explain xkcd - User contributions [en]

Talk:2916: Machine

2024-04-07T20:38:23Z

198.41.236.152:

rather late for an april fools comic innit? also there doesn't seem to be anything exciting in this one lol, none of the usual cool exploration easter eggs, as far as i could tell at least [[Special:Contributions/172.71.178.76|172.71.178.76]] 16:41, 6 April 2024 (UTC)Erfaniom

: We're exploring crowdsourced human creativity here, in a way, so it can be a lot more interesting then Randall's exploration comics, at least for me, because i did take two years of GCSE psychology and enjoyed it. [[Special:Contributions/172.64.238.130|172.64.238.130]]

Just popped over using Chrome on Android and all I see is four "missing picture" logos spinning around, plus another down the bottom right... [[Special:Contributions/141.101.68.193|141.101.68.193]] 18:13, 6 April 2024 (UTC)
:Okay, followup: it behaves quite differently on the non mobile site. You get two entry points with red balls and yellow balls and you need to place the various gizmos to direct the balls to the correct exit point. Once enough have correctly passed to turn the red X into a green tick, you have the option to submit. If you do, once you have named your design it will be added to the grid with other submissions all of which exist to push red and yellow balls around. (if you come across "Memories of Ragnarok", that's mine) [[Special:Contributions/172.71.134.207|172.71.134.207]] 18:27, 6 April 2024 (UTC)
::The number of inputs appears to vary between 1 and 4, each of a different color, with one color-coded output for each. [[User:Claire Kholin|Claire Kholin]] ([[User talk:Claire Kholin|talk]]) 18:49, 6 April 2024 (UTC)

On the "machine" section, you see lots of "under construction cells". Perhaps this will develop as more are submitted. I notice the "under construction tape" has "DJIA" and "31415", perhaps a reference to "dow jones industrial average" and the first five digits of pi. [[User:Zeimusu|Zeimusu]] ([[User talk:Zeimusu|talk]]) 18:37, 6 April 2024 (UTC)
:Whenever someone submits a cell, it fills in one of the under construction cells. [[User:Claire Kholin|Claire Kholin]] ([[User talk:Claire Kholin|talk]]) 18:49, 6 April 2024 (UTC)

I wanted to add an image for each object, but do not have the necessary access, can someone who has access add the images that I linked in the table so they can be included? [[User:Claire Kholin|Claire Kholin]] ([[User talk:Claire Kholin|talk]]) 18:49, 6 April 2024 (UTC)

I found a discussion with some guy talking about the API at https://euphoria.leet.nu/room/xkcd/ ; this could be useful for the wiki.

<code>
[c+1] now time to try fucking with the api
[c+1] https://incredible.xkcd.com/
[userwithnoaccount] 404
[c+1] it seems there are numbered machines under incredible.xkcd.com/machine/x
[c+1] returns a grid of individual machinlets
[c+1] which are uids like 3a7af27c-5389-5dcb-b660-3feab6be2ceb
[c+1] they're stored at urls like incredible.xkcd.com/folio/3a7af27c-5389-5dcb-b660-3feab6be2ceb
[c+1] there appear to be 33 machines total
[c+1] the json it returns seems to refer to these as "versions"
[c+1] $ curl -s https://incredible.xkcd.com/machine/21 | jq ".version"
21
[c+1] there is a machine/0, but it's all null
[c+1] going to https://incredible.xkcd.com/machine/current redirects to the current machine
[c+1] $ curl -sL https://incredible.xkcd.com/machine/current | jq ".version"
35
[c+1] wait, is that the *total* number of mahcines?
[c+1] i would've thought there'd be more
[c+1] this whole think is rather esoteric
[c+1] Written in rust, too: https://rapier.rs/
[c+1] Uh oh.
https://i.hypercone.us/?v=8e283d
[c+1] HMMM
https://i.hypercone.us/?v=079f8f
[c+1] it seems there is no limit
[c+1] i've uploaded a ~50M title
</code>

[[Special:Contributions/172.70.57.146|172.70.57.146]]

