Timeline for Is Grothendieck a computer?
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 27, 2013 at 14:31 | comment | added | Omar Antolín-Camarena | Why are simplicial sets more "computery" than abstract simplicial complexes? | |
| Dec 11, 2010 at 22:47 | comment | added | Daniel Moskovich | @Gil Kalai: The computeroid closest to home might be Farjoun! I was thinking Bousfield, Kan, Curtis, May, and Quillen, although I'm probably overlooking important people. Sepaking of which, another example of an idea more natural to computers would be abstraction of the polynomial Hirsch conjecture. I think a "computer idea" means, among other things, "to strip a geometric/topological problem of all its geometry, and to transform it into a combinatorial problem about sets, boxes, and arrows". A computer would never think geometrically, but only in terms of arrays, pointers, and data sets! | |
| Dec 10, 2010 at 21:02 | comment | added | Gil Kalai | I dont understand the computer human distinction here and why simplicial sets are natural to computers. Anyway, dear Daniel, who are the computeroids most associated to the simplicial set idea through the ages? | |
| Dec 10, 2010 at 15:49 | comment | added | Harry Gindi | @Mariano: We've had plenty of conversations on IRC. I've never said anything like that to you? I'm surprised! | |
| Dec 10, 2010 at 14:05 | comment | added | Mariano Suárez-Álvarez | I don't think I had ever heard simplicial sets called extremely pretty before... | |
| Dec 10, 2010 at 12:55 | comment | added | Daniel Moskovich | @Harry- That's what I meant! Simplicial complexes are still a human idea... but simplicial sets are the computer idea, and are extremely pretty. @Minhyong- I would argue that simplicial sets go far beyond simplicial complexes (despite the existence of geometric realization), and are therefore "more fundamental". Braids form a simplicial set (face-map = deleting a strand, degeneracy= cabling)- but I have no idea how they might form a meaningful simplicial complex. | |
| Dec 10, 2010 at 4:59 | comment | added | Minhyong Kim | As I understand it, a simplicial complex in fact is, in some sense, how objects are encoded in computer-adided design. Furthermore, it might be argued that it is simplicial complexes that are fundamental, and the move to simplicial sets might have been made by any old computer, once it was required to consider morphisms. The proof that this is a good model for spaces, I agree is far more involved. | |
| Dec 10, 2010 at 3:55 | comment | added | Harry Gindi | The insight behind simplicial sets is, I think, a bit deeper than that. The motivation you've given is for simplicial complexes. It's completely non-obvious from a homotopy perspective that simplicial sets should be able to model spaces so well up to homotopy. | |
| Dec 10, 2010 at 2:58 | history | answered | Daniel Moskovich | CC BY-SA 2.5 |