explain xkcd - User contributions [en]

166: Misusing Slang

2023-10-31T00:21:25Z

47 Radians Felsius:

{{comic
| number = 166
| date = October 4, 2006
| title = Misusing Slang
| image = misusing_slang.png
| titletext = It slowly dawns on us that our parents knew exactly what they were doing.
}}

==Explanation==
[[Randall]] expresses excitement for the time in the future where he can intentionally misuse modern-day slang in order to make nearby teenagers feel uncomfortable. He illustrates this by using the word "pwned," the past tense of "pwn" (from "own," as in to defeat completely): "The noob was pwned by the pro."

Many teenagers believe their parents to be not "with the times," however Randall suggests that parents actually ''do'' know what the words mean, but are acting otherwise in order to mess with their heads for their personal amusement. The title text reinforces this, as every generation has had some form of slang that they used, and it could be possible that this practice has been continued for a good while. It also suggests that the parents of teenagers may be "pwning" their children by intentionally misusing these modern-day slang.

==Transcript==
:The best part of getting older is gonna be intentionally misusing slang around teenagers just to watch them squirm.
:Cueball: Oh man, that song is so pwned!
:Teenager: ''twitch''

{{comic discussion}}
[[Category:Comics featuring Cueball]]
[[Category:Language]]
[[Category:Multiple Cueballs]]

2251: Alignment Chart Alignment Chart

2023-10-12T00:17:25Z

47 Radians Felsius:

{{comic
| number = 2251
| date = January 6, 2020
| title = Alignment Chart Alignment Chart
| image = alignment_chart_alignment_chart.png
| titletext = I would describe my personal alignment as "lawful heterozygous silty liquid."
}}

==Explanation==
"Alignment" and "alignment charts" come from tabletop roleplaying games, most prominently ''{{w|Dungeons & Dragons}}''. Every character has an {{w|Alignment (Dungeons & Dragons)|alignment}}, which very roughly identifies their tendencies. The most widely used alignment system was introduced in the ''{{w|Dungeons & Dragons Basic Set}}'' in 1977 and has been reused in many (but not all) subsequent editions of the game. This system uses two perpendicular axes, each divided into three levels (for a total of nine categories). The two axes are:
* Lawful/neutral/chaotic: this axis says whether a character is strongly devoted to, indifferent about, or categorically opposed to following established rules.
* Good/neutral/evil: this axis says whether a character is generally inclined to commit good deeds or evil deeds.

In this system, the "lawful" attribute is independent from the "good" attribute. Lawful alignment means that a character is committed to a set of rules, which can refer to actual established laws, or to something like a rigid personal code, a set of traditions, or a chain of command, while a chaotic alignment means that a character has no interest in those, and may actively oppose them. The good vs evil scale is generally based on a character's concern for the lives and well-being of others; a good character will actively seek to help others and prevent harm, while an evil character will have no such concern and may actively harm others. Being 'good' is assumed to be independent of being 'lawful'. For example, a character who actively breaks laws to help those who are unjustly imprisoned or oppressed would be considered to be "chaotic good". In both cases, a neutral alignment can indicate a character's indifference to a concept, or that their commitment is conditional, or that they consciously seek to balance both sides. A character with the "neutral neutral" alignment is called a true neutral.

An alignment chart is a grid that divides the alignments, usually for the purpose of putting descriptions or particular characters on it. Alignment charts are frequently used as a [https://knowyourmeme.com/memes/mcdonalds-alignment-chart meme template], where humorous or absurdist things are organized into different alignments. In addition to the "classic" Dungeons and Dragons alignment chart, there are a number of variant alignment charts in use as meme templates. Many keep the three-by-three grid structure but replace the lawful-neutral-chaotic and good-neutral-evil axes with descriptions.

This comic claims to be a meta-alignment chart, where nine "alignment charts" are themselves sorted into the nine Dungeons and Dragons alignments, following the use of alignment charts to humorously classify abstract concepts. However, these "alignment charts" are mostly diagrams used in academic classifications, which are being treated as if they were blank meme templates. There are two levels of absurdity here: first, the idea of using these diagrams to classify things they were never intended for, and second, the conflation of chaos as a physics concept and an assigned moral weight as it applies to each of these classification systems.

