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bio website isomorphism.es
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ὰγεωμὲρητος μηδϵὶς ϵἰσίτω

The philosopher kings of Plato's Republic were to learn Geometry at the acme of their preparation to rule. The reasoning was not only due to Plato's geometrical view of Nature but also his view of abstraction.

Without taking sides on this particular philosopher—how much more would he have valued modern geometry? I'm interested in learning mathematics from this perspective: experiencing how "the most different" human language influences my thoughts about the everyday world.

(By the everyday world I mean love, money, and human diversity — things that seem far away from serious professional text.) In particular I'd like to be able to think up novel and creative ideas about non-mathematical things, using modern mathematical shapes.

Besides this broad personal project, I am also interested in applying modern mathematics to economic theory.


12h
awarded  Yearling
Apr
23
comment Intuition behind Alexander duality
I sometimes understand an idea better by seeing how it's used than by seeing it described. Here's Robert MacPherson using Alexander duality at minute 21; HTH someone.
Mar
24
comment Visualization of the real projective plane
ℝℙ¹ is the space of lines through the origin so I just imagine a line nailed into the origin spinning around. (Reminding myself when it reaches noon it's already been there at 6:00 since unlike a ray the line is bi-directional hence $a=-a$.)
Mar
23
comment Visualizing functions with a number of independant variables
Often in my experience it's not necessary to show 5-way interactions – a 5-input function is really separable, with interesting interactions being 2-way but rarely 3-way. It also pays, imo, to look for ways to reduce dimensionality when you don't absolutely have to use necessarily overwrought visualisation techniques (Chernoff-Fleury faces, symphonies) which, like a time-lapse not over time, are entertaining but not super clear.
Mar
22
comment Intuitive crutches for higher dimensional thinking
I like the idea of "more neighbours" in higher-D euclidean space. Geoff Hinton joked about being in a grocery store buying pizza. Tomato sauce and cheese were near the pizza-dough, but sardines were not. "Unfortunately it's not at 16-dimensional grocery store", because then everything related to pizza-dough could be next to pizza-dough. So I think of ℤ³ as a graph with each vertex having 6 edges. In ℤⁿ each node has 2n edges.
Mar
15
revised Motivation for concepts in Algebraic Geometry
improved formatting
Mar
15
suggested approved edit on Motivation for concepts in Algebraic Geometry
Feb
17
revised What is DAG and what has it to do with the ideas of Voevodsky?
improved formatting
Feb
17
suggested approved edit on What is DAG and what has it to do with the ideas of Voevodsky?
Nov
28
comment What's a groupoid? What's a good example of a groupoid?
ok, right. So passing in a circle (like the Von Trapp family with Baroness Schräder) would work better than football, where movement up the field and other competitive factors would break the invertibility.
Nov
19
revised How to write popular mathematics well?
added 44 characters in body
Nov
19
revised How to write popular mathematics well?
added 21 characters in body
Oct
19
comment What's a groupoid? What's a good example of a groupoid?
I guess if this is true, then passing in (European) football also is more like a groupoid than a group. Only the person with the ball can pass to any teammate (or "negative pass" to any opponent). Yes?
Sep
30
revised How to write popular mathematics well?
head/heart
Sep
30
answered How to write popular mathematics well?
Sep
30
comment Cures for mathematician's block (as in writer's block)
Does it need to be science? I think it could be even further afield—history, art, anything that renews one's sense of curiosity and wonder at the world…
Sep
30
answered Category theory sans (much) motivation?
Sep
30
revised Mathematical definition of running
not Cartesian
Sep
30
comment Mathematical definition of running
@Noah Yes, you do remember that correctly. canyon23.net/math/1985thesis.pdf (found Kevin Walker's thesis via the E.A.T. book of Robert Ghrist. Dr Ghrist has done some work on robots not bumping into each other [braid theory] which may be what you had in mind?)
Sep
30
answered Mathematical definition of running