5 ms·

So, a few question to all the number-as-shapes-in-head-representators out there: What happens in front of your inner eye when you do more complicated operations

So, a few question to all the number-as-shapes-in-head-representators out there: What happens in front of your inner eye when you do more complicated operations like exponentials, modulo, ...? Do you have distinct visualisation for certain ways to represent a number (roots, fractions and so on) too? And do these representations help you when you solve a problem where you don't have to "count" anything, like when you have to write a proof or something?

hamaluik 5y ago
I don't see things the exact same way as the author, though similar (simplest way I could describe it is things like addition are filling up tanks of liquid of [usually] 10^n size, though a little more amorphous and yet "jelly" than what you would normally think of as liquid? I'm finding it hard to describe). Exponentials get represented as a third dimension; where basic arthimetic is 1 or 2d depending on the context, exponentials go into a third dimension if that makes sense. Modulo is the leftovers / splash-out when I pour one number into several smaller containers. Fractions are simply fractional amounts of a tank of liquid (i.e. 2/3 is simply a measuring cup filled to the 2/3 line type of thing), but I can't ever picture them very accurately for weird fractions. "Improper" fractions are basically the same as modulo.. almost as if they're unstable in my head and automatically "pour" themselves into more tanks that fill as needed until some remainder is left. I don't have a visualization for roots, which is probably why I'm generally so bad at them. The representations helped in engineering school for getting a "feeling" about a formula; it was often very easy to notice if an equation I was massaging had gone off the rails. For a pure proof however (not that I did much of that), it was useless.
- deleted 5y ago
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- drBonkers 5y ago
  Can you tell me more about your visualization of exponentiation? Your modulo visualization helps me, I think.
pramodbiligiri 5y ago
There's a book which describes studies done on this topic [1]. I haven't read it in full, but I found it useful to know how other people have looked at this issue. [1] - https://www.amazon.in/Visual-Thinking-Mathematics-Marcus-Giaquinto/dp/0199575533 https://www.amazon.in/Visual-Thinking-Mathematics-Marcus-Gia...

hamaluik 5y ago

I don't see things the exact same way as the author, though similar (simplest way I could describe it is things like addition are filling up tanks of liquid of [usually] 10^n size, though a little more amorphous and yet "jelly" than what you would normally think of as liquid? I'm finding it hard to describe). Exponentials get represented as a third dimension; where basic arthimetic is 1 or 2d depending on the context, exponentials go into a third dimension if that makes sense. Modulo is the leftovers / splash-out when I pour one number into several smaller containers. Fractions are simply fractional amounts of a tank of liquid (i.e. 2/3 is simply a measuring cup filled to the 2/3 line type of thing), but I can't ever picture them very accurately for weird fractions. "Improper" fractions are basically the same as modulo.. almost as if they're unstable in my head and automatically "pour" themselves into more tanks that fill as needed until some remainder is left. I don't have a visualization for roots, which is probably why I'm generally so bad at them. The representations helped in engineering school for getting a "feeling" about a formula; it was often very easy to notice if an equation I was massaging had gone off the rails. For a pure proof however (not that I did much of that), it was useless.

deleted 5y ago
[deleted]
drBonkers 5y ago
Can you tell me more about your visualization of exponentiation? Your modulo visualization helps me, I think.

pramodbiligiri 5y ago

There's a book which describes studies done on this topic [1]. I haven't read it in full, but I found it useful to know how other people have looked at this issue. [1] - https://www.amazon.in/Visual-Thinking-Mathematics-Marcus-Giaquinto/dp/0199575533 https://www.amazon.in/Visual-Thinking-Mathematics-Marcus-Gia...