Hacker News Reader

Comment by tylerhou | Hacker News Reader

> I no longer have to haul the pyramid blocks up the ramp myself... what I bring to the party is intuition and understanding.

Hauling the pyramid blocks is what gives people intuition and understanding. It is true that school systems usually have way too much computation -- it is easier to test and grade computation. But the only way that you were able to use computer algebra systems fluently is because you had internalized how algebra worked by hand. If we tell students that they no longer need to learn how to solve equations we are seriously depriving them of a mathematical education.

View on HN

Maybe. As a parallel, I know C# and F#. They are programming languages. They are built on top of Microsoft products like the JIT and more basically Assembly language.

I have no idea how assembly works - in my years of experience I’ve never had an issue that required I dig that deep into it. Does that mean I can’t be effective with higher-level tooling because I do not know the absolute basics?

The entire point of a programming language design is to give you an abstracted environment with a complete coherent semantics so that you don't need to understand what's going on under the hood.

You can be effective at using C# and F# to solve other problems specifically because they are very well designed at the goal of abstracting over the lower level hardware. But if your goal is to build an intuition of how programming languages themselves are implemented and how computer hardware works, then, using those languages will be counter productive.

If you're trying to use math to solve arithmetical problems, then by all means using AI to help. But if you're trying to advance the math field itself, then actually knowing how math works is probably essential.

Put in more concrete terms: if someone wants to be a working mathematician without learning the fundamentals of math, then how do they even know what prompts to the AI are worth writing? In what way are they adding any value to the process at all?

I never said one should not know the fundamentals of mathematics, I was trying to express it’s a damned lot easier when once understood you can delegate the lesser aspects to machinery. Abacus, calculator, computer, CAS, now AI: the mathematician’s understanding and intuition are still fundamental, but the instruments they can rely upon are levelling the playing field (and indeed, it is a great field in which to play).

First of all, programming isn't necessarily a very skilled task as being a mathematician.

Secondly, I've encountered compiler bugs many times, so it is very helpful.

That's the difference between a senior and a junior: the junior goes to the senior and the senior figures it out. You can remain a junior at any age.

While true that doing things the hard way is critical to learn a discipline, the OP’s point is about what is possible with AI once you’ve built those skills and intuition. I think in the future it will be common for those passionate about a discipline to strategically avoid AI until they’ve “built the muscles.”

Exactly. I learnt to haul the blocks myself, but it has always been an uncertain and effortful exercise; now I can move them around as effortlessly as if I were playing Tetris.

This might be clumsy but I will say it anyway. If music is math, how do you explain people who have innate musical abilities without formal academic training in notation, music theory, circle of fifths, etc.

Well i can tell you what i think: music isn't math and whoever told you that is wrong.

To further underline the point: entire cultures' musical traditions don't follow the circle of fifths, or notation as you're likely familiar with it, or even notes that follow the kinds of ratios you might use to describe western musical scales of any kind. The mathematical representations of western music were applied in retrospect, math never played any role in the development of western music anyway.

So considering math was never a factor in the development of western music and the math used to describe western music doesn't even apply universally, i just can't really consider "music is math" to be a meaningful statement at all

Rhythm, the core of global music, is math.

2,000 year old Chinese music uses sanfen sunyi. You take a pipe length, cut it by a third, then extend the new one by a third, alternating. Hey look.....a petatonic scale.

Arabic music pitches even more. The maqam system uses intervals that fall between Western half steps, often called "quarter tones," Some used "commas" which divide the whole tone into 9 parts. This gives you octave with about 53 steps.

Math isn’t music, even in a metaphorical sense. The argument by analogy fails at the first hurdle.

Just to make sure I follow, do you mean the "music is math" idea fails, or that my question does? I'm not saying math has nothing to do with music. Frequency ratios and rhythmic divisions are clearly there. My point is that you can have deep musical ability without ever thinking in those terms, which suggests music is more than the math that describes it.

I’m saying that though argument by analogy is very persuasive, “math is music” is a metaphor that is fundamentally unsound as the grounds for reasoning from. I’m not talking about the mathematical aspects of music (which, as you correctly point out, can be found to exist) but that music is performative and aesthetic, whereas mathematics is all about internal consistency.

Sheet music is no more music than mathematical notation is mathematics. (Indeed both notations have roots in the same kind of two-dimensional seventeenth century calligraphic tradition.) However, as you point out, mathematics is indeed the study of patterns, structures, and relationships, and music is not. It is a structure and has relationships, but it is not a “metaphor of metaphors” as mathematics is. Case in point: modern visual art post-photography is much more affine to music than mathematics is, because after depiction became not quite trivial but literally photographic from the daguerreotype onwards, the role of the visual arts became the solicitation of emotion and the conveyance of narrative. Music has syntax, indeed it has very many, but it is not the study of syntaxes in the manner in which mathematics is.

Also there is some instinctual understanding of the work moving a big heavy rock takes, and how to do it. No such corollary for algebra and hence some civilizations never discovered or understood it.

a scale?

Have you ever heard of concrete, aka “the stone for projects too large to be assembled in blocks”?

Reply on news.ycombinator.com