A digitizable theory, a theory that can be represented by using discrete digits, like for example the letters and numbers in equations or in theorems. And the continuum, the non discrete kind of... something, in which everything goes arbitrarily "smoothly". (Notice: not infitinitely smoothly but arbitrarily smoothly - this is way not the same, and that's a common mistake than many physicists do so many times!) And perhaps it is just because all our theories are digitizable after all, that they can't really grasp the continuum.
Much like here. You could turn the "digits", the small squares of the "coordinates system" as small as you wish, but they are still not able to really grasp the circle. You just get a more or less "pixelated curve", nor a real arbitrarily smooth one.
Jump over to photography and think again about digital and analog. No, not for damning the digital technology, not at all. For even analog photography was never really analog. Its "digits" are the light absorbing molecules that form the bilf at the end. There is nothing "finer" than them, and since quantum dynamics we alll know that the whole world is digital. The digits are so small that we perceive them as "continuous", but they are discrete in reality. And nonetheless we thought of that kind of perfect thing, called "the continuum", and we search for its nature, even if it is only a product of our minds. We use "real numbers", like for example π (3.14......), that are generated by the idea of the existence of perfectly "continuous" circles, and we stand astound in front of what we already found of them.
Perhaps the analog photography could be said to be exactly this: The search for a world of which we know that we will never find. But it is worthy to be searched.
I know that you talk the pure truth always when you say what you think, Yazeed. It is only that I find some disadvantages here too, like for example that kind of "absence of good contures", which may also be just my own impression. Anyway, thanks a lot.
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