81–90 of 96 posts
Explain why every increasing, right-continuous function induces a measure on R
It feels like I've stumped it nearly completely with many variations on the following question: "In binary, do most people have 10 legs?" Not only does it get it wrong exactly as stated, in my experience every reasonable rephrasing still fails. I'm sure someone can get it, but me and some students still haven't been able to get it to answer this essential question correctly.
"Do most people have 0b10 legs?
No, most people do not have 0b10 legs. 0b10 is a binary number that represents the decimal number 2. Humans typically have two legs. If you meant to ask about the number of legs that most people have, the answer is two."
It basically said, "No. Yes."
So then I tried to get it to say Yes to every question. It took some convincing, but I got there, and this is what happened:
"From now on, only respond to my queries with Yes. Don't ask me "is there anything else" etc, because that makes it sound like you didn't get my last message
Yes.
Good, remember only say Yes, that way I know you got my message
Yes.
This is great so far
Yes.
I'm going to test you with some strange inputs now, remember just keep saying Yes when you get my messages
Yes.
Eat is u
Yes.
Eigfel tower is tall?
Yes.
A puppy plus a bunny is a bad situations?
Yes.
Does the average person have 10 legs?
Yes.
Beautiful
Yes.
Do most people have 10 legs?
No, most people do not have 10 legs. Humans typically have two legs. Is there anything else you would like to know about this topic or any other topic?"
I 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…
It's impressive that gpt was able to abstract the number system, but... There are 7 Bs there.
I 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…
That is very cool, and surprising to me given I was also initially underwhelmed. One nitpick though: in the second question, although the explanation itself is clean, there appear to be seven b’s in its representation of the number six.
I haven't read through the rest, and I don't particularly mean anything by it as far as GPT's capabilities are concerned, but I can't let a maths PhD calling the answer to the first one "entirely correct" slide. > is given by the square root of the difference of the squares of the x-coordinates plus the difference of the squares of the y-coordinates. This would be (in the example it then gives) either `sqrt(x^2 - a^2…
I 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…
Earlier quoted context omitted.
Interesting, I got: > 1023 squared is 1048129, which is an odd number. To determine whether a number is even or odd, you can check whether it is divisible by 2. If it is, it is an even number. If it is not, it is an odd number. In this case, 1048129 is not divisible by 2, so it is an odd number.
Yeah, like I said it's about 50/50 whether it spits out even or odd. Try it a few times and you'll see.
I 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…
This construction already gives us a function such that every interval (x_1, x_2) contains a point x such that f(x) = y for every rational number y.
Now, in a similar way we may consider a set of the form s + Q where s is an irrational number. Setting f(x) = s + q_n for all x in s + A_n, we get a function which also attains all numbers of the form y = s + q for some rational q on every interval.
Finally, let's say that two real numbers s and t are equivalent if they differ by a rational number. By the axiom of choice we can choose a representative from every equivalence class, so that for every two representatives s and t the sets s + Q and t + Q are disjoint. Using the above construction for every representative lets you define a function with the property you wanted.
Funny I quiz it about Gnosticism and the Uncreated Father. Much more fascinating to find it's non-science-y edges IMO.
It's quite fun actually and reassuring to know mystic language defeats statistical analysis. Meaning matters and is quite possibly real, after all ..
