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> Took me way too long to figure out that signal just means function. If I was going to teach Fourier concepts, I would have no problem talking about signals i
by lutusp 13y ago
> Took me way too long to figure out that signal just means function.
If I was going to teach Fourier concepts, I would have no problem talking about signals initially, at the stage when I wanted the students to acquire an intuitive grasp of the topic before discussing the technical aspects.
But I think that way about most mathematical topics -- I think creating a visual analogue of, as well as some enthusiasm for, a topic is a very desirable first step as we move toward the formal and disciplined part.
- j2kun 13y agoThis is exactly why I struggle to learn physics. I get intuition by playing with the mathematical objects themselves, not by guessing what their interpretations might do in the wild (guided by other, unrelated, and likely wrong intuition). But then again I have trained myself to go into new situations devoid of intuition so I don't confuse myself.
- lutusp 13y ago> I get intuition by playing with the mathematical objects themselves, not by guessing what their interpretations might do in the wild ... This is why string theory is in such a mess -- too much focus on the mathematical, too little on the physical. At the moment, string theory can explain anything, including any number of imaginary universes. It's worth remembering that Einstein (in a manner of speaking) pictured his theories before turning them into mathematics, and made frequent uses of the gedankenexperiment (thought experiment) approach, in which he would imagine a physical embodiment for an idea to see how it held up. Obviously in modern times, the mathematical form of a theory is the bottom line and cannot be dismissed. But to have significance in reality it should be partnered with a very clear physical analogue.