Does the use of the word signal spawn from its application in communications theory? I've never found it strange using the word signal but it might be because of my EE background. Frequency domain and time domain never irked me either :/

"Signal" has always bugged me because it has the connotation of a function of time, whereas historically the Fourier series were first used to represent functions of space.

But the point is that the transform shows you two representations, one time-based, the other frequency-based, of the same signal.

And notice that time is a component in each of these.

It doesn't need to be time- and frequency- based. For example in quantum mechanics you transform from position to momentum space. I think the complaint was that the word "signal" excludes this later case while "function" is more general.

EE here, same for me. Although, it is true that the first two classes of my signal theory course consisted entirely of restating high school results, with "signal" replaced for "function"...

Function to me implies something with known characteristics. I suppose this is true when performing analytic FTs, but I think signal makes more sense when dealing with unknown inputs and numerical solutions. Regardless the relationship (or distinction) should be made clear when learning!

This is a good distinction to make. The term "signal" implies an information carrier (as in the expression "the signal in the noise"), which in light of information theory can be interpreted to mean an unknown variation (as modelled by, e.g. a stochastic process). This is philosophically distinct from the interpretation of a mathematical function as analytically defined and completely known.

Except that EEs like to explicitly restrict the word "signal" to mean only the known inputs, and call the rest "noise."

s/known inputs/desired outputs/ ?

> 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.

This 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.

> 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.