Tuesday, April 26, 2016

Visualizing Turbulence in Van Gogh.

Mathematics Education
Environmental & Science Education
Edward Hessler

Vincent van Gogh [Public domain],
via Wikimedia Commons

Unexpected Math in Art

Natalya St. Clair joined her interests in studio arts and mathematics while an undergraduate at Scripps College. She has created three TED-Ed lessons, one of which is about the unexpected mathematics in Vincent Van Gogh's "Starry Night."

In introducing the lesson St. Clair quotes something Nobel Prize (1932) physicist Werner Heisenberg is reputed to have said on his death bed: “When I meet God, I am going to ask him two questions: why relativity? And why turbulence? I really believe he will have an answer for the first.” The quote is very similar to one made by British fluid dynamicist Horace Lamb.

Heisenberg's Dissertation on Laminar to Turbulent Flow

Heisenberg's Ph.D. was on the transition from laminar to turbulent flow. The thesis was brilliant; his performance during its defense led to a grade of C and a brief description of this episode may be found here. He had failed basic questions (e.g., how a storage battery works) on physical phenomena as well as in experimental physics. These simply had never interested him. There was also a deep split in the department between experimentalists and theoreticians which was represented on Heisenberg's examining committee.

The problem was far from trivial. Heisenberg's advisor, Arnold Somerfeld said "I would not have proposed a thesis of this difficulty as a dissertation to any of my other pupils". The results were in doubt for about a quarter of a century when they were finally confirmed.

Whether true or not, the quote attributed to Heisenberg draws attention to the difficulty of the mathematics.  St. Clair's lesson is about the value of art in depicting the way turbulence looks. It may be seen here.

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