ok. i figured out a way to prove my point.
if you took 100 ice creams and you said, how many different ways could these be arranged on a shelf? in other words, how many 'realities' could there be in terms of each of these ice creams having a particular place?
that would be 100 factorial, or 100 x 99 x 98 x 97 and down the line, which is obviously a lot.
if you took 100 ice creams and you said: a gold, silver and bronze medal will be given to three of these ice creams, how many possibilities would there be?
that would be 100 x 99 x 98 (three numbers for three places), which is obviously considerably less than the previous.
if you took 100 ice creams and you said, choose 100 ice creams out of these 100 ice creams. how many possibilities would there be? in other words, if their placement didn't matter at all, how many possibilities would there be? though the answer should be obvious, let's look at it mathematically:
that would be 100 x 99 x 98 x 97 and all the way down the line, divided by exactly the same: 100 x 99 x 98 x 97 and all the way down the line.
that only equals one possibility.
therefore, permutations vs. combinations proves that the whole point of hierarchy and contests may be to increase the number of imagined or possible 'realities' that can exist for all of us. without that, there would only be one reality: that in which we all simply 'are' and cannot escape from that existence.
but to emphasize the significance of place for every single one, vs. just three places, for example, increases the number of imagined or possible realities for all of us exponentially. and so this is a good mathematical example of the kind of scale - or values - that 'true imagination' requires.
some of this is obvious as spiritual concept, but i'm trying to memorize these math formulas
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