The Tarpit

10:30 PM

@cairdcoinheringaahing The ? just because of APL. Despite finishing my undergrad in math though, I've never encountered another symbol, that I can think of, which I associate with randomness... Why?

caird coinheringaahing

@AviFS Adding a randomness command in a new(ish) language

AviFS

I imagine pseudo-randomness, with chaos theory, is talked way more about in physics (and obv. CS) than in math. And I've never encountered a theoretical purely-random function

The closest to that would be the non-deterministic automata in my Theory of Computing course

So maybe the symbols 'NP', haha

caird coinheringaahing

Isn't the orientation of electrons supposed to be completely random?

And that's how qubits work?

@AviFS I've decided to go with ? (see the convo in TNB) FYI

AviFS

@cairdcoinheringaahing Very good point. I guess in quantum computing, too!

So maybe 'Q'

caird coinheringaahing

I want to stay way from letters as much as possible

AviFS

10:34 PM

But I think ? makes the most sense, and is the most intuitive on a million different levels!

caird coinheringaahing

It's primarily math notation, and letters don't really factor that much into math

AviFS

@cairdcoinheringaahing Of course! I was kidding!

I definitely vote ?

caird coinheringaahing

Also, I should be ashamed to call it "math" and not "maths" :P

AviFS

@cairdcoinheringaahing Haha, you Brit!

caird coinheringaahing

Is it just me, or does anyone else kinda feel "better" at coding when they're drinking a beer? Like idk what it is, but I instantly feel more focused and my thought processes are clearer if I'm drinking a beer

@AviFS Well, my parents say I'm basically an American cause of my speech colloquialisms :P

AviFS

10:37 PM

@cairdcoinheringaahing Haha, I've always wanted to try, but never had a chance

@cairdcoinheringaahing That's too funny!

caird coinheringaahing

@AviFS You're in the UK for uni right? You can drink over here

AviFS

Am turning 21 in a month and I only just got here...

@cairdcoinheringaahing True, but just a semester abroad

Got here in January

caird coinheringaahing

If you're in Edinburgh, it's very easy to get absolutely f-ed up

AviFS

And couldn't buy it myself because I didn't get the right ID

So just had it parties, clubs, gatherings and such

caird coinheringaahing

The bar/club scene there is mad

@AviFS How do you mean?

AviFS

10:39 PM

@cairdcoinheringaahing Actually, I guess I could. I just needed my passport, which I didn't like carrying around

caird coinheringaahing

@AviFS Do you have a US driving license? Pretty sure most shops/bars take them

AviFS

Anyway, I went to a few pubs, but never bought any to bring back to the dorm and code, is all I meant ⍨

caird coinheringaahing

@AviFS Fair enough

AviFS

@cairdcoinheringaahing It's very silly, but they don't take 'em

Lyxal

@cairdcoinheringaahing I know I'm as late as anything to the party, but I didn't get a chance to answer (blame sleep for that). No, I don't use regex when parsing... When I was first reading tutorials on how to make programming languages, they said regex is a big no no. And I can kinda see why: sometimes syntactic structures can be more complicated than regex can handle.

caird coinheringaahing

10:40 PM

@AviFS Really?? I always thought they would

@Lyxal Interesting

AviFS

Each state has a different driving license. I'm from Cali, so they definitely could verify it. But as a matter of principle they don't because I think they don't want to need training in how to read 50 different cards

caird coinheringaahing

I have 2 languages that are almost entirely parsed via regex

And all of my "more complicated" languages use regex at some point in parsing/tokenising

@AviFS I'd have thought it'd be a simple of checking for a hologram and that the age matches

AviFS

Any thoughts on the SB tree lang?

Did you guys get a chance to see my conversation with the great @AdHocGarfHunter?

Lyxal

@cairdcoinheringaahing yet my 4 don't make a single reference to regex

caird coinheringaahing

@Lyxal Different preferences

AviFS

10:42 PM

@cairdcoinheringaahing Yeah, didn't seem right to me

caird coinheringaahing

Add++, the one I use the most, I think only uses regex to check whether a command is infix, prefix or postfix

AviFS

@cairdcoinheringaahing Definitely considered better practice not to use it. But definitely easier to do so

caird coinheringaahing

@AviFS glances at code Yeah... better practice...

