I remember chatting with about AI a few months ago about the issue of foreign RAM sticks being able to cooperate with websites to serve different files/instructions, undetectably. Scary stuff.
The idea that FFT's decomposition is non-optimal is surprising. What the new bound means is we basically were looking at the problem and its structure incorrectly, and therefore implicates other problems for which we have used recursion to get to our currently-best bounds.
Almost no interesting math problems are just sitting there alone in their little corner. Getting a hint like that is a big deal.
Is it surprising though? If you assume constant time when it doesn't exist (in this case arbitrary precision arithmetic), it should be obvious that you will be able to devise algorithms that are faster than the commonly accepted best results.
If you can do arithmetic on arbitrarily large integers in constant time, you can sort lists in linear time.
I find it highly ironic that many people here seem to believe mathematicians should just accept LLM proofs, but software projects shouldn't accept LLM code.
Why? Is it because most programmers can get paid from a company and not most drawers or musicians? Is it that programmers don't give enough free code on Github, or that their PRs don't wax and wane about how beautiful they found their specific bugfix to be?
If you see the whimsical in a PR changing some column name in a table in a billing system, or you feel the magic and fantasy of a REST API, or yet, God forbid, the emotional undertones of fixing a NPE because the previous change did not consider that a field was optional, then you may have trouble to perceive the difference.
I, at least, never wrote a stock management system to explore the depth of human emotions.
Hmm. I had an issue once with numpy shape mismatch errors appearing after 18+ hours of computation. Frustrating, because it could be caught at compile time.
Later, I learned some typelevel programming (in Scala), and by encoding a digital (binary) adder and multiplier at the type level, I showed -- at least to myself -- it was possible to compute and check linear algebra shapes at compile time (without a compiler plugin). It was rather magical and funny to think that I just embedded basic digital logic in such a higher-abstraction world.
It was slow for the inputs I cared about, so I added some optimizations, like an if-statement at the type level, for example, so that it bit-shift for multiplying powers of 2 (multiplication for tensor products). The compile time difference being palpable was a testament to how "some 'ideas' are surprisingly close to others" (err, 'ideas' ~ 'numbers' in this case). There is a connection to the p-adic numbers here, courtesy of dyadics, and some connection to the more-natural "last-mile" problem.
I agree that solving logic puzzles is very fun. I even pointed at things such as Advent of Code in my original reply. Computer programming can be very fun and satisfying to do. It is the reason why I became a software developer.
But it is not the same sort activity as writing a short story, or composing a a symphony, or painting a still-life. Those are done with different purposes. Art is something done with the purpose of exploring emotions, aesthetic beauty, question societal norms, etc.
The closest programming gets to that is if you are writing a jingle for advertisement, or drawing a signpost, or writing a technical article.
I disagree. It's not just a logic puzzle. If I haven't communicated that to you, that's also my failure. I've written stories short and long as well. It's a different kind of art.
"Art is something done with the purpose of exploring emotions, aesthetic beauty, question societal norms, etc."
I apologize if my emotions and aesthetics are not communicated, but I can only say that they were there. As for societal norms, I doubt that "embedding digital logic in types" is a "norm" of the programming society.
And though it's an appeal to patterns, I will have to bring up the general repeated failure of humanity to recognize art.
I apologize if I don't have the same sort of emotional response to embedding linear algebra validation at the compilation step as I do when I watched Mononoke Hime, or when I read The Picture of Dorian Grey.
While your tale sounded pretty interesting, it is the same sort of interesting as solving a math puzzle. I enjoy math puzzles.
Yep, and that's fine. I just think that for the people who do treat something as art, that I'd want to respect their opinion and emotions. Photography was not art, and now is.
Whatever moves people, however people wish to express themselves, whatever people find beautiful, all that is "art" to me. There's much which is art to others, perhaps, that I would not understand as art for myself.
I have to disagree, because this would stretch the meaning of the word "art" ao much that it becomes meaningless. Given your definition, anything can be art. Filing my taxes can be art, sweeping the floor can be art, taking out the trash can be art, making a butt print in my office chair can be art.
Art is something done with the express purpose of aesthetic appreciation, eliciting emotional responses and so on.
Nature for example can be beautiful, and certainly can draw out emotional responses from people. But unless we bring religion into the mix, it is not made with any purpose, it simply is.
The closest thing I think of programming as art is obviously videogames, if I consider that game mechanics are added with the undeniable purpose of inspiring in the player emotional response, it can certainly be done with aesthetics in mind, and I can think of a few examples where it is used to question norms.
"making a butt print in my office chair can be art." -- There were literally butt prints displayed at the Whitney a couple months ago. Just because it's in resin, so what? If I have fun making butt prints on my chair, is that worse because I didn't seal the form?
I am a programmer who likes aesthetics. I think about how aesthetic it is to not have to deal with certain production incidents for certain blocks of code because the typelevel computation tells me it would be a compiler bug if it screwed up. I like the feeling of realizing those 100 LOC could just be 10.
I sometimes tell people of when I came down from Mt. Fuji, there were wispy clouds and grand nature below me, picturesque like a painting. At that time, I likened it to the beauty I felt when I was first learning Haskell. But I say it because I expect it to be a rare kind of sentiment.
The thing with art and music is that they are easy to appreciate, and the appreciation grows deeper with more consideration. I love reading the placards in museums and attempting to understand why the artist did what they did, I like it more than even looking at the piece itself.
Code (and math, for that matter) is almost the same except for one key difference: they are not easy to appreciate without deliberate training, training which is often far to the side of anything most people need/want to deal with.
> The thing with art and music is that they are easy to appreciate
> Code (and math, for that matter) is almost the same except for one key difference: they are not easy to appreciate without deliberate training, training which is often far to the side of anything most people need/want to deal with.