Had quite a lot of fun, added a few 'successful' machines to the grid. Noted that whenever I try to use the Prism that (after a short delay) the comic-pane blanks and I need to refresh the page/get a completely new 'challenge' to start from scratch, so I'm just not using the prism at all (used most of the other items, in combination or 'just the one across the whole board', whichever seems most fun). But it doesn't seem to do what I'd like it to do, which is sort multiple colours from the same inflow into different outflow directions. Which would be ''very'' useful in a 'crossroads' situation, the general solution of directing them cross-path being too prone to random collisions. Also might be useful in the 'submitted machine grid', as I note that errors propagate, whereas adding a filter on all inputs would clean out (dispose of/send off to a valid gate?) the rogue balls. Anyway, gonna have to come back to this later when there's more time... Maybe then I'll even have something useful to add to the Explanation. [[Special:Contributions/172.70.163.31|172.70.163.31]] 19:03, 6 April 2024 (UTC)

The balls appear to be different weights. I just saw a machine that used fans to separate yellows from greens and blues in a sort of 'wheat from the chaff' manner to direct them to their correct outputs. I wonder what other hidden tricks are included. [[Special:Contributions/172.68.1.159|172.68.1.159]] 19:40, 6 April 2024 (UTC)

They're not all accepted, though it makes you think they are. Or something else more complex is going on we haven't realized yet. I made a machine that was working reliably, submitted it, and saw it on the overall grid. Reloading from a different browser I found the same location of the machine, with the same surroundings, but my machine had been replaced. It's nowhere else on the grid either. The first browser still shows it (but not after a reload with a cache clear). I'm not sure if there's some kind of "save" event that needs to happen beyond seeing your machine in the broader one, or if all user collaboration is an illusion, or if the system changes its mind about us somehow.

: Yeah, i've been seeing this too. Please tell me if you find any of my machines, images at https://i.hypercone.us/?v=22d562 , https://i.hypercone.us/?v=ad8e3a , and https://i.hypercone.us/?v=8d4d6a . I want to be one of the few to have added Catalan and Spanish to the grid. [[Special:Contributions/172.71.134.164|172.71.134.164]] 20:56, 6 April 2024 (UTC)

I've added some more observations to the page. Also, a guess which is too uncertain to put on the main page: The ball launcher for the yellows on the far left side misses a lot, and the yellow container isn't the one on the left. So I think the whole machine with crossing streams will result in the colors being sorted in their container order, and possibly have the streams combined and deposited at the bottom just above the containers. --[[Special:Contributions/172.71.147.100|172.71.147.100]] 21:07, 6 April 2024 (UTC)

has anyone seen the boat at the very bottom? [[User:Mushrooms|Mushrooms]] ([[User talk:Mushrooms|talk]]) 21:21, 6 April 2024 (UTC)

trying to see it on Firefox for Ubuntu and it just tells me to "visit xkcd.com to view" - THAT'S WHERE I AM?! Tried clearing website data (but not my entire cache) and that didn't help. Is there something I'm missing?

Oooh, just had one with four ball-entries (four colours) and ''three'' exits (one caters for two arrows). Pity it's rather complicated to get entries to exits (even if I can merge two of the streams). Might have to give up on it, but I'd like to have seen how it fits in with the 'submited grid'. i.e. someone else gets a two-colour introduction spot. [[Special:Contributions/162.158.74.119|162.158.74.119]] 22:37, 6 April 2024 (UTC)
:Me again. I'm just refreshing the page, looking at the pattern of entries/exits (just a dozen or so screens in, getting some repeats of pattern, indicating that it's going back to tiles it was suggesting before, probably depends on how many others are contributing and extending...)
:Found another 'double-colour' example. Two yellows ''from the same side'', which probably means that there's a two-yellows been asked to exit from the neighbour (will check shortly).
:Quickly adapting from my spreadsheet notation, "R, Y, G, B" in order, each "(Entry, Exit)", I've been using <dir> of L/R/T/B and a number (nominally percentage, though seems to include only values of 20, 30, 50, 70 and 80, so it ''might'' be more 1/6..5/6?) relating to the distance along from L to R (for T/B) or T to B (for L/R).
:This line is therefore (0,0)(L20+L70,R30+B70)(R80,L80)(T70,L50) ... no reds, two yellow pairings, a red pairing, a blue pairing. Would require at least two path-crossings (but I was going to calculate those things later, and double-colours might confuse my intended simple line-intersection calculation).
:...anyway, spent some time on this message, which might mean I'll get into a 'new batch' of available patterns as people have succeeded some of the challenges that I've been 'swiping left'. [[Special:Contributions/172.70.162.20|172.70.162.20]] 19:28, 7 April 2024 (UTC)
:...very next click: (0,0)(T30+L20,R20+R70)(R80,L80)(R50,B50), which is clearly the actual left-neighbour of the above. [[Special:Contributions/172.70.162.19|172.70.162.19]] 19:32, 7 April 2024 (UTC)
:Ok, stopped my refreshing to [https://imgur.com/a/OMFOmzy 'solve' a screen]. First of all I routed both yellows entries (right-upper and upper-right) to one yellow exit (middle-left) and gradually teased the greens across (lower-left to middle-right), as that way I was avoiding a criss-cross of balls, but the the other yellow exit (left-lower) was, of course, invalid.
:Changed it to drop one stream of yellows down towards the lower exit, across the rapidly firing greens (added a fan to filter away the occasional yellow that gets bounced over there, not much of an opportunity to filter falling-greens out of the yellow exit, so apologies to whoever gets the sceen below). Submited as "Two Yellows, One Green!", whether or not that'll save (apparently, I should continue to contribute and not refresh/close, or else the server will not keep the solution?).
:Interestingly, all four adjacent tiles are "Under construction", and if I scroll up... *DARN* the comic has blanked out (nothing there between the upper PREV/RANDOM/NEXT buttons and the lower ones, just whitespace). This may mean that it did not save. This is the kind of 'page crash' I get when I try using a Prism or get too many balls rattling around on top of a Black Hole. Perhaps it doesn't like that I'm scrolling into an Under Construction that shouldn't be there? (But then, why ''is'' it there?)
:Anyway, all extra information for everyone.
:I'll just refresh the page and go back and do some more entry/exit mapping, maybe? [[Special:Contributions/172.70.162.20|172.70.162.20]] 20:17, 7 April 2024 (UTC)

