nk

Physics PhD anno 2015.
CV @ big evil company.
Kullback-Leibler does not equal Leibler-Kullback.
Sophie Ellis-Bextor was never my girlfriend.
Wiener measurer.

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I'm not a 23yo Indian webdev. But I aspire to post as if I was one.
I will get there. And with the help of Thiel, maybe I'll also become the former.

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@rtchromaaeraa Lashes and lip fillers do work if you don't recognize that it has been done. Basically, you don't know when it worked, as in that case you didn't see the trick.

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@doxa_ty @woarna_is_right well in the lambda calculus, you'd then write
exists := λx(∃y=x)

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Gaussian elimination is when you find out more than just the mean and variance

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@doxa_ty @woarna_is_right the lambda binding the argument was more what I was asking

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@nihilunbounded @sclv scooped

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@nrunje (June 2023)

Motorola Moto G6 Play

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@alz_zyd_ The n'th polynomial is propto n times the antiderivative \int^x of 1, so without dropping differentiable functions themselves, you'll probably not get rid of polynomials popping up.

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@NoahChrein evidently

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@honor5947 I'm the opposite - if I estimate my chance of, say, an accident only being 1 to 50, my mind irrationally rounds it down to 0.
Bit weird, since thus e.g. my fear of heights doesn't kick as early as it should.

All that said, here's some fitting lyrics for u
https://t.co/ddvKqVxZ3u

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@honor5947 I ordered a metal box ... using my debit card checked in to google pay. Right after the card stopped working, but I didn't connect the dots. Today I got a physical letter from the bank, them falsely conjecturing my card must have been stolen and exploited.
https://t.co/PfN9Z6Adyx

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time for +$8k more compute

[Dr. Elisabeth Wagner @ehwagner]

Wenn Mädchen gerne basteln: "Sie ist sehr kreativ!"
Wenn Jungen gerne basteln: "Er ist handwerklich begabt!"

Sie hat ein niedliches Hobby - er hat Potenzial.

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fyi

The ambiguity doesn't hurt either.

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@littmath @alz_zyd_

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@thomasahle @JustDeezGuy Con(T) is independent of strong sound T,
so T+Con(T) and T+¬Con(T) have models.
They are relative consistent wrt T.

For W weaker than T,
V := W+¬Con(T)
is still consistent. And V proves T inconsistent.

E.g.
HA+¬Con(PA)
is constructive, in a conventional sense, but not sound
:(

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@radokirov how suddenly it all happed

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@thomasahle @JustDeezGuy (I should say sacrosanct is the computable world because it has those computable semantics. Sacrosanct is the classical world for people who want more theorems be proven that the other world won't let them. I agree that we would get by without, probably, say for physics.)

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@JustDeezGuy There's a few ways in which one could approach this question, but maybe the elaboration of the following phenomenon helps:

Enumerate the Turing machines (to be ran on some input) and for n:ℕ and b:{0,1}, denote by H(n, y) the predicate that's true if the n'th Turing machine halts with y.
(For our purposes, H is basically the Kleene predicate, if you want to read it up.)
By Turing, no computable function realizes this, i.e. there's no
f_H : ℕ → {0,1}
such that you can hand it any n whatsover, and in finite time it would return 1 for halts and 0 for doesn't.

A theory T with Comprehension and terms for entities S⊂ℕ (set theory, second-order arithmetic,...) and can translate predicates (expressions of the logic) into graph entities. E.g., for 2-ary P over ℕ×{0,1} define
G_P := {(n, y) ∈ ℕ×{0,1} | P(n, y)}
G_P ⊂ ℕ×{0,1}
This is really the reification of the 2-ary predicate,
(m, z) ∈ G_P ⟺. P(m, z)
If P(n, 0) and P(n, 1) never hold at once, then LEM for P,

P(n, y) ∨ ¬P(n, y)
is equivalent to G_P being a function graph:
For each n, there's y such that (n, y) ∈ G_P, and by exclusion it's unique.
So classical T with sufficient Comprehension always believes G_H is a function.

ZF (and much weaker classical theories) thinks/proves that there is a function on ℕ that given n return 1 iff the n'th Turing machine halts.
No problem with that conceptually, but it means T can't have purely computable semantics. The "sets of pairs" definition of "functions" cannot "be about" python codes. Or about Gödel's recursive functions.
Sacrosanct, as you say, are computable semantics as a possibility.

(And this is not just LEM, but also the entity formation/Comprehension. You can have super weak 2nd-order arithmetics that still have computable semantics. But then little induction power.)
Now the "constructive counterparts of ZF", that I mentioned, doesn't have LEM.

It has comprehension and so has G_H.
It proves G_H ⊂ ℕ×{0,1}.
But it doesn't think/prove
G_H ∈ {0,1}^ℕ
From a classical viewpoint, it's function space are super sparse.
(It's ℕ^ℕ is uncountable for itself, although classical ZF would disagree with it about that. Also, then, the constructive {0,1}^ℕ injects into 𝒫(ℕ), but not vice versa. 𝒫(ℕ) actually holds predicates that aren't like evaluate-able functions from a constructive viewpoints.)
tl;dr, the constructive world has much tamer ℕ^ℕ than Cantor's classical set theory.
More elaborately, classical arithmetic Z2 and the world of computable functions validate a lot of constructive counterparts of ZF. So, coming back to what I said, if classical arithmetic is fine, then so are basically all ZF axioms. And so barring Z2, the delta is LEM.

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@maybeKonsti Alleinerziehend-Poll wäre nun interessant

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@AndrewSabisky Having been in many many dozen math courses, I knew that ofc just doing something "good" was not the main driver in how people choose to spend their live. Recently, the understanding that many mathematicians have of themselves, and willingness to be leeches, still shocks me.