[HN Gopher] Loader's Number
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Loader's Number
Author : lisper
Score : 52 points
Date : 2025-04-05 16:18 UTC (6 hours ago)
(HTM) web link (googology.fandom.com)
(TXT) w3m dump (googology.fandom.com)
| tromp wrote:
| Last year I ported Loader's construction to Haskell [2] in order
| to better understand it, and managed to shrink the code down to
| under 232 bytes [1]. That work was also featured in a video that
| youtuber CodeParade made about the Quest To Find The Largest
| Number and its followup [3].
|
| [1]
| https://github.com/tromp/AIT/blob/master/fast_growing_and_co...
|
| [2] https://codegolf.stackexchange.com/questions/176966/golf-
| a-n...
|
| [3] https://www.youtube.com/watch?v=kQLcoSuMKHg&t=10s
| rvnx wrote:
| In that thread, I see for example, another challenge linked on
| that page:
|
| > Write the shortest possible program (length measured in
| bytes) satisfying the following requirements:
|
| > infinite memory and runtime
|
| > no input
|
| > output is to stdout
|
| > execution eventually terminates
|
| > total number of output bytes exceeds Graham's number
|
| This sounds like a loop and that's it ?
|
| I'm struggling to see the challenge or discovery there ?
| zimpenfish wrote:
| Given (from what I remember from Numberphile) you can't write
| Graham's number down in the observable universe, how are you
| going to make sure that the loop terminates after outputting
| Graham's number of bytes? Because you definitely can't put
| `if count > G` in there...
| rvnx wrote:
| Ok, that makes it much more interesting, I get it now. It's
| the "execution eventually terminates" that is tricky. Thank
| you!
| knome wrote:
| >it is so large that the observable universe is far too small
| to contain an ordinary digital representation of Graham's
| number, assuming that each digit occupies one Planck volume,
| possibly the smallest measurable space. But even the number
| of digits in this digital representation of Graham's number
| would itself be a number so large that its digital
| representation cannot be represented in the observable
| universe. Nor even can the number of digits of that number--
| and so forth, for a number of times far exceeding the total
| number of Planck volumes in the observable universe
|
| How do you write the halt condition for your loop in the
| minimal number of bytes?
| tromp wrote:
| Amazingly, this can be done in literally a bit over 6 bytes,
| shorter than an empty for-loop in many languages...
| HumanOstrich wrote:
| Can you provide any examples?
| HeliumHydride wrote:
| https://codegolf.stackexchange.com/a/263884/
| throwaway81523 wrote:
| > This sounds like a loop and that's it ?
|
| No, the execution is required to eventually terminate. The
| challenge is to find the shortest possible program that
| generates at least G bytes of output and then stops, where G
| is Graham's (extremely large) number. This is sort of like
| the Busy Beaver problem.
| tromp wrote:
| Both Graham's Number and Loader's Number appear as lower
| bounds in the functional Busy Beaver at
| https://oeis.org/A333479
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