The title text describes Randall's alignment as "lawful heterozygous silty liquid" which references the true neutral, neutral good, lawful good, and lawful neutral charts in the Alignment Chart Alignment Chart. Lawful is the left side of an alignment chart, heterozygous is the top right or bottom left of a Punnet Square, silty is the bottom right of a soil chart, and liquid is the top right of a phase diagram. As such, the title text describes Randall's alignment as between Lawful Neutral and Neutral Good on this chart.

{| class="wikitable"
!Alignment
!Chart
!Explanation
|-
|Lawful Good
|{{w|Soil texture|Soil chart}}
|This chart shows the USDA classification of soil types by their relative proportions of sand, clay and silt. The chart is a ternary diagram (very common in geology), so soils with more clay plot towards the upper corner, soils with more sand to the bottom left, and soils with more silt to the bottom right. This chart has been used humorously as an alignment chart ([https://www.reddit.com/r/PrequelMemes/comments/8wakd4/anakin_soil_reference_chart/ for example]) and may have been the inspiration for Randall to use scientific diagrams as alignment charts. In addition to being Lawful Good, this grid cell is also the upper left cell of the chart and will be read first, making it a good place to put this chart as a "jumping off point". [https://what-if.xkcd.com/83/ What If 83 "Star Sand"] cites Randall as "...very satisfied with this chart, it's like the erosion geology edition of the electromagnetic spectrum chart..."
|-
|Neutral Good
|{{w|Punnett square}}
| Punnet squares are a visual method of determining what traits an organism might have based on the traits of the organism's parents. It relies on the principle that a trait is either dominant (indicated with capital letters) or recessive (indicated with lowercase letters). The exact combination of dominant or recessive genes that a child organism receives from their parents determines their traits. Heterozygous and homozygous refers to the pairs of alleles in an organism’s genotype, indicating mixed or same alleles, respectively. Randall later uses "heterozygous" in the title text. Note that it is possible for a phenotype to be expressed the same between some heterozygotes and homozygotes, e.g., persons with genotypes heterozygous "Aa" and homozygous "AA" will both express blood type A.
Therefore, the Punnett Square is a good chart because it is both a simple and true geometric predictor of inheritance, but it tends to be neutral because of complicating factors such as polygenic inheritance; these and other factors will cause genotypic frequency to deviate from expected 1:2:1 patterns.
|-
|Chaotic Good
|{{w|IPA vowel chart with audio|IPA vowel chart }}
|This chart shows the relationship between different vowels according to the {{w|International Phonetic Alphabet}}. The position of the vowel on the chart serves roughly as an indicator of the position of the tongue in the mouth of the speaker. As different vowel sounds are created by changes in different parts of the mouth, including lip roundness which is expressed in the chart implicitly as an invisible third dimension, vowel identification is qualitative and often up to interpretation, and vowel expression can change dramatically from region to region or even person to person within the same language, the categories described by the chart might be considered chaotic. The chart is missing the near-open central vowel [ɐ] and the open central vowel [ä] (often written as /a/).
|-
|Lawful Neutral
|{{w|Phase diagram}}
|A phase diagram shows the equilibrium phases of matter present for a particular temperature, pressure, and composition. The diagram included is a unary phase diagram of a typical material that has a solid, liquid, and gas phase depending on the temperature and pressure for a fixed composition. Phase diagrams are useful for understanding how a material may change as its conditions change. For example, the air pressure of Mars is such that there is no temperature at which liquid water can exist in equilibrium on its surface. Water exists as ice until the temperature reaches a point where it sublimates directly into steam.

This phase diagram does not specify what material is depicted, but it is certainly ''not'' the phase diagram of water. On this diagram, compressing the liquid phase will transform the material into a solid, which is how most materials behave, but the solid/liquid phase line for water tilts the opposite direction. This is why water ice floats on liquid water, for example.

Phase diagrams follow the laws of thermodynamics and concern themselves with the order in which things ''should'' be, so they are inherently lawful.
|-
|True Neutral
|Alignment chart
|All alignment charts are neutral unless humans contaminate them. The chart in this cell has the same overall shape as the Alignment Chart Alignment Chart in the comic. It's important to note that this is called the Alignment Chart Alignment Chart alignment chart. However, that may be [https://xkcd.com/745/ doing 'doing "doing it wrong" wrong' wrong].
|-
|Chaotic Neutral
|CIE chromaticity diagram
|The {{w|chromaticity}} diagram is a chart of colors. Visible colors form a shape like a triangle with two bulging sides in the diagram. The curved line within the diagram shows the chromaticities of {{w|Black body|black bodies}} over a range of color temperatures. The chromaticity diagram shows colors independent of luminance.
The chart is not a simple geometric shape, so it is labeled as chaotic. Points on the diagram can be specified as combinations of three underlying illuminants (the colors of which may not all be visible). It can also be described in polar form with angle and radial distance from some central point, where the maximum radial distance depends on the angle.
The fact that the colors may not show properly on a screen, making the diagram incorrect, may also contribute to its chaotic aspect, as well as the fact that the official standard is behind a paywall.
|-
|Lawful Evil
|Political compass
|[https://www.politicalcompass.org/ Political Compass] separates ideas about governance into economic and social political thought. For example, Gandhi and Stalin supposedly both had similar economic perspectives (collectivist) but radically different social perspectives (libertarian vs authoritarian).

