6,378 karma · joined October 22, 2017
Really, same thing goes for most other disciplines. So many kids learn 4 years of algebra without having the slightest clue that this all is building to something called "Calculus" that they don't understand what it is.
It seems like Ibis uses DuckDB on its backend (by default) and has Polars support as well. Given this, maybe see if Ibis works better for you than polars. If you very specifically need polars, using that will for sure be better. DuckDB is faster than polars and it has great polars support, so depending on how Ibis is implemented it might be "better" than polars as data frame lib.
The problem that's usually not told to kids is that decidability has different sort of implications to classical mathematics and constructive mathematics. Since most undergrad programs only teach mainstream math (i.e. classical) and don't even mention constructive logic, decidability becomes a black magic situation for some confused students.
Here's the crucial part: decidability really only has material impact on our reasoning if we're in some kind of constructive setting. Undecidability does not and cannot have any impact on the results of classical mathematics, period, but it does have effect on the proofs of those classical theorems. It can also have impact on classical mathematics if we're reasoning classically but describing results in constructive settings (e.g. this is what happens when we do computability theory in classical mathematics).
In short, classically we're always allowed to work around undecidability by using an "oracle". But it can be important to state that we can only do it this way (similar to how we can state the need to use the axiom of choice).
One way to re-phrase Aristotle's law of excluded middle (forall P, P or not P) is to say: "every relation is decidable" which is how you would postulate it in homotopy type theory: https://agda.github.io/agda-stdlib/master/Axiom.ExcludedMidd...
This doesn't mean in classical mathematics every relation "literally" is decidable. Classical mathematics can still study constructive settings by creating a computational model (e.g. Turing Machine model). But it does mean that in classical mathematics every relation effectively is indistinguishable from decidable relations since given a statement like "Program P will halt" you are always allowed to say "either (program P will halt) or (program P won't halt)" regardless of our impossibility to prove one of the cases in general.
Also note that we call this kind of constructive reasoning "neutral constructive mathematics" which is when we operate in a constructive reasoning setting (like Agda's type theory above) but allow ourselves to say things like "AxiomOfChoice implies ExcludedMiddle" etc, read: https://ncatlab.org/nlab/show/neutral+constructive+mathemati...
[1] It's a personal preference but Agda is simply a much better language with almost limitless metaprogramming which allows me to write proofs close to as they'd appear in prose math papers. It has a smaller ecosystem though. I've never seen a proof in any other language I personally didn't think would be much more readable/simpler in Agda.
The way formalists (mainstream mathematical community) dealt with the foundational issues was to study them very closely and precisely so that they can ignore it as much as possible. The philosophical justification is that even though a statement P is undecidable, ultimately speaking, within the universe of mathematical truth, it's either true or false and nothing else, even though we may not be able to construct a proof of either.
Constructivists on the other hand took the opposite approach, they equated mathematical truth with provability, therefore undecidable statements P are such that they're neither true nor false, constructively. This means Aristotle's law of excluded middle (for any statement P, P or (not P)) no longer holds and therefore constructivists had to rebuild mathematics from a different logical basis.
The issue with Principia is it doesn't know how to deal with issues like this, so the way it lays out mathematics no longer makes total sense, and its goals (mathematical program) are found to be impossible.
Note: this is an extreme oversimplification. I recommend Stanford Encyclopedia of Philosophy for a more detailed overview. E.g. https://plato.stanford.edu/entries/hilbert-program/
Isn't this going a bit too far? Sure they didn't have a modern writing system like Mayans, or even proto-writing systems like Inca's quipu but we do have hard evidence of Teotihuacan society communicating language with painted symbols (e.g. findings in La Ventilla). It's unclear to me how we can say they didn't leave writing to future generations (especially assuming probably there were a lot more stuff that was lost to time than we can see)
Also, this comment seems to slightly misunderstand what the GP said imho. Yes writing is a new invention, but e.g. paintings in Lascaux are about 17k years old. Which means even before Catalhoyuk level civilizations, humans were leaving symbols for later generations to look and decipher. This is the same "archival" process GP is talking about. Humans leave a message to future generations. It seems like our biology must prime us to do it, because we see it universally. Whether the messages we leave are writing, painting, music or whatever... humans still produce things for people that'll come after them. But animals are incapable of doing so, even if a Bonobo is roughly as intelligent as a human, it's not like it can transmit any kind of information to future generations, so every generation of Bonobos need to learn either from scratch or from their community. So, perhaps ironically, part of being human-smart is having human-precise hands that can paint/write. Without this ability, we end up like bonobos, elephants, dolphins etc perhaps smart but for all they know their parents were the Adam and Eve.
