My wife was hosting a baby shower at our house and one of the games was to guess how may gum balls were in a glass jar. Well I love those kinds of problems so immediately I supplied open AI with the details. Chat GPT studiously calculated the volume of the jar and the volume of each gumball and divided them. 165. I went to write that on the sheet and stopped. But there is lots of air in the jar. It assumed the space was somehow all used.
I pointed this out and got this response: "You are correct that the packing density of spheres is an important factor to consider when determining how many spheres can fit in a given space." It then provided a full page of formulas and calculations and came up with 121. Big difference.
I asked it why it did not think about packing density the first time. "I apologize for not taking into account the packing density of spheres in my initial response. As an AI language model, I strive to provide accurate and helpful responses to the best of my abilities. However, I am not perfect and can sometimes miss important details or make mistakes. I appreciate your feedback and thank you for bringing this to my attention."
Wow, at least it is honest about its ability. I decided to do some further test. I made up a simple problem any human adult or child could solve without doing any math.
How many 2" diameter circles fit inside a 4" circle without overlapping?
I will not bore you with the pages of calculations, but the final answer of 7 was a surprise. I told it the right answer was 2. "I apologize for my mistake. You are correct that only 2 non-overlapping 2" diameter circles can fit inside a 4" circle." The math it provided looked very impressive, but the answer was stupid.
So I asked it how many would fit in a 6" circle. After much calculation it concluded the answer was 3. When I told it the answer was 5 it again admitted to having messed up and agreed the answer was 5. I knew 5 would fit, but guessed 7 might fit as well. I looked it up. No, the answer is 5 unless I make the smaller circles 1.99" instead of 2", then 7 would fit.
So I asked it how many would fit in a 5" circle. It said 4. I explained that a human can easily know the 2" and 6" case without doing any math, but the 5" problem was harder to do without math. The answer was either 3 or 4, but I was not sure. I asked it based on its first two failures on simple problems how sure it was on this problem.
"In the case of the current question, I can confirm that the maximum number of non-overlapping 2" diameter circles that can fit inside a 6" diameter circle without overlapping is indeed 5, and the maximum number that can fit inside a 5" diameter circle is 4."
I am beginning to understand why something that talks like a human and makes mistakes like a human should not be trusted any more than you would trust a 3rd grader to get the answer right.
By the way, there were 154 gumballs in the jar. Chat was wrong both times, but it was right about 4 2" circles fitting in a 5" circle, according to www.engineeringtoolbox.com. Lots to think about.
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