Timeline for What is Chemlambda? In which ways could it be interesting for a mathematician?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 23, 2020 at 13:58 | history | edited | Marius Buliga | CC BY-SA 4.0 |
added 404 characters in body
|
| May 22, 2018 at 8:42 | comment | added | Marius Buliga | In case anybody interested, I opened the github repository EM which contains a working draft for an article which treats emergent algebras as a term rewrite system, with the final goal to rigorously connect emergent algebras with chemlambda. I don't know if it will work collaboratively, but I give it a try. | |
| May 17, 2018 at 18:18 | comment | added | Marius Buliga | I don't know. What is interesting about SR is that it's like hyperbolic geometry for somebody who wants to understand more about the axiom of parallels. In knot theory, topology, physics there's lots of graphical tools based computations. Very high level though. All of them, SR included (which is new and low level) look almost like the same graph rewrites, variously decorated (typed?). So I don't know but I guess chemistry is even more intriguing. Maybe is a trend after the historically first models of computation based on words. | |
| May 16, 2018 at 16:08 | comment | added | Qfwfq | Thank you. Yes, I know sub-riemannian geometry is a very active area of research; but I was wandering if also other kinds of geometric structure (holomorphic, symplectic, algebraic, ...) could give rise to analogous rewriting systems interpretations. If the answer is yes then it'd be natural to ask how these other "computation models" look like; if it's no or it's not known yet, then one could ask -as I did- which peculiarities of sub-riemannian geometry (as opposed to other equally widely studied geometric structures) lead to graphical models of computation. | |
| May 16, 2018 at 7:36 | comment | added | Marius Buliga | Sub-riemannian geometry is fascinating. A SR manifold is metrically a fractal but it is also smooth with respect to a differential calculus discovered by Pierre Pansu. It appears in physics too: non-holonomic manifolds (i.e. bikes on roads) are SR, the unit sphere in a complex Hilbert space is SR, the Heisenberg groups are the equivalent of linear SR spaces, a sort of non-commutative version of a vector space. Nothing from the fundamentals of differential geometry and calculus works like expected. | |
| May 15, 2018 at 23:20 | vote | accept | Qfwfq | ||
| May 15, 2018 at 23:19 | comment | added | Qfwfq | (...) I find it quite surprising that sub-riemannian geometry had something to do with computation! Do you think that analogous phenomena could be found in other domains of mathematics (not obviously related to computation)? What are, essentially, the features of sub-riemannian geometry that ultimately lead to the "emergent" structures? | |
| May 15, 2018 at 23:14 | comment | added | Qfwfq | So, chemlambda has a set of local rules (that can be chosen to be random or deterministic) that, given a molecule, produce another molecule until eventually the process halts. And this formalism is Turing complete: can perform any computation. Also it is a simplified formalism that resembles (but is not identical to) certain structures that appear in sub-riemannian geometry and amount to a graph rewriting system but are not known to be Turing complete. (...) | |
| May 15, 2018 at 22:57 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
minor typo
|
| May 15, 2018 at 22:57 | comment | added | Qfwfq | Wow an answer from the author. Thank you very much for spending the time for writing it! Especially the last paragraph is new to me (I mean, I didn't get it by very quickly skimming through the online material). | |
| May 15, 2018 at 22:13 | history | answered | Marius Buliga | CC BY-SA 4.0 |