model to Battery Park City. Then you use it to interpolate or extrapolate to Park Ave. The price per square foot is implied from the market price of the Battery Park City apartments; it’s not the realized construction price per square foot because there are other variables – exposure, quality of construction, neighborhood – that are subsumed into that one implied number.
Calibration is dangerous; it’s always the fitting a wrong model to the only world we know, and then using it to extrapolate or interpolate. The closer your model to the behavior of the world, the less dangerous your extrapolation.
The Aim of Financial Models
The way property markets use implied price per square foot illustrates the functions of financial models more generally.
Models are used to rank securities by value.
Apartments have manifold features. Implied price per square foot can be used to rank and compare many similar but not identical apartments. It provides a simple one-dimensional scale on which to begin ranking apartments by value. The single number given by implied price per square foot doesn’t truly reflect the value of the apartment; it provides a starting point after which more qualitative factors must be taken into account.
Models are used to interpolate from liquid prices to illiquid ones
In finance, models are used less for divination than in order to interpolate or extrapolate from the known prices of liquid securities to the values of illiquid securities at the current time – in the example above from the Battery Park City price to the Park Ave. value. The Black-Scholes model proceeds from a known stock price and a riskless bond price to the unknown price of a hybrid, an option, similar to the way one estimates the value of fruit salad from its constituent fruits.
No model is correct – a model is not a theory – but models can provide immensely helpful ways of initial estimates of value.
Models transform intuitive linear quantities into nonlinear dollar values
In finance a model is also a means of translating acquired intuition into dollar values. The apartment-value model transforms price per square foot into the value of the apartment. It’s easier to begin with an estimate of price per square foot because that quantity captures so much of the variability of apartment prices. Similarly, it’s easier to convert one’s intuition about future volatility into current options prices than it is to guess at the appropriate prices themselves.
8. THE ONE LAW OF FINANCE
Research papers in quantitative finance look superficially like those in natural science, but the similarity is deceptive. There are no deep laws or theories in finance that can be expressed in mathematics.
The one law you can rely on in finance is the law of one price, which roughly put, dictates: “If you want to know the value of a financial security, use the known price of another security that’s as similar to it as possible.”
The wonderful thing about this law – it’s valuation by analogy – when compared with almost everything else in economics, is that it dispenses with utility functions, the unobservable hidden variable whose ghostly presence permeates most of faux-quantitative economic theory.
The law of one price is not a law of nature. It’s a general reflection on the practices of human beings, who, when they have enough time and enough information, will grab a bargain when they see one. The law usually holds in the long run, in well-oiled markets with enough savvy participants, but there are always short- or even longer-term exceptions that persist.
How do you use the law of one price to determine value? If you want to estimate the unknown value of a target security, you must find some other replicating portfolio, a collection of more liquid securities that, collectively, is similar to, i.e. has the same future payoffs as the target, no matter how the future turns out. The target’s value is then simply that value of the replicating portfolio.
Where do models enter? It takes a model to demonstrate similarity, to show that the target and the replicating portfolio have identical future payoffs under all circumstances. To demonstrate the identity of future payoffs, you must (1) specify what you mean by “all circumstances,” for each security, and (2) you must find a strategy for creating a replicating portfolio that, in each future scenario or eventuality, will have payoffs identical to those of the target. That’s what the Black-Scholes options model does – it tells you precisely how to replicate an option out of stocks and bonds, under certain assumptions. It’s like a recipe that tells you how to make fruit salad – an option – out of fruit, the stocks and bonds. And, ingeniously used, it tells you how to do the inverse – to figure out the value of one type of fruit given the price of other fruits and fruit salad.
