(Negative probabilities, infinite towers of negative energy states, or a breakdown in causality are the common issues that arise.)
Single particle Klein-Gordon equation?
Yep!
I have been casually reading these notes which so far have been a great friendly review of a bunch of stuff I once knew or half-knew or felt like I should know but didn’t or etc.
I’m not near it either. As far as I can tell, the paper takes the concept of “probabilistic logic” (of which I think fuzzy logic is one variety?) as a given, and concerns itself with the idea that a probabilistic logic can be given a “truth predicate” that avoids Tarski’s undefinability theorem (which applies to non-probabilistic logics).
I have no idea if this is a new concept, and it may not be, but I don’t think it’s something you'd have to do when coming up with a probabilistic logic.
I recommend Ada because I am a bigger fan of that book than most people, and less of a big fan of GEB than most people.
GEB is a weird book. Hofstadter says that “the point” was supposed to be about his idea that consciousness is the result of strange loops, and has expressed frustration that so few people got that. However, relatively little of the book is actually about those ideas directly — a lot of it consists of either whimsical word/logic games, or of Hofstadter’s long and very detailed exposition of Godel’s Incompleteness Theorems (which I guess he considers necessary because they provide prototypical examples of strange loops).
So, if you like the whimsical Lewis Carroll-like stuff, and are up for several hundreds of pages (IIRC) explaining Godel, then read GEB. If you’re less interested in those things than in Hofstadter’s big idea about strange loops and consciousness, you might actually want to skip GEB and read the book he wrote specifically about that (caveat: I haven’t read it myself).
Ada is also a book that doesn’t click with everyone, but it’s definitely worth a try. (Note that the first three chapters are much more dense and confusing than the rest of the book, so don’t give up there.)
Hope that helps!
That does help, thank you!
Maybe I will put down GEB in favor of Ada….
Having said that, are there books on math for interested laypeople that you’d recommend?
Love and Math by Edward Frenkel is a really great math book for a popular audience, in that it explains some really abstract concepts, does it in a friendly way with plain language, but still really gets the concepts across without dumbing them down or replacing them with metaphors. It’s about the Langlands program, if that sounds interesting. It also gives you a good sense of what the experience of mathematical work is like.
I recommend Ada because I am a bigger fan of that book than most people, and less of a big fan of GEB than most people.
GEB is a weird book. Hofstadter says that “the point” was supposed to be about his idea that consciousness is the result of strange loops, and has expressed frustration that so few people got that. However, relatively little of the book is actually about those ideas directly – a lot of it consists of either whimsical word/logic games, or of Hofstadter’s long and very detailed exposition of Godel’s Incompleteness Theorems (which I guess he considers necessary because they provide prototypical examples of strange loops).
So, if you like the whimsical Lewis Carroll-like stuff, and are up for several hundreds of pages (IIRC) explaining Godel, then read GEB. If you’re less interested in those things than in Hofstadter’s big idea about strange loops and consciousness, you might actually want to skip GEB and read the book he wrote specifically about that (caveat: I haven’t read it myself).
Ada is also a book that doesn’t click with everyone, but it’s definitely worth a try. (Note that the first three chapters are much more dense and confusing than the rest of the book, so don’t give up there.)
Hope that helps!
rikerist replied to your post: rikerist replied to your post: So what…
dude remind me again what u are doing for ur thesis? computational fluid mechanics stuff?
Yeah, stuff having to do with elegant/efficient representations of the mixing due to turbulence in simplified codes that don’t explicitly resolve turbulence
Today in class the Professor presented a few criticisms of von Neumann-Morgenstern and Savage axioms saying they’re not very well descriptive of human decisionmaking and…
I mean, yes?? And????
Those aren’t descriptive theories. If you want a descriptive theory you go after Kahneman and Tversky’s Prospect Theory. Utilitarianism and whatnot are prescriptive theories, saying what an agent should act like, if they followed the axioms. Whether the axioms are desirable or not is another conversation altogether, but saying they’re not descriptive is a completely irrelevant criticism.
Utility functions are used frequently in economics, and (as I understand it) the VNM axioms are part of the standard justification of this. (Some people find “people are rational” easier to swallow than “people have utility functions because I say so.” Note that von Neumann and Morgenstern first introduced them in a book called Theory of Games and Economic Behavior.)
But of course this is not very descriptively realistic. There’s a long history of argument in economics about whether or not assuming rational agents is a sensible “modeling approximation” even if it isn’t realistic. But in any case, economists do use this stuff descriptively.
(So I guess one could say that “the VNM axioms are prescriptive” is a good prescriptive theory, but not a good descriptive one!)
“Et in Arcadia Ego” -Comic Sans
In my head, Alanis Morissette just sang: “and isn’t it ergodic …”
thought doesn’t usually satisfy conservation laws tho (i.e. a thought may have multiple consequences). otoh you might go backwards and try to interpret fluid dynamics using linear logic? idk
Yeah, if interpreted as logic this has the weird consequence that the system can’t believe “A –> B” and “A –> C” at the same time if B and C aren’t the same.
I guess that’s why I said the implication doesn’t have to be necessarily logical? It’s more like “B is the thing that is natural for me to think about immediately after I have thought about A.” Maybe I should call them “transitions,” not “implications.” Like if you have a Turing machine in one state, there’s only one other state it’s going to transition to
I guess the property of “thinking” that ends up being captured is that I feel like various ideas are connected, but thinking about an idea usually just leads me to think next about one connected idea, not all connected ideas. (The conservation of tracer mass reflects a “working memory of constant size” – the amount of idea-stuff I can think about at any given time is the same at all times.)
With tracer diffusion, thinking about an idea leads me to think a little bit about all related ideas, but there is still a general direction of the “train of thought” (advection).
I guess what I should say is that velocity field at a given time represents all possible trains of thought I could be having at that time. I’m not sure if this can be interpreted as belief about logical implication.
What I’m curious about is how the dynamics (vorticity conservation) produces an evolution over time from one “set of possible trains of thought” to another, and whether this has any natural interpretation. If we start with several vortices in distinct parts of the domain, representing several looping “trains of thought” I could be stuck in, what does their subsequent interaction mean?
