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12:18 AM
Hello, I was doing some multivariable limits and my teacher suggested converting to polar using x=rcos(θ) and y=rsin(θ) to check if the limit exists (as it measures the limit from all directions). I was working on a problem in which I know the limit doesn't exist, and can't figure out how to parametize to polar.
Do you even need to do that? Try approaching on the line y=0 and on the line y=x @AfronPie
Remember that $(\sin x)/x\to1$
Ah, ok that makes sense. for the y=0 line I got the limit to be 1, while for y=x it is 2. I was just tempted to parametrize as the denominator was $x^2+y^2$ (it seemed like a good idea).
Thanks @AkivaWeinberger
12:45 AM
@AfronPie Yeah that was my first thought too but I realized the numerator would be $(\sin(r\cos\theta)+\sin(r\sin\theta))^2$
which isn't a hundred percent useful
Yup same
Thanks again
2 hours later…
2:22 AM
@AkivaWeinberger there is a valid identity there, actually. See the real-valued formulae here: Jacobi-Anger expansion
(That said, valid does not mean productive)
That seems incredibly unproductive yeah
but yeah that's cool thanks
I thought it was gonna be something using the sum-of-trig identities
which would give 2sin[(rcos+rsin)/2]cos[(rcos-rsin)/2] I think?
And then $\cos(\theta)\pm\sin(\theta)$ is something involving $\cos(\theta\pm\frac\pi4)$ or something similar
Doesn't seem like a useful road
@rapasite yes
What's the hardest problem whose solution was known to the Greeks?
Maybe superlatives don't make good questions
What are some hard problems whose solutions were known to the Greeks?
(I haven't actually gone through Elements so I'm not so familiar with what's in there)
I know they knew the surface area and volume of a sphere
The fact that they could do stuff with spherical triangles is pretty cool in my book
(I mainly have Menelaus in mind for that )
Oh for some reason I thought he was German, 'cause of the name
Mene"lay-us", not Mene"louse"
(or me-NE-la-os/osh in Modern Greek)
(but Euclid is efKLEEthees(h) in Modern Greek so whatever)
2:49 AM
@Semiclassical a n g e r y
@rapasite yes
3:07 AM
The 21st century, much more than any other, is the age of hyperbole.
αιλ σήγλω βαιηνντηούνω, μούτσω μας και κουαλκηαίρ ώτρω, αις λα αίρα δαι λα υπέρβολε
Why did you do this
I see what you did, I just wanna know why
because they say Greek sounds like Spanish
3:16 AM
The phonologies are remarkably similar
or are you asking why I chose the long vowels
Same vowels and /ɣ/, /ð/
I had to think for a few seconds for "ch"
I suppose τσ will do
That's how they do loanwords
oh nice
also some people pronounce "ch" like "ts" sometimes
3:17 AM
The /s/ in Greek is retracted so it almost sounds like /ʃ/ anyway
'Bar' in Greek is ΜΠΑΒ
No other way to write /b/
(since β is /v/)
(and not /β/ because that would make too much sense)
how would they transliterate "ei" as in "veintiuno"?
εϊ @LeakyNun
oh, that exists
Ex: πρωτεΐνη
(Diaeresis and accent on the same letter)
hmm, they transliterate uno dos tres as ουνο ντος τρες
3:25 AM
What about seis
word-initial "d" doesn't undergo lenition in Spanish I suppose
Utterance-initial, at least
@AkivaWeinberger the source only has ουνο ντος τρες :P
item 146
ooh I found another sauce
I was about to
3:28 AM
They use an accent mark - if it's on the first letter in a digraph then it separates
(and if it's on the second letter then it remains a digraph)
Accent marks in Greek, unlike Spanish, are required for any word with more than one syllable
Note: διέθ, not διέσ
ούνο δος τρες κουάτρο θίνκο σέις σιέτε ότσο νουέβε διέθ όνθε δόθε τρέθε κατόρθε κίνθε διεθισέις διεθισιέτε διεθιότσο διεθινουέβε βέιντε
βέιντε is a little suspicious
because ντ = d?
@LeakyNun Word-medially I think it can also be /nd/?
