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Had a panic attack during a coding assignment and now every time I think about that problem I just start spacing. Noice.
Also dear companies: if you wanna ask your interviewees about trying to deduce a theorem out of nowhere, maybe do it in the first test and not in the last one. Cause that’s a shot in the dark to someone who’s not a mathematician and id feel waaay less frustrated if I didn’t give you 6 hours of my life just to end up with an arbitrary task like this.5 -
As I was browsing pornhub, I started reading articles about AI, dick still in hand, and went down the rabbit-hole (no pun intended) of self referential systems and proofs. This is something I do frequently (getting off track, not beating off, though I have been slacking recently).
Now I'm no expert but my neurotic DID personality which prompted this small reading binge DOES think it is an expert. And it got me thinking.
Godel’s second incompleteness theorem says that "no sufficiently strong proof system can prove its own consistency."
Then utilizing proof by contradiction, systems that are "sufficiently strong" should produce truth outputs that are monotonic. E.g. statements such as "this sentence is a lie."
Wouldn't monotonicity then be proof (soft or otherwise) that a proof system is 'sufficiently strong' in the sense that Godel's second theorem meant?
Edit: I WELCOME input, even if this post is utterly ignorant and vapid. I really don't know shit about formal systems or logic. Welcome any insight or feedback that could enlighten me.1 -
This formula from Gödel's incompleteness theorem. It basically says there is no hope to ever know if your program is correct ... 😁
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Just finished up some math homework
One of the problems involved finding the side lengths of a triangle
Spend a good 20 minutes fucking around with the law of sines and the law of cosines before I realized it was a right triangle, and so I could use the Pythagorean theorem
I'm an idiot3 -
Theorem 2.71 All software is shit.
Corollary 3.14 So stop the braindead OS wars. All OS are shit, too.
Proof. The only software that can stay beautiful and clean is software that is never used. Maybe if you are Dijkstra or live in a Haskellian world, you might come away with it, but for the rest of us our artifacts have to interact with other artifacts or are build upon strange historically grown systems, they have to deal with users who will put it to creative use.. and in the process we also actually might have to alter some state.
Or put another way: code is a social construct. Like science are the beliefs and superstitions grown by a scientific community, software is the montainous dunghill produced by our laborious efforts to make shit even work. Of course this only piles the stack higher and higher until you can already smell it from the moon. -
The Pythagorean theorem is pretty important. You should be able to represent it graphically because it shows that you are a thinking creature to the point of math.
Works also if you have no other common basis for communication, not even mimics. That might well save you from a live autopsy in case you get abducted by aliens because it would make them curious.1 -
https://brilliant.org/wiki/...
Is a fascinating breakdown for anyone interested in complex numbers but intimidated by complex *math*.
They really go over it step by step. Take a look -
On science and religion. Inspied by a comment in another rant, credits to @Commodore and @cjbatz
According to Godel's incompletness theorems, aritmetics is incomplete and inconsistent. Therefore, any science based on aritmetics (dude, like, every) is also.
Therfore, as a mathematician, I must accept that there are things that cannot be proven by current science, and that there are statements that are true and false at the same time in current science.
So, science can't prove religious beliefs? It cant prove P vs NP either. It might someday. Science couldn't prove earth wasn't flat for a looong time. Or Pythagoras theorem.
But more importantly, if science can prove something, doesn't mean it can't prove the exact oposite.
This way of thinking allows for any and all ridiculous beliefs, under the shield of "it might be proven one day" or "doent't mean opposite isn't true also" but kerp in mind that there are complete and consistent sciences and proofs in them. Check if something's been proven to exist or not exist without doubt.11 -
If we can transform the search space or properties of a product into a graph problem
we could possibly use Kirchhoff's theorem to reveal products which are 'low complexity'
in particular search spaces, yeah?
Now according to
https://en.wikipedia.org/wiki/...
"n Cycle Space, A family of sets closed under the symmetric difference operation can be described algebraically as a vector space over the two-element finite field Z 2 {\displaystyle \mathbb {Z} _{2}} \mathbb{Z } _{2}.[4] This field has two elements, 0 and 1, and its addition and multiplication operations can be described as the familiar addition and multiplication of integers, taken modulo 2"
Wouldn't this relate to pollards algorithm, because it involves looking for factors of coprimes modulo N or am I mistaken?
Now, according to wikipedia, "in a group, the additive identity is the identity element of the group, is often denoted 0, and is unique."
If we make the multiplicative identity of our ring or field a tuple of the ratio of a/b for some product p, or a (and a/w, where w is the square root of p), or any other set such that n*m allows us to derive a or b, we could reduce the additive identity to the multiplicative identity, making the ring trivial. Solving for p would then mean finding a function from R to R, mapping every number to 0, i.e. finding the additive identity.
Now in a system with a multiplication operation the distributes over addition, the "additive
identity annihilates ring elements", so naturally, the function that maps to 0, gives us
our additive identity, we need only find the subset, no?
Forgive me if I'm wrong, but shouldn't this be convertible to a graph search?
I'm WAY out of my depth here so if anyone is familiar and can enlighten me I'd be grateful.
It's all unknown unknowns to me.
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