AviFS

@cairdcoinheringaahing Haha, just what the people say, IDK. I didn't come up with it :D

Note I said considered

Alright, hiatus for me

caird coinheringaahing

TBH I think I almost always have import re or import regex, cause if I don't use regex in the interpreter, I have regex/string processing commands in the language

@AviFS o/

Lyxal

10:45 PM

@AviFS imma have to do that too

AviFS

@Lyxal :(

@cairdcoinheringaahing Shoot! I always contradict myself. Am doing something else

@cairdcoinheringaahing But have to ask: what does that mean?

Seen it a bunch...

caird coinheringaahing

It's a wave

AviFS

@cairdcoinheringaahing ?

caird coinheringaahing

Usually waving goodbye if someone's leaving

Occasionally used for other purposes in certain rooms

AviFS

@cairdcoinheringaahing Hmm... still don't see

@cairdcoinheringaahing An empty face and one arm?

caird coinheringaahing

10:48 PM

The o is the head, and the / an arm

AviFS

Like half of: \o/?

@cairdcoinheringaahing Right! Thanks :)

caird coinheringaahing

There's also \o, \0, \O and their mirrors

AviFS

@cairdcoinheringaahing Makes sense!

@cairdcoinheringaahing Am back but afraid we lost @Lyxal

caird coinheringaahing

sees Lyxal join

AviFS

Here they are

Lyxal

10:58 PM

My hiatus was called breakfast

AviFS

> Any thoughts on the SB tree lang?
Did you guys get a chance to see my conversation with the great @AdHocGarfHunter?

caird coinheringaahing

If/when I take a hiatus it should be sleep :P

AviFS

Or on Brainmuck?

Or on anything else you might be interested in?

caird coinheringaahing

@AviFS TBH I'm not sure I fully understand SB, so I don't really have any thoughts

Sorry :/

AviFS

Including any of your own thoughts?

caird coinheringaahing

10:59 PM

I barely know what a binary tree is

AviFS

@cairdcoinheringaahing It's unbelievably embarrassing, but I'm not sure I do either...

We'll have to wait for AdHoc

caird coinheringaahing

IIRC they're based in NYC, so its 19:00 for them

AviFS

This is about as much as I actually have decided:

> Semi-concrete: For two different languages, I'm thinking about playing with number representations. One would encode and manipulate only surreal numbers. The other would be based on the Stern-Brocot tree. It would only have fractions and they could only be manipulated through traversing the tree.

caird coinheringaahing

@AviFS Remind me what surreal numbers are again?

AviFS

Stern–Brocot tree

In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree. The Stern–Brocot tree was discovered independently by Moritz Stern (1858) and Achille Brocot (1861). Stern was a German number theorist; Brocot was a French clockmaker who used the Stern–Brocot tree to design systems of gears with a gear ratio close to some desired value by finding a ratio of smooth numbers near that value. The root of the Stern–Brocot tree corresponds to...

Everything in that conversation was AdHoc's ideas as to how it might look

But any ideas you have about a language based on SB representations of numbers (fractions), or it's tree, are equally great

@cairdcoinheringaahing Not sure I understand it well enough to explain very well

caird coinheringaahing

11:04 PM

googling

AviFS

Essentially another number system, which I always find fascinating

Surreal number

In mathematics, the surreal number system is a totally ordered proper class containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field. If formulated in von Neumann–Bernays–Gödel set theory, the surreal numbers are a universal ordered field in the sense that all other ordered fields, such as the rationals, the reals, the...

caird coinheringaahing

Well, there's a book by Donald Knuth on it, so that's always a good sign

AviFS

But with math stuff, Wikipedia is always impossible

Lyxal

Last time I saw an esolang based on just numbers, it was intcode.

caird coinheringaahing

Yeah, I got lost very quickly

@Lyxal What about 7?