As politics is how laws are made, this is inherently lawful. Representing all politics in terms of two very general axes is not only a gross oversimplification, it is often used to put one's favored ideology as far away from Hitler or Stalin. This common use of a fallacy similar to the straw man makes this chart evil.

Like the USDA soil chart, the political compass has actually been [https://knowyourmeme.com/memes/political-compass used as an alignment chart], largely to mock the original political compass chart.
|-
|Neutral Evil
|{{w|QAPF diagram|QAPF rock diagram}}
|This diagram is used to classify coarse-grained felsic (low magnesium and iron) igneous rocks by the relative volumes of the minerals quartz, alkali feldspars, plagioclase feldspars, and feldspathoids in the rock. It consists of two ternary diagrams - quartz and feldspathoid minerals cannot coexist (they will react to form feldspars) so only three of these components will be in any given rock. Rocks in the upper triangle of the diagram contain quartz, with rocks with more quartz plotting closer to the top, while rocks in the lower triangle contain feldspathoids, with rocks with more feldspathoids plotting lower. Rocks closer to the left corner of the diagram contain more alkali feldspar and rocks closer to the right corner contain more plagioclase feldspar. The field on the diagram for granite is labeled in the comic, but each area outlined on the diagram has its own rock name (monzonite, syenite, granodiorite, etc.). All the rocks that the QAPF diagram is used to classify look superficially like granite, but their chemistry, mineralogy, and origin differ.
The QAPF diagram and the names of the more obscure rock types on it can be somewhat arcane, which may be why it is considered evil here.
|-
|Chaotic Evil
|Omnispace classifier
|The other eight diagrams shown in this comic, squished together into one, with the shapes of the diagrams corresponding to those of the originals. The diagram is labeled chaotic, since it does not have a simple geometrical shape. Probably self-referential humor, in that the diagram created for this comic is considered to be chaotically evil.
|}

An alignment chart was also featured in [[2408: Egg Strategies]], which was published exactly one year later.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

[A 3×3 grid of squares. Each square contains a label at the top and a drawing of a chart, and each square has a caption below it. From left to right, a row at a time:]

----

Soil Chart

[describe this chart here]

* Clay
* Silty Clay
* […]

Lawful Good

----

Punnett Square

A 2x2 grid with a capital or lowercase R at either the left or top of each row and column, and each square containing the two letters of its row and column.

Neutral Good

----

IPA Vowel Chart

[describe this chart here]

Chaotic Good

----

Phase Diagram

[describe this chart here]

Lawful Neutral

----

Alignment Chart

[A 3×3 grid of nine empty squares, each with an unreadable label below it.]

True Neutral

----

CIE Chromaticity Diagram

[describe this chart here]

* Green
* Yellow
* …

Chaotic Neutral

----

Political Compass

[describe this chart here]

Lawful Evil

----

QAPF Rock Diagram

[The diagram is a rhombus with each corner labeled: ‘Q’ at the top, ‘A’ at the left, ‘P’ at the right, and ‘F’ at the bottom. The diagram is divided into trapezoids and triangles, each with labels. The writing in most subdivisions are unreadable. The readable subdivisions:]
* Granite (around the top left)
* Basalt (just below the right corner)
* Foidolite (at the bottom)

Neutral Evil

----

Omnispace Classifier

Chaotic Evil

[describe this chart here]

{{comic discussion}}



[[Category:Charts]]
[[Category:Biology]]
[[Category:Chemistry]]
[[Category:Physics]]
[[Category:Geology]]
[[Category:Language]]
[[Category:Fiction]]
[[Category:Politics]]
[[Category:Recursion]]

