Everything about the exact timbre of your voice is captured in the waveform that represents it. To the extent that the sampling rate and bit depth are good enough to mimic your actual voice without introducing digital artefacts (something analogous to a pixelated image) that’s all it takes to reproduce any sound with arbitrary precision.

Timbre is the result of having a specific set of frequencies playing simultaneously, that is characteristic of the specific shape and material properties of the object vibrating (be it a guitar string, drum skin, or vocal chords).

As for how multiple frequencies can “exist” simultaneously at a single instant in time, you might want to read up on Fourier’s theorem and watch 3Blue1Brown’s brilliant series on differential equations that explores Fourier series https://www.youtube.com/watch?v=spUNpyF58BY

Yes digital media, and computers in general, are miracles of science and engineering. Is there some reason digital audio in particular inspires you in this way, as opposed to digital images?

Long list of numbers in sequence. Each represents how far away from equilibrium the speaker cone should be, at each point in time, as it vibrates back and forth.

Tough-guy Ted “Bundy” Nugent also shat on himself to dodge the Vietnam draft.

Why do bots

Suddenly appear? 🐦

I heard some of the really wealthy Silicon Valley types kit out their own private laboratory and hire chemists.

That’s how the salesman guy got Homer to buy the Mister Plow truck lol

https://zombo.com/

Localsend - it’s like airdrop but for android, linux, windows, and mac.

I can’t help feeling a lot of these new motorized doodads are total deathtraps. I used to have a 40mph kaabo electric scooter and although it was mega fun, I sold it before it had a chance to kill me. Small wheels, poor geometry for stability, small caster angle, intoxicatingly high power - it’s a recipe for disaster.

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There are many structures of proof. A simple one might be to prove a statement is true for all cases, by simply examining each case and demonstrating it, but as you point out this won’t be useful for proving statements about infinite cases.

Instead you could assume, for the sake of argument, that the statement is false, and show how this leads to a logical inconsistency, which is called proof by contradiction. For example, Georg Cantor used a proof by contradiction to demonstrate that the set of Natural Numbers (1,2,3,4…) are smaller than the set of Real Numbers (which includes the Naturals and all decimal numbers like pi and 69.6969696969…), and so there exist different “sizes” of infinity!

For a method explicitly concerned with proofs about infinite numbers of things, you can try Proof by Mathematical Induction. It’s a bit tricky to describe…

• First demonstrate that a statement is true in some 1st base case.
• Then demonstrate that if it holds true for the abstract Nth case, then it necessarily holds true for the (N+1)th case (by doing some clever rearranging of algebra terms or something)
• Therefore since it holds true for the 1th case, it must hold true for the (1+1)th case = the 2th case. And since it holds true for the 2th case it must hold true for the (2+1)=3th case. And so on ad infinitum.

Wikipedia says:

Mathematical induction can be informally illustrated by reference to the sequential effect of falling dominoes.

Bear in mind, in formal terms a “proof” is simply a list of true statements, that begin with axioms (which are true by default) and rules of inference that show how each line is derived from the line above.

Exactly. I’m thinking of dying for a few years so I can save up enough to get on the property ladder. Just waiting for a decent grave to come up on the outskirts of town where the rents aren’t too high.

Lemmy is succeeding just fine right now.

Reddit’s “content” is way more rage-baiting, fake AITA stories, culture wars both-sideisms, publicfreakout schadenfreude, and basic-tier iFunny memes, re-posted by waves of bots. All reddit is “succeeding” at is being a firehose of diarrhea.

I prefer Lemmy’s slant towards technology-related news, and polite discussion in earnest without painfully unfunny “and my axe” responses.