AviFS

11:06 PM

@cairdcoinheringaahing Conway invented it and told Knuth on a napkin, before publishing. Knuth got his permission, went away and locked himself up in a hotel for a week, during which he wrote that novel

Lyxal

@cairdcoinheringaahing i didn't remember 7 because i never had to write an interpreter for it

AviFS

Wait, maybe not before publishing, it did come up in the book on games with Hackenbush and two other authors. Anyway, the point was it was if not the first book, one of them, on it

mathworld.wolfram.com/SurrealNumber.html

@cairdcoinheringaahing Recommend ^^^

caird coinheringaahing

I'll take a look, thanks

AviFS

@cairdcoinheringaahing It's just 2 paragraphs :)

Just an overview, not explanation

caird coinheringaahing

@AviFS In the middle of something rn tho :p

AviFS

11:08 PM

Basically they're of the form { L | R } where L & R are sets of other surreal numbers

Lyxal

@AviFS clicks link...*gets immediately distracted by the idea of using wolfram to apply bilateral filter to dog image*

AviFS

So you start with the most basic possible which is {|} or {⍬|⍬} and from there you recursively make larger and larger ones. It can be shown that they not only represent all real numbers, but also all ordinals and it's thought to be the most natural system with well-defined operations which has all of them

AKA, you can actually work with 'infinities' as numbers

The simplest infinity is ⍵, that is it's larger than any real number, but you can still have √⍵, ⍵^2, ⍵+1, etc.

You can also have 1/⍵, the smallest number greater than 0

caird coinheringaahing

I don;t like new representations of standard math :P

AviFS

Well, smaller than any other positive real number, that is

caird coinheringaahing

Unless its to absolutely blow someone's mind :D

AviFS

11:13 PM

Because you can have 1/(⍵^2), and such

@cairdcoinheringaahing Don't really understand the ordinal/infinities very well but it's not much different from SB for practical purposes

It would only be used for small, finite numbers. So basically the primitives would be you either append another surreal number to the left hand side or the right hand side

caird coinheringaahing

@AviFS Bruh, just subtract 0.000....0001 from it, and it's smaller :P

AviFS

Because remember, they look like { L | R }

So { 1 3 5 | 2 4 6} →

\ :  { 1 3 | 2 4 6}
/ :  {1 3 5 | 2 4}
<7:  {1 3 5 7 | 2 4 6}
>8:  {1 3 5 | 2 4 6 8}

Just made up the /\<> notation for cutting/appending left/right. But basically those would be the primitives to manipulate the numbers

Anyway, SB is really easy! At least by comparison

Infinite Fractions - Numberphile

►

caird coinheringaahing

@AviFS Given that I still don;t understand surreal numbers, I guess I almost don;t understand SB then?? :P

AviFS

@cairdcoinheringaahing I don't understand surreals, and I've looked at every source I could find including downloading the books (thank God for libgen). Honestly, I'm sure Knuth's would do it since he wrote it for children. And with enough time/energy so would Conway. But Knuth's book bored the heck out of me. He's no good at novels IMO, and the tone is unnervingly religious, for me. I always knew he was, but sheesh!

They sort of find the rules of surreals on ten-commandment-like tablets, and then these teenagers decode it on an abandoned island while they fall in love with each other. But it's written like a play, where it's just dialogue back and forth. I lost patience because most of it is fluff, with some stuff where they're enamored with each other, and mathematics and such, and the math itself is spread too thin for my liking so it was hard to skim out the meat of it.

@cairdcoinheringaahing Surreals are a whole 'nother thing. SB is really elegant and simple though, I swear! You know how accessible Numberphile is and they cover it there in 5

caird coinheringaahing

11:28 PM

Mathematics have never been known for their ability to interact well with other people

@AviFS Never been a fan of Numberphile tbh

AviFS

@cairdcoinheringaahing Contemporary books dedicated to exposition tend to be good though, IMO. Anything before around the 80s-ish though is out of touch, afaict, even among the exposition. Except for Martin Gardner, who's amazing!

caird coinheringaahing

@AviFS TBH I'm fairly partial to Simon Singh

AviFS

Eg. I tried this book at my grandparents titled 'Mathematics for the Millions.' Supposed to be accessible to highschoolers

I still find it boring and inaccessible

Lyxal

@AviFS this?

