Just now found paper on internet that uses Lambert's W for these pronlems. Haven't read it, but it's intro for students so I may have chance to understand it: The strange properties of the infinite power tower. Luca Moroni, 2019. I can use L's W, with great difficulty, but had no clue was useful here. 1:30
In fact it would be interesting to try the "x^x^x^... = 3" because that is an equation which has no solution. The largest possible number that x^x^x^... can equal to is 2.71828... (e) where 'x' equals e^(1/e). Any higher input and the output is infinity. So it would be interesting to see if ChatGPT4 realizes that the equation does not neecssarily have a solution to begin with.
Honestly, these are quite difficult problems. I wasn't able to solve it. So you could say chatgpt-4's understanding of math is equivalent to an average STEM student. I bet, most of us don't know the trick that simplifies the problem. May be it's a piece of cake for mathematicians because they have seen it before, but for the average STEM student, it is not. PS: An average STEM student may excel in school tests and be satisfied with it, but an exceptional STEM student tries to solve olympiad-level problems
Yes you are right the problem is not a standard result, but given that it was trained on maths papers I was expecting it to be able to spot this. Interestingly, it understood the tower power trick, but failed afterwards on the easy bit that would be clear to a high school student after the infinite tower power is gone. It goes to show that it doesn't seem to reason like we think it can, even if does a jolly good job of appearing to be very reasonable.
@@eternity_hour Yes, not perfect reasoning (but attempts are being made in the research community). But I was able to make it (GPT 3.5 based model) come up with the correct answer by hinting. That said, it is easy for an average STEM student to come up with the answer once the trick is known. Not so with the AI.
I've got a longer recording where I go into more detail - I just wanted this to make a short example. You're right about LaTeX - I was trying to get Manim to work with LaTeX but found rendering was taking an age. Thanks for your feedback - I'm just starting out on YT and would love to grow this into a bigger project - better visuals will surely follow.
Just now found paper on internet that uses Lambert's W for these pronlems. Haven't read it, but it's intro for students so I may have chance to understand it: The strange properties of the infinite power tower. Luca Moroni, 2019.
I can use L's W, with great difficulty, but had no clue was useful here. 1:30
In fact it would be interesting to try the "x^x^x^... = 3" because that is an equation which has no solution. The largest possible number that x^x^x^... can equal to is 2.71828... (e) where 'x' equals e^(1/e). Any higher input and the output is infinity. So it would be interesting to see if ChatGPT4 realizes that the equation does not neecssarily have a solution to begin with.
I'll try it!
Honestly, these are quite difficult problems. I wasn't able to solve it. So you could say chatgpt-4's understanding of math is equivalent to an average STEM student. I bet, most of us don't know the trick that simplifies the problem. May be it's a piece of cake for mathematicians because they have seen it before, but for the average STEM student, it is not.
PS: An average STEM student may excel in school tests and be satisfied with it, but an exceptional STEM student tries to solve olympiad-level problems
Yes you are right the problem is not a standard result, but given that it was trained on maths papers I was expecting it to be able to spot this. Interestingly, it understood the tower power trick, but failed afterwards on the easy bit that would be clear to a high school student after the infinite tower power is gone.
It goes to show that it doesn't seem to reason like we think it can, even if does a jolly good job of appearing to be very reasonable.
@@eternity_hour Yes, not perfect reasoning (but attempts are being made in the research community). But I was able to make it (GPT 3.5 based model) come up with the correct answer by hinting.
That said, it is easy for an average STEM student to come up with the answer once the trick is known. Not so with the AI.
Thanks for your comments - I'll try nudging it more next time. Don't forget to subscribe to see more uploads
@@eternity_hour Subscribed :)
Why don't you try to interact with it and see if it understands its mistakes ? Also try to use LaTeX for math formulas
I've got a longer recording where I go into more detail - I just wanted this to make a short example. You're right about LaTeX - I was trying to get Manim to work with LaTeX but found rendering was taking an age.
Thanks for your feedback - I'm just starting out on YT and would love to grow this into a bigger project - better visuals will surely follow.