If you combine a bunch of these silly claw things in the middle by just spamming it, it begins to lag and do some chaotic collisions, even without balls colliding on it. It's curious how it does that seemingly randomly though. I wonder how calculations are added and if there's a tiny sprinkle of RNG. (Also, errors occur and say something about damaging recursion in the Rust programming language, so I guess we know how it was made. It's also pretty weird how there's not a lot of opening combinations? It's possible that the machine loops over in chunks of gears or something (that's what I'll call them). ([[User talk:Leo|talk]]) 13:15, 7 April 2024 (UTC)

If you place a black hole in the centre of a wheel, it makes the wheel behave unpredictably between resets. Sometimes it's almost normal, sometimes it's a lot faster than usual, and sometimes it's stopped but launches balls that touch it with extreme force. I was able to use this to submit a machine which didn't actually let a single ball through after being submitted. https://i.hypercone.us/?v=928bcd [[Special:Contributions/162.158.33.149|162.158.33.149]] 01:19, 7 April 2024 (UTC)

The page says that (and I have taken note of) the ball hue is ''coded'' to certain values, but is there a logic to those values that might be derived from the colour (either as RGB triplet or HSV/other colourspace definition). For example, the two ball-types with zero green component in their makeup are 'unit density' (green is far heavier "green+red" is far lighter, so it's not a simple relationship, unless it converts from °hue, in some way) and the only secondary colour exhibits non-zero drag. There's the possibility that it just derived from "we need different properties, we need different colours, we have no reason to connect either with other deliberately" or even some non-mathematical symbology (fire=red, water=blue(?), earth=green, air(/sunlight?)=yellow). But it makes me wonder what combination of properties cyan/magenta balls might have, if added. (Or is the choice of those four colours constrained, anyway? Though R/G colorblindness is already something of an accessibility failure, if anyone suffers that.) [[Special:Contributions/172.69.194.205|172.69.194.205]] 17:02, 7 April 2024 (UTC)

[https://pastebin.com/7PAiLnyF Python script to get the URL and title of each Cell in the current machine]

[https://pastebin.com/xBhywGde Result of running that script at the moment] (encoded with ROT13 because pastebin wouldn't let me save it otherwise)

[https://pastebin.com/jN5MP2za Result of running that script on the first 42 machines], at least on these it looks like the only difference is that one cell is added each time? [[Special:Contributions/172.71.99.195|172.71.99.195]] 17:22, 7 April 2024 (UTC)

I've submitted four now, none of which was accepted. I tend to spend a lot of time getting them just right. Any hints as to what the acceptance criteria might be? Or do I just stink at this?
[[Special:Contributions/172.69.59.204|172.69.59.204]] 19:47, 7 April 2024 (UTC)

