Diamond Holographic Principle and D-Emergent Time

SPEAKER_00: hello and welcome everyone to actin flab today is may 6 2021 and we're really excited to have shauna dobson back for math stream 2.1 this is going to be a fun discussion diamond holographic principle and d square immersion time maybe you'll teach us how to pronounce it and what it is so thanks again for coming on this stream and really looking forward to it so please take it away SPEAKER_01: Thank you so much, Daniel. I just want to say your community is so supportive and I'm so happy to be back for a second talk. You are all working on some of the most, you know, profound ideas here. And so I'm really excited and thank you for having me. Yay. All right. So this talk, I'm going to go a little bit into the more like the diamond part. Cause I got some feedback on what are these diamonds and what was she talking about? And so I was really excited that D square is actually D diamond for emergent time. So, um, I'll try to do my best to lay all these out. Please ask, like Daniel was saying, questions every, you know, 10 slides or something like that. I'm happy to answer it. I'm also trying to constellate and weave together this sort of kind of grand unified picture. So there's some drawings in here, and I hope that it's fun. Okay, so let's go. I'll be talking about the diamond holographic principle in D-diamond emergent time. Yay. Okay. So the goal, I sort of talked about this last time, but not too, too in detail. Um, today I'm going to actually weave together this kind of new math with a active inference and let's try to put it together and all work together. So the goal is like to take the holographic principle, which were, you know, um, all aware of, which was like begotten by Maldacena's, you know, beautiful gauge gravity duality between anti-de Sitter space and conformal field theory. I have an idea to sort of reinterpret it in terms of continuous K theory and something I'm going to call pro-emergence. So a pro-object is is um a specific object kind of in category theory that's being used everywhere and it's sort of this idea of sewing together a bunch of um kind of smaller things that are self-contained to get a grand object and it's sort of built into the very structure i thought oh this is a great idea so i talked about k theory a little bit last time which is this beautiful construction by grothendieck to actually look at um classifying very difficult objects using isomorphism classes of the spaces. So it's like, oh, we can tell if two spaces are equivalent based on their equivalence relations. And I thought that's a very, very, very nice, higher way of looking at things. And there's a new work by Efimov talking about continuous K-theory. So, again, this idea of sort of sewing together maybe smaller K-theories to build a bigger object. So, for this pro-emergence, right, I am fascinated by time, and I want us to kind of get into it, right? how does active inference see these sort of time streams? Like, are there little local times with little thicknesses around them? What is this? So in this idea of mine, this pro-emergence, you have a doubly emergent time that's emergent on two fronts. So you have a local singular condensed time, which is sort of the time that we all experience. It's very like, you know, I'm presenting to your lovely community, 9.06 a.m. This is like Shanna's now, right? But there's also like you know, Alpha Centauri now and the unicorn constellation now, right? So there's all these different nows and who's now is what. So you have these like local singular time, and then you're going to have actually have this global, what I'm going to try to push for is a non-locality in the diamonds, right? So to rephrase the holographic principle and kind of upgrading ADS, which is anti-de Sitter space, which is the bulk, which has gravity in it, I'm going to try to actually rebuild that from the six-factor formalism. So that's what you see in this figure with these sort of six columns. is the six…