Friday, April 22, 2016

Hidden dimensions

"What dimension are we working in?" I prompt the student in my office.  "One." "Which means the Hamiltonian must be..."

I've been talking about "boxes" in one-dimension, three-dimensional vibrational breathing modes — spherically symmetric molecules that expand and collapse like stars going nova — and molecular wavefunctions that sit in four, twelve, or fifty-two dimensional spaces.

But what does it mean to be between (integer) dimensions?  Fractional dimensions are a way of describing the complexity of mathematical objects, such as this Sierpinski triangle being assembled on Bryn Mawr's green.  It has a dimension of log23 or about 1.58.

It looks like we are working in 2 dimensions but it's not quite. Where did the missing .42 dimension go?

Math Man has long dreamed of constructing an enormous Sierpinski triangle, math writ large.  All the pieces fell into place earlier this spring and on Sunday the game is on, a 9th level Sierpinski triangle build at the Wagner Free Institute of Science (a very cool space).

K'Nex donated about half the 30,000 some odd pieces needed.  After the event the pieces will get packed up into kits for teachers.  You can support the project here.

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