Τα μαθηματικά είναι διεγερτικά!
2014-02-13
Τελευταία δημοσίευση: 11:48Διάφορα
Σε μερικούς ανθρώπους δεν υπάρχει διαφορά είτε βλέπουν ένα πίνακα του Βαν Γκογκ, είτε ακούνε Μπαχ, είτε κοιτάζουν το Πυθαγόρειο Θεώρημα.
Τα μαθηματικά μπορούν να γοητεύσουν κάποιον -κατά προτίμηση έναν μαθηματικό που τα καταλαβαίνει- τόσο πολύ που να διεγερθούν οι ίδιες περιοχές του εγκεφάλου του, οι οποίες ενεργοποιούνται και στη θέα ή την ακρόαση ενός μεγάλου έργου τέχνης.
Αυτό διαπίστωσε μια νέα βρετανική επιστημονική έρευνα, σύμφωνα με την οποία όσοι θεωρούν πραγματικά όμορφες τις εξισώσεις, τις βλέπουν σαν αυθεντικά έργα τέχνης. Η νέα μελέτη ενισχύει τη θεωρία ότι υπάρχει μια ενιαία νευροβιολογική βάση για την ομορφιά και την αισθητική αντίληψη του ωραίου.
Οι ερευνητές, με επικεφαλής τον καθηγητή Σεμίρ Ζέκι του Εργαστηρίου Νευροβιολογίας Wellcome του University College του Λονδίνου, που έκαναν τη σχετική δημοσίευση στο περιοδικό «Frontiers in Human Neuroscience» (Σύνορα στην Ανθρώπινη Νευροεπιστήμη), σύμφωνα με το BBC, χρησιμοποίησαν την τεχνική της λειτουργικής μαγνητικής απεικόνισης (fMRI) για να μελετήσουν την εγκεφαλική δραστηριότητα 15 εθελοντών μαθηματικών, την ώρα που αυτοί καλούνταν να δουν 60 μαθηματικές εξισώσεις και να τις αξιολογήσουν ως όμορφες, άσχημες ή ουδέτερες.
Η μελέτη έδειξε ότι η εμπειρία του «μαθηματικά ωραίου» καταγράφεται στην ίδια συναισθηματική περιοχή του εγκεφάλου (στον μέσο κογχομετωπιαίο φλοιό), όπου αποτυπώνεται και γίνεται η επεξεργασία του «ωραίου» στην μουσική ή τη ζωγραφική.
«Σε πολλούς από εμάς οι μαθηματικές εξισώσεις φαίνονται ξερές και ακατανόητες, όμως για έναν μαθηματικό μια εξίσωση μπορεί να ενσωματώνει την πεμπτουσία της ομορφιάς. Η ομορφιά μιας εξίσωσης μπορεί να προέρχεται από την απλότητά της, τη συμμετρία της, την κομψότητά της ή την έκφραση μιας αναλλοίωτης αλήθειας. Για τον Πλάτωνα, η αφηρημένη ποιότητα των μαθηματικών εξέφραζε το αποκορύφωμα της ομορφιάς», δήλωσε ο Σεμίρ Ζέκι.
Το πείραμα έδειξε ότι οι εξισώσεις που συστηματικά γεννούν την πιο έντονη αισθητική απόλαυση, είναι η ταυτότητα του Όιλερ, το Πυθαγόρειο θεώρημα και οι εξισώσεις Κοσί-Ρίμαν.
Πηγή: ΑΠΕ-ΜΠΕ
Mathematics: Why The Brain Sees Maths As Beauty
Mathematics 2: Why The Brain Sees Maths As Beauty
Mathematics: Why the brain sees maths as beauty
Brain
scans show a complex string of numbers and letters in mathematical
formulae can evoke the same sense of beauty as artistic masterpieces and
music from the greatest composers.
Mathematicians were shown "ugly" and "beautiful" equations while in a brain scanner at University College London.The same emotional brain centres used to appreciate art were being activated by "beautiful" maths.
The researchers suggest there may be a neurobiological basis to beauty.
The likes of Euler's identity or the Pythagorean identity are rarely mentioned in the same breath as the best of Mozart, Shakespeare and Van Gogh.
The study in the journal Frontiers in Human Neuroscience gave 15 mathematicians 60 formula to rate.
One of the researchers, Prof Semir Zeki, told the BBC: "A large number of areas of the brain are involved when viewing equations, but when one looks at a formula rated as beautiful it activates the emotional brain - the medial orbito-frontal cortex - like looking at a great painting or listening to a piece of music."
The more beautiful they rated the formula, the greater the surge in activity detected during the fMRI (functional magnetic resonance imaging) scans.
"Neuroscience can't tell you what beauty is, but if you find it beautiful the medial orbito-frontal cortex is likely to be involved, you can find beauty in anything," he said.
A thing of great beauty
Euler's identity: Does it get better than this?
Continue reading the main story
“Start Quote
Prof David Percy Institute of Mathematics and its ApplicationsAt first you don't realise the implications it's a gradual impact, perhaps as you would with a piece of music and then suddenly it becomes amazing as you realise its full potential.”
It is a personal favourite of Prof David Percy from the Institute of Mathematics and its Applications.
He told the BBC: "It is a real classic and you can do no better than that. "It is simple to look at and yet incredibly profound, it comprises the five most important mathematical constants - zero (additive identity), one (multiplicative identity), e and pi (the two most common transcendental numbers) and i (fundamental imaginary number).
"It also comprises the three most basic arithmetic operations - addition, multiplication and exponentiation.
"Given that e, pi and i are incredibly complicated and seemingly unrelated numbers, it is amazing that they are linked by this concise formula.
"At first you don't realise the implications it's a gradual impact, perhaps as you would with a piece of music and then suddenly it becomes amazing as you realise its full potential."
He said beauty was a source of "inspiration and gives you the enthusiasm to find out about things".
The hugely influential theoretical
physicist Paul Dirac said: "What makes the theory of relativity so
acceptable to physicists in spite of its going against the principle of
simplicity is its great mathematical beauty. This is a quality which
cannot be defined, any more than beauty in art can be defined, but which
people who study mathematics usually have no difficulty in
appreciating."
He said he loved a "small thing [mathematician Pierre de] Fermat did". He showed that any prime number that could be divided by four with a remainder of one was also the sum of two square numbers.
So 41 is a prime, can be divided by four with one left over and is 25 (five squared) plus 16 (four squared).
"So if it has remainder one it can always be written as two square numbers - there's something beautiful about that.
"It's unexpected why should the two things [primes and squares] have anything to do with each other, but as the proof develops you start to see the two ideas become interwoven like in a piece of music and you start to see they come together.
He said it was the journey not the final proof that was exciting "like in a piece of music it's not enough to play the final chord".
He said this beauty of maths was missing from schools and yet amazing things could be shown with even primary school mathematical ability.
In the study, mathematicians rated Srinivasa Ramanujan's infinite series and Riemann's functional equation as the ugliest of the formulae.
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