Yeah, I do understand your point of view. I'm just doubting if it applies universally, like you may superimpose that assumption on the thinking caveman, but is the thinking caveman really doing the same?
Yes, technique is one thing, but being really good at throwing spears doesn't make you really good at math, is my argument. And most people will encounter maths in a formal setting while lacking the broader perspective that everything is technically "math".
Yet, we need to see the argument from the common person's view, if we're talking about calculus and learning in the traditional sense. The view you stated is quite esoteric and doesn't generalize well in this setting imo.
It's like a musician saying they see music in every action, but to most non-musicians (even if the stated thing is kind of true) that doesn't make a lot of sense etc.
> but is the thinking caveman really doing the same?
Are you projecting a continuous space onto a binary one? You'll need to be careful about your threshold and I'm pretty sure it'll just make everything I said complete nonsense. If you must use a discrete space then allocate enough bins to recognize that I clearly stated there's a wide range of rigor. Obviously the caveman example is on the very low end of this.
> It's like a musician saying they see music in every action, but to most non-musicians (even if the stated thing is kind of true) that doesn't make a lot of sense etc.
Exactly. So ask why the musician, who is certainly more expert than the non-musician has a wider range? They have expertise in the matter, are you going to just ignore that simply because you do not understand? Or are you going to try to understand?
The musician, like the mathematician, understands that every sound is musical. If you want to see this in action it's quite enlightening[0]. I'm glad you brought up that comparison because I think it can help you understand what I really mean. There is depth here. Every human has access to the sounds but the training is needed to put them together and make these formulations. Benn here isn't exactly being formal writing his music using a keyboard and formalizing it down to musical notes on a sheet (though this is something I know he is capable of).
Learn the rules like a pro, so you can break them like an artist.
His abstract nature to a novice looks like something they could do (Jackson Pollocks is a common example) but he would have told you he couldn't have done this without first mastery of the formal art first.
I know this is confusing and I wish I could explain it better. But at least we can see that regardless of the field of expertise we find similar trains of thought. Maybe a bridge can be created by leveraging your own domain of expertise
Maybe I can put it this way: gibberish is more intelligible when crafted by someone who can already speak.
Yes, technique is one thing, but being really good at throwing spears doesn't make you really good at math, is my argument. And most people will encounter maths in a formal setting while lacking the broader perspective that everything is technically "math".
Yet, we need to see the argument from the common person's view, if we're talking about calculus and learning in the traditional sense. The view you stated is quite esoteric and doesn't generalize well in this setting imo.
It's like a musician saying they see music in every action, but to most non-musicians (even if the stated thing is kind of true) that doesn't make a lot of sense etc.