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Agree with this; also, it feels like you are reading out the same theories I have somewhere in my brain and that's a weird sensation. A related theory: being g

by ajkjk 3y ago

Agree with this; also, it feels like you are reading out the same theories I have somewhere in my brain and that's a weird sensation. A related theory: being good at math, especially mental math, correlates with aphantasia (not being able to see pictures in your head). People who can see images in their head learn to do arithmetic early on with visual algorithms, which are fundamentally not good for understanding as well as rather error-prone (because the brain remembers gestalts, not finicky details like where a decimal is). Aphantasiacs are forced to learn to do math differently, and use some different part of the brain as 'scratch space'. In my case it's the language brain: calculations which are set aside live in the same part of your brain that can repeat what was said a moment to you without understanding it. Turns out, though, that this verbal part is quite _accurate_ at remembering things, and this makes it easier to juggle multi-step calculations without paper.

xigency 3y ago
> A related theory: being good at math, especially mental math, correlates with aphantasia (not being able to see pictures in your head) This is the kind of condition I wonder if I have. Because on one hand, if I do a visualization exercise I would describe it as foggy at best. Then again, I struggle to understand how our brains could be wired that differently from person to person, that we could have or lack certain mental senses. I would suggest that everyone has some latent capability, whether they recognize it or not. After all the visual cortex is quite important. In the context of your example, those good at mental math might see a chalkboard like image of the problem with all the detail. Those who struggle might be distracted visualizing the items that are being counted themselves, and all their detail. For another riddle, consider the question of whether one recognizes their thoughts as an internal monologue or not, and how that relates to communication and action.
- ajkjk 3y ago
  I would emphasize that people who are good at mental math tend to not see a chalkboard, while those are less good at it tend to. Relying on visualization is, I have noticed from asking around, a weakness. Of course it's just anecdotal but the pattern seems pretty pronounced to me. (I polled a hundred people at one point and saw this pattern reflected in the responses) I agree, though, that visualization is probably latent even in people who can't do it. I notice it when half asleep for instance.
- halfcat 3y ago
  > those good at mental math might see a chalkboard like image of the problem with all the detail Experiments with chess players and memorization shed some light on this. DeGroot’s research showed the average person is quite poor at recalling chess positions from real games, while chess masters have almost perfect recall even after seeing the board for only a few seconds. However, when the chess masters were given completely random arrangements of pieces on the board (as opposed to positions from real chess games), they were no better than the average person. This and other experiments suggest it’s not a visual snapshot, but functional knowledge and chunking, such as knowing pawns typically protect one another in diagonal chains, etc. I recall from talking with high rated chess players, they rarely visualize the board in the mind’s eye, but they just know things without thinking, like, a bishop on d3 attacks the square h7 and not h6. Not from rote memorization, but from playing and seeing that sacrificing a bishop on h7 is a thematic attacking pattern.
  - ajkjk 3y ago
    Incidentally, that's one of those anecdotes that sounds deep but is really perfectly obvious if you play chess at a moderate level, or, like, ask someone who does. It would be much more surprising if it didn't work that way (chunking the board into patterns).
thorncorona 3y ago
> being good at math, especially mental math, correlates with aphantasia as someone who used to do math competitions as a kid, everyone I knew who was "good" at mental math had a good number sense, a big bag of tricks for doing different things with numbers, and practiced with their bag of tricks.
- ajkjk 3y ago
  I did math competitions also, but I'm not really talking about the specialized tricks like fast multiplication or square root algorithms. I'm just talking about basic stuff, like computing tips or taking percents. Most people simply cannot add or multiply numbers in their accurately, by any method.
ChainOfFools 3y ago
We are definitely aware of the same phenomenon! Check out a reply I made elsewhere in this thread which addresses compensatory recruiting of ones verbal/ audio immediate recall as an extension of working memory store.

by ajkjk 3y ago

xigency 3y ago

> A related theory: being good at math, especially mental math, correlates with aphantasia (not being able to see pictures in your head) This is the kind of condition I wonder if I have. Because on one hand, if I do a visualization exercise I would describe it as foggy at best. Then again, I struggle to understand how our brains could be wired that differently from person to person, that we could have or lack certain mental senses. I would suggest that everyone has some latent capability, whether they recognize it or not. After all the visual cortex is quite important. In the context of your example, those good at mental math might see a chalkboard like image of the problem with all the detail. Those who struggle might be distracted visualizing the items that are being counted themselves, and all their detail. For another riddle, consider the question of whether one recognizes their thoughts as an internal monologue or not, and how that relates to communication and action.

ajkjk 3y ago
I would emphasize that people who are good at mental math tend to not see a chalkboard, while those are less good at it tend to. Relying on visualization is, I have noticed from asking around, a weakness. Of course it's just anecdotal but the pattern seems pretty pronounced to me. (I polled a hundred people at one point and saw this pattern reflected in the responses) I agree, though, that visualization is probably latent even in people who can't do it. I notice it when half asleep for instance.
halfcat 3y ago
> those good at mental math might see a chalkboard like image of the problem with all the detail Experiments with chess players and memorization shed some light on this. DeGroot’s research showed the average person is quite poor at recalling chess positions from real games, while chess masters have almost perfect recall even after seeing the board for only a few seconds. However, when the chess masters were given completely random arrangements of pieces on the board (as opposed to positions from real chess games), they were no better than the average person. This and other experiments suggest it’s not a visual snapshot, but functional knowledge and chunking, such as knowing pawns typically protect one another in diagonal chains, etc. I recall from talking with high rated chess players, they rarely visualize the board in the mind’s eye, but they just know things without thinking, like, a bishop on d3 attacks the square h7 and not h6. Not from rote memorization, but from playing and seeing that sacrificing a bishop on h7 is a thematic attacking pattern.
- ajkjk 3y ago
  Incidentally, that's one of those anecdotes that sounds deep but is really perfectly obvious if you play chess at a moderate level, or, like, ask someone who does. It would be much more surprising if it didn't work that way (chunking the board into patterns).

thorncorona 3y ago

> being good at math, especially mental math, correlates with aphantasia as someone who used to do math competitions as a kid, everyone I knew who was "good" at mental math had a good number sense, a big bag of tricks for doing different things with numbers, and practiced with their bag of tricks.

ajkjk 3y ago
I did math competitions also, but I'm not really talking about the specialized tricks like fast multiplication or square root algorithms. I'm just talking about basic stuff, like computing tips or taking percents. Most people simply cannot add or multiply numbers in their accurately, by any method.

ChainOfFools 3y ago

We are definitely aware of the same phenomenon! Check out a reply I made elsewhere in this thread which addresses compensatory recruiting of ones verbal/ audio immediate recall as an extension of working memory store.