[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 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.

An example of an interesting computation requiring a vast finite computer is AIXI-tl.]

An 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.

We 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. 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.

Thus, in a practical sense, computations that would require sufficiently large finite amounts of computation are pragmatically equivalent to computations that require 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.

An example of an interesting computation requiring a vast finite computer is AIXI-tl, or Andrew Critch's parametric bounded analogue of Lob's Theorem.