"Everything that exists must be implemented" -> fascinating statement! “The trouble is, you think you have time.” – Fake Buddha Quote ;)
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"infinity leads to ugly outcomes" >> this is the heart of where we disagree. Infinity is the perfect elegance (and ugliness etc.) - how i see it.
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Infinity is a wonderful tool if you want to make stuff, a cornucopia: shake it a little, and things fall out of it without limit, but it is also infinitely hard to make by itself. No finite process can create an infinity, but once you have it, you can easily create universes.
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I agree regarding axiomatic systems. Regarding the world, I‘m less sure.
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How would you scrape an infinite amount of bits via your observational interface?
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