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Not disagreeing, but just to add on the other side of the coin: language can be a driver for thought and ideas. This might feel wishywashy without an example, b

Not disagreeing, but just to add on the other side of the coin: language can be a driver for thought and ideas. This might feel wishywashy without an example, but I usually feel that I need to reinterpret algebraic manipulation that I have done to understand what significance they have. So in a way, I allowed myself to be a mechanical executer through the rules of algebra/calculus I've used, and then I re-engaged my intuition to understand what is happening. It might even be my unwillingness to accept the mechanical approach purely that poses a big hindrance to fast tracking a lot of learning in this domain I have to do. Maybe I should just shut up and calculate as they say, but it's hard. This just makes it all the more true that learning "languages" is the best way to become smarter. "Smarter" is a weird personal word here, but I'm at a loss for a better way to put it. What am going for is: languages can be an abstract lever that allows our limited cognitive potential to build culturally, which is distinct and will definitely interact with the knowledge ladder, but in a distinct way. "Languages" here are more general than just the textual/oral/syntactic, and am not talking about Russian/Arabic/French either.

TuringTest 7y ago
> I usually feel that I need to reinterpret algebraic manipulation that I have done to understand what significance they have. So in a way, I allowed myself to be a mechanical executer through the rules of algebra/calculus I've used, and then I re-engaged my intuition to understand what is happening. That's a sensible approach, but it works because you're executing mechanical in a well-defined problem domain, so there's an intuition attached to each term used, and you can build an overall intuition. You might as well use random mechanical transformations over an algebra and they wouldn't make any sense, just like if you attached random dictionary words forming grammatically correct sentences. I see usage of formal languages as mathematicians and philosophers making "very precise sentences", i.e. being extremely precise with the meaning attached to each term so that it remains consistent among all the transformations of discourse (in fact, there's a formal theory of meaning which does exactly that). But the main value of such exercise is in knowing what you want to express, not in the fact that you're being extremely precise while doing it; the latter can help you convince others of what you're saying, but they need to agree to the original axioms of your theory, otherwise they'll just be able to point very precisely where they think you are wrong.

TuringTest 7y ago

> I usually feel that I need to reinterpret algebraic manipulation that I have done to understand what significance they have. So in a way, I allowed myself to be a mechanical executer through the rules of algebra/calculus I've used, and then I re-engaged my intuition to understand what is happening. That's a sensible approach, but it works because you're executing mechanical in a well-defined problem domain, so there's an intuition attached to each term used, and you can build an overall intuition. You might as well use random mechanical transformations over an algebra and they wouldn't make any sense, just like if you attached random dictionary words forming grammatically correct sentences. I see usage of formal languages as mathematicians and philosophers making "very precise sentences", i.e. being extremely precise with the meaning attached to each term so that it remains consistent among all the transformations of discourse (in fact, there's a formal theory of meaning which does exactly that). But the main value of such exercise is in knowing what you want to express, not in the fact that you're being extremely precise while doing it; the latter can help you convince others of what you're saying, but they need to agree to the original axioms of your theory, otherwise they'll just be able to point very precisely where they think you are wrong.