The Nineteenth Byte

Usually I've seen the * character used for convolution in written mathematics, which I'm sure Luis et al would approve of replacing this silly multiplication operator ;)

orlp

^ is a notational approximation, ** is a logical approximation (repeated multiplication)

weatherman115

3:15 PM

Here it is

github.com/PySlither/Slither

Fatalize

** is both

since * is not multiplication

orlp

as I said before, it is

it's the closest thing we have in ASCII to the centre dot

Fatalize

you're just used to * being multiplication ;)

weatherman115

Me too

I always use it when doing multiplication

trichoplax

Knuth's up-arrow notation

In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. It is closely related to the Ackermann function and especially to the hyperoperation sequence. The idea is based on the fact that multiplication can be viewed as iterated addition and exponentiation as iterated multiplication. Continuing in this manner leads to iterated exponentiation (tetration) and to the remainder of the hyperoperation sequence, which is commonly denoted using Knuth arrow notation. == Introduction == The ordinary arithmetical operations of addition,...

orlp

3:17 PM

now we just need notation for repeated up-arrow notation

El'endia Starman

@trichoplax I wonder if it's possible for me to define an operator that can be chained endlessly in Pytek...

orlp

and notation for repeated repeated up-arrow notation :D

@El'endiaStarman your lexer can do that

El'endia Starman

@orlp Simple! One up arrow is equivalent to exponentiation, so it's easy enough to do ^^ for two up arrows, ^^^ for three, etc.

orlp

you can have a lexer translate *** to (*, 3), **** to (*, 4)

weatherman115

I hate my slow typing

Fatalize

3:19 PM

anyway, reserving ^ for xor is stupid, this operator is a lot less used than power

orlp

@El'endiaStarman no, you miss my point

weatherman115

Case in point

FryAmTheEggman

@orlp en.wikipedia.org/wiki/Conway_chained_arrow_notation#Properties

weatherman115

Well, I've got to go read Fahrenheit 451

orlp

a ^ b, a ^^ b, a ^^^ b, ..... a {n times ^ } b

then repeated-up-arrow is a | n, which is a {n times ^} a

then we can repeat that!

Fatalize

3:20 PM

Knuth's up-arrow notation

In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. It is closely related to the Ackermann function and especially to the hyperoperation sequence. The idea is based on the fact that multiplication can be viewed as iterated addition and exponentiation as iterated multiplication. Continuing in this manner leads to iterated exponentiation (tetration) and to the remainder of the hyperoperation sequence, which is commonly denoted using Knuth arrow notation. == Introduction == The ordinary arithmetical operations of addition,...

a ^² b

orlp

@Fatalize yes, you see, but now we've just deferred the problem

what if I want to do that n times?

conway's chain notation solves that... until we want to repeat chains!

2 -> 2 -> 2 -> 2 -> ... (n times) ... -> 2

then what if we want to repeat that?

it's a never ending cycle of repetition

El'endia Starman

This reminds me of Vsauce's recent video on orders of infinity...

Kenny Lau

meta-meta-meta-uparrow

meta*n-uparrow

Fatalize

"what if we want to repeat that?" no point in inventing notations for things you don't use anyway

orlp

@KennyLau that's good, but what if I want to repeatedly use meta*n-uparrow?

Kenny Lau

3:23 PM

well

meta^n-uparrow

orlp

@Fatalize you've come to the wrong place if you wanted useful things :P

@KennyLau same question :P

Kenny Lau

well

meta(meta^n)-uparrow

FryAmTheEggman

Couldn't it just be triadic? f (base, value, meta-arrow-ness)

orlp

@KennyLau what if I want to repeat n metas?

meta(meta(meta(meta(meta...

@FryAmTheEggman ah, but what if I want to repeatedly do f(f(f(f(f(f(f(f(base, value, ...?

Kenny Lau

@orlp I ran out of notation

or not

meta(^n

Eᴀsᴛᴇʀʟʏ Iʀᴋ

3:25 PM

f^2(.........)?

trichoplax

@KennyLau I believe that was the goal :P

Eᴀsᴛᴇʀʟʏ Iʀᴋ

I've alway seen f o f = f^2(x)

El'endia Starman

f^f(n)

FryAmTheEggman

Hmm, variadic? f(base, value, first-meta-ness, second-meta-ness, ...)

