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text: '[summary: An unphysically large finite computer is one that's vastly larger than anything that could possibly fit into our universe. In a practical sense, computations that would require sufficiently large finite amounts of computation are pragmatically equivalent to computations that require [1mk hypercomputers], and serve a similar purpose in unbounded analysis: they let us talk about interesting things and crisply encode relations that might take a lot of unnecessary overhead to describe using *small* finite computers. Nonetheless, since there are some mathematical pitfalls of considering infinite cases, reducing a problem to one that only requires a vast finite computer can sometimes be an improvement.\n\nAn example of an interesting computation requiring a vast finite computer is [1ml].]\n\nAn unphysically large finite computer is one that's vastly larger than anything that could possibly fit into our universe, if the *character* of physical law is anything remotely like it seems to be.\n\nWe might be able to get a googol ($10^{100}$) computations out of this universe by being clever, but to get $10^{10^{100}}$ computations would require outrunning proton decay and the second law of thermodynamics, and $9 \\uparrow\\uparrow 4$ operations ($9^{9^{9^9}}$) would require amounts of computing substrate in contiguous internal communication that wouldn't fit inside a single [Hubble Volume](https://en.wikipedia.org/wiki/Hubble_volume). Even tricks that permit the creation of new universes and encoding computations into them probably wouldn't allow a single computation of size $9 \\uparrow\\uparrow 4$ to return an answer, if the character of physical law is anything like what it appears to be.\n\nThus, in a practical sense, computations that would require sufficiently large finite amounts of computation are pragmatically equivalent to computations that require [1mk hypercomputers], and serve a similar purpose in unbounded analysis - they let us talk about interesting things and crisply encode relations that might take a lot of unnecessary overhead to describe using *small* finite computers. Nonetheless, since there are some mathematical pitfalls of considering infinite cases, reducing a problem to one guaranteed to only require a vast finite computer can sometimes be an improvement or yield new insights - especially when dealing with interesting recursions.\n\nAn example of an interesting computation requiring a vast finite computer is [1ml], or [131]'s [parametric bounded analogue of Lob's Theorem](http://intelligence.org/files/ParametricBoundedLobsTheorem.pdf).',
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