bio  website  isomorphism.es 

location  Great Cacapon, WV  
age  
visits  member for  4 years 
seen  yesterday  
stats  profile views  196 
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.
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 
Sep 24 
awarded  Autobiographer 
Sep 18 
answered  What is a good introductory text for moduli theory? 
Sep 11 
comment 
Heuristic behind the FourierMukai transform
also math.stackexchange.com/questions/1002/… 
Sep 4 
comment 
Wikipedia's definition of constant sheaf is wrong
@KevinBuzzard OK, but realistically people do expect Wikipedia to be right, and they expect maths textbooks to be right, and they expect the maths on Wikipedia to be right. It's up to people who know what a sheaf is (and what better forum to alert them) to correct WP, of course. 
Jul 24 
comment 
Au revoir, law of excluded middle?
I can't remember all of my original philosophical objections but for example "A sea battle will occur tomorrow" is neither true nor false today. (One could make a timelogic, but meanwhile {T,F,?} should replace {T,F} in PC.) Or consider any linguistic ambiguity; vague predicates, ambivalent feelings, words that sortof fit the situation but notreally or maybekindasorta fit.…

Jul 24 
comment 
Au revoir, law of excluded middle?
I'm surprised that coming from philosophy you would say excludedmiddle is so undeniable. For me it was through philosophical objections that I wanted to deny EM (to deny that it must work in all cases ¬⊨P∨¬P ; not to deny it in each case ⊨¬(P∨¬P) ).

Jun 27 
comment 
Algebraic Geometry for nonmathematician
The only "shortcut" I know of would be to play around with SURFER : imaginary.org/program/surfer. It shows you the roots of polynomials over 3 letters. Since varieties and algebraic curves are fundamental in AG this gives you a peek at the topic. Also an analytical statement about intersections (from eg lecture 1 of Vakil) can be envisaged with eg.

Jun 7 
comment 
Homological algebra and calculus (as in Newton)
It sounds like an isomorphism theorem for functors: replacing map(•) with surj(bij(inj(•))) .

Jun 7 
comment 
Homological algebra and calculus (as in Newton)
When I think of ∂ I'm necessarily thinking about the fundamental theorem of calculus: take I=[0,1] then $\int_I D[f] = f \vert_{\partial I}$. So wouldn't ∂² then be evaluating $f$ on ∂(∂(I))=∅, which is a strange enough notion that I'm not sure what one would want to do to make sense of it. My way of thinking about it doesn't yield anything nice like $f''$ resulting from ∂∂I, which may make it a bad idea. 