This not even remotely close to true. Like not even a little bit. I use Cursor and Gemini for work daily and I'd be hard pressed to think AI is a "better" programmer than any professional software engineer. Sure it makes writing code faster and more efficient, because you just click tab and three lines are written for you. It absolutely isn't better than me at coding though.
The claim about math is even more unbelievable than the claim about coding. We still don't have a single theorem proved and published by a LLM without human aid. LLMs barely follow a discussion in basic topology. It's incredibly ridiculous to state they're better than 99% of people. More like 0% of mathematicians and maybe 50% of college freshman.
Our society has a pathological obsession with productivity.
PS: Not associated with DuckDB team at all, I just love DuckDB so much that I shill for them when I see them in HN.
Art progresses with extreme restrictions. The same way Schoenberg put seemingly absurd restrictions in his music ((very roughly) don't repeat the same note before playing every other note etc...) to create something radically novel, we as software developers can do so to advance our art as well.
[1] This method is the anti-thesis of the common "never rewrite a working program" software development methodology. Here, the experiment is to see what happens if we always rewrite, and never add or modify, i.e. refactors are never allowed, instead if things need changing we need to re-design the whole thing top-bottom with the new understanding.
I'd be curious to hear the argument that people legally working or studying here aren't "subject to jurisdiction" of. People on H1B for a while file the exact same taxes citizens file (because they're US persons for tax purposes). Not sure how are they legally not subject to jurisdiction of?
If you're making Western classical music in classicist, romanticist or modernist style, the model of music you have will carry a lot of information about harmony and the application of harmonic techniques throughout the piece. Given a core musical idea you can then apply peripheral techniques (such as orchestration) to build a full piece. E.g. when people study counterpoint, the model of music originates from vertical harmony of notes and when they can be used with respect to each other. The assumption is that orchestration is something that'll be separately developed "skinning" the composition. E.g. a common technique in this tradition is composing a piece for piano four hands and then orchestrating it (e.g. Holst's "The Planets" symphony was composed this way).
However, this stops being a useful model once you step into other musical traditions. In some cultures harmony would be like how Western music treats orchestration, peripheral to composition (like how extreme speed is irrelevant to Newtonian mechanics because it was never designed for near lightspeed motion). So you'd first design timbres, and have an idea about how timbres interact, timbres change, transform to each. You may have a theory of counterpoint of timbres. Once you have this, you can apply any standard "harmony skin" on the composition and you have a piece. This is not even restricted to non-Western music. If you look at the postmodernism in Western music you'll find instances of it. Easy example: a lot of people say that Philip Glass "makes the same music" again and again, what is being missed is the point he's trying to convey is that even if you pick the exact same 4 chords you can still create variation in music via other means. It just won't be different from the traditional harmony-centric Western musical model.
By the way, I studied CS and my full-time job is a Software Engineer. So I doubt our disagreement comes from my background in computer science.
Also I'm a composer with extensive knowledge of how to make, orchestra, and mix acoustic or electronic music. This thread has an extreme Western bias, just because something is studied in a particular way from Western music theory perspective, it doesn't mean it has to be that way.
Check my comment here: https://news.ycombinator.com/threads?id=gnulinux#42368137
Check my comment here: https://news.ycombinator.com/threads?id=gnulinux#42368137
Any and all formal, mathematical, informal theory about music can be called music theory. Music theory is about modeling music. Period. It does not matter if it's about harmony, rhythm, pitch, form, timbre, dynamics, or some other aspect of music. Whether it helps with understanding music, composing music, improvising music etc is a separate topic. Music theory neither has to be about practical music making skills, nor it has to be about music of a particular artistic tradition. It just needs to present some model that can be a helpful tool in some musical context. Maybe what you call "audio engineering" is a specialized skill for some musical traditions, but for musical traditions where the expressive content primarily comes from timbre and synthesizers are common instruments, it will be an essential music making skill.
* Ernest Hemingway's novel "A Farewell to Arms"
* Ludwig Wittgenstein's essay "Some Remarks on Logical Form"
* The first part of the 14th edition of Encyclopædia Britannica
* William Faulkner's novel "The Sound and the Fury"
* René Magritte's painting "The Treachery of Images"
* Wassily Kandinsky's painting "Upward"
* "Un chien Andalou", directed by Luis Bunuel and cowritten by Salvador Dali
* "The Cocoanuts", the first film of the Marx Brothers
* the first "Silly Symphony" cartoons, including "The Skeleton Dance".
Not a bad year at all!