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.
A derivative is linearisation, and differential calculus is essentially linear algebra, ... See Freya Holmér - Why Can't You Multiply Vectors? and Freya Holmér on Continuity of Splines . See also the MIT OCW page: Matrix Calculus For Machine Learning And Beyond (Alan Edelman, Steven G. Johnson) Subscribe to The Julia Programming Language . Alan Edelman talking about expressing mathematics as computer code. The idea is that you can use computer languages to communicate mathematical ideas precisely to other people. See my comments about functional programming languages here: https://prooftoys.org/ian-grant/hm/ Subscribe to TEDx Talks .
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) => ...
I think this is the first time they've actually publicly announced anything about this project. See these posts: Eron Woolf on Why Open Source is Failing Matt Mikhailov and Vincent McKibbon on The Problem with Open Hardware Jason Kridner talking About BeagleBoard.org and Software Development . See these places: https://danielc.dev/rk/ https://github.com/petabyt/rk https://github.com/futo-org/ret See also https://pine64.org/devices/pinebook_pro/ . Subscribe to FUTO . See https://github.com/nir9/low-level-learning-resources/tree/master/setups/debian . Subscribe to Nir Lichtman . If you're looking for a cool init process, try https://ctx.graphics/terminal/ . See Artful Bytes - When to Use a RTOS and How to Create a Successful Open Source Project .
[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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