zlacker

It's about as interesting as the other answers proposed in TFA, and it gets to the meat of it: they are all just representations invented by people, and there's nothing stopping us from inventing our own representations that fit into 64 bits (or 1 bit).

>>pphysc+(OP)
No, it doesn’t. The question is “what is the largest non-trivial number you can represent with some constraint on size of its expression”. It’s a really old question, and saying “infinity” as an answer misses the point. Saying you can invent an arbitrary number system also misses the point by simply not answering. If you need to spend a bunch of bytes explaining your new system, did you really use 8 bytes?

It just feels really bad faith.

>>toxik+06
What is "really bad faith" about saying "An ON bit indicates the value 'googolplex'?"

Computing is fundamentally about decoding bit strings as different arbitrary representations that are meaningful to humans.

>>pphysc+(OP)
Not really. The specialness of TFA's constructions is that the interpreter does not need to have any knowledge of the large numbers a priori.

>>pphysc+t7
Even the word "googolplex" is quite a bit longer than the lambda calculus program in question...

>>tromp+Zc
The actual bit is just 1 though, the word "googolplex" is in the accompanying documents for interpreting the bit.

The course on reading and using lambda calculus is similarly longer than than the actual lambda calculus expression

>>dumbo-+M7
Alternative contructions don't have to either - eg. "The bit 1 represents running the algorithm from TFA"

>>8note+Ie
That's precisely identical to declaring the number in the interpreter.

>>8note+ue
> The course on reading and using lambda calculus is similarly longer than than the actual lambda calculus expression

I'm not sure what a "course on reading and using" has to do with description complexity? In any case, it takes 206 bits to implement a binary lambda calculus interpreter (that's Theorem 1 in http://tromp.github.io/cl/LC.pdf )