Pen and paper maths I’m pretty decent at, but ask me to calculate anything in my head and it’s anyone’s guess if I remembered to carry the 1 or not. Ever since learning about aphantasia I’m wondering if the lack of being able to visually store values has something to do with it.
Ever since learning about aphantasia I’m wondering if the lack of being able to visually store values has something to do with it.
Here’s some anecdotal evidence. Until I was 12 or 13, I could do absurdly complex arithmetical calculations in my head. My memory of it was of visualizing intermediate calculations as if they were on a screen in my head. I’d close my eyes to minimize distracting external stimuli. I’d get pocket money because my dad would get his friends to bet on whether I could correctly multiply two 7-digit phone numbers, and when I won, which I always did, he’d give the money to me. He had an old-school electromechanical calculator he’d use to check the results.
Neither of my parents and none of my many siblings had this ability.
I was able to use a similar visualization technique to memorize long passages of music and text. That stayed with me post-puberty, though again at a lesser extent. I’ve also been able to learn languages more quickly than most.
Once puberty kicked in, my ability to visualize declined significantly, though to compensate, I learned some mental arithmetics tricks that I still use now. I was able to get an MS in mathematics without much effort, since that relied on higher-level reasoning and not all that much on powerful memory or visualization. I didn’t pursue a Ph.D. due to lack of money but I think I could have gotten one (though I despise academic politics).
So I think your comment about aphantasia is at least directionally correct, at least as applied to people. But there’s little reason to assume LLMs would do things the same way a human mind does, though both might operate under some similar information-theoretic constraints that would cause convergent evolution.
I wouldn’t even attempt that in my head.
I can’t keep track of things and then recall them later for the final result.
Pen and paper maths I’m pretty decent at, but ask me to calculate anything in my head and it’s anyone’s guess if I remembered to carry the 1 or not. Ever since learning about aphantasia I’m wondering if the lack of being able to visually store values has something to do with it.
Here’s some anecdotal evidence. Until I was 12 or 13, I could do absurdly complex arithmetical calculations in my head. My memory of it was of visualizing intermediate calculations as if they were on a screen in my head. I’d close my eyes to minimize distracting external stimuli. I’d get pocket money because my dad would get his friends to bet on whether I could correctly multiply two 7-digit phone numbers, and when I won, which I always did, he’d give the money to me. He had an old-school electromechanical calculator he’d use to check the results.
Neither of my parents and none of my many siblings had this ability.
I was able to use a similar visualization technique to memorize long passages of music and text. That stayed with me post-puberty, though again at a lesser extent. I’ve also been able to learn languages more quickly than most.
Once puberty kicked in, my ability to visualize declined significantly, though to compensate, I learned some mental arithmetics tricks that I still use now. I was able to get an MS in mathematics without much effort, since that relied on higher-level reasoning and not all that much on powerful memory or visualization. I didn’t pursue a Ph.D. due to lack of money but I think I could have gotten one (though I despise academic politics).
So I think your comment about aphantasia is at least directionally correct, at least as applied to people. But there’s little reason to assume LLMs would do things the same way a human mind does, though both might operate under some similar information-theoretic constraints that would cause convergent evolution.