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The largest number representable in 64 bits

tromp.github.io

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Re: The largest number representable in 64 bits

#71

Post by xelxebar »

Busy Beaver gets a lot of love, but the fast growing hierarchy is both constructive and can go way, way, waaaaay beyond current known BB bounds. This makes their size much more viscerally apparent than gesturing vaguely at BB(BB(BB(100))) or whatever, IMHO.

David Metzler has this really cool playlist "Ridiculously Huge Numbers" that digs into the details in an accessible way:

https://www.youtube.com/playlist?list=PL3A50BB9C34AB36B3

By the end, you're thinking about functions that grow so fast TREE is utterly insignificant. Surprisingly, getting there just needs a small bit of machinery beyond Peano Arithmetic [0].

Then you can ponder doing all that but making a tiny tweak by replacing succesorship with BB. Holy cow...

[0]:https://en.wikipedia.org/wiki/Theories_of_iterated_inductive...

Re: The largest number representable in 64 bits

#72

Post by tdb7893 »

ShroudedNight wrote: post #67
tdb7893 wrote: post #65

Earlier quoted context omitted.

Are you talking about that people could just click on the link then not actually read it? The thing is that clicking on the link then closing is serves as both a slight barrier to entry targeted at the people who comment without reading and also a reminder that there is an actual article to comment on. It's not going to fix discourse but the theory behind it is to be a slight nudge to get people who don't click to at…

Wouldn't browser prefetching subvert these small frictions to entry?

I think I've seen sites trying to track outbound clicks recently, has prefetching made that impossible? I don't know the implementation but I've seen the browser sending requests that track clicks while investigating other stuff (idk whether it's working accurately though).

Edit: to be clear, it's not like I've researched this proposal since I don't work for social media companies. It's just a feature I wish I could have on my posts.

Re: The largest number representable in 64 bits

#74

Post by [deleted] »

tromp wrote: post #32

Please no more comments to the extent of "i can define a much larger number in only 1 bit". What makes my blog post (hopefully) interesting is that I consider tiny programs for computing huge numbers in non-cheating languages, that are not specifically equipped for doing so.

[deleted]

Re: The largest number representable in 64 bits

#75

Post by librecell »

i take so much for granted.

every time i’m hacking around with no idea what the program might be, i really should be working on a “thank you, world!” program,

to cultivate gratitude and humility

all those whose work has made it such that i can say “hellos commonlisp what is the most positive fixnum or word or whatever!” or totally not even think about that let alone complex allocations that seem to happen automatically relative to me

they’re cool as f**! i should do well not to forget this.

thank you for sharing

Re: The largest number representable in 64 bits

#76

Post by omoikane »

tromp wrote: post #32

Please no more comments to the extent of "i can define a much larger number in only 1 bit". What makes my blog post (hopefully) interesting is that I consider tiny programs for computing huge numbers in non-cheating languages, that are not specifically equipped for doing so.

A better title might have been "fastest growing function with 64bit arguments". The main value of this article is really the various functions that take larger strides to cover a finite range that's significantly larger than 2^64-1.

Re: The largest number representable in 64 bits

#77

Post by pinkmuffinere »

cortesoft wrote: post #3

This feels like the computer science version of this article: https://www.scottaaronson.com/writings/bignumbers.html

> You have fifteen seconds. Using standard math notation, English words, or both, name a single whole number—not an infinity—on a blank index card. Be precise enough for any reasonable modern mathematician to determine exactly what number you’ve named, by consulting only your card and, if necessary, the published literature.

Lol, we used to do this with my (extremely nerdy) friends group in college when we 'inducted' new members! I never knew that it was from something, I just thought it was tradition. We had some great entries -- a circle of nines with no beginning and ending, a very good drawing of a wolf, many protest entries, somebody accidentally wrote 1^1^1^1^1^... before realizing their folly, etc. Great times.

Re: The largest number representable in 64 bits

#78

Post by ted_dunning »

bmacho wrote: post #18
tromp wrote: post #14

Earlier quoted context omitted.

To find the largest number that is computable by a program of at most 64 bits in a non-cheating language; i.e. one that's not geared toward producing large numbers.

Do you have a mathematical formulation, or? Ultimately you seem to pick a random definition of computing and size and then work with that?

The article described why the choices were neither random nor particularly arbitrary.

Re: The largest number representable in 64 bits

#79

Post by cwillu »

cortesoft wrote: post #3

This feels like the computer science version of this article: https://www.scottaaronson.com/writings/bignumbers.html

I get what you're trying to say, but the computer science version of that article is very clearly https://www.scottaaronson.com/papers/bb.pdf
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