dellamonica

6 ms·

1.
by dellamonica 3mo ago
The point of the AI with respect to checking is to translate a natural language theorem and its proof into the formal system. Most of known math is not formalized because it is very hard to do so.
2.
by dellamonica 4mo ago
It is extremely well known. Lots of people have tried to solve it and it stood basically stuck for 80 years. It is getting harder every day to downplay these models. Given its elementary nature (very easy to state), you can bet that a lot o
3.
by dellamonica 3y ago
The ellipse can be also encoded by just the lengths along each axis and then by a rotation in R^n (which is just a unitary matrix multiplication). So in essence, for the problem in the original post there are three pieces of information nee
4.
by dellamonica 3y ago
Every ellipse can be encoded by the matrix A (and the geometric concept is generalized to arbitrary dimensions). Not sure I follow the physics analogy though. A unit ball is a specific case of an ellipse where A is the identity matrix. Perh
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by dellamonica 3y ago
Yes, if you don't use dotnet and is already used to Unix tooling then it is a tough sell, but otherwise the integration with dotnet is quite good.
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by dellamonica 3y ago
I mean, the entire dotnet is available, you can do anything in PS though obviously that is not always the smart call. It has been very useful to me to use as a REPL on my own C# libraries, I can instantiate and use types from these librarie
7.
by dellamonica 3y ago
What is wrong with PowerShell core? *PS core is the one based on the new versions of dotnet.
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by dellamonica 3y ago
It's rather difficult to provide a good formalization but let me give it a shot. Suppose that mathematicians write papers with pen and paper in a subset of natural language without ambiguity (you wish!). What they write as proofs can b
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by dellamonica 3y ago
First of all, thank you for a thorough response. I'll need to take time to read it (and the refs in your other reply) with the care it deserves. Basically I'm talking about the subset of proofs that could be done with pen and pape
10.
by dellamonica 3y ago
No misunderstanding about NP here for sure. As I said, this is about as much of a thesis as Church Turing is about what can be computed. I have no clue about CiC, lean and whatnot. It was never my field and I don't doubt there can be s
11.
by dellamonica 3y ago
Right, and this is also the current status of handmade mathematics. All we know is that we did not find a proof yet with everything that has been tried. This typically means that a problem is harder the more stuff has been thrown at it and
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by dellamonica 3y ago
Could you give me a reference? This is not something I'm familiar with. Can you claim that this equivalence proof is not in NP, without requiring this specific encoding? I would be very surprised to learn that there is no encoding wher
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by dellamonica 3y ago
Then in that target language, found by a clever human, you could do the same type of enumeration... My whole point is that humans simply cannot process/create by themselves any truly long proof (we can obviously create a process for th
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by dellamonica 3y ago
This is all very interesting but it seems that we're just taking different views on what is the instance size. If it is the length of the theorem statement in some suitable encoding and the goal is to find a proof, of any possible len
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by dellamonica 3y ago
Of course it would, you would enumerate lengths too. If the lengths need to be larger than polynomially bounded then we can be sure it would never be found by a human anyway.
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by dellamonica 3y ago
It doesn't require anything like that. Math proofs are of NP complexity. If you had access to a non deterministic Turing machine you could enumerate all possible proofs of a given length and check them all in poly time. That does not s
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by dellamonica 3y ago
Without digging too much, I don't think such an argument could be made by this paper. A non trivial lower bound on a concrete problem in a general computation framework would be a marvel on its own. As another example of what I mean, t
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by dellamonica 3y ago
It might be possible to compute whether the start and end States are connected without constructing the actual path. As usual non trivial lower bounds on computation are basically non existent. As an example, we can determine whether a numb
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by dellamonica 3y ago
It does though. My gmail account has a dot. For some reason someone with a similar name to mine must have for believed his address was the non dotted version of mine and to this day I keep getting emails addressed to this other person... an
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by dellamonica 3y ago
There has been a push for using Source Generators to move stuff that relies on reflection to compile time code generation. JSON serialization is (mostly) supported in this mode with perf advantages as well. This does not address pre-existin
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by dellamonica 3y ago
It can get really tricky: using reflection you could read a string from any input and create a generic type instantiation that never happens in the source code. How would the code for that type be present in an AOT scenario? There are also
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by dellamonica 3y ago
There are lots of techniques that use randomness to show the existence of objects with desired properties. Some of them rely on the "first moment" (expectation) which seems to be what you are saying. These tend to be the simpler o
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by dellamonica 4y ago
That would make a great Black Mirror episode... and a terrible dystopia if it becomes reality.
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Building GPT-3 applications – beyond the prompt(medium.com)
3 points by dellamonica 4y ago|3 comments
25.
by dellamonica 4y ago
I think the basic idea is that the hash has a fairly uniform probability distribution, so knowing the prefix means you can estimate its location in a sorted list. For instance if we were talking about n random sequences of digits then if yo
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by dellamonica 4y ago
It does not matter at a high level but I think the distinction is that there should be only one black box in the proof, which is precisely the thing being reduced. Every other instruction/call used n the algorithm must be known to be c
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by dellamonica 4y ago
Don't waste your time like I did. This person does not have a clue.
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by dellamonica 4y ago
Right... have a good day.
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by dellamonica 4y ago
I'll bite, what is the false statement that you keep alluding to? Because the vacuous "if" statement that you claimed to be false is absolutely a truth in logic. Compute and implements are different words, nobody is arguing t
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by dellamonica 4y ago
You are the one failing basic logic. Your statement is logically true but vacuous because your conditional is false! If <absurd condition> then <some even more absurd thing> is a perfectly sound logic statement. I explained alre

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