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> This sounds like being familiar with an example of an abstract idea is as ["pretty much" as] useless as not knowing anything about it Right! > I am not pers

> This sounds like being familiar with an example of an abstract idea is as ["pretty much" as] useless as not knowing anything about it Right! > I am not persuaded that thinking concretely is akin to rejecting abstractions, as you seem to be. I'm not arguing against thinking concretely. I'm arguing against highlighting the syntax of English sentences and math formulas just because some people couldn't parse them, let alone semantically analyze them, otherwise. > Notice that in the course of your argument, you keep bringing concrete math examples to make your point. Of course. As I previously said, examples serve to illustrate a general concept. > it's a pretty trivial idea to show which parts of a natural language phrase correspond to (...) Indeed. > You can do it with colors, or gesturing, or whatever. You can do it with your brain. > Your WORD for a number causes you to be faster or slower at arithmetic. So I think using unfamiliar symbols might also make a difference. Um, wat. Operating on a number doesn't require thinking of the word you use for that number. > However, even in the realm of natural language, humans will have a hard time understanding utterances with nested quantifiers, negation, and clauses. And they systematically let people graduate from high school in this pathetic state? Maybe I got it wrong: Don't sue your elementary school. Sue your country's education ministry.

gugagore 9y ago
> And they systematically let people graduate from high school in this pathetic state? You're being nasty. There's nothing pathetic about recognizing that almost everyone experiences limits in their cognition. If you don't, then that must be very nice. Perhaps you misunderstood. People can understand a sentence with a few levels of negation, quantification, embedded clauses, but not too many. And sentences in math are often more complex than sentences in casual speech. You made a bold claim that math syntax is equivalent to natural language syntax, and I am demonstrating why that claim is wrong, or at best not relevant to coloring math expressions. I understand you are claiming they are formally be the same (who knows, since no one has completely formalized "The Math Language" or probably any natural language, but I understand your point in the context of baby first order logic syntax). And I am claiming that that doesn't matter. > I'm arguing against highlighting the syntax of English sentences and math formulas just because some people... No one is saying you should colorize every textbook or every anything, so I don't understand what you are arguing. > You can do it with your brain. Yeah, and you need to feed your brain some input. There are lots of ways you can encode the same information. If you suddenly no longer had vision, someone could read to you unambiguously every math expression you needed, but I bet you're going to suffer a hit in your math performance. Despite using your brain. > Um, wat. Operating on a number doesn't require thinking of the word you use for that number. Obviously. A computer operates on a number without having a "word" for a number. (Well...). And some humans are better at being computers than other humans. That's not responding to my point that shows that people must be thinking about words, because you can measure delays when the words aren't very good, like the number words in German or French. Yeah, I agree it's "Um, wat" in an interesting way, but I fear you're just dismissing it.

gugagore 9y ago

> And they systematically let people graduate from high school in this pathetic state? You're being nasty. There's nothing pathetic about recognizing that almost everyone experiences limits in their cognition. If you don't, then that must be very nice. Perhaps you misunderstood. People can understand a sentence with a few levels of negation, quantification, embedded clauses, but not too many. And sentences in math are often more complex than sentences in casual speech. You made a bold claim that math syntax is equivalent to natural language syntax, and I am demonstrating why that claim is wrong, or at best not relevant to coloring math expressions. I understand you are claiming they are formally be the same (who knows, since no one has completely formalized "The Math Language" or probably any natural language, but I understand your point in the context of baby first order logic syntax). And I am claiming that that doesn't matter. > I'm arguing against highlighting the syntax of English sentences and math formulas just because some people... No one is saying you should colorize every textbook or every anything, so I don't understand what you are arguing. > You can do it with your brain. Yeah, and you need to feed your brain some input. There are lots of ways you can encode the same information. If you suddenly no longer had vision, someone could read to you unambiguously every math expression you needed, but I bet you're going to suffer a hit in your math performance. Despite using your brain. > Um, wat. Operating on a number doesn't require thinking of the word you use for that number. Obviously. A computer operates on a number without having a "word" for a number. (Well...). And some humans are better at being computers than other humans. That's not responding to my point that shows that people must be thinking about words, because you can measure delays when the words aren't very good, like the number words in German or French. Yeah, I agree it's "Um, wat" in an interesting way, but I fear you're just dismissing it.