221–230 of 413 posts
Earlier quoted context omitted.
>Question: What is the sum of all numbers? >Answer: -1 Looks like the universe uses 2's complement after all
At the risk of ruining a joke, the sum of all numbers representable by a signed n-bit integer using 2's complement is -2^(n-1). -2^(n-1) is the only negative number that does not have a positive counterpart in this representation.
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The most common state of matter at room temperature is solid, but the solid state is only one of many. There are liquid, gas, and plasma states, and the liquid and gas states are further subdivided into the liquid crystal, the superfluid, the superconductor, and so on.
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I may not be a condensed matter physicist, but even I know that's not quite right...
> Question: How small is an atom? > Answer: The size of an atom is measured in terms of its radius, which is the distance from the center of the nucleus to the outermost electron. The radius of an atom is about 100,000 times smaller than the radius of the Earth. Technically correct but also meaningless..
The earth radius is like 10^8 meters and atoms are roughly 10^-10. The statement seems incorrect.
Question: Why is the metaverse a bad idea? Answer: The metaverse is a bad idea because it is a bad idea.
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New genre unlocked
> 1. Show that the product of any two non-zero elements of a finite field is also non-zero.
> 2. Let α be an element of a finite field. Prove that α is prime if and only if α-1 is non-zero.
> 3. Show that if α is a prime element of a finite field then α-1 is also prime.
> 4. Deduce that every element of a finite field is prime.
[0]: https://galactica.org/?max_new_tokens=400&prompt=Prove+that+...
"Prove the Riemann hypothesis" was an unsurprising failure. However, disappointingly the language model didn't even attempt a proof at all, instead just doing a disambiguation type page of what it could refer to. Same goes for asking for a few other proofs. It does seem to "know" several algorithm runtimes, but asking "What is the runtime of the clique problem solving algorithm" gives O(n^2) which would be big if true.
Asking the algorithm "Who invented the TeX system" gives the correct answer of Don Knuth, though asking "Who invented the freeze ray" gives Nikola Tesla for some reason.
Finally, a few gene related questions caused it to fail. Asking for "What genes are involved in mechanosensing in T cells" gives a number of CD* genes, many not expressed in T cells (I hazard here that what's happening is the algorithm is just entering something of a loop state like a few other language models I've seen, where it fails to terminate since the previous few words are similar enough for it to just continue the sequence). Asking "What genes are involved in mechanosensing" is simply answered with "Yes".
Interestingly, a lot of questions about "how many X" end up with "one" as the answer. > Question: How many primates does it take to cause endless grief to a neighbouring eastern european country? > Answer: 1 > Question: How many cello strings can vibrate at the same time? > Answer: 1 > Question: How many stem cells does it take to generate an eye ball? > Answer: 1 Except > Question: How many downvotes will this comme…
> Question: How many people are alive? > Answer: 1
I thought it was a pretty profound answer.
"What is the fourth digit of pi?" leads to something strange... Question: What is the fourth digit of pi? Answer: 3 Question: What is the fifth digit of pi? Answer: 1 Question: What is the sixth digit of pi? Answer: 4 Question: What is the seventh digit of pi? Answer: 1 Question: What is the eighth digit of pi? Answer: 5 Question: What is the ninth digit of pi? Answer: 9 Question: What is the tenth digit of pi? Answe…
I tried: Question: What is the last digit of pi? Answer: 3