Might be free variation
I don't know about that
3:30 AM
In any case I don't think you can enforce /nt/
hey we just did a Rosetta stone thing
@AkivaWeinberger and θίνκο not σίνκο
Santorini = /s̠a(n)doɾ̠ini/?
@LeakyNun Right 'cause ceceo
za ce ci zo zu = /θ/
sa se si so su = /s/
> Santorini (Greek: Σαντορίνη, pronounced [sandoˈrini])
> It may be an alveolar approximant [ɹ] intervocalically
A little American-sounding
(Full quote:
> The only Greek rhotic /r/ is prototypically an alveolar tap [ɾ], often retracted ([ɾ̠]). It may be an alveolar approximant [ɹ] intervocalically, and is usually a trill [r] in clusters, with two or three short cycles.[8]
3:35 AM
> [o voˈɾʝas ˈco̯iʎoz ˈmalonan | ʝa to ˈpços aptuz ˈðʝo ˈineo̯ ðinaˈtoteɾos | ˈota ˈnetiçe napeˈɾasi apo broˈstatus | ˈenas taksiˈðʝotis pu̥ foˈɾuse ˈkapa]
From Wikipedia's example sentence
> broˈstatus
what's the [ç] corresponding to?
Nonsyllabic /i/ after a voiceless consonant I think
what is [ˈnetiçe]?
Ο βοριάς κι ο ήλιος μάλωναν για το ποιος απ’ τους δυο είναι ο δυνατότερος, όταν έτυχε να περάσει από μπροστά τους ένας ταξιδιώτης που φορούσε κάπα.
@LeakyNun ν έτυχε
"όταν έτυχε" = [ˈota ˈnetiçe] interesting
so they do they German thing with the ch
fronting before front vowels
3:38 AM
Oh so I was wrong about nonsyllabic /i/
That's just /j/ as usual
ha, they converged!
/ɣ/ fronts to /ʝ/ though
a merger in plain sight!
> This also accounts for Greeks having trouble disambiguating voiced stops, nasalised voiced stops, and nasalised voiceless stops in borrowings and names from foreign languages; for example, d, nd, and nt, which are all written ντ in Greek.
wait why is "ταξιδιώτης" pronounced [taksiˈðʝotis]?
ʝ instead of ç?
3:42 AM
δ is voiced
oh right
Notice all the sandhi as well
I dunno what acoustically the spaces in the IPA transcription refer to
but they're clearly not the same as the word boundaries in the orthography
Like French?
Except without the dropping consonants
Conlang idea: the only consonants are /h̪͆/, /s/, /sʲ/, /ʂ/, /ɕ/, /ʃ/, /ɬ/, and /ɧ/
@AkivaWeinberger are you jewish?
like religiously?
3:53 AM
and the only vowels are /ə/ and /ə̥/
@LeakyNun Yes
can I ask you a religious question?
is Hebrew the original language?
and do you know Jews who insist that?
3:55 AM
I haven't discussed it with them though
Everyone knows the true original language is Sanskrit though
(it's actually Tamil)
and have you heard of people trying to connect the meanings of triliteral roots to the individual letters?
I probably heard that somewhere
like how A means strong and L means something I forgot so A-L is god
I know Kabalah attaches a lot of meaning to the letters making up the words for things
I'm really not the person to ask about Kabalah though
3:59 AM
You could probably find people who do a similar sort of thing with hanzi to be honest
(Would probably be easier, too)
so 90% of the Chinese characters are formed from a radical denoting meaning and a word denoting pronunciation
Fun fact: the letter 'chet' used to refer to two separate phonemes that merged
Phonosemantic compounds, yeah
@AkivaWeinberger well a lot of mergers happened in Hebrew
This one happened in early Biblical Hebrew
@AkivaWeinberger so I don't know if you were referring to that
or maybe you're talking about things like fengshui
and I don't really know about that
4:01 AM
Don't know what that is
@AkivaWeinberger Biblical Hebrew also. just look at https://en.wikipedia.org/wiki/Semitic_languages#Consonants
leaky original how?