Kenny Lau

@FryAmTheEggman And then repeat that?

FryAmTheEggman

3:26 PM

Couldn't you just add one more argument if you wanted to repeat it?

Fatalize

Continuing that xor discussion, ^ isn't even a used symbol for xor in math

Kenny Lau

and then if I want to have n arguments?

trichoplax

@Fatalize I'd like to see a symbol which reflects the symmetry of repeated operation

FryAmTheEggman

What do you mean by n arguments? A different argument for each meta level?

Sp3000

For xor they probably looked at ⊻ and went "Hmm, ^ is close enough, right?" "No, wouldn't everyone confuse that with AND?" "Well, do YOU have any better ideas?"

orlp

3:28 PM

regardless of what operation you come up with, I can always come up with a function that grows faster by repeated application

⊕ is what cryptography papers use for XOR

the logic behind it is that it's addition without carry

so it's a plus sign with a circle around it

(\oplus)

trichoplax

Does anyone use multiplication without carry?

orlp

you thought BB(n) grew fast? try BB(BB(n))

Kenny Lau

It's called and @trichoplax

orlp

@trichoplax yes

@KennyLau no

it's multiplication of polynomials over GF(2)

(XOR is addition of polynomials over GF(2))

trichoplax

For bitwise?

orlp

3:32 PM

@trichoplax can you rephrase?

trichoplax

Well, "phrase" since I didn't bother phrasing it the first time :)

orlp

I don't know what you mean with "for bitwise?"

trichoplax

I mean is the (2) because we're talking about bitwise and?

orlp

sorry I apologize (partly)

GF(2) addition is XOR, multiplication is AND

but that's only for a single bit

(hence field size 2)

trichoplax

Ah I see

orlp

3:34 PM

however, for larger fields

e.g. GF(2^64) for 64 bits

addition is still XOR

but multiplication becomes polynomial multiplication, and it's no longer simple AND

trichoplax

Right

orlp

it's also not unambiguous

you have to choose your multiplication operation

because you need to reduce the polynomial multiplication modulo some irreducible polynomial

this is for example why there's multiple flavours of CRC (cyclic redundancy check)

you have CRC-32, CRC-32C (Castagnoli), CRC-32K
(Koopman {1,3,28}), CRC-32K2
(Koopman {1,1,30}), which differ by choice of irreducable polynomial

Eᴀsᴛᴇʀʟʏ Iʀᴋ

3:53 PM

@Downgoat :D I got the cheddar install script!

zyabin101

@EᴀsᴛᴇʀʟʏIʀᴋ \o/ Where?

Eᴀsᴛᴇʀʟʏ Iʀᴋ

DIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" && pwd )"
command="git clone github.com/cheddar-lang/Cheddar.git; cd Cheddar; eval npm install;echo 'alias cheddarrepl=\"node $DIR/Cheddar/dist/interpreter/tests/t_repl.js\"' >> ~/.bash_profile"

if [ -f ~/.bash_profile ];
then
   if grep -q 'cheddarrepl' ~/.bash_profile
	then
		echo "Script already ran, or remove the any mentions of `cheddarrepl` from your .bash_profile."
	else
		if [ ! -d ~/Cheddar ];
		then
			eval $command
		else
			echo "Please delete the Cheddar directory before retrying."

bash only right now

i need to upload

Quill

that should all be a node script inside package.json

zyabin101

@Quill Then we can't use the script easily.

Quill

well you can save it as a .sh file in the repo

zyabin101

3:58 PM

@Quill ^^

It must be available using a curl command

Something like

Quill

and then add "dowhatever": "bash whatever.sh" to the package.json

zyabin101

curl install.cheddar.vihan.org

And it has to be in a command such as

bash -c `curl install.cheddar.vihan.org`

Also, some people don't have npm. :P

Welp, apparently, all Node users have npm.

But it must be available at ease.

Someone has also to create cpm install cheddar :P

orlp

4:18 PM

now it's day 2 of typing on the new keyboard, back to 40 wpm

But it can go down to 20 when I have to type multiple words in a row with letters that I struggle with.

I struggle with the right hand and 'b' because I always had my right hand on hjkl instead of jkl;.

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