Most of the mathematical complexity in finance involves the description of the range of future behavior of each security’s price. Trying to specify all circumstances always reminds me of the 1967 movie Bedazzled, starring Peter Cook and Dudley Moore. In this retelling of the German legend of Faust, Dudley Moore plays a short-order cook at a Wimpy’s chain restaurant in London who sells his soul to the devil in exchange for seven chances to specify the circumstances under which he can achieve his romantic aims with the Wimpy’s waitress he desires. Each time that the devil asks him to specify the romantic scenarios under which he believes he will succeed, he cannot get them quite specific enough. He says he wants to be alone with the waitress in a beautiful place where they are both in love with each other. He gets what he wants—with a snap of the devil’s fingers, he and his beloved are instantly transported to a country estate where he is a guest of the owner, her husband, whom her principles will not allow her to betray. In the final episode, he wishes for them to be alone together and in love with each other in a quiet place where no one will bother them. He gets his wish: The devil makes them both nuns in a convent where everyone has taken a vow of silence. This difficulty is the same difficulty we have when specifying future scenarios in financial models—like the devil, markets always eventually outwit us. Even if markets are not strictly random, their vagaries are too rich to capture in a few sentences or equations.
So die the dreams of financial theories. Only imperfect models remain.
9. THE RIGHT WAY TO USE MODELS
Given that finance’s best tools are shaky models, the best strategy is to use models as little as possible, and to replicate making as little assumptions as you can. Here are some other rules I’ve found to be useful as a practitioner.
Avoid too much axiomatization
Axiomatization is for mathematics. Finance is about the real world. Every financial axiom is pretty much wrong; the practical question is: how wrong, and can you still make use of it?
Good Models are Vulgar in a Sophisticated Way
In physics it pays to drop down deep, several levels below what you can observe (think of Newton, Maxwell, Dirac), formulate an elegant principle, and then rise back to the surface to work out the observable consequences. In financial valuation, which lacks deep scientific principles, it’s better to stay shallow and use models that have as direct as possible a path between observation of similarity and its consequences.
Markets are by definition vulgar, and correspondingly the most useful models are wisely vulgar too, using variables that the crowd uses, like price per square foot, to describe the phenomena they observe. Build vulgar models in a sophisticated way.
Of course, over time crowds and markets get smarter and the definition of vulgarity changes to encompass increasingly sophisticated concepts.
Sweep Dirt Under The Rug, But Let Users Know About It
One should be very humble in applying mathematics to markets, and be extremely wary of ambitious theories, which are, when you face facts, trying to model human behavior.
Whenever we make a model of something involving human beings, we are trying to force the ugly stepsister's foot into Cinderella's pretty glass slipper. It doesn't fit without cutting off some essential parts. Models inevitably mask as well as expose risk. You must start with models and then overlay them with common sense and experience.
The world of markets doesn’t exactly match the ideal circumstances a model assumes, but a robust model allows a savvy user to qualitatively adjust for those mismatches. A user should should know what has been assumed when he uses the model, and he should know exactly what has been swept out of view.
Think of Models as Gedanken Experiments
It’s impossible to make a correct financial model. Therefore, I like to think of financial models as gedanken experiments, like those Einstein carried out when he pictured himself surfing a light wave or Schrodinger when he pictured a macroscopic cat subject to quantum effects.
I believe that’s the right way to use mathematical models in finance, and the way experienced practitioners do use them. Models are only models, not the thing in itself. So, we can’t expect them to be truly right. Models are better regarded as a collection of parallel thought universes you can explore. Each universe should be consistent, but the actual financial and human world, unlike the world of matter, is going to be infinitely more complex than any model you make of it. You are always trying to shoe-horn the real world into one of the models to see how useful an approximation that is.
Beware of Idolatry
The greatest conceptual danger is idolatry, imagining that someone can write down a theory that encapsulates human behavior and relieves you of the difficulty of constant thinking. A model may be entrancing but no matter how hard you try, you will not be able to breath true life into it. To confuse the model with a theory is to embrace a future disaster driven by the belief that humans obey mathematical rules.
Financial modelers must therefore compromise, must firmly decide what small part of the financial world is of greatest current interest, decide on its key features, and make a mock-up of only those. A model cannot include everything. If you are interested in everything you are interested in too much. A successful financial model must have limited scope; you must work with simple analogies; in the end, you are trying to rank complex objects by projecting them onto a low-dimensional scale.
In physics there may one day be a Theory of Everything; in finance and the social sciences, you have to work hard to have a usable Model of Anything.
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