There appears to be a new object: a cat that bats things that touch it.
[[Special:Contributions/172.69.214.39|172.69.214.39]] 20:17, 7 April 2024 (UTC)

Is anyone else experiencing the bug where prisms cause the comic to disappear (leaving only the white background where it was) after a while? It makes viewing the whole machine basically impossible. (On further testing it appears to be firefox-exclusive.) [[Special:Contributions/172.70.162.38|172.70.162.38]] 20:31, 7 April 2024 (UTC)

== Level scrolling bug ==

When one views the whole machine, and scrolls down far enough, everything just disappears, and the comic is completely unresponsive. Has anyone else seen this? [[Special:Contributions/198.41.236.152|198.41.236.152]] 20:38, 7 April 2024 (UTC)

Talk:2835: Factorial Numbers

2023-10-13T09:38:17Z

198.41.236.152:

Number systems aren't real math, at least not serious math. They're an affectation. 99.9% of math is number-system-independent, so nobody should care about them. [[Special:Contributions/172.70.46.108|172.70.46.108]] 22:30, 29 September 2023 (UTC)

: Of course it's "real math." There aren't that many applications, but so what? Math isn't about applications. Besides, there are some. Maybe not specifically for factorial base, but for some place systems. The only thing "dirty" about decimal is the arbitrariness of ten. Considering place systems in general is just considering special kinds of sums. Certainly, "serious" mathematicians are interested in proving numbers normal in specific bases, or in every base. [[User:EebstertheGreat|EebstertheGreat]] ([[User talk:EebstertheGreat|talk]]) 01:55, 30 September 2023 (UTC)

: A great deal of interesting maths can be found in and around he various arrangements of digits in number systems, surely. AzureArmageddon 07:54, 30 September 2023 (UTC)

I thought this was a complete joke, until coming here. The "factorial number system" exists?! [[Special:Contributions/162.158.90.249|162.158.90.249]] 22:38, 29 September 2023 (UTC)
:Yup, complete news to me too... What's REALLY weird: the night before this comic I was tutoring a friend's daughter in math, and I happened to teach her what factorials are! (News to me there's a number system, though)... [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 04:59, 1 October 2023 (UTC)

I wanted to add a link to a converter, but the one I found is https://www.dcode.fr/factorial-base which is quite ugly with lots of adds and a bit counter-intuitive.--[[User:Pere prlpz|Pere prlpz]] ([[User talk:Pere prlpz|talk]]) 23:42, 29 September 2023 (UTC)

This needs simplifying a bit. Came here because I had no idea what was going on, and after a quick scroll through the prose, the main thing I learned was "it's 'cause you're dumb". May be true but I still don't get what Randall's factorial system is....[[User:Alcatraz ii|Alcatraz ii]] ([[User talk:Alcatraz ii|talk]]) 01:25, 30 September 2023 (UTC)
==Fractions==
I have actually considered this system, though not with any illusion of its being useful. Any system "exists", just as any number "exists". A system where 1 = decimal 1, 10 = decimal 29, 100 = decimal 493 , exists in the monetary system of the Harry Potter world. An actual system existed where 1d = 1d, 1/- = 12d, £1/-/- = 240d.

It's only on seeing that someone else had come up with this system, that it's occurred to me to consider fractions. Any rational number has a finite number of places after the "factoradic" point. Anything with infinite repetition after the point is irrational.
1⁄2 = 0.1
1⁄3 = 0.021
1⁄4 = 0.0121
1⁄5 = 0.01041
1⁄6 = 0.011
1⁄7 = 0.0032061
1⁄8 = 0.0031
1⁄9 = 0.002321
1⁄10 = 0.0022
π = 11.003156502.....1
e = 10.11111111111111111111.....1 [[Special:Contributions/198.41.236.185|198.41.236.185]] 09:34, 13 October 2023 (UTC)

Factorial base also allows to finitely represent all rational numbers - no constant base is capable of that! [[Special:Contributions/172.68.238.76|172.68.238.76]] 01:55, 30 September 2023 (UTC)
: Unless you use a division sign. But yes, only radix numerals of a variable base with infinite series of factors of every prime can even theoretically finitely represent arbitrary rationals without invoking existential quantifiers. [[Special:Contributions/172.71.147.26|172.71.147.26]] 06:43, 30 September 2023 (UTC)