the Jews believe the world has been created with the word
> Biblical Hebrew as of the 3rd century BCE apparently still distinguished the phonemes ġ /ʁ/ and ḫ /χ/, based on transcriptions in the Septuagint. As in the case of /ɬ/, no letters were available to represent these sounds, and existing letters did double duty: ח /χ/ /ħ/ and ע /ʁ/ /ʕ/. In both of these cases, however, the two sounds represented by the same letter eventually merged, leaving no evidence (other than early transcriptions) of the former distinctions.
guess what language that word would have been in
4:03 AM
"... and G-d said, let there be light"
Different people will give different levels of literalness to that
but I don't really see a problem in believing that Proto-Semitic existed and evolved into Hebrew and friends
Re: Sanskrit (or Tamil) being the world's first language, though — which are surprisingly common claims — it turns out that with the power of nationalism you can argue anything
There's a lot of people who believe "I speak a language therefore I'm an expert in linguistics"
(See also: "I have a brain so I'm an expert in psychology" and "I have a body so I'm an expert in medicine")
(Maybe that last one is not as common)
@AkivaWeinberger stares at essential oils
Fun fact: They're called that because they contain the "essence" of the plant
It's basically a bad pun
4:08 AM
well the problem is that Hebrew is a Canaanite language (closed related to Phoenician) but the Hebrews are supposed to have originated from outside Canaan
Hm never thought about that
but Abraham (and sons) are able to converse with the locals pretty well
if im not mistaken, i think it was the lingua franca of the time in the region
but triple check me on that
so Hebrew can't be the original language!
When Joseph spoke to his brothers and they thought he was an Egyptian official what language did that happen in
why not?
4:10 AM
I imagine Egyptian... Did Joseph have an accent?
here's another fun thing to ponder -- while the New Testament is written in Hebrew, the Koran is written in Arabic. The Muslims accept the Hebrew Bible and the New Testament as the word of G-d. Why did G-d cross over to Arabic in the Koran?
It's such a shame Escher never saw aperiodic tilings (like the Penrose tiling)
'cause doubtless he would've used them in his art
@JoeShmo 'Cause the Hebrew versions are corruptions or something like that?
to them
Re: Escher, it's neat how his circle limit stuff came about
'cause he wanted some way to portray the infinite in a finite space
and experimented with some ideas and couldn't quite get something he was satisfied with
and then randomly saw an illustration by Coxeter (I think) in some math talk
of a hyperbolic tiling
and immediately realized that that was the solution to his problem
idk how much of it is modern reinterpretations.. still. Quite difficult to ignore the fact and the deed -- the language of choice of both the Hebrew bible is.. Hebrew.
and he asked Coxeter how he drew it, Coxeter IIRC gave some incomprehensible answer that assumed Escher had more mathematical background than he did, and eventually Escher figured out how to do it on his own
(He wanted a straightedge-and-compass construction)
The infinite in a finite space
not sure what im looking at though
4:20 AM
Right so anyway I dunno what he would've done with an aperiodic tiling but I'm sure he would've had fun with it
i see an elephant in distress
@JoeShmo Are you familiar with Escher's "Circle Limit" series?
Or his tiling stuff in general
At home I have a coffee table book full of Escher prints
Great artist
yeah vaguely
impossible staircase constructions etc.?
He did that too @JoeShmo
^Circle Limit IV
Angels and demons tesselating
These are neat
especially the fish turning into the birds
alright. gotta hit the bed. good night everyone!
4:25 AM
Here's a previous attempt at an infinite tiling
He didn't feel satisfied with it because it had an artificial outer boundary
he is a wonderful artist
so it still felt "partial" (you could complete it infinitely outwards)
whereas with the Circle Limit stuff he eventually did there's no artificial boundary
well the irony is that he is constrained to finitely many recursive drawings
He's a fan of tilings changing as you move along them, I guess
like so^
@AkivaWeinberger איל גﬞודיאו־איספאנײול איס לה לינואה פﬞאבﬞלאדה די לוס גﬞודיוס ספﬞרדים ארונגﬞאדוס די לה איספאנײה איניל 1492. איס אונה לינגואה דיריבﬞאדה דיל איספנײול אי פﬞאבﬞלאדה די 150,000 פירסונאס אין קומוניטאס אין ישראל, לה טורקײה, אנטיקה יוגוסלאבﬞײה, לה גריסײה, איל מארואיקוס מאיורקה, לאס אמיריקאס, אינטרי מונגﬞוס אוטרוס לוגאריס
4:29 AM
^the same but not a video
"Favlada"? Sounds Portuguese, interesting @LeakyNun
I'm gonna learn a song in Ladino for my choir at some point
Dunno the phonology. I think they still have a /v/ and /b/ (unlike Spanish where they're merged)
It's a shame Judeo-English never developed. It would be interesting to see how the orthography would work
(Is that song in 9/8?)