2840: Earth Layers

2023-10-12T00:02:35Z

47 Radians Felsius:

{{comic
| number = 2840
| date = October 11, 2023
| title = Earth Layers
| image = earth_layers_2x.png
| imagesize = 585x627px
| noexpand = true
| titletext = The Earth's magnetic field is primarily generated by currents in the liquid outer core, though some geophysicists argue that an unexplained mismatch with models suggests that the Kinder toy contains a magnet.
}}

==Explanation==
{{incomplete|Created by a KINDER SURPRISE - Please change this comment when editing this page. Like this? Do NOT delete this tag too soon.}}

This comic reimagines the internal structure of the earth, mixing the real geological layers of the planet with fictional ones. Some of the fictional layers are appropriated from the layers of other objects that have cross-sectional diagrams, such as the layers of a piece of fruit, an eyeball, or a building.

{| class="wikitable"
! Layer
! scope="col"| Explanation
|-
! scope="row"| Lithosphere/Crust (50/50 Blend)
| The {{w|lithosphere}} and {{w|Earth's crust|crust}} are two different parts of the surface of the Earth and cannot be mixed together.{{citation needed}}
|-
! scope="row"| {{w|Upper mantle}}
| An actual layer of the earth's structure.
|-
! scope="row"| Deep mantle
| A pseudo-correct layer of the earth's structure. There is a layer called the {{w|lower mantle}}, which could be what Randall refers to.
|-
! scope="row"| Filler
| This suggests there is space in the earth that was empty, so the creator(s) added some filler to fill up the extra space.
|-
! scope="row"| Vitreous humor
|Vitreous humor ({{w|vitreous body}}) is the transparent gel inside the eye, located between the lens and the retina.
|-
! scope="row"| Mechanical/HVAC layer
| {{w|HVAC}} is an abbreviation for heating, ventilation, and air conditioning - the system used to heat or cool a building. Tall buildings can have a "HVAC floor" or "utilities floor" between regular floors, like an extra layer.
|-
! scope="row"| Guacamole
| {{w|Guacamole}} is a dip or sauce made from avocados. Originating in the Mayan Empire, It often includes onions, tomatoes, and spices. Notably, guacamole is a major component of seven layer dip, and are shown here to be the seventh layer (from the surface).
|-
! scope="row"| Cytoplasm
|{{w|Cytoplasm}} is the "flesh" of both eukaryotic and prokaryotic cells; a jelly-like substance that fills all the otherwise empty space within the cell.
|-
! scope="row"| Cork
|Due to the proximity of the cork layer and the insulation layer, this may possibly be referencing {{w|Cork (material)|cork}}-lined walls, which while not the most popular choice for wall lining, does have [https://www.jstor.org/stable/27135713 a considerable history]. Another potential reference could be the fact that baseballs (another spherical shape) have a layer of cork in them (though it is usually in the center).
|-
! scope="row"| Insulation
|Probably a reference to the {{w|building insulation}} installed in the walls and ceilings of buildings.
|-
! scope="row"| Seeds
|Part of a fruit.
|-
! scope="row"| {{w|Pith}}
|Part of a tree trunk or the thick spongy layer of the skin of a citrus fruit
|-
! scope="row"| Nougat
|{{w|Nougat}} is a family of confections made with sugar or honey, roasted nuts, whipped egg whites, and sometimes chopped candied fruit.
|-
! scope="row"| {{w|Outer core}}
| An actual layer of the earth's structure.
|-
! scope="row"| {{w|Inner core}}
| An actual layer of the earth's structure.
|-
! scope="row"| Secret core
| The "next layer" that is secret and only certain people, like Randall, know about it.
|-
! scope="row"| Kinder toy capsule
| A {{w|Kinder (brand)|Kinder}} toy is a reference to two chocolate egg-shaped confections by the Kinder brand, the {{w|Kinder Joy}} and {{w|Kinder Surprise}}. Both contain small toys within it, though the Kinder Surprise was banned in the US because it exceeds the limit of non-food that can be inside a food item (although it is widely believed that it's because it can be a choking hazard, despite the fact that you'd have to be swallowing a chicken egg-sized confectionery in a single mouthful for that to happen; the toys, on the other hand, may contain brightly coloured small pieces that can pose a choking hazard). Randall's punch line of the comic is that there is a hidden toy at the center of the Earth. The title text elaborates on this further, stating that due to an "unexplained mismatch" with other models, some geophysicists argue that the hidden toy is - or at least contains - some form of magnet.

