This is spooky. Maybe AGI is within our lifetime. Does anybody else here look forward to life as a paperclip?
I quiz ChatGPT about math
61–70 of 96 posts
Re: I quiz ChatGPT about math
#62[deleted]
Re: I quiz ChatGPT about math
#63I was actually very impressed with some math questions it was able to answer for me: S: If flabb means three, snabb means four, and whabb mean five, what is flabb plus whabb? If flabb means three, snabb means four, and whabb means five, then flabb plus whabb would be equal to three plus five, or eight. In this made-up numbering system, the words “flabb,” “snabb,” and “whabb” represent the numbers three, four, and fiv…
> There are a few reasons why people may argue about the answer to a mathematical question like “8 / 2(2+2)”. One reason is that there is more than one wav to interpret the question and arrive at a different answer. For example, some people may interpret the question as “8 / (2 * (2+2))” and arrive at an answer of 1, while others mav interpret it as “(8 / 2) * (2+2)” and arrive at an answer of 16. Wow, this is kinda…
Regarding the issue of "mav", it looks like the poster used screen capture followed by some image-to-text OCR routine (possibly tesseract). This feels like an OCR fail.
Re: I quiz ChatGPT about math
#64I just tried doing this myself JFZ: how do we know there are infinitely many primes ChatGPT: One way to show that there are infinitely many prime numbers is to use the fact that the set of prime numbers is infinite to show that there must be an infinite number of composite numbers as well. Composite numbers are positive integers that have at least one positive integer divisor other than 1 and itself. For example, 4 i…
> (seems hand wavey, and probably wrong though I can't figure out where the flaw is)
The flaw is here:
> Since there are infinite sequences of composite numbers, and each composite number is the product of at least two prime numbers (for example, 12 is the product of 2 and 6, which are both prime numbers), there must be an infinite number of prime numbers as well.
This doesn't establish that the prime numbers are distinct. The infinite sequence of even numbers has a single prime number in it, for example.
Re: I quiz ChatGPT about math
#65I'd still rather google these questions. you get the same material (google+gpt3 scraping+processing the same internet), but a choice of how its presented - a video, a "ELI5" explanation, an animated illustration, the comprehensive treatment on a Wikipedia page, etc.
And you are learning from a person, in a community, etc. Potential of beginning to belong to something as you learn. And be pointed to other contexts, other perspectives, other bodies of related learning.
And less of a queasy feeling about accuracy, since you know the source a bit better. Hard to be a critical reader with gpt3, anything it says is suspect to a degree.
No reason gpt3 can't foster this kind of thing, by citing sources etc. But it does run the risk of biting the hand that feeds it. If the summaries are good enough, fewer people rewarding ppl building websites to provide sharing of knowledge ...
Re: I quiz ChatGPT about math
#66I tried asking ChatGPT about a math question I thought of that I don't know the answer to:
Is there a function f: R -> R such that for all real x1, x2 and y where x1 I was hoping it might at least point me in the right direction but, although it always attempts a proof, most of its answers contain something trivially incorrect like "A set cannot be infinite, therefore..."
That said, it did give me a reasonable proof that such a function can't exist if it has to be continuous, because of a thing called the intermediate value theorem, which I hadn't heard of before. But when I asked about noncontinuous functions, it went back to bullshitting.
(If anyone here does know the answer, I'd love to hear it!)
Re: I quiz ChatGPT about math
#67There's another very simple test you can put ChatGPT through: Ask it to multiply some small numbers which it will most likely get right. Then ask it to multiply some large numbers and it will most likely be wrong by an order of magnitude or more. My layman's explanation is that because the space of likely answers is much smaller for small numbers than for larger ones the probability of finding the same multiplication in its corpus is high and the result likely correct. The larger the numbers the less likely it is to find the same multiplication or find an inference (for example both numbers begin with a 2, the result is likely starting with a 4) that is correct for all digits.
Re: I quiz ChatGPT about math
#68I tried asking ChatGPT about a math question I thought of that I don't know the answer to: Is there a function f: R -> R such that for all real x1, x2 and y where x1 I was hoping it might at least point me in the right direction but, although it always attempts a proof, most of its answers contain something trivially incorrect like "A set cannot be infinite, therefore..." That said, it did give me a reasonable proof…
You're looking for the Conway base 13 function (https://en.wikipedia.org/wiki/Conway_base_13_function).
Re: I quiz ChatGPT about math
#69I tried asking ChatGPT about a math question I thought of that I don't know the answer to: Is there a function f: R -> R such that for all real x1, x2 and y where x1 I was hoping it might at least point me in the right direction but, although it always attempts a proof, most of its answers contain something trivially incorrect like "A set cannot be infinite, therefore..." That said, it did give me a reasonable proof…
[deleted]
Re: I quiz ChatGPT about math
#70If ChatGPT is what we can expect from AI I’m quite afraid. It seems to be usually correct but often spectacularly and confidently wrong. I hope we never give this technology decision making power.
Adding a confidence score to every answer doesn't look like an insurmountable problem.
It generates text. It has no idea how “correct” its output is. The best it can ever do is give you information about how likely the output is to follow the input based on its corpus. That may or may not correlate with correctness.
For the sake of argument ignore issues with the correctness of the corpus itself. Imagine that the model produces a 50 word answer. Inserting the single word "not" in the answer may only change the likelihood score by a small amount either way, but it could completely change the meaning of the answer.