I feel like Michael when Oscar is trying to explain what a “surplus” is.[[Special:Contributions/162.158.186.241|162.158.186.241]] 04:12, 30 September 2023 (UTC)
:Bruh, same, and I'm a stats major. This "explanation" sorely needs a couple paragraphs of ELI5 introductory exposition for English majors between the first and second sentences. [[Special:Contributions/172.69.134.16|172.69.134.16]] 13:11, 5 October 2023 (UTC)

== The warning is complete nonsense, just remove it ==

bots cant be escorted out of somewhere just remove the stupid warning [[Special:Contributions/162.158.203.109|162.158.203.109]] 04:28, 30 September 2023 (UTC)

: you must be new here - [[Special:Contributions/108.162.216.143|108.162.216.143]] 15:51, 30 September 2023 (UTC)

: The nonsense is part of the fun. AzureArmageddon 07:52, 30 September 2023 (UTC)

::im deleting it {{unsigned ip|162.158.203.80|11:16, 30 September 2023}}‎

:::Premature elision. Still has a purpose (as does signing your contributions here). [[Special:Contributions/172.71.178.208|172.71.178.208]] 14:58, 30 September 2023 (UTC)
:::<nowiki>*</nowiki>sigh* As has been stated, you MUST be new here. The "incomplete" tag goes on new comics while their descriptions are still in flux. When the bot creates the empty description page, it does so with the Incomplete warning, labelled with its name. On the first edit, someone ALWAYS changes the name to some silly gag that's related to the comic, often pretending it's the name of the bot that created the page for us. In this case the comic shows Cueball being escorted out, so the joke is the bot is being escorted out. If you're not going to have a sense of humour, why are you here? Just leave the editing to others in the meantime. :) (Oh, and as the user above noted, make sure to end your comments with <nowiki>~~~~</nowiki> (4 tildes), like it says at the top of the editing text box you type in). :) [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:13, 1 October 2023 (UTC)
:Okay, now the Incomplete warning needs to stay up forever. :) [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:13, 1 October 2023 (UTC)
::nope
:In case you weren’t aware, this wiki has a tradition of humor. This is one of its examples. [[Special:Contributions/172.68.58.134|172.68.58.134]] 12:56, 2 October 2023 (UTC)

== The "adic" part of factor-adic numbers ==

It's not explicitly mentioned in the comic but the "adic" in the name "Factor''adic''™" implies that the number system extends the factorial number system by being in some way "adic" as discussed in [https://youtube.com/watch?v=tRaq4aYPzCc this YouTube video on the Veritasium channel] and so negative numbers would have a truly wacky representation that violates the intent of the title text's pronouncement by requiring an infinitely long representation requiring infinite digits (1, 2, 3, 4, ..., 9, A, B, C, ..., ''infinite digits''). AzureArmageddon 08:00, 30 September 2023 (UTC)

: The "adic" in factoradic doesn't actually relate to p-adic numbers of any kind. Rather, both factoradic and p-adic numbers use the suffix -adic to refer to the concept of adicity, which is "The number of arguments or operands a function or operation takes" according to Wiktionary. Each place value of a p-adic number had p possibilities, and each place value in the factoradic system has a number of possible arguments determined by the factorial of the place. Factoradic would be better called "factorary" since it's more similar to ordinary n-ary number systems, but I guess it just isn't. [[Special:Contributions/172.69.205.130|172.69.205.130]] 20:43, 30 September 2023 (UTC)

:: Ah, today I learned. AzureArmageddon 15:35, 1 October 2023 (UTC)

== Title text ==
The title text references that 10! = 3,628,800 (base 10), and so for numbers greater than or equal to that, you would have to add a tenth digit in order to display them in this system. The question is asking whether you would then proceed to using letters of the alphabet such as one does in [https://en.wikipedia.org/wiki/Hexadecimal hexadecimal] to which the reply is that numbers above this amount are simply illegal. The trouble comes when you try to write down the number 10 * 10! = 36,288,000 (base 10) in this system. For 10!, the notation is 1000000000 , so 9 * 10! would be 9000000000, and then to get 10 * 10!, you would have to write A000000000 because 10 * 10! < 11!. In fact, since this is the first "illegal" number, you could "legally" allow up to 10 * 10! - 1 = 36,287,999 (base 10) in the system (which would be written as 9987654321 = 9 * 10! + 9 * 9! + 8 * 8! + ... + 2 * 1! + 1 * 1!) without the need to introduce any letters. I also want to point out that the reference in the comic to 9 being reserved for big numbers is due to no number needing a 9 to write it down in this system until 9 * 9! = 3265920 which is written 900000000. Since numbers above 10! are not allowed, this means that only the 9! digit is legally allowed to hold a 9, and it only applies to numbers in that high range of 3265920 to 3628799.[[Special:Contributions/172.71.166.230|172.71.166.230]] 15:01, 30 September 2023 (UTC)
:I feel the current in-Explanation explanation about that already covers this, with the addition of the validity that the digit that could need to be >9 could still be any digit 0..9 without needing to invoke the 11th digit. (Maybe a few tweaks, but not sure what you're trying to add here.) [[Special:Contributions/172.70.86.148|172.70.86.148]] 15:13, 30 September 2023 (UTC)

