Corpus evidence — top 10 passages

Most-relevant passages from the entire indexed corpus (67,286 paragraph chunks across YouTube transcripts, PubMed, arXiv, archive.org, Stanford Encyclopedia of Philosophy, OpenAlex, and more) ranked by semantic similarity (bge-small-en-v1.5).

1. 01 · yt0.840

   Um, so anyway, this is this is what one finds. This is just looking at each each picture here is a different possible underlying rule. So they're in a sense different artificial physicses and the question is what do they all do? So many of them do very simple things but my all-time favorite science discovery is the one numbered 30 there rule 30 and if you look at what it does has a very simple uh kind of rule for how it's constructed but yet you started off in just one black cell it makes this pattern that seems kind of complicated. When I first saw this I kind of thought well if I run it long…

   yt/OWyugUdBups-stephen-wolfram-computation-at-the-foundations-of-everything/transcript.txt

2. 02 · blog0.812

   With \(r = 1\), there are 8 possible neighbors (see Fig. 4 above) to be mapped to \({1, 0}\), giving a total of \(2^8 = 256\) rules. Starting with random initial conditions, Wolfram went on to observe the behavior of each rule in many simulations. As a result, he was able to classify the qualitative behavior of each rule in one of four distinct classes. Repeating the original experiment, we simulated the evolution of two rules for each class of Wolfram’s scheme. 2.3 The Classes of the 256 Rules Class 1 rules leading to homogeneous states, all cells stably ending up with the same value: Rule 25…

   blog/plato-stanford-edu/cellular-automata.md

3. 03 · yt0.806

   And if you take a random pattern in nature, you can always say, I can compile this pattern into what I want it to be. You see a bunch of say leaves tumbling or you see a bunch of molecules in brownian motion in the surface of your table. Uh couldn't we compile this interpret it as a sequence of mental states? And the thing is every compilation step would require a new function. >> And if you see these leaves then one state and the tumbling of the leaves is now compiled into one thought.

   yt/IzbtOzXMLOo-joscha-bach-anders-sandberg-ai-consciousness-and-the-cyborg-/transcript.txt

4. 04 · yt0.801

   So I started thinking well okay what can can we write programs that will reproduce what happens in the natural world and uh then the next question was well you know the programs we're used to writing are big complicated things that are set up for some particular purpose we have in mind but what about programs in the wild what about programs which are just sort of picked at random enumerated very simple programs what do such programs typically do and so that got me into asking that question and so I started looking at very simple programs. Here's an example of of one. This is a creature called …

   yt/OWyugUdBups-stephen-wolfram-computation-at-the-foundations-of-everything/transcript.txt

5. 05 · pubmed0.788

   In this paper we explore several fundamental relations between formal systems, algorithms, and dynamical systems, focussing on the roles of undecidability, universality, diagonalization, and self-reference in each of these computational frameworks. Some of these interconnections are well-known, while some are clarified in this study as a result of a fine-grained comparison between recursive formal systems, Turing machines, and Cellular Automata (CAs). In particular, we elaborate on the diagonalization argument applied to distributed computation carried out by CAs, illustrating the key elements…

   pubmed/PMID-30655222-self-referential-basis-of-undecidable-dynamics-from-the-liar/info.md

6. 06 · yt0.780

   You might   term it the cut-and-paste construction.  It's where you take models of space-time,   like relatively well-behaved models, like  something like a Minkowski space-time, and what   you're going to do is you're going to cut slits  here, and you're going to glue things together.   You're going to create wildly crazy topologies in  this way. They're going to be standard models of   GR. They're going to count as models of GR,  but they're going to be wildly unphysical. Now, those folks, Penrose, Geroch, others,&nbs…

   yt/iGOGxaZZHwE-it-s-not-that-we-don-t-know-it-s-that-we-can-t/transcript.txt

7. 07 · yt0.775

   You you set these are the rules that we are we adopt to prove things. Then you what Gödel shows is an amazing thing. I always thought it was amazing. There is a statement which you by virtue of your trust in these rules, you can see that it's true. Yet, you can't prove it by the rules. Now, I found this absolutely amazing because it means you're you don't use the rules to to understand things because how do you know this thing is true? Well, you know it's true but because you trust the rules. Well, it's you're you're if you're using the rules, then how do you know that using the rules only giv…

   yt/OoDi856wLPM-sir-roger-penrose-stuart-hameroff-collapsing-a-theory-of-qua/transcript.txt

8. 08 · blog0.774

   Cellular Automata (Stanford Encyclopedia of Philosophy) Stanford Encyclopedia of Philosophy Menu Browse Table of Contents What's New Random Entry Chronological Archives About Editorial Information About the SEP Editorial Board How to Cite the SEP Special Characters Advanced Tools Contact Support SEP Support the SEP PDFs for SEP Friends Make a Donation SEPIA for Libraries Entry Navigation Entry Contents Bibliography Academic Tools Friends PDF Preview Author and Citation Info Back to Top Cellular Automata First published Mon Mar 26, 2012; substantive revision Fri Dec 15, 2023 Cellular automata (…

   blog/plato-stanford-edu/cellular-automata.md

9. 09 · yt0.773

   Um I will say the um uh turns out and it took about 50 years for me to sort of straighten this out that actually that original question that I had about the second law of thermodynamics is all about computational irreducibility in the end. So if if we take uh you know something gas molecules in the box bouncing around becoming more random, we can look at sort of a space-time picture of that, we can kind of simplify it a bit and we can end up with something that's just one of these cellar automaton systems where we just have a a grid of cells and we're just updating cells according to the value…

   yt/OWyugUdBups-stephen-wolfram-computation-at-the-foundations-of-everything/transcript.txt

10. 10 · arxiv0.773

    To respect physics and nature, cellular automata (CA) models of self-organisation, emergence, computation and logical universality should be isotropic, having equivalent dynamics in all directions. We present a novel paradigm, the iso-rule, a concise expression for isotropic CA by the output table for each isotropic neighborhood group, allowing an efficient method of navigating and exploring iso-rule-space. We describe new functions and tools in DDLab to generate iso-groups and iso-rules, for multi-value as well as binary, in one, two and three dimensions. These methods include filing, filteri…

    arxiv/2008.11279-isotropic-cellular-automata-the-ddlab-iso-rule-paradigm/info.md