271–280 of 681 posts
Can't even ctrl+f the conversation, wish openai would fix that
Obsidian Web Clipper has a nice reader mode that works for ChatGPT transcripts (disclaimer: I made it)
Earlier quoted context omitted.
> https://en.wikipedia.org/wiki/Transmission_Control_Protocol compare to > https://en.wikipedia.org/wiki/Rees_algebra Most people, especially non-tech technical people, could crash through the TCP article and come out the other side with at least a high level understanding of it. Most people, even technical ones, could not even get through the first line of the rees article, heck the first statement of the article. A…
"The Rees algebra is an algebra over Z[t^−1]" Such a small sentence and yet it means very little to me. I understand some constituent pieces, but I don't understand what Z is here other than a 'ring' and I don't really grasp how t^-1 converts this into a generalized family of algebra. It would take me a lot of effort to understand this and use it practically. I find that fascinating because it really is such a small…
In lean4, even without mathlib4, TCP/IP is way more code than a Rees algebra.
Math uses dense notation that is gigaoverloaded, and the disambiguating context was historically the leisure and proximity to have someone explain what the lexemes even mean.
lean4 is proving to be very revealing as an uncorruptible referee on a lot of things, including the relative difficulty of computer science and complex analysis.
-- A Rees algebra over ℤ[t⁻¹] is this.
-- That's it. That's the whole thing.
structure ReesAlgebra where
coeffs : Array Int -- integers, indexed by grade
-- grade k means the coefficient sits at t^k
-- negative indices are the t⁻¹ part
-- The "algebra" part: you can add them
def ReesAlgebra.add (a b : ReesAlgebra) : ReesAlgebra :=
⟨a.coeffs.zipWith b.coeffs (· + ·)⟩
-- And multiply them (convolution, same as polynomial multiplication)
def ReesAlgebra.mul (a b : ReesAlgebra) : ReesAlgebra :=
sorry -- it's Array.foldl over index pairs (i,j) summing into slot (i+j)
-- exactly how you'd multiply polynomials in a job interview
-- That's the entire mathematical content of
-- "The Rees algebra is an algebra over Z[t^{-1}]"
--
-- Compare: a minimal TCP SYN handshake in Lean4 would be
-- ~200 lines before you even get to retransmission.
--
-- The notation is the gate, not the math.Earlier quoted context omitted.
Your translation only makes intuitive sense to you because you are well versed in programming. I suspect if I showed a non-technical person with no background in either math or programming they would think both are nonsense until you explained it to them
My example was contrived, I'm sure some smart people could come up with a SQL-esque language that is even more readable to non-technical folks than programming syntax. At a certain point though, your layman has to know the "atomic" (as in, you can't break them down further) mathematical concepts like "functions" and "infinity": `sum function(x) from x=0 to x=infinity`
And if you think about how summation would look in Lisp or APL (which some smart people use to this day), I am not even convinced your argument for the "sum function" notation being superior holds in general.
Math has some of the most insanely dense and impenetrable nomenclature. I can generally keep my head mostly above water or at least near the surface reading from most STEM fields, perhaps leaning on google/wikipedia a bit, but man, mathematics just so quickly decouples from all common tractable understanding it's insane. Sorry it's a bit of an aside, but I imagine many other otherwise "technical" folks feel the same…
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Maybe? At the end of the day, even if they are some insane oracle (pun intended), they're still bounded by training data and how it relates to the real world. Even if they're a near perfect tool, we are still the interface between them and our lived experience. If that stops being the case then why do we care about the output? This assumes it doesn't graduate to just killing all of us and doing it's own thing, but wi…
they're still bounded by training data and how it relates to the real world. Yes and no. They can extrapolate and build upon the training data, as was the case with the last dozens of math proofs
To put it differently, if you have some idealized model in front of you that can do anything a team of humans can do, what do you say to it? It's still just a model that takes an input and provides an output.
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Again, you are underestimating how much effort it takes to understand how an 8086 CPU works. There are a lot of foundational concepts that you are simply assuming the person already understands. That may be a reasonable assumption for a CS undergraduate, but the average person does not understand binary arithmetic, registers, memory addressing, instruction execution, calling conventions, or even what a CPU is doing a…
> There is an enormous amount of computer science that most programmers are completely unfamiliar with, especially within academic CS: programming-language theory, type theory, formal semantics, compiler theory, algorithmic research, complexity theory, distributed computing theory, verification, cryptography, computational geometry, numerical methods, and so on. Being proficient in one narrow area does not automatica…
Because otherwise if you think about it all of computing is Maths but with computers...
I don't think people who read the Wireless Fidelity spec can understand any of it in a weekend or anything even to a rough extent.
Similarly with websockets, quic etc. the most you can take away without much prior knowledge is what it does which maps into Maths as well.
Math has some of the most insanely dense and impenetrable nomenclature. I can generally keep my head mostly above water or at least near the surface reading from most STEM fields, perhaps leaning on google/wikipedia a bit, but man, mathematics just so quickly decouples from all common tractable understanding it's insane. Sorry it's a bit of an aside, but I imagine many other otherwise "technical" folks feel the same…
People in their second year of graduate school only get to about the early 20th century in terms of understanding. Third year is getting to about the mid-century. Fourth and fifth years get kind of to modern times but with increasingly smaller breadth.