Which is what makes the headline bait. We start with "The largest number representable in 64 bits" (which obviously depends on the representation, and as the baited comments point out, if that's freely settable, we can just set it arbitrarily high). But the body then moves the goalposts to "using a Turning machine", "using a Turing machine with specific parameters fixed", to "lambda calculus", etc.

This is now (at least) "The largest number representable by a Turning machine of fixed parameters that can then be squeezed into 64 bit."

(I don't remember my lambda calc, so … eh.)

So HN can't do this because I don't think it tracks all clicks but I've been of the opinion for a while that most social media should have the option for posts to not allow people to comment unless they've actually clicked on the link.

Surely you've been on HN long enough to know people just read the headline. Not that it would stop all sniping, but that headline doesn't even include "program" (or "compute").

An interesting follow-up question is, what is the smallest number unable to be encoded in 64 bits of binary lambda calculus?

Question: but how many different numbers can you fit in 64 bits using your encoding (sorry I understand the general approach but I have no idea how that fast hierarchy works). I guess it's still 2^64 different numbers?

So basically you have a very low density of representable numbers (2^64 / w218), I wonder how quickly it grows as you use more and more 1-bits, and is there even a correlation between the bit pattern and the corresponding number value?

I think "representable" is misleading. Nice post, though.