Right, but that seems to imply you had to give up spending the time and attention elsewhere. There are definitely times where spending time with a certain person is pretty close to a terminal goal. And in that case “spending” seems to be a bit of a misleading word.
dandelion4
Karma: 20
Agreed. However, humans also don’t have an internal multiplication algorithm, but can nonetheless use a scratchpad to multiply accurately (in extreme circumstances :P). I’ve chosen multiplication as an example here because it’s maybe the “simplest” thing GPT-4 can’t consistently do.
What I’m finding interesting here is that GPT-4 knows how to break down multiplications (it can write perfect recursive code for multiplying large numbers). It also knows about chain of thought prompting. How close is it to being able to just… directly use the algorithms it knows? What’s the minimum amount of prodding needed? The following prompt is an upper bound on how hard it is to teach GPT-4 accurate multiplication:To multiply large numbers accurately, it helps to break down the problem. We will demonstrate multiplying 191241 by 741122. Set a = 19, b = 12, c = 41, d = 74, e = 11, and f = 22. We can then write 191241 * 741122 = (10^4 a + 10^2 b + c) * (10^4 d + 10^2 e + f). Expanding this out, we obtain 10^8 ab + 10^6 (ae + bd) + 10^4 (af + be + cd) + 10^2 (bf + ce) + cf. We can now calculate all these products: ab = 19 * 74 = 1406 ae = 19 * 11 = 209 bd = 12 * 74 = 888 af = 19 * 22 = 418 be = 12 * 11 = 132 cd = 41 * 74 = 3034 bf = 12 * 22 = 264 ce = 41 * 11 = 451 cf = 41 * 22 = 902 Now we can calculate the sums inside parentheses: ae + bd = 209 + 888 = 1097 af + be + cd = 418 + 132 + 3034 = 550 + 3034 = 3584 bf + ce = 264 + 451 = 715 We can now factor to avoid having so many zeroes: 10^8 ab + 10^6 (ae + bd) + 10^4 (af + be + cd) + 10^2 (bf + ce) + cf 10^2 (10^2 (10^2 (10^2 ab + (ae + bd)) + (af + be + cd)) + (bf + ce)) + cf Now we substitute in: 10^2 (10^2 (10^2 (10^2 * 1406 + 1097) + 3584) + 715) + 902 = 10^2 (10^2 (10^2 (140600 + 1097) + 3584) + 715) + 902 = 10^2 (10^2 (10^2 (141697) + 3584) + 715) + 902 = 10^2 (10^2 (14169700 + 3584) + 715) + 902 = 10^2 (10^2 (14173284) + 715) + 902 = 10^2 (1417328400 + 715) + 902 = 10^2 (1417329115) + 902 = 141732911500 + 902 = 141732912402 The final answer is 141732912402. Use the exact same method to multiply 183112 * 994531.(It correctly follows the procedure to obtain
182110560472.) Is there a shorter prompt that accomplishes the same thing?
50⁄50 is sort of an obvious Schelling point norm? If neither of you want to give into blackmail and have to agree to get any money at all, it seems like a relatively symmetric situation. But interesting question…