This is your brain on mathematics
anthonybonato.com
This is your brain on mathematics
1–10 of 25 posts
Re: This is your brain on mathematics
#2This will probably sound wacky but here's what I think:
There are two steps to conveying a thought in a language:
1. recall the grammar rules and vocabulary 2. form the sentence
The steps are fundamentally different in that the first one is an exercise in recollection whereas the second one is a "creative" process of some sort.
To prove a mathematical fact you go through the same two steps:
1. you recall all the past mathematical knowledge 2. you deduce the fact in a creative process of meshing together the facts you just recalled
So conveying a thought in a language is sort of analogous to proving a mathematical fact.
But clearly when doing math step 2 is given the spotlight whereas when you are talking in a foreign language step 1 is by far the hardest.
Re: This is your brain on mathematics
#3This will probably sound wacky but here's what I think: There are two steps to conveying a thought in a language: 1. recall the grammar rules and vocabulary 2. form the sentence The steps are fundamentally different in that the first one is an exercise in recollection whereas the second one is a "creative" process of some sort. To prove a mathematical fact you go through the same two steps: 1. you recall all the past…
just out of curiosity, how many human languages do you speak fluently?
Re: This is your brain on mathematics
#4This will probably sound wacky but here's what I think: There are two steps to conveying a thought in a language: 1. recall the grammar rules and vocabulary 2. form the sentence The steps are fundamentally different in that the first one is an exercise in recollection whereas the second one is a "creative" process of some sort. To prove a mathematical fact you go through the same two steps: 1. you recall all the past…
just out of curiosity, how many human languages do you speak fluently?
3
Re: This is your brain on mathematics
#5This will probably sound wacky but here's what I think: There are two steps to conveying a thought in a language: 1. recall the grammar rules and vocabulary 2. form the sentence The steps are fundamentally different in that the first one is an exercise in recollection whereas the second one is a "creative" process of some sort. To prove a mathematical fact you go through the same two steps: 1. you recall all the past…
With spoken languages, don't you typically get to the point where #1 is a no-op? I don't ever do it consciously in English. I rarely do it in French. I often spend far more cycles on determining the correct vocabulary for what I want to say.
Re: This is your brain on mathematics
#6This will probably sound wacky but here's what I think: There are two steps to conveying a thought in a language: 1. recall the grammar rules and vocabulary 2. form the sentence The steps are fundamentally different in that the first one is an exercise in recollection whereas the second one is a "creative" process of some sort. To prove a mathematical fact you go through the same two steps: 1. you recall all the past…
I think it would be more accurate to say there are 3 steps in both:
1) Recall the grammar/rules of the output language (for both natural language and formal languages).
2) Form the idea of what it is you want to express in your head using your internal language (usually your first natural language).
3) Encode the idea you have in your mind using the formal rules from step 1.
Step 1 is usually internal and subconscious for natural languages that you can communicate in freely and to an extent this is even the case for other languages and even programming languages.
For your first natural language, step 1 is usually done behind the scenes by your brain automatically, or these rules are already present in your brain in a usable form, and step 3 is trivial because you are just expressing the idea which is already in this language in your mind.
Re: This is your brain on mathematics
#7This will probably sound wacky but here's what I think: There are two steps to conveying a thought in a language: 1. recall the grammar rules and vocabulary 2. form the sentence The steps are fundamentally different in that the first one is an exercise in recollection whereas the second one is a "creative" process of some sort. To prove a mathematical fact you go through the same two steps: 1. you recall all the past…
With spoken languages, don't you typically get to the point where #1 is a no-op? I don't ever do it consciously in English. I rarely do it in French. I often spend far more cycles on determining the correct vocabulary for what I want to say.
I didn't mean to imply that the steps are done consciously.
What I meant was that there is more recalling involved (more of step 1) when you want to say something than when you want to prove something. Of course you are not aware of it. The brain does it subconsciously.
Re: This is your brain on mathematics
#8Earlier quoted context omitted.
With spoken languages, don't you typically get to the point where #1 is a no-op? I don't ever do it consciously in English. I rarely do it in French. I often spend far more cycles on determining the correct vocabulary for what I want to say.
I didn't mean to imply that the steps are done consciously. What I meant was that there is more recalling involved (more of step 1) when you want to say something than when you want to prove something. Of course you are not aware of it. The brain does it subconsciously.
Curious, because I'm not a mathematician: is it typical to say "proof" something versus "prove" something? I noticed you used that twice now. My brain keeps autocorrecting it, but I'm ignorant and would love to update my rules if needed. :)
Re: This is your brain on mathematics
#9Earlier quoted context omitted.
I didn't mean to imply that the steps are done consciously. What I meant was that there is more recalling involved (more of step 1) when you want to say something than when you want to prove something. Of course you are not aware of it. The brain does it subconsciously.
Curious, because I'm not a mathematician: is it typical to say "proof" something versus "prove" something? I noticed you used that twice now. My brain keeps autocorrecting it, but I'm ignorant and would love to update my rules if needed. :)
No. I make that typo all the time though. It's just that due to my accent I do not differentiate between "prove" and "proof" and always voice the words as "proof" so I always write "proof".
Re: This is your brain on mathematics
#10This will probably sound wacky but here's what I think: There are two steps to conveying a thought in a language: 1. recall the grammar rules and vocabulary 2. form the sentence The steps are fundamentally different in that the first one is an exercise in recollection whereas the second one is a "creative" process of some sort. To prove a mathematical fact you go through the same two steps: 1. you recall all the past…
Have you ever listened to humans talk? Most sentences are improper, they're riddled with disfluencies, and usually they don't even finish what they're saying.