I would argue that this exists on a spectrum. There's lots of art and music that's pretty difficult to appreciate without deliberate training, and indeed there are whole categories of music which we would probably call music for musicians.
For example, the album Kind of Blue by Miles Davis is loved by many and is considered by most people to be the best gateway record into the world of jazz, because it's easy to listen to and appreciate. An album like Sketches of Spain, and especially an album like Bitches Brew, are more difficult for the average non-musician listener to get into.
An even more out-there example for music is Allan Holdsworth. In certain circles, he's a well-known and well-regarded name, considered highly influential. Most people have no idea who he is or what he did. (A bit like that cutaway in Family Guy where they jumped to Benjamin Disraeli and he simply said: "you don't even know who I am!").
Similarly, in art and painting, you often need training to understand why something was especially impressive. Now that we have photography, some old paintings can feel "boring" if you don't know how to appreciate the level of difficulty in producing a near-photorealistic work in the 1700s.
Conversely, some math is very easy to appreciate without training! I had a buddy who I got excited about math simply by explaining the Fibonacci sequence and the golden ratio, then showing trivial examples of how they appear in nature. My friend got lit up about math that day in a whole new way.
Coding is not really programming. It is certainly a highly adjacent skill, but coding is not the same as programming. To quote Leslie Lamport, coding is to programming as typing is to writing.
> The thing with art and music is that they are easy to appreciate
I get what you mean (and agree w.r.t. math/code) but notably, I think appreciation for a lot of things still accumulates if you put in the work.
As an amateur violist, I can attest that I gained a totally new appreciation for most of the pieces I've studied and played in an orchestra in the past.
This not only includes "unknown" classical music from different eras, but also the obvious (popular) candidates like Beethoven's 6th, Dvořak's 9th and Grieg's "Peer Gynt" suites.
And there's a lot of great music one needs to get into first; for expample: I love Tool songs exactly for that, and there are certainly more obscure artists :)
So, I suspect the thing about maths and code is mainly just caused by the fact that people can go through life just fine without really interacting with them on the level required to develop the smallest bit of "taste" (as opposed to e.g. music).
And to think that all this knowledge comes from a small subset of music, specifically rooted in European classical music. Music worldwide even uses different scales.
I think you're overestimating the "appreciability" of art and music. I would say most people don't have the training to understand or enjoy the majority of the most important critical works in art or music from the last 100 years, if not longer.
>I think you're overestimating the "appreciability" of art and music. I would say most people don't have the training to understand or enjoy the majority of the most important critical works in art or music from the last 100 years, if not longer.
I think you're gonna need to unpack how you define "most important" and "critical" here.
It's quite easy to see most people enjoying a lot of art and music (I personally wouldn't include much 'understand' in my own definition of 'appreciate' here).
The more you study something the more you can have nuances or less-widespread angles by which to appreciate it, that will lead you to appreciate different things, but that's not the same as requiring that study to appreciate it.
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From another angle: critics have claimed that the Beatles were less important than various less-popular or more-niche musicians of their era since the 60s (from many different angles, even then). Is there a point where sustained higher popularity negates that criticism? Does time overwhelm niche more-highly-trained criticism at some point?
Most people do not understand the skill or craft required in aspects of art and music. They do not appreciate it. They may enjoy it in general but cannot appreciate the technical aspects without the background or education. For example, they may enjoy bold colors without realizing the colors come straight from the tube and the artist did no real work in selecting those colors or they may not appreciate the order and precision of brush strokes to achieve certain mark making shapes.
There's not much more satisfying than looking a a codebase, and mentally soaring through all its concept and files, peering down, feeling clean and happy the whole way. :)
Related, I've wasted so much time in my life, typing things that don't matter at all to anyone but myself. I suppose there are worse vices!
Mixed blessing indeed. As a young programmer, many times I complained about being asked to put warts in my perfect architecture, until I realized I'm not being paid to make museum pieces, I'm being paid to solve business problems.
I don't program anymore, but I learned you still can enjoy the beauty of your Mount Fuji when the business needs a pizza stand in the middle of the trail.
Seeing the core of my Mount Fuji stable and supporting more stands around for years is a satisfaction itself.
I personally feel like the second any art becomes a "job", it ceases its magic for them.
I don't think that artists would feel the same way about their art if they were put in corporate cubicasl with little agency to build art that "sells" because it increases the bottom line.
I think this is why in the video game industry many people burn out. They join for the passion and leave soulless.
A collective of workers in a field can very much decide what they want to get payed for. Craftsmen did exactly that for centuries, and that's in fact what makes them being known for quality and is thus in fact their business moat.
I totally agree that it takes some deliberate training to appreciate it.
But saying that out loud feels kind of lame to me.
Making something that connects with a ton of people is really hard too.
Beatles, Michael Jackson
But yeah! I really do get what youre saying.
Good point, I think a better way to have said it would be something like: to almost everyone, there's some music or graphic which resonates with them emotionally, and this has been true for thousands of years. There are very few such admirers for code, which has also only existed for a few decades. Perhaps worse is that it is mainly a profession for even most programmers, and not something they automatically see as expression.
Strange. That's like saying no one cares about the technicals of art, just how they feel about looking at an image.
As a consumer of graphics and music, let me "agree" for just a moment. I might not care how the music or image came to me. I just care that I like the final product. Which is why most paintings are trash, because I prefer highly saturated colors.
...I suppose this is somewhat true of many people already.
*For now. If a company were to degrade something, it shouldn't be so obvious that the "goodwill" was just a reallocation. Just a good strategy. For example, it allows them to claim that they're "just going from 150% to 125% usage allowance, which is still more than 100%".
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