seems like it
35 mins ago, by Akiva Weinberger
Re: Sanskrit (or Tamil) being the world's first language, though — which are surprisingly common claims — it turns out that with the power of nationalism you can argue anything
@AkivaWeinberger we get the same dose in HK
@AkivaWeinberger Not often you see someone compose music to a painting
where people say that Cantonese has a history of 1000 years while Mandarin only a few hundred years
so Cantonese is more authentic
There's a demand/Mandarin pun somewhere
but I forget what it is
@AkivaWeinberger so f>h happened after 1492!
(ferrum > hierro, filium > hijo, etc)
4:42 AM
from Cantar de mio Cid, 12th century

Ya sennor glorioso, padre que en çielo estas,
Fezist çielo e tierra, el terçero el mar,
Fezist estrelas e luna, e el sol pora escalentar,
Prisist encarnaçion en Sancta Maria Madre,
Fezist = hiciste
sennor = señor
nn = ñ
I wonder if that was pronounced as a gemminate or what
> Many words now written with an ⟨h⟩ were written with ⟨f⟩ in Old Spanish, but it was likely pronounced [h] in most positions (but [ɸ] or [f] before /r/, /l/, [w] and possibly [j]). The cognates of the words in Portuguese and most other Romance languages have [f].
Like /hu/=[ɸu] in Japanese
> The palatal nasal /ɲ/ was written ⟨nn⟩ (the geminate nn being one of the sound's Latin origins), but it was often abbreviated to ⟨ñ⟩ following the common scribal shorthand of replacing an ⟨m⟩ or ⟨n⟩ with a tilde above the previous letter. Later, ⟨ñ⟩ was used exclusively, and it came to be considered a letter in its own right by Modern Spanish. Also, as in modern times, the palatal lateral /ʎ/ was indicated with ⟨ll⟩, again reflecting its origin from a Latin geminate.
Modern Spanish's respecto vs respeto distinction is interesting
also calidad vs cualidad
5:10 AM
@LeakyNun Can you spot the pattern in the design
not really
Hint: time flows down and to the left
@AkivaWeinberger self-demonstrating statement right there
@Semiclassical Yes
@AkivaWeinberger it seems that a grid is determined by the three grids on the line above it
000 -> 1
001 -> 1
010 -> 1
011 -> 0
100 -> 0
101 -> 0
110 -> 0
111 -> 1
5:18 AM
The seed is a single pixel (offscreen)
Rule 30 is a one-dimensional binary cellular automaton rule introduced by Stephen Wolfram in 1983. Using Wolfram's classification scheme, Rule 30 is a Class III rule, displaying aperiodic, chaotic behaviour. This rule is of particular interest because it produces complex, seemingly random patterns from simple, well-defined rules. Because of this, Wolfram believes that Rule 30, and cellular automata in general, are the key to understanding how simple rules produce complex structures and behaviour in nature. For instance, a pattern resembling Rule 30 appears on the shell of the widespread cone snail...
ooh nice
@LeakyNun Reading the right-hand side from the bottom up we get 1000111, which is a unique identifier of the rule
Oh wait I think it's the color-reversed version of Rule 30
Rule 135?
@AkivaWeinberger guess the rule ;)
Start from random seed, shift everything by 1?
So I guess somewhere around 256/3
why 256/3?
5:25 AM
I dunno I want binary 101010 or something
hint: the emoticon
Rule 170 (which is about 256*2/3 so not too far off)
What's it to do with the emoticon
if you zoom in the image you'll see that it doesn't shift everything by 1
look at the top row
Oh… adds them?
The top-left and top-right?
Hm no
Rule 1
Hm wait
No, 101->1
Rule 34?
