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bio website isomorphismes.tumblr.com
location Great Cacapon, WV
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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.


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 time-logic, but meanwhile {T,F,?} should replace {T,F} in PC.) Or consider any linguistic ambiguity; vague predicates, ambivalent feelings, words that sort-of fit the situation but not-really or maybe-kinda-sorta fit.…
Jul
24
comment Au revoir, law of excluded middle?
I'm surprised that coming from philosophy you would say excluded-middle 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 non-mathematician
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.
Jun
3
comment Badiou and Mathematics
on the arXiv: arxiv.org/abs/1406.0059v1 arxiv.org/abs/1301.1203 might be better than Wikipedia for a relatively technical yet also politically fraught subject.
Jun
3
revised Why is the gradient normal?
re-read OP's question
Jun
3
revised Why is the gradient normal?
picture was gone
Jun
3
comment Why is the gradient normal?
@G.T.R. Thanks for heads-up. I no longer remember what original image I was trying to use so I'll just add a few others.
May
22
comment Elementary+Short+Useful
Niles Johnson posted a very nice talk of this sort on youtube: nilesjohnson.net/hopf.html complete with excellent visuals (at the end) accompanied by high-energy music. Basically a Hopf-sphere disco ball.
May
22
comment Elementary+Short+Useful
@PhilIsett One can easily show that the sum of two uniforms is triangular. One can also use Excel and thereby invoke some experimental mathematics.
May
22
comment Elementary+Short+Useful
...and if I wanted to introduce equivalence-relations to undergraduates, I'd definitely use the piano (modes, white-keys & black-keys, scales, the octave...)
May
19
comment Coboundaries and Gluing in Cech Cohomology - Intuition?
Penrose gave a concrete example of cocycle and coboundary in the tribar: jstor.org/stable/1575844
May
19
comment Coboundaries and Gluing in Cech Cohomology - Intuition?
Here's my drawing of a coboundary: tmblr.co/ZdCxIy-JEnZC based on Ghrist's EAT.
May
9
comment Teaching homology via everyday examples
Was it from Chichilinsky? papers.ssrn.com/sol3/papers.cfm?abstract_id=1375205
Mar
31
comment Is there something like a Heyting Ring?
Don't join and meet each constitute group operations?
Mar
25
revised What are some examples of colorful language in serious mathematics papers?
corrected spelling
Mar
23
answered How does an academic mathematician educate him/herself about job opportunities outside academia?
Feb
15
comment How to respond to “I was never much good at maths at school.”
The stronger I bear in mind that my goal is to connect with someone and not to defend maths, the better I do. I look for any possible response except disagreeing with them. Also—someone who hates "maths" doesn't hate "representation theory" or "topology". "I think about knots all day" sounds much better than "Every day of my life is like the homework you hated". If it must be broached, I would emphasise the total lack of overlap between what I love and what they were forced to do as a youth.
Feb
15
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