== Radix Economy ==
Someone got in there just before I did, about (from a quick scan of what's been added) "economical" use of Factorial-based variable radices. (I was planning both the test code and the explanation for this, whilst travelling.) My short way of putting it is that (apart from values of zero or one, which represent identically in Factorial-based notation to any other notation in base of 2+) the Factorialised method initially is using up 'places' quicker until the point at which it has reached a 'magnitude' equal to its base-normal 'original' (i.e. only when there are N glyphs made available under Factoradic notation does it not rush through the 'magnitude' quicker than the base-N number). And ''then'', it needs to work up into the more 'efficient' higher-order digits in order to pull back the disadvantages of its lower-order ones and equal, then be shorter than, any given value's respective base-N form. 
Now, I've done some very rough calculations (started hitting numbers for which I really need to convert everything into high-precision large-number data types, which needs me to rewrite one or two elements of my existing code) and looked at the successive changes of magnitude, in each base, and checked the calculated Factoradic length (with the assumption that there are enough extended glyphs to represent every digit singly, unlike the comic Title Text speculation). 
By my reckoning, Base-2 is more efficient at 20fact (compare with 1002, =410); Base-3 breaks better at
3111fact (100003, =81); Base-4: 540220fact (10000004, =4096); Base-5: 533340021fact (10000000005, =1953125); Base-6: 90967344000fact(1000000000006, =362797056); Base-7: 7ABAA086002001fact(1000000000000007, =678223072849); Base-8: D73A256860540220fact(100000000000000008, =281474976710656); Base-9: B1HEA65678836651220fact(100000000000000008119, =1350851717672992000) ...but at this point, the conversion of decimal to its base-9 form (and that powers of 9 should ''never'' have trailing zeros!) shows I may very well have hit a limit to normal large-number precision, so I really can't trust the subsequently derived base-10 values. 
But, in case anyone wants it, the following is my (Perl, but should be easily convertible into most medium-to-high level code dialevts) en-Factoriadialising function.
sub factadic { my ($n,$place)=(@_,1);
return () unless $place;
if ($n>=fact($place+1)) { return factadic($n,++$place) }
my $digit=0; my $base=fact($place);
while ($n>=$base) { $digit++; $n-=$base; }
my @return=($digit,factadic($n,$place-1));
return @return;
}
You call it as <code>factadic(''<value>'')</code>. Or <code>factadic(''<value>'',''<minimum_digits>'')</code> to start with the assumption of at least a minimum number of digits, but it'll start by shifting the default minimum of 1 into the <script>$place</script> variable if you don't give it that (there are other ways that you can/must do that, of course), and it will still always expand that to the degree necessary in the first phase of 'diving in' as far as it needs to in order to agree with the <code>fact()</code> function (factorial calculator, a trivial coding issue that I only use here like this because I alreadu set it up for another bit of code). 
It returns an array (@-variable, in Perl) of digits, in standard most-to-least-significance order, that you can convert to a glyphwise notation in any way that you wish (or do a string conversion within the function, at each stage of building it up). ...and I'm presenting a ''slightly'' less optimised version of it here (some of the Perl-tricks I originally used don't translate well into some non-Perl) and, yes, the <code>while ($n>=$base)</code> loop could be done using modulus and integer-division, but it's a fairly trivial part of the looping process. 
If you have any ''real'' problems with it, it's probably going to be if you're hitting any recursion-depth limits (especially as it uses roughly twice as many recursive calls as the eventual notation-length it produces). I also have a 'stack-based' version (loops round as it shifts in enough 'slots', then works back down again assigning the place-values) which avoids such trouble, but that's coded in a slightly esoteric Perlish way that I'm not sure most of you'd appreciate. ;) [[Special:Contributions/141.101.76.77|141.101.76.77]] 20:25, 30 September 2023 (UTC)
: Probably a double precision floating point accuracy limitation, you can only get up to 2^53 = 9007199254740992 before many modern programs start getting numerically fuzzy. But what weirds me out is you seem to have gotten 1350851717672992900 out of what should have been 9^19 = 1350851717672992089, instead of a nearby float of 1350851717672992768 or 1350851717672993024. What is it with things rounding to decimal like that? [[Special:Contributions/172.71.147.84|172.71.147.84]] 11:43, 1 October 2023 (UTC)
::One 'solution' is to <code>use Math::BigFloat</code> (or similar), in the Perl, and make hold such sensitive and large-tending values. Alternately, implement an array of digits in a raw manner (can be of entirely arbitrary base, explicitly, plus arbitrarily long; well, as long as one doesn't hit ''other'' data limits!) and make your own long-division/etc algorithms. Or pack bitwise/bytewise data as a 'string', with suitable overloaded/replacement mathematical functions. But it all adds extra coding effort, of course. And I rarely share my various hacked-together bits of Perl, because they either work but look horrible or they don't work (and probably look strange, even to me - hence why I've failed to discover why they don't work!). [[Special:Contributions/172.71.98.87|172.71.98.87]] 19:39, 1 October 2023 (UTC)
: Just analyzed the growth rate; For base x, the length can be estimated by 1/2+e*x-e-1.487*ln(x). Maybe a more sniped nerd can get more precision, or even an exact solution; but this is within a digit of the result up to around base 10^13, and then I start running into precision problems in general, so I'm just putting this here as a good enough guess. [[Special:Contributions/172.71.146.129|172.71.146.129]] 13:20, 1 October 2023 (UTC)

