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Last Build Date: Wed, 18 Apr 2018 23:20:39 +0000
Wed, 18 Apr 2018 23:20:39 +0000
That's a good idea. Actually Spencer Breiner should do it, since it's his workshop... but I'll be happy to get some of the fame and glory. (image)Wed, 18 Apr 2018 22:00:15 +0000
JB, thanks very, very much for posting this. What an intense experience those two days must have been! As the saying goes, "Like drinking water from a fire hose." And thanks to the organizers and participants. ---- Segueing to a slightly different topic, IMO a message to the Categories mailing list, with a link to http://www.appliedcategorytheory.org/nist-workshop-slides/ would be a very good idea. Would you be willing to post such a message? If for some reason you do not want to, I will see if Bob Rosebrugh would accept such a message from me, but it seems more appropriate for you to submit such a message. Thanks.Wed, 18 Apr 2018 19:07:48 +0000
Here’s the schedule for the ACT 2018 Adjoint School: (image)Wed, 18 Apr 2018 05:47:42 +0000
Here are links to the slides and videos for most of the talks from "Applied Category Theory: Bridging Theory & Practice". They give a pretty good picture of what went on. Spencer Breiner put them up here; what follows is just a copy of what's on his site.Tue, 17 Apr 2018 07:22:07 +0000
The Petri nets are familiar to the Chemist, though maybe not necessarily under that name :-). I see that you arrived at that by what we would call "reaction kinetic" considerations. When I started to think about it I had a different approach: just regard the thermodynamic equilibria. So the basic question is about the types of the products and not how long it takes to get them. That would be something like a "reaction mechanism network". (A side note here: what you write about the term "species" in Chemistry is entirely true, but there is another thing that can be mentioned, chemists are well trained to strictly separate between "particle/molecule,atom" and "compound" hierarchy. There is usually a set of terms which forms a partition with this respect and "species" strictly speaking belongs to the particle/molecule subset). So I thought about compounds (anything what you can put into any type of container) as the elements of the set $latex A=\{a,b,\dots\}$. And the binary operation (lets write it multiplicative for the moment) being a perfect mixture followed by infinite time. Then reactions read for example like $latex ab=cd$. Its clear that $latex aa=a$, you mix the compound with itself and nothing happens. (The nice feature of multiplicativity here I find is that total amounts do not appear, only concentrations.) Also $latex ab=ba$ is clear. But except closed-ness, there is nothing more. So my conclusion was its a CI-magma. What is missing are different reaction conditions at which we wait for the thermodynamic equilibrium. So I thought you get that by a set of indexed morphisms, the indices are the reaction conditions, I think its basically temperature and pressure, maybe some EM radiation. This morphism conserves idempotency and commutativity (besides closedness), so I thought one might call it "homomorphism" (but I am not sure). An interesting feature of this formalization is, that one can for example model that there is a difference between pouring $latex a$ into $latex b$ and $latex b$ into $latex a$, which seems to contradict commuativity at first glance, but thats not true: pouring a into b means essentially starting with $latex (((ab)b)b)b$ and going via $latex a((((ab)b)b)b)$ and $latex a(a((((ab)b)b)b))$ to $latex a(a(a((((ab)b)b)b)))$, which is $latex \ne b(b(b((((ba)a)a)a)))$ in a CI-magma. So in that approach "kinetics" would enter from an more algebraic side the buisnes. Would it make sense to you?Tue, 17 Apr 2018 06:42:47 +0000
Interesting, thank you very much!Mon, 16 Apr 2018 21:48:18 +0000
A common approach these days is to use a strict symmetric monoidal category where different substances (usually called 'species') are objects, the tensor product is denoted $latex +$ and a typical morphism would a reaction like this: $latex A + B \to C + D + D $ This is a tiny bit like a commutative idempotent magma, but different. You can read more in Section 25.2 here: • John Baez and Jacob Biamonte Quantum Techniques for Stochastic Mechanics, World Scientific Press, Singapore, 2018. (Draft available on the arXiv.)Mon, 16 Apr 2018 20:56:01 +0000
I had myself some thoughts about the mathematics of chemical reactions. My bases was to note that the set of substances with the a binary operation is a "commutative idempotent magma" (CI-magmas), for obvious reasons. Reaction conditions are not included in this picture, so one way to introduce them would be some "homomorphism" taking care for that. I dunno if much results from that (the lit. on CI-magmas as far as I can see is sparse) but anyway I think this is at least a concise picture of the structure of the beast. Got some take on that?Fri, 13 Apr 2018 01:29:17 +0000
Here’s the schedule of the ACT2018 workshop: (image)Mon, 09 Apr 2018 04:06:00 +0000
[…] John Baez elaborates on the sequence of ‘hyperdiamonds’, together with mentioning an alternative three-dimensional structure called the triamond, here. […]