bio  website  isomorphism.es 

location  Great Cacapon, WV  
age  
visits  member for  4 years, 4 months 
seen  yesterday  
stats  profile views  220 
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 nonmathematical 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 bidirectional hence $a=a$.) 
Mar 23 
comment 
Visualizing functions with a number of independant variables
Often in my experience it's not necessary to show 5way interactions – a 5input function is really separable, with interesting interactions being 2way but rarely 3way. It also pays, imo, to look for ways to reduce dimensionality when you don't absolutely have to use necessarily overwrought visualisation techniques (ChernoffFleury faces, symphonies) which, like a timelapse 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 higherD euclidean space. Geoff Hinton joked about being in a grocery store buying pizza. Tomato sauce and cheese were near the pizzadough, but sardines were not. "Unfortunately it's not at 16dimensional grocery store", because then everything related to pizzadough could be next to pizzadough. 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 