Factorial numbers is new to me... It sounds more like a coding system than a number system, LOL! "The door code is 4503 in factorial! Figure it out!" (I'd write this on the bottom of the comments as usual, but I don't want to get mixed up with that ill-thought out and unsigned coding sample Algorithm and table that I KNOW must be mangled when published because the wiki refuses to honour single Newlines. Clearly the author didn't take a peek at what it looks like when published EDIT: Correction, wow, the wiki spotted the code and marked it as such automatically (for now), wow!) :) [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 04:59, 1 October 2023 (UTC)

All the stuff about economy / efficiency doesn't seem to really have any direct relation to the comic, so I'd suggest it doesn't really belong in the explanation, but should be confined to the comments, or at least to a trivia section. Not least because it dives off into a lot of technical stuff that ''itself'' requires explanation for a significant part of the readership. As it is, it's doing more to confuse than to explain.[[Special:Contributions/172.70.85.218|172.70.85.218]] 09:02, 2 October 2023 (UTC)
:I sort of agree, in that I had planned something similar about 'notation economy' as a Trivia-like addendum, before others got there before me. But there could at least be something to be said that by reserving higher-digits(/dissalowing them in lower values), Cueball/Randall is sacrificing conciseness for (one idea of) aestheticism. (And that's without going into 'how much storage it takes to store each digit', which I wasn't going into. So rather than the idealised radix being base-'e', I would have said the idealised base was whatever base-number exceeded the highest value, so it was just one (different) single squiggle for ''everything''. Obviously, there's necessary entropy in the choice of differentiatable squiggles/encoding, though, which is why I also appreciate the current Explanation's blurb.) [[Special:Contributions/172.70.90.52|172.70.90.52]] 10:15, 2 October 2023 (UTC)

NiceGuy1 the wiki uses standard markdown, if you preface with 6 spaces, it will automatically recognize it as a code snippit. I appologize if my contribution was ill-thought out, though i have gone back and signed it. [[User:Drinkcoffeeandcode|Drinkcoffeeandcode]] ([[User talk:Drinkcoffeeandcode|talk]]) 20:06, 4 October 2023 (UTC)
:I called it "ill-thought out" for having no tags or markup, and thus figured it would be all mangled. :) I was mistaken. Good to know, except I don't see myself ever sharing code (I figure people generally aren't hanging out in a coding environment to just run random code like that. I myself don't have any place to try it these days, and if I did I don't prefer C so probably wouldn't have a C environment anyway). But the last time I wrote someone after an unsigned comment, some idiot manually marked it as mine (WHY would I reply to myself?), which I removed, and I don't know how to manually write someone else's sign in (and didn't want to hunt one down to SEE and learn how), so it's probably STILL unsigned. Usually when there's an unsigned comment someone who knows how checks the edit history to find the IP or name to add it. :) Oh, and usually if you want to reply to someone, you put a colon and place your reply below theirs (like this). :) [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 04:29, 7 October 2023 (UTC)

== Factoradic Algorithms ==

there are several ways to compute the factoradic of a base 10 number, depending on the choice of language
the length of the program will be demonstrably bigger. Dynamically typed languages, like perl can likely
perform this in one or two lines, where as a language like c++ will be longer.