|}

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:The layers of the Earth

:Lithosphere/crust (50/50 blend)
:Upper mantle
:Deep mantle
:Filler
:Vitreous humor
:Mechanical/HVAC layer
:Guacamole
:Cytoplasm
:Cork
:Insulation
:Seeds
:Pith
:Nougat
:Outer core
:Inner core
:Secret core
:Kinder toy capsule

{{comic discussion}}

[[Category:Comics with color]]
[[Category:Geology]]
[[Category:Food]]

Talk:2835: Factorial Numbers

2023-10-01T18:36:44Z

47 Radians Felsius:

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 the various arrangements of digits in numbers 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)

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)

== 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)

== 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)
: 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)

== 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 the radix 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(to_string(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

2835: Factorial Numbers

2023-09-30T16:01:38Z

47 Radians Felsius:

{{comic
| number = 2835
| date = September 29, 2023
| title = Factorial Numbers
| image = factorial_numbers_2x.png
| imagesize = 628x481px
| noexpand = true
| titletext = So what do we do when we get to base 10? Do we use A, B, C, etc? No: Numbers larger than about 3.6 million are simply illegal.
}}

==Explanation==
{{incomplete|Created by a VARIABLE-BASED BOT BEING ESCORTED OUT OF THE COMPUTER SCIENCE DEPARTMENT BY SECURITY - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

This comic is based on the {{w|factorial number system}}, which is a way of writing integers or real numbers using {{w|factorial|factorials}} instead of powers. Unlike the 'proper' version of this system, [[Randall]]'s version does not include the rightmost digit that adds no information, since it is always 0.

A factorial is a product of positive integers. For instance, four factorial, written '4!', means 4×3×2×1 = 24. These can be used to write numbers in a strange way.

Normally, numbers are represented in a positional system with a constant base, especially base ten. This means that each digit in a number has a place value based on its position, and that value is a power of ten. For instance, the number 137 usually means 1×10² + 3×10¹ + 7×10⁰, i.e. one hundred, three tens, and seven units. We say that the 1 is in the hundreds place, the 3 in the tens place, and the 7 in the ones place (or units). The same number could be written in base sixteen as 89, meaning 8×16¹ + 9×16⁰, i.e. eight sixteens and nine units. The 8 is in the sixteens place, and the 9 is in the ones place.

In a "factorial base," instead of each place value being an escalating power of some constant base, each place value is an escalating factorial. The amount to multiply each place value by to get the next place value increases by 1 each time. So that same number (137 in base 10) could be written 10221, meaning 1×5! + 0×4! + 2×3! + 2×2! + 1×1!. We could say there is a 1 in the 120s place, a 0 in the 24s place, a 2 in the 6s place, another 2 in the 2s place, and a 1 in the ones place.

In normal base-n notation, n digits are used, running from 0 to n–1. For instance, in base ten, we use the ten digits {0,...,9}. In base sixteen, we need sixteen digits, so we use {0,...,9,A,...,F}. Any of these digits can be used in any position. But in factorial base, each position needs an increasing number of different digits to express all n-digit numbers. The comic labels each position with the equivalent base that would allow the same digits, e.g. the place value 3! is "base 4" because it uses the digits 0 to 3.

For instance, with just two digits, we can express some numbers with the digits 0, 1, and 2, like 21 = five. But we can't express 30 = six. As a result, Randall jokes that since we only have ten digits {0,...,9}, we can only express numbers with up to nine digits, making larger numbers "illegal." Randall believes that would make the largest "legal" factorial base number 987654321 = 9×9!+8×8!+7×7!+6×6!+5×5!+4×4!+3×3!+2×2!+1×1!, which in base ten is 3,628,799 (which he calls "about 3.6 million"). In fact, adding one to this number gives 1000000000, which still doesn't require any digits larger than 9, but he may wishes to stay away from the mere possibility of representing the digit that ''ought'' to use another symbol. The first number that actually cannot be represented with our usual ten symbols {0,...,9} comes right after 9987654321, which in decimal equals 36,287,999.

In the comic, the top example represents 3×720 + 5×120 + 3×24 + 0×6 + 1×2 + 1×1, after calculating each factorial accordingly, which gives the decimal value of 2835, [[2835|this comic's number]].

