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.
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).
> It may be an alveolar approximant [ɹ] intervocalically
Ooh
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]
> 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.
> 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.
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")
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
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?
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)
@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
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
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,
> 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].
> 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
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...
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.
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