Διαισθητική μεγαλοφυία
Οι χαοτικές δίνες που χαρακτηρίζουν τα αριστουργήματα του Βαν Γκογκ ακολουθούν με ακρίβεια τις μαθηματικές περιγραφές των αναταράξεων σε ρευστά υλικά, όπως οι στροβιλισμοί του νερού σε ένα ταραγμένο ρυάκι ή οι πραγματικοί ανεμοστρόβιλοι, διαπιστώνουν έκπληκτοι οι φυσικοί.Το παράξενο μάλιστα είναι ότι η στατιστική υπογραφή της δυναμικής των ρευστών ανιχνεύεται μόνο στους πίνακες που ζωγράφισε η διαταραγμένη μεγαλοφυία όταν ήταν πνευματικά ασταθής, και όχι στην «ήρεμη» περίοδο της ζωής του, όταν ακολουθούσε φαρμακευτική αγωγή για τις κρίσεις του.
Πρόκειται για ένα ακόμα παράδειγμα καλλιτέχνη που εντελώς διαισθητικά είχε αντιληφθεί τη δυναμική των φυσικών φαινομένων, επισημαίνει άρθρο στο Nature.com. Μαθηματικά μοτίβα φράκταλ, για παράδειγμα, είχαν στο παρελθόν εντοπιστεί στα έργα του Αμερικανού ζωγράφου Τζάκσον Πόλοκ.
Ψυχωτική διαίσθηση«'Ταραγμένο' είναι το βασικό επίθετο που χρησιμοποιείται για να περιγράψει το έργο του Βαν Γκογκ» σχολιάζει ο φυσικός Χοσέ Λουί Αραγκόν, επικεφαλής των ερευνητών στο Εθνικό Αυτόνομο Πανεπιστήμιο του Μεξικού. «Προσπαθήσαμε αυτό να το ποσοτικοποιήσουμε» εξηγεί.
Η ανάλυση των πινάκων στον υπολογστή αποκάλυψε ένα μοτίβο φωτεινών και σκοτεινών περιοχών που ακολουθούν τις εξισώσεις του Αντρεϊ Κολμογκόροφ, του Σοβιετικού επιστήμονα που τη δεκαετία του 1940 κατάφερε να περιγράψει έστω και εν μέρει τη δυναμική του στροβιλισμού των ρευστών.Οι ταραγμένοι ουρανοί στην Έναστρη Νύχτα (1889) και στο Δρόμος με Κυπαρρίσι και Αστρο (1890), μεταξύ άλλων, παρουσιάζουν τη λεγόμενη «κλιμάκωση Κολμογκόροφ», εξισώσεις που δίνουν την πιθανότητα δύο οποιοδήποτε σημεία του ρευστου να έχουν μια δεδομένη διαφορά ταχύτητας.Οι πίνακες αυτοί ζωγραφίστηκαν λίγο πριν ο Βαν Γκογκ αυτοκτονήσει σε ηλικία 37 ετών.
Την περίοδο εκείνη, ο ζωγράφος υπέφερε από ψυχωτικά επεισόδια, παραισθήσεις και επεισόδια απώλειας της συνείδησης, πιθανώς συμπτώματα επιληψίας.Αντίθετα, μετά τον αυτοακρωτηριασμό του αφτιού του, ο Βαν Γκογκ φαίνεται ότι είχε χάσει τη μαθηματική του ακρίβεια, όπως δείχνουν για παράδειγμα τα αυτοπορτραίτα του 1888. Την περίοδο εκείνη ο καλλιτέχνης βρισκόταν σε κατάσταση «απόλυτης ηρεμίας» λόγω του βρωμιούχου καλίου που του χορηγήθηκε.
«Πιστεύουμε ότι ο Βαν Γκογκ είχε μια μοναδική ικανότητα να απεικονίζει αναταράξεις σε περιόδους παρατεταμένης ψυχωτικής αναστάτωσης» σχολιάζει ο Αραγκόν.Οι ερευνητές εξέτασαν έργα και άλλων ζωγράφων αναζητώντας τη στατιστική υπογραφή του Κολμογκόροφ, όμως η διαισθητική ικανότητα του Βαν Γκογκ φαίνεται ότι ήταν μοναδική. Η διάσημη Κραυγή του Έντβαντ Μουνχ, για παράδειγμα, είναι γεμάτη από παρόμοιες δίνες, οι οποίες δεν ακολουθούν όμως τις μαθηματικές εξισώσεις.
Η μελέτη δημοσιεύεται στο διαδικτυακό αρχείο arXiv.org.
Van Gogh painted perfect turbulence
The disturbed artist intuited the deep forms of fluid flow.
Vincent van Gogh is known for his chaotic paintings and similarly tumultuous state of mind. Now a mathematical analysis of his works reveals that the stormy patterns in many of his paintings are uncannily like real turbulence, as seen in swirling water or the air from a jet engine.
Physicist Jose Luis Aragon of the National Autonomous University of Mexico in Queretaro and his co-workers have found that the Dutch artist's works have a pattern of light and dark that closely follows the deep mathematical structure of turbulent flow.
The swirling skies of The Starry Night, painted in 1889, Road with Cypress and Star (1890) and Wheat Field with Crows (1890) — one of the van Gogh's last pictures before he shot himself at the age of 37 — all contain the characteristic statistical imprint of turbulence, say the researchers.
These works were created when van Gogh was mentally unstable: the artist is known to have experienced psychotic episodes in which he had hallucinations, minor fits and lapses of consciousness, perhaps indicating epilepsy.
