Kogasa

Well, we knew he was a shitbag beforehand, so that’s not really what’s in question

I’m not a physicist, I don’t know one way or another. But it’s possible that there’s a leading explanation for the formation of the universe based on a mathematical model that predicts exactly one big bang.

Based on the comment you’re replying to, I assume they would say “no, nothing materialized from nothing because there wasn’t a ‘before’ in which nothing could have existed”

It wouldn’t have been published, and he’s only relatively famous if you’re a topologist, but it was Charlie Frohman. Not that it must carry the same weight for you, but I value his insight highly, even if it’s just a quip.

Yes, but it proves that termwise comparison with the harmonic series isn’t sufficient to tell if a series diverges.

The assumption is that the size decreases geometrically, which is reasonable for this kind of self similarity. You can’t just say “less than harmonic” though, I mean 1/(2n) is “slower”.

Quoting a relatively famous mathematician, linear algebra is one of the few branches of math we’ve really truly understood. It’s very, very well behaved

Lived in Iowa for a few years, there were a few authentic Mexican places, just not as many as Americanized ones.

Yes, with Iosevka font

Google it? Axiomatic definition, dedekind cuts, cauchy sequences are the 3 typical ones and are provably equivalent.

I’m fully aware of the definitions. I didn’t say the definition of irrationals was wrong. I said the definition of the reals is wrong. The statement about quantum mechanics is so vague as to be meaningless.

That is not a definition of the real numbers, quantum physics says no such thing, and even if it did the conclusion is wrong

U good?

Your first two paragraphs seem to rail against a philosophical conclusion made by the authors by virtue of carrying out the Turing test. Something like “this is evidence of machine consciousness” for example. I don’t really get the impression that any such claim was made, or that more education in epistemology would have changed anything.

In a world where GPT4 exists, the question of whether one person can be fooled by one chatbot in one conversation is long since uninteresting. The question of whether specific models can achieve statistically significant success is maybe a bit more compelling, not because it’s some kind of breakthrough but because it makes a generalized claim.

Re: your edit, Turing explicitly puts forth the imitation game scenario as a practicable proxy for the question of machine intelligence, “can machines think?”. He directly argues that this scenario is indeed a reasonable proxy for that question. His argument, as he admits, is not a strongly held conviction or rigorous argument, but “recitations tending to produce belief,” insofar as they are hard to rebut, or their rebuttals tend to be flawed. The whole paper was to poke at the apparent differences between (a futuristic) machine intelligence and human intelligence. In this way, the Turing test is indeed a measure of intelligence. It’s not to say that a machine passing the test is somehow in possession of a human-like mind or has reached a significant milestone of intelligence.

https://academic.oup.com/mind/article/LIX/236/433/986238

I don’t think the methodology is the issue with this one. 500 people can absolutely be a legitimate sample size. Under basic assumptions about the sample being representative and the effect size being sufficiently large you do not need more than a couple hundred participants to make statistically significant observations. 54% being close to 50% doesn’t mean the result is inconclusive. With an ideal sample it means people couldn’t reliably differentiate the human from the bot, which is presumably what the researchers believed is of interest.

Only if you’re trying to get a numerical point evaluation. For example, one can use Fourier series to represent complex signals in terms of sine waves, and then reproduce the sine waves with hardware to reproduce the original signal. This is how a simple synthesizer produces different kinds of tones.

What you have described is technology beyond the imagination of the men of my time

What century is it

You tell em Admiral

Would not be surprised if it’s getting confused about a wallet sponsorship