AviFS

@cairdcoinheringaahing Def. contemporary. Born '64. Martin Gardner's the only one I know in math who wrote really well in the times that my physic-professor-grandparents were buying exposition books in math

Obviously in physics there's way more like Feynman

caird coinheringaahing

11:34 PM

I've never really read many math books that were'nt textbooks

I think I have <10 math books on my bookshelf

AviFS

@Lyxal Hmmm... not sure. That one actually looks reasonable and I can't find the right cover. Maybe it was an older edition? Definitely looked older than '68, IDK

@cairdcoinheringaahing Only bc of my grandparents did I when I was younger. So I started getting lots of mathemagic books

Things like this, too

Nothing heavyweight. Again, never got farther than fibonacci, phi, GoL and mathematically-self-working magic trick sorts of things

Tons of esoteric sequences, constants, automata, magic tricks, jokes and such, but nothing more difficult than those

@cairdcoinheringaahing Not even for 5 minutes?

caird coinheringaahing

@AviFS Nah, I always found their videos too "dumb it down"

I like being challenged, even in subjects I have basically no prior knowledge

AviFS

Basically, just a way to construct a binary tree (tree with two children per node) such that each fraction appears once and only once

caird coinheringaahing

Imagine thinking that 2/4 equals 1/2 :P

AviFS

Therefore, every fraction can be represented by a binary string with this encoding. You start at the root, 1/1, and 0 means left; 1 means right. So 110 represents 5/2

caird coinheringaahing

11:43 PM

Just list the possible values a/b for all a, b

AviFS

@cairdcoinheringaahing It does! That's what's so neat!

Only 1/2 comes up; 2/4 never will

caird coinheringaahing

See, right now, you might as well be just be writing a sentence, then scrambling the words

AviFS

Forgot to mention, thanks: Each fraction only ever shows up in its most reduced form

@cairdcoinheringaahing ?

caird coinheringaahing

I know what each word means, but together, I have no clue what you're saying

AviFS

Few more examples:
0: 1/2
1: 2/1
10: 3/2
01: 2/3

0110: 5/1
1100: 7/3

@cairdcoinheringaahing Which part?

caird coinheringaahing

11:46 PM

@AviFS The whole thing. Like, have you ever looked at a sentence and gone "I know what all those words individually mean, I know what they mean when you put any of them together, but I have absolutely no clue that this sentence is saying"?

AviFS

@cairdcoinheringaahing Yeah, but I re-read what I said and I'm not sure which part is doing that. So I need some direction

caird coinheringaahing

@AviFS In all likelihood, it's my lack of knowledge, rather than anything specific that you've said

AviFS

@cairdcoinheringaahing The 5 min. vid is easier, but less details. By far, the best written bit on SB is from my favorite math book ever, and Knuth is the first co-author since one of you was excited about that

caird coinheringaahing

Imma just stick to the math I know for now

AviFS

The full book is Concrete Mathematics: A Foundation of Computer Science - 2nd Edition, which you can find on Libgen if you like

caird coinheringaahing

11:53 PM

Maybe expand my Calculus knowledge

AviFS

But I carefully spliced out the phenomenally written chapter on SB for you:

caird coinheringaahing

@AviFS I'll read it, but don;t expect me to grasp it :P

AviFS

Darn, how to upload a PDF?

I don't want to use github

caird coinheringaahing

I'd just copy and paste

If it's too long, press shift+enter at the start

That's how I sent my Long Message™

AviFS

Stern-Brocot Numbers from Concrete Mathematics

@cairdcoinheringaahing ?

It's a PDF

caird coinheringaahing

11:57 PM

Yeah, but you can usually select+copy+paste sections of a PDF

AviFS

@cairdcoinheringaahing Much too long for that

@cairdcoinheringaahing Ignore the impossible calculus at the beginning of the page. It's the chapter on Relative Primality which start at the bottom of first page

Promise it's way more interesting than silly calculus

Or I can just start again:

Transcript for