The simplest algorithm is to generate the digits from right to left one at time by dividing the number by a per-iteration-incrementing radix starting from 2 (because 1 is simply '0', we start from 2), taking the result and repeating until the quotient reaches zero:

#include <iostream>
#include <algorithm>
using namespace std;
int factoradic(int num) {
string digits;
int radix = 2;
while (num != 0) {
digits.push_back(((num % radix)-'0'));
num /= radix++;
}
reverse(digits.begin(), digits.end());
return atoi(digits.c_str());
}

Using Randall's values we can confirm it is correct:

int main(int argc, char* argv[]) {
for (int i = 21; i < 26; i++)
cout<<i<<" - "<<factoradic(i)<<endl;
for (int i = 5038; i < 5042; i++)
cout<<i<<" - "<<factoradic(i)<<endl;
for (int i = 999998; i < 1000002; i++)
cout<<i<<" - "<<factoradic(i)<<endl;
return 0;
}

max@laptop:~/$ ./factoradic
21 - 311
22 - 320
23 - 321
24 - 1000
25 - 1001
5038 - 654320
5039 - 654321
5040 - 1000000
5041 - 1000001
999998 - 266251210
999999 - 266251211
1000000 - 266251220
1000001 - 266251221

Came back to sign code sample after seeing NiceGuy1's comment. [[User:Drinkcoffeeandcode|Drinkcoffeeandcode]] ([[User talk:Drinkcoffeeandcode|talk]]) 20:02, 4 October 2023 (UTC)

I would love to have some kind of explanation as to why this number system exists/what it's used for in the real world. (Even if that explanation is just "there's no practical purpose, mathematicians just love doing this stuff".) [[Special:Contributions/172.70.134.87|172.70.134.87]] 14:55, 2 October 2023 (UTC)

Would it be too much of a fandom crossover to edit / annotate the last word of the explanation (at time of commenting, the word "senary") to "seximal"? Or, given that we are discussing intentionally silly base systems, just the '''right''' amount of a fandom crossover? [[Special:Contributions/172.71.242.176|172.71.242.176]] 08:14, 5 October 2023 (UTC)
:: "Fandom crossover" with what, exactly? Just humour for Beavis & Butthead/Quagmire-style "sex, hee hee" people (such as myself), or is there some actual fandom you're referring to? As it is, I would have thought the proper word WOULD have "sex" in it, like sextillion does... :) [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:41, 7 October 2023 (UTC)
::: I'm assuming the jan Misali fandom. The guy is mostly known for his videos on constructed languages, but he also has strong opinions on base 6. As a reference, see his site [https://www.seximal.net/ seximal.net].

Can I politely note that your algorithm potentially has no end? num is never 0 because you're always dividing and never subtracting. My perl attempt goes through every radix up to around 180 before giving up. (Leave out the atoi and you'll see what I mean.) I might recommend capping radix at 9. [[User:Hymie|Hymie]] ([[User talk:Hymie|talk]]) 12:20, 9 October 2023 (UTC)

== Category ==

There should be a category where presenters are escorted by security, or are about to be.--[[Special:Contributions/162.158.87.153|162.158.87.153]] 12:27, 6 October 2023 (UTC)
: You may be right, I recall several (none specific come to mind, but I know it's a scenario Randall clearly enjoys). [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:41, 7 October 2023 (UTC)

== Notation ==

[[wikipedia:Factorial number system]] uses the 3121! style notation. Should probably be used in the explanation, together with the 8310 notation. --[[Special:Contributions/162.158.87.154|162.158.87.154]] 12:42, 6 October 2023 (UTC)
: "In this article, a factorial number representation will be flagged by a subscript '!'", that sounds like it's not a standard notation, just one THAT editor used for THAT article to clarify things when explaining it. [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:44, 7 October 2023 (UTC)
::It's used at least in a *Scientific American* article from 4 years ago: https://blogs.scientificamerican.com/roots-of-unity/its-factoradical/