Imaging trying to determine the length of a fractal bounary, i.e. the length of a line with infinitely going number of "yet another smaller deviation of each of its segments from a smooth curve". Much like having a saw and adding a smaller copy of its teeth on the sides of each one ot it, then adding an even smaller copy on the sides of the already added yopies, and so on. So you get an infinitely "zig-zagged" line.
Many times the lenth of such a line is not finite (not as surpricing), many times it is not even definable (more surprising) and many other times... it can be calculated very easily. (Now, this is surprising!) BTW, though a line should always have a dimension of 1, such lines have... broken dimensions! Like for example 1.7 or 3/2 and similar. (Fractal comes from fracture, ey?) So, it is easy to think of one- and two- and three-dimensional things, but that we would also have 1.7-dimensional things is quite unexpected. Yet they are there.
Photographically it does have its problems again, but I am not sure what could be done better. What is the most important thing to improve here?
Yin and Yang, you say.... which in its most general form is: This and the other, ey? And so I aso have to wonder about something in mathematics, which is that in mathematics the "discovery" and the "invention" are... one and the same. It speaks about "other discoveries or inventions" like Yin and Yang, and it also speaks about its own self. And such things like the "natural abstraction" become self-contained.
Imagine, you generate the notion of "distance" which is based on the concept of a straight line, which itself is nothing else than having looked around "realizing" that "there is" something that has the "meaning" of a distance, and... now what? Did you "discovered" or did you "invented" that concept? The abstraction from the natural was surely there since you kept "only what is important" and neglected such things like "color" or "thickness", etc from the concept of distance, and that was great to do so! But in doing this you assumed first that it had a "natural meaning" which is somewhat troublesome, when you take into consideration that it was exactly the natural that you took for such an abstraction, and there is no "colorless" and "thicknessless" straight line in this nature. ;-)
So did you invented that or doid you discovered that? Mathematics goes the path of saying that... it doesn't matter. Such an invention or discovery exists within your mind, and so the distinction between the two is unnecessary.
Well... thanks a lot for inducing that stream into my mind, Avi!
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