Aight now I get it
5:31 AM
Fun fact: the station design was meant to honor Conway
It was supposed to be "inspired by Conway's Game of Life"
but they couldn't figure out a good design from that
so they went with the similar looking Wolfram Rules instead
which has very little to do with Conway
(except for both being cellular automata I guess)
(One 1D, the other 2D)
Also Conway wasn't told about any of this until it opened
Rule 110 is known to be Turing complete, fun fact
I think Rule 30 is conjectured to be
what does Turing complete mean?
You could turn an algorithm into a sequence of pixels, run Rule 110 on it for a bit, halt when it reaches some special state, and convert the output into an answer
I think?
No comment on any of the conversions involved being efficient to compute
> Matthew Cook presented his proof of the universality of Rule 110 at a Santa Fe Institute conference, held before the publication of NKS. Wolfram Research claimed that this presentation violated Cook's nondisclosure agreement with his employer, and obtained a court order excluding Cook's paper from the published conference proceedings. The existence of Cook's proof nevertheless became known.
Bit of a dick move on Wolfram's part
> The function of the universal machine in Rule 110 requires a finite number of localized patterns to be embedded within an infinitely repeating background pattern.
Interactions between "streams"
called "spaceships" in the article
possibly by analogy with the similar concept in the Game of Life
@LeakyNun Isn't it interesting how the universe can simulate itself
aka we can build computers (out of pieces obeying the laws of physics) which can simulate physics
can it?
5:46 AM
This is what video games do
oh yeah isn't there an argument that uses that to argue that we're in a simulation
because we can create many simulations
We don't know for sure about quantum mechanics being simulatable
and statistically you're more likely to be in a simulation because there's only one "real" universe
and we don't know what the ultimate theory of everything is
Reminds me of the question: "How do we know that we're awake"
How do we know that we're not asleep right now and that this isn't a dream
Once someone challenged me to prove it to them
and I came up with this really clever proof
and they were convinced that we were in fact awake
…and then I woke up.
"Prove to me we're awake right now." "Pfft, I could do that in my sleep! …wait"
6:32 AM
can we write this in the form of sets of R

$x>1\Rightarrow x^2>9$

can we say that is$ ]3,+\infty[$?
thank you
If I understand correctly, yes
no it's (-infty,1] U (3,infty)
Well, my last night dream took that one step further:
I died without realising I have died
Any body ever herd about God particle
The way it pull that narrative off (almost) is that when I woke up in the middle of the night, the room and vision is so distorted that it looks nothing like my real life room. Before I hit the light switch, I thought I am still dreaming while in fact I am dehydrating
Put it simply, the brain masked the sense of dehydration, which my consciousness misinterpret it as me dying, with a dream state so that even real life is part of the dream
If I did die, the brain will probably go hyperdrive on this and I will not be able to tell the difference between real life and dream as my body functions shut down one by one
6:47 AM
@Secret You're always five minutes away from death, but the counter resets every time you take a breath
Fun fact: the word "boson" (the type of elementary particle) was named after Indian physicist Satyendra Nath Bose (1894–1974)
@Secret Neat mnemonic: you can last 3 minutes without air, 3 days without water, and 3 weeks without food
(and about a week without sleep, but I dunno how to fix that into the mnemonic)
Death will probably feel like dizziness and confusion, to the point that you won't even notice it when life ends
It'll all be fuzz
or static
I dunno
7:04 AM
Yes there are many amazing fact about his theories
@Secret I think this is new
8:42 AM
it is
and it is relaxing
9:13 AM
is there an algorithmic way to generate all elementary functions
I'm thinking of something along the lines of
Start with a set of $\{ c, \alpha x \}$
The constant and linear function
Apply every unary elementary function to that set and add them to the set
And then apply every binary operation with every pair of elements from that set
Every time with different factors

\{ \alpha x, c \} &\to& \{ \alpha x, c, (\alpha x)^n, e^{\alpha x}, ... \} \\
&\to& \{ \alpha x, c, (\alpha x)^n, e^{\alpha x}, \alpha x + c, \alpha x + (\beta x)^n, ... \}
seems like it would work but be fairly inefficient because of getting the same class of functions
ie $x \times x \sim x^2$

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