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 Originally Posted by OngBonga
Take pi as an example. This is a number that is directly related to the number 1 in that pi is the circumference of a circle with a diameter of 1. Since pi is famously irrational, there is no way of perfectly visualising this ratio. Thus, in a quantised universe, pi is an impossible number. Perfect circles don't exist. This is philosophy.
But 1 exists, and so does 2. No philosophy required, no mental gymnastics. Just quantised energy, actual physical matter.
I guess I get where you're coming from, but it still doesn't seem like a proof to me.
If an empty set exists, then I can imagine an empty set within that empty set, and I have created nothing, nor invoked a universe or atoms or energy levels. All that requires is that I can imagine partitioned nothingness. If partitioned nothingness isn't an absolutely absurd idea, then IDK what is.
Nonetheless, that's all we need. Anything which can springboard us into a constructing a sequence. Nesting empty sets within empty sets and labeling their "nested depth" is adequate. All we need is a notion of sequence. What we call each step in the sequence becomes the number line, whether it's one, two, three, or eins, tzwei, drei, or whatever.
From that you get all of math. Not exactly, but you get addition, subtraction, multiplication, division, exponentiation, complex numbers, rationals, irrationals, etc. You don't get *all* of math, but you get a nice huge chunk of it.
But still, using numbers is a sapient way of understanding things. What's to say it isn't some defect in humanity that keeps us from seeing that everything truly is 1, as many spiritual leaders have assured us..?
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