For completion of the examples shown in the panel, the numbers up to 200 in this variable base are:

1=1
2=10
3=11
4=20
5=21
6=100
7=101
8=110
9=111
10=120
11=121
12=200
13=201
14=210
15=211
16=220
17=221
18=300
19=301
20=310
21=311
22=320
23=321
24=1000
25=1001
26=1010
27=1011
28=1020
29=1021
30=1100
31=1101
32=1110
33=1111
34=1120
35=1121
36=1200
37=1201
38=1210
39=1211
40=1220
41=1221
42=1300
43=1301
44=1310
45=1311
46=1320
47=1321
48=2000
49=2001
50=2010
51=2011
52=2020
53=2021
54=2100
55=2101
56=2110
57=2111
58=2120
59=2121
60=2200
61=2201
62=2210
63=2211
64=2220
65=2221
66=2300
67=2301
68=2310
69=2311
70=2320
71=2321
72=3000
73=3001
74=3010
75=3011
76=3020
77=3021
78=3100
79=3101
80=3110
81=3111
82=3120
83=3121
84=3200
85=3201
86=3210
87=3211
88=3220
89=3221
90=3300
91=3301
92=3310
93=3311
94=3320
95=3321
96=4000
97=4001
98=4010
99=4011
100=4020
101=4021
102=4100
103=4101
104=4110
105=4111
106=4120
107=4121
108=4200
109=4201
110=4210
111=4211
112=4220
113=4221
114=4300
115=4301
116=4310
117=4311
118=4320
119=4321
120=10000
121=10001
122=10010
123=10011
124=10020
125=10021
126=10100
127=10101
128=10110
129=10111
130=10120
131=10121
132=10200
133=10201
134=10210
135=10211
136=10220
137=10221
138=10300
139=10301
140=10310
141=10311
142=10320
143=10321
144=11000
145=11001
146=11010
147=11011
148=11020
149=11021
150=11100
151=11101
152=11110
153=11111
154=11120
155=11121
156=11200
157=11201
158=11210
159=11211
160=11220
161=11221
162=11300
163=11301
164=11310
165=11311
166=11320
167=11321
168=12000
169=12001
170=12010
171=12011
172=12020
173=12021
174=12100
175=12101
176=12110
177=12111
178=12120
179=12121
180=12200
181=12201
182=12210
183=12211
184=12220
185=12221
186=12300
187=12301
188=12310
189=12311
190=12320
191=12321
192=13000
193=13001
194=13010
195=13011
196=13020
197=13021
198=13100
199=13101
200=13110

Note the apparent gap at 24 (4!) and 120 (5!) - apparent for those of us who are used to decimal numbers.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon. - Still needs a lot of deconstruction/reconstruction work on the [Poster:] to make it properly Transcripted (no tables, ideally!), but have improved the surrounding markup/descriptions}}
:[Cueball is standing in front of a large poster. There are two uniformed officers (a Ponytail and a further Cueball, wearing badged hats) approaching Cueball.]
:[Poster:]

:Variable-base Factoradic™ numbers
:{|
|Base 7||Base 6||Base 5||Base 4||Base 3||Base 2
|-
|3||5||3||0||1||1
|}

:Left side

:{| class="wikitable"
|Base 10||Factoradic
|-
|1||1
|-
|2||10
|-
|3||11
|-
|4||20
|-
|5||21
|-
|6||100
|-
|7||101
|-
|
|-
|21||311
|-
|22||320
|-
|23||321
|}

:Right side

:{| class="wikitable"
|Base 10||Factoradic
|-
|24||1,000
|-
|25||1,001
|-
|
|-
|5,038||654,320
|-
|5,039||654,321
|-
|5,040||1,000,000
|-
|
|-
|999,998||266,251,210
|-
|999,999||266,251,211
|-
|1,000,000||266,251,220
|-
|1,000,001||266,251,221
|}

:Cueball: Small numbers like seven or nineteen shouldn't use big numerals like "7" or "9".
:Cueball: I mean, "9" is the biggest numeral we have! It should be reserved for '''''big''''' numbers.
:Cueball: Small numbers should be written with small numerals like "1" or "2".
:Cueball: That's why my variable-base system uses...Hey! No, listen!
:[Caption under the comic:] Factorial numbers are the number system that sounds most like a prank by someone who's about to be escorted out of the math department by security.

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Characters with hats]]
[[Category:Math]]
[[Category:Self-reference]] 
[[Category:Comics featuring Ponytail]] 
[[Category:Multiple Cueballs]]

2835: Factorial Numbers

2023-09-29T23:02:50Z

47 Radians Felsius:

2835: Factorial Numbers

2023-09-29T23:01:12Z

47 Radians Felsius: