bio | website | isomorphism.es |
---|---|---|
location | Great Cacapon, WV | |
age | ||
visits | member for | 4 years, 3 months |
seen | 14 hours ago | |
stats | profile views | 216 |
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.
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 |
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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 |
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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 |
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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 |
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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? |