"We think that van Gogh had a unique ability to depict turbulence in periods of prolonged psychotic agitation," says Aragon.
In contrast, the Self-portrait with Pipe and Bandaged Ear (1888) shows no such signs of turbulence. Van Gogh said that he painted this image in a state of "absolute calm", having been prescribed the drug potassium bromide following his famous self-mutilation.
Measured chaos
Scientists have struggled for centuries to describe turbulent flow — some are said to have considered the problem harder than quantum mechanics. It is still unsolved, but one of the foundations of the modern theory of turbulence was laid by the Soviet scientist Andrei Kolmogorov in the 1940s.
He predicted a particular mathematical relationship between the fluctuations in a flow's speed and the rate at which it dissipates energy as friction. Kolmogorov's work led to equations describing the probability of finding a particular velocity difference between any two points in the fluid. These relationships are called Kolmogorov scaling.
Aragón and colleagues looked at van Gogh's paintings to see whether they bear the fingerprint of turbulence that Kolmogorov identified. "'Turbulent' is the main adjective used to describe van Gogh's work," says Aragn. "We tried to quantify this."
Darkness and light
The researchers took digital images of the paintings and calculated the probability that two pixels a certain distance apart would have the same brightness, or luminance. "The eye is more sensitive to luminance changes than to colour changes," they say, "and most of the information in a scene is contained in its luminance."
Several of van Gogh's works show Kolmogorov scaling in their luminance probability distributions. To the eye, this pattern can be seen as eddies of different sizes, including both large swirls and tiny eddies created by the brushwork.
Van Gogh seems to be the only painter able to render turbulence with such mathematical precision. "We have examined other apparently turbulent paintings of several artists and find no evidence of Kolmogorov scaling," says Aragon.
Edvard Munch's The Scream, for example, looks to be superficially full of van Gogh-like swirls, and was painted by a similarly tumultuous artist, but the luminance probability distribution doesn't fit Kolmogorov's theory.
The distinctive styles of other artists can be described by mathematical formulae. Jackson Pollock's drip paintings, for example, bear distinct fractal patterns.
Visit our newsblog to read and post comments about this story.
Aragón I., et al. Preprint http://www.arxiv.org/abs/physics/0606246 (2006).
The disturbed artist intuited the deep forms of fluid flow.
Vincent van Gogh is known for his chaotic paintings and similarly tumultuous state of mind. Now a mathematical analysis of his works reveals that the stormy patterns in many of his paintings are uncannily like real turbulence, as seen in swirling water or the air from a jet engine.
Physicist Jose Luis Aragon of the National Autonomous University of Mexico in Queretaro and his co-workers have found that the Dutch artist's works have a pattern of light and dark that closely follows the deep mathematical structure of turbulent flow.
The swirling skies of The Starry Night, painted in 1889, Road with Cypress and Star (1890) and Wheat Field with Crows (1890) — one of the van Gogh's last pictures before he shot himself at the age of 37 — all contain the characteristic statistical imprint of turbulence, say the researchers.
These works were created when van Gogh was mentally unstable: the artist is known to have experienced psychotic episodes in which he had hallucinations, minor fits and lapses of consciousness, perhaps indicating epilepsy.
"We think that van Gogh had a unique ability to depict turbulence in periods of prolonged psychotic agitation," says Aragon.
In contrast, the Self-portrait with Pipe and Bandaged Ear (1888) shows no such signs of turbulence. Van Gogh said that he painted this image in a state of "absolute calm", having been prescribed the drug potassium bromide following his famous self-mutilation.
Measured chaos
Scientists have struggled for centuries to describe turbulent flow — some are said to have considered the problem harder than quantum mechanics. It is still unsolved, but one of the foundations of the modern theory of turbulence was laid by the Soviet scientist Andrei Kolmogorov in the 1940s.
He predicted a particular mathematical relationship between the fluctuations in a flow's speed and the rate at which it dissipates energy as friction. Kolmogorov's work led to equations describing the probability of finding a particular velocity difference between any two points in the fluid. These relationships are called Kolmogorov scaling.
Aragón and colleagues looked at van Gogh's paintings to see whether they bear the fingerprint of turbulence that Kolmogorov identified. "'Turbulent' is the main adjective used to describe van Gogh's work," says Aragn. "We tried to quantify this."
Darkness and light
The researchers took digital images of the paintings and calculated the probability that two pixels a certain distance apart would have the same brightness, or luminance. "The eye is more sensitive to luminance changes than to colour changes," they say, "and most of the information in a scene is contained in its luminance."
Several of van Gogh's works show Kolmogorov scaling in their luminance probability distributions. To the eye, this pattern can be seen as eddies of different sizes, including both large swirls and tiny eddies created by the brushwork.
Van Gogh seems to be the only painter able to render turbulence with such mathematical precision. "We have examined other apparently turbulent paintings of several artists and find no evidence of Kolmogorov scaling," says Aragon.
Edvard Munch's The Scream, for example, looks to be superficially full of van Gogh-like swirls, and was painted by a similarly tumultuous artist, but the luminance probability distribution doesn't fit Kolmogorov's theory.
The distinctive styles of other artists can be described by mathematical formulae. Jackson Pollock's drip paintings, for example, bear distinct fractal patterns.
Visit our newsblog to read and post comments about this story.
Aragón I., et al. Preprint http://www.arxiv.org/abs/physics/0606246 (2006).
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