2023-09-16 00:29:51 <concrete_houses> nice
2023-09-16 05:10:02 <KipIngram   > Wow - projective geometry looks really useful for graphics.
2023-09-16 08:02:52 <KipIngram   > So, I ran across this math package called Geogebra.  Managed to get a version installed on my notebook.
2023-09-16 08:03:25 <KipIngram   > It's pretty cool - you can do "geometric constructions" with it, among other things - it's really good at understanding what you're trying to get it to do.
2023-09-16 08:04:30 <KipIngram   > Here's a screen shot of one I did:
2023-09-16 08:04:33 <KipIngram   > https://imgur.com/a/0hqP1uC
2023-09-16 08:04:49 <KipIngram   > The idea is that you pick the first pair of lines, then draw all the rest based on those.
2023-09-16 08:05:37 <KipIngram   > One of those lines stays in the same place as you move earlier cnstruction points around - that was the gist of the particular thing being studied.
2023-09-16 08:06:59 <KipIngram   > The idea is that the first thing you pick is "a point outside that circle."  Then you do a bunch of other stuff, until you wind up with that final line, which is called the "polar" of the initial point.  Changing all the decisions you made in the middle doesn't change it.
2023-09-16 08:15:57 <FUZxxl      > Geogebra is cool
2023-09-16 08:16:05 <FUZxxl      > we used it in highschool a lot
2023-09-16 08:26:33 <KipIngram   > It looks pretty handy to have on tap for occsional "tinkering."  I also used it to look at level curves of a surface (x^3+y^3+3*x*y = 0).  Did a real nice job of that.  Again, it seems to "know what you're wanting from it" - someone thought the interface through really well.
2023-09-16 08:27:56 <FUZxxl      > yeah
2023-09-16 09:28:58 <veltas      > I love affine transformations and all that stuff
2023-09-16 17:05:53 <KipIngram   > I think it's really neat how there are levels of all this stuff - affine, projective, etc.  Each one requiring that you have more "capability."  Wildberger describes projective work as the stuff you can do with only a straight edge (not ruled, no compass, no square, etc.)  I like the way he tries to teach these things working at the "minimal" level, so that you wind up with the most general results.
2023-09-16 17:09:00 <KipIngram   > In a projective situation you can subdivide a line, and thereby "create yourself a ruler," and you can then transfer that ruling to another parallel line.  But, you can't tranfer a ruling to a line with a different direction.
2023-09-16 17:09:34 <KipIngram   > So, you can measure along any given directions, but you can't relate the lengths fo things with different orientations.
2023-09-16 17:10:53 <KipIngram   > In the more general, less capable settings it's harder to prove things, but if you can prove something it's better than proving it in a "higher tier."
2023-09-16 17:11:55 <KipIngram   > All of math is structured this way, starting with set theory and building up more involved things layer by layer.
2023-09-16 17:13:56 <KipIngram   > I think topological spaces is the next layer after set theory.
2023-09-16 17:14:20 <KipIngram   > Only new ideas you add there are "adjacency" and "connectivity."
2023-09-16 17:14:28 <KipIngram   > "nearness."
2023-09-16 17:16:09 <KipIngram   > That's where you get the idea that a donut and a coffee mug are the same thing:
2023-09-16 17:16:11 <KipIngram   > https://cems.riken.jp/wp-content/uploads/2013/03/A080_FurusakiT-Fig.jpg
2023-09-16 18:55:17 <KipIngram   > You know, I do have to give Wildberger credit for one thing.  I'm watching his course on hyperbolic geometry.  The usual approach has sinh() and so on flying around almost immediately - as soon as you start talking about the distance between points.  Wildberger takes a more fundamental approach - it's pure arithmetic, ratios, etc. all the way.
2023-09-16 18:55:40 <KipIngram   > And things like sinh() involve a LOT of details that he completely dodges having to assume.
2023-09-16 18:56:22 <KipIngram   > sinh(x) is basically an infinite series if you try to get at it arithmetically.
2023-09-16 18:57:19 <KipIngram   > I've seen this pattern in his work a lot - he often has to work harder to prove various things, but in the end his development is just a lot more "satisfying."
2023-09-16 18:57:46 <KipIngram   > Precisely because he DOESN'T import any "high caliber machinery" from outside his development.
2023-09-16 18:59:24 <KipIngram   > Also, as far as I can tell the standard development of hyperbolic geometry restricts the discussion to points inside the circle, but according to him everything he builds will be equally valid for points outside the circle too.
2023-09-16 19:00:53 <KipIngram   > Hyperbolic geometry is essentially the geometry of special relativity.
2023-09-16 20:48:23 <KipIngram   > This is fairly interesting:
2023-09-16 20:48:26 <KipIngram   > https://antidelusionmechanism.org/files/CircularWave2.pdf
2023-09-16 20:51:24 <KipIngram   > That has Wildberger's parametrization of the unit cicle in it.
