Re: [math-fun] Vladimir Arnold Dies at 72; Pioneering Mathematician
I was also saddened to learn, a few days ago, of Arnol'd's death. Although I never met him, I was first introduced to his work via the wonderfully fun book with Avez, "Ergodic Problems in Classical Mechanics" -- which is a compendium of interesting facts that, despite the intimidating title, require very little background to appreciate (more accurately, a bachelor's in math would easily do). Another beautiful book is his "Mathematical Methods in Classical Mechanics", whose first chapter shows how to make rough estimates of various aspects of an animal, like the speed it can run, in terms of its linear size S, . (For example, its volume is proportional to S^3.) One thing he mentioned is the power of S that the height an animal can jump is proportional to. Do you want to guess? --Dan << FYI -- Arnold was one of my favorite mathematicians; I really enjoyed his work on orbits. His (English translated) books are quite readable.
________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx
On Fri, Jun 11, 2010 at 1:13 PM, Dan Asimov <dasimov@earthlink.net> wrote:
I was also saddened to learn, a few days ago, of Arnol'd's death.
Although I never met him, I was first introduced to his work via the wonderfully fun book with Avez, "Ergodic Problems in Classical Mechanics" -- which is a compendium of interesting facts that, despite the intimidating title, require very little background to appreciate (more accurately, a bachelor's in math would easily do).
Another beautiful book is his "Mathematical Methods in Classical Mechanics", whose first chapter shows how to make rough estimates of various aspects of an animal, like the speed it can run, in terms of its linear size S, . (For example, its volume is proportional to S^3.) One thing he mentioned is the power of S that the height an animal can jump is proportional to. Do you want to guess?
Well, it seems to me that the mass is proportional to S^3, the muscle force is proportional to the cross-section of the muscle which is like S^2, and the distance the force has to operate is proportional to S, so height = (force * distance) / (mass) should be proportional to S^0. That seems roughly right: a flea and I can both raise our center of mass by on the order of half a meter or something. --Joshua
participants (2)
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Dan Asimov -
Joshua Zucker