7:41 A consistency requirement would be connected to more than just one individual's knowledge though. I'm sure there is a better one, I just don't know what it is! [8:31 But it's connected with how the reference measurement is established [14:11 Oh, he says as much himself! [18:23 and confirms it explicitly! ]]]
25:59 Regularities one expects are always conditioned on some context. I expect the apple to fall, but not if it's on a shelf, for example. So ultimately our expectations are conditioned by our abilities to prepare experimental conditions. When our expectations are not met the most likely reasons are that the [experimental] conditions were not in fact met, or there were [experimental] conditions that we thought were universal but which turned out not to be, and these are novelties. I have the feeling that this can be shown to be consistent with Popper's falsifiability criterion for scientific knowledge: universal laws are those things that happen just because there is no particular reason why anything else should happen. The second law of thermodynamics is perhaps the best example.
59:42 [I made a comment on this, regarding the nature of the many particular things other than mass, but YouTube deleted it because it had a link to Popper talking about exactly this.] Newton's Law of Gravitation was derived from what Newton called "Inductive Reasoning" (Isaac Newton: "In [experimental] philosophy particular propositions are inferred from the phenomena and afterwards rendered general by induction": Principia, Book 3, General Scholium, at p. 392 in Volume 2 of Andrew Motte's English translation published 1729.) The law does not tell you the conditions under which this "particular aspect of things" (i.e. gravitational mass) is observed, nor even the phenomena that represent it because observations of these things are "theory laden" in Popper's terminology, and the growth of knowledge proceeds by conjectures and refutations, so we are continually testing existing knowledge against new experience. But that does not tell us how to proceed in the case when observations apparently contradict our theories: we have to make a choice about what is in error: theory or observation, and it is not always clear. It would be nice of the consistency requirement could help with this.
I mean, how to get the best of the two different philosophies of computation. One is based on typed programming languages and the other on engineering with diagrams . This is about practical computing and the cost and feasibility of software development in general. Here is the problem: We have a lot of algorithms which can all be described abstractly using some sort of pseudocode, or perhaps using some particular language (usually Python!). These algorithms are often well-studied and a lot is known about them in terms of their computational complexity in time and space. Substantive practical software systems invariably employ many such algorithms, often implemented in libraries with more or less well-specified APIs. But very few of these libraries are capable of interoperating because they are either packages written in some specific programming language like Java or Haskell, say, or they are written in C and used as object code, or they are written in an interpreted language like Sc...
Listening to Freya Holmér last night I started to get glimmers of an idea I had long ago about how to represent vector spaces in computational processes using this recursive abstract type : abstype 'a point = POINT of {getx : 'a vector, diff : 'a point -> 'a point, move : 'a point -> 'a point, scale : 'a -> 'a point, proj : 'a point -> 'a} with fun new i (op +) (op -) (op * ) dot = let fun self x = POINT {getx = x, move = fn (POINT pr) => (self (x + (#getx pr))), diff = fn (POINT pr) => self (x - (#getx pr)), scale = fn i => (self (x * i)), proj = fn (POINT pr) => ...
Just testing stuff: SVG You can click on the blue circle: MathML There is not much you can do with this. See Mathematical Markup Language 1.01 Specification 7.1.5 Mixing and Linking MathML and HTML . It's the big problem of how you compose languages. a x 2 + b x + c = 0 You can click on the discriminant: x = − b ± b 2 − 4 a c 2 a 2D Canvas Sound Beep! WebGPU Next level Parser expression grammar compiler: https://peggyjs.org/online.html Devine Lu Linvega's unxtal assembler/debugger: https://wiki.xxi...
[8:31 But it's connected with how the reference measurement is established [14:11 Oh, he says as much himself! [18:23 and confirms it explicitly! ]]]
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