2023-09-16 20:52:09 <KipIngram   > If you asked a hundred scientists or engineers to parametrize the unit circle, you'd get back at least 99 answers "x = cos(t), y = sin(t)" and more likely a hundred.
2023-09-16 20:52:33 <KipIngram   > But if you pick some random t and calculate that it will turn out it's not REALLY on the unit circle - it's only "close to it."
2023-09-16 20:53:13 <KipIngram   > Wildberger's expression lets you pick any integer t - positive or negative, and it cranks out a point exactly on the circle.  And all such points correspond to SOME value of t.
2023-09-16 22:11:33 <gordonjcp   > KipIngram: any non-zero integer t
2023-09-16 22:11:37 <gordonjcp   > surely?
2023-09-16 22:12:35 <gordonjcp   > oh, maybe not
2023-09-16 22:13:42 <gordonjcp   > yeah it can, because you can pick a combination of r and t that blows up without special care
2023-09-16 22:48:18 <veltas      > What is it with Forth200x and hiding everything they do
2023-09-16 22:48:45 <veltas      > They write all these documents and I have to spend hours trawling the web looking for up to date documents
2023-09-16 22:52:30 <veltas      > They've got a website but the latest document is from 2019
2023-09-16 22:52:47 <veltas      > Well now I've found this https://github.com/Forth-Standard/forth200x/blob/master/basis/forth.pdf
2023-09-16 22:52:55 <veltas      > From 2022
2023-09-16 22:57:01 <veltas      > And still no recognizers
2023-09-16 22:59:50 <veltas      > And yet committee members like to act as if it's a well founded thing.
2023-09-16 23:00:08 <veltas      > Just because there's a committee and they have regular meetings doesn't mean it exists, it doesn't exist if they don't do releases or even provide draft copies
2023-09-16 23:00:41 <veltas      > It's just a kind of weird sprititual experience for the people on the committee at this point
2023-09-16 23:01:00 <Zarutian_iPad> fascinating in a sense
2023-09-16 23:17:14 <veltas      > Also I just dislike the whole recognizer thing, it's not very Forthy
2023-09-16 23:17:42 <veltas      > The only thing like that which works in a Forthy way is retro's prefix system
2023-09-16 23:38:55 <vms14       > i wonder why they do own the forth standard when the language was invented by chuck
2023-09-16 23:39:10 <vms14       > which even dislikes this standard xd
2023-09-16 23:39:42 <vms14       > it's like stealing something is not yours
2023-09-16 23:40:01 <vms14       > and even making it look ugly to the guy you stole it from
2023-09-16 23:40:12 <veltas      > They don't own it I don't think
2023-09-16 23:40:50 <veltas      > They just make a standard, they're not even ISO or ANSI
2023-09-16 23:40:51 <vms14       > they kind of do at the end
2023-09-16 23:40:59 <vms14       > they decide what goes and what not
2023-09-16 23:41:20 <vms14       > even knowing chuck dislikes what they do
2023-09-16 23:41:35 <thrig       > this might be like those French or Spanish language police that everyone ignores
2023-09-16 23:42:03 <veltas      > Some Forths go by it, but not most
2023-09-16 23:42:09 <vms14       > still i kind of understand
2023-09-16 23:42:20 <veltas      > And it's hard to track something that only insiders seem to be able to keep up with
2023-09-16 23:42:34 <vms14       > the desire of forthwrights to have a common forth so they can share code and alike
2023-09-16 23:43:28 <veltas      > I don't think that's the intention of the committee
2023-09-16 23:43:54 <veltas      > I think that was the intention originally but standards always diverge from that path eventually
2023-09-16 23:44:31 <vms14       > so now the motivation is just to irritate chuck
2023-09-16 23:44:59 <veltas      > I don't think Chuck follows what they do at all so probably doesn't care
2023-09-16 23:45:15 <veltas      > Chuck probably moaned about ANS, that was released in 1994
2023-09-16 23:45:33 <veltas      > Honestly I would be surprised if he knows about Forth 2012 or 200x at all
2023-09-16 23:45:59 <veltas      > There were earlier standard attempts he might have moaned about
2023-09-16 23:48:04 <vms14       > then you mean it's like the comitee lost its original goals and is now like walking in random directions?
2023-09-16 23:49:19 <vms14       > about being forthy... as far as i know the standard wasn't forthy from the start
2023-09-16 23:50:23 <vms14       > this ans vs not ans stuff reminds me a bit about lisp vs scheme
2023-09-16 23:50:38 <vms14       > but in a reverse way
2023-09-16 23:53:19 <veltas      > It's gotten less and less forthy over time