[HN Gopher] The largest number representable in 64 bits
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       The largest number representable in 64 bits
        
       Author : tromp
       Score  : 43 points
       Date   : 2023-04-23 15:37 UTC (7 hours ago)
        
 (HTM) web link (googology.fandom.com)
 (TXT) w3m dump (googology.fandom.com)
        
       | repsilat wrote:
       | TFA neglected to mention that floats have an "infinity" value,
       | quite a bit larger than any 64 bit busy-beaver.
       | 
       | (And before anyone says it's not a number, call `isnan` with an
       | infinity and get back to me :)
        
         | SAI_Peregrinus wrote:
         | I don't believe IEEE 754 specifies _which_ infinities it
         | encodes as its positive and negative infinity. I 'd tend to
         | treat it as the surreal equivalence class {0,1,2...|}, but it
         | might be any of the others.
        
           | stephencanon wrote:
           | IEEE 754 is very clear that the infinities are the endpoints
           | of the extended real line (and hence also the extended
           | integers, which matches your assumption).
        
             | SAI_Peregrinus wrote:
             | Thanks, clearly it's been too long since I read the spec.
        
         | tromp wrote:
         | Fixed:-)
        
         | IEEE754 wrote:
         | Correct.
        
           | petters wrote:
           | Username checks out. There is an other article about fp32 vs
           | fp16 the front page for you as well!
        
       | jll29 wrote:
       | One large number that fits in 64 bits is:
       | F^^^^^^F = 15 ^ .... ^ 15       12345678       [8*8=64 bit]
       | 
       | According to Conway and Guy (1996) The Book of Numbers, p. 60,
       | the arrow notation, defined by Knuth in (1976), is such that
       | m^n is  m x m x ...x m,       m^^n is m^m^ ...^m,       m^^^n is
       | m^^m^^ ... ^^m,
       | 
       | and so on, with n copies of m in each case, and the expression
       | being evaluated from the right.
        
         | tromp wrote:
         | That is however inconceivably smaller than the number in the
         | article, which exceeds Graham's number.
        
       | pipo234 wrote:
       | The intro got me thinking of MDL model selection. I.e. to express
       | X you can choose a language L that can represent X, and rather
       | than focusing on the conciseness of just L(X) (which for some
       | powerful L might be a single bit) it's more fair to also take the
       | length of the language itself into account.
       | 
       | Then this question would be rephrased as something along the
       | lines of "what language would fit into 64 bits and leave enough
       | enough bits to describe a huge value in that language? And which
       | would represent the largest value?"
       | 
       | https://en.wikipedia.org/wiki/Minimum_description_length
        
         | tromp wrote:
         | That just begs the question: in what language do you describe
         | the language L? In terms of features, the language I use was,
         | together with combinatory logic, the first language ever
         | proposed for formalising computation back in the 1930s, so it's
         | about as non-arbitrary as can be...
        
           | pipo234 wrote:
           | Very good point!
        
       | mcdonje wrote:
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       | 
       | If you don't want to host your own blog, consider putting it on
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         | Fandom/Wikia is so bad that I have to use lynx or something
         | like textise.net to browse it on mobile without uBlock Origin.
        
           | rootw0rm wrote:
           | My addon collection for Firefox nightly consists of ublock
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           | Here's the custom collection info for anybody who wants to
           | use it:
           | 
           | 16881813
           | 
           | xenoglyph
        
           | Asooka wrote:
           | I personally use Fennec with uBlock on mobile.
        
         | networked wrote:
         | There is an alternative front end for fandom.com called
         | BreezeWiki. It is open source (written in Racket!), and like
         | with other open source alternative front ends, volunteers run
         | their own instances. Here is the story link on one instance:
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         | https://antifandom.com/googology/wiki/User_blog:JohnTromp/Th...
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         | BreezeWiki source code: https://gitdab.com/cadence/breezewiki.
        
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         | ummonk wrote:
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       (page generated 2023-04-23 23:01 UTC)