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They're saying you can't find a ruler accurate enough to be sure the number you measure is sqrt(2) and not sqrt(2) for the first 1000 digits then something else. And eventually, as…

Non-physicst here. Hopefully someone can correct me or elaborate. My understanding is that what's being described is smaller scale decoherence inside the proton. Normally, the univ…

He's not making it up and there's no reason for that tone. Strings are more straightforward to isolate compared to vocals/horns/etc because they produce a near-perfect harmonic ser…

Agreed. My experience is GPT5 is significantly better at large-scale planning & architecture (at least for the kind of stuff I care about which is strongly typed functional systems…

Why are you monitoring your colleagues’ water intake?

These models still have guardrails. Even locally they won't tell you how to make bombs or write pornographic short stories.

Bell's Theorem (1964) describes an inequality that should hold if quantum mechanics' randomness can be explained by certain types of hidden variables. In the time since, we've repe…

I believe that those who justify cruelty with rhetoric and spread hate will one day look into the mirror and be horrified at what they see.

The sharpest cries of, "that's not thinking!" always seem to have an air of desperation about them. It's as if I'm special, and I think, and maybe thinking is what makes me special…

> Part of this problem is also because courses have (in my experience) rarely rewarded actual knowledge or understanding It doesn't matter. There is literally no assignment you can…

megaparsec (1 million parsecs)

This is exactly what I got wrong when I started learning jazz piano as an adult. My wife is a lifelong musician and I got to the annoying point where I'd be playing and she'd walk …

Yet it remains true that not having magic evil talismans in my house makes it very unlikely that my family or I get cursed by accident.

I didn't say and don't believe those things.

> changing how you in particular perceive the world does not actually change the world that you are a part of It's impossible to change yourself without changing the world, because…

What is this "statement" you speak of? (if (= 2 2) :OK :nope)

> otherwise it wouldn't be possible to have so much done inside such a small volume, with such small amounts of energy That's interesting. Could you share your source?

This feels a lot like a standard line of muddy thinking we see in youtube videos about consciousness (for example): "we don't understand brains, and we don't understand quantum mec…

Like all writing, proofs have a target audience. If you don't know what a Galois group or a modular form is, it's not the author's job to teach you. Formal verification is getting …

> That's a pretty extreme interpretation. Anyone who downloads the IDE can create and publish a game. If kids are using the tool, making fun games, and sharing them with other peop…

I think this is correct. I play Go at a strong amateur level, and on the 19x19 board, I can often fully recall 200+ move games against "normal" opponents, because the moves tell a …

Here's Mike Battaglia playing a cover of "House of the Rising Sun" on a 31 EDO synth setup which I always loved: https://www.youtube.com/watch?v=IlZv13YZzSM

I'm not sure if you intend this as a helpful analogy for an undergrad or as an argument in favor of groups/homomorphisms being created to match reality, but I don't think it applie…

Definitions are created to be useful or interesting or both, and sometimes those specifiers overlap with physical reality. But that doesn't mean they're created to match reality or…

Mathematicians don't "believe" in real numbers. They're part of an abstract logical framework, not a statement about the nature of reality. Mathematical objects arise from definiti…