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	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=2983:_Monocaster&amp;diff=356136</id>
		<title>2983: Monocaster</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=2983:_Monocaster&amp;diff=356136"/>
				<updated>2024-11-07T16:06:21Z</updated>
		
		<summary type="html">&lt;p&gt;172.71.134.31: /* Explanation */ Nostalgia for the old blue and red steel tubes, long before &amp;quot;cast aluminium yuppy kick-scooters&amp;quot; revived the general form...&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 2983&lt;br /&gt;
| date      = September 9, 2024&lt;br /&gt;
| title     = Monocaster&lt;br /&gt;
| image     = monocaster_2x.png&lt;br /&gt;
| imagesize = 536x673px&lt;br /&gt;
| noexpand  = true&lt;br /&gt;
| titletext = My competitors say the tiny single tiny caster is unsafe, unstable, and offers no advantages over traditional designs, to which I say: wow, why are you guys so mean? I thought we were friends!&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
A caster, also spelled castor, is a small unpowered wheel, usually attached to a swiveling base. They are typically found on carts and office chairs to make them easy to move, and may be placed on heavy appliances to facilitate movement.&lt;br /&gt;
&lt;br /&gt;
Randall has proposed a variant of the skateboard with only one caster on the bottom, the titular &amp;quot;monocaster&amp;quot;, and devoted most of the comic to a {{w|Perceptual mapping|perceptual map}} showing the variety of wheeled vehicles. Market strategists and investors use such diagrams as a simple way of representing important differences between products or companies, but where a consumer might be more concerned with features like speed, cost, ease of use, or carrying capacity, this map focuses on the number of wheels (horizontal axis) and the diameter of those wheels (vertical axis).&lt;br /&gt;
&lt;br /&gt;
Each axis uses a logarithmic scale, which is convenient for making the map look more evenly filled but also visually exaggerates the size of the &amp;quot;key gap&amp;quot; that the monocaster is filling, which can be described as &amp;quot;vehicle with a single wheel smaller than 25 cm&amp;quot;. The nearest competitors appear to be a two-wheel skateboard sometimes called a {{w|caster board}} (wheel diameter under 8 cm) and a single-wheel self-balancing board resembling a {{w|Onewheel}} (diameter around 25 cm). The Onewheel is sometimes described as a {{w|monowheel}} (though these are traditionally larger like the &amp;quot;1920s monowheel&amp;quot; on the upper left). Randall appears to have combined these two names to create the monocaster. This gives up several of the competitors' features - the caster board's two wheels provide enough stability to propel the vehicle manually, while the Onewheel's single wheel is wide (assisting with sideways balance) and powered by a self-balancing mechanism.&lt;br /&gt;
&lt;br /&gt;
The result resembles a {{w|Balance board#Sphere-and-ring|&amp;quot;Sphere-and-ring&amp;quot; balance board}}, or other types, though these provide limited locomotion potential. The joke depends on the caster's obvious impracticality in this role: the hole in the market was open ''for a reason''. The obvious drawback to any single-wheeled vehicle is that it's difficult to balance: the rider has to avoid falling forward or backward, as well as to either side. This is a major reason why one-wheeled vehicles are uncommon to begin with, but those vehicles which do exist compensate by using relatively large wheels, driven either by human power or a motor, which creates rotational inertia and allows the rider to balance simply by leaning forward. &lt;br /&gt;
&lt;br /&gt;
A single, small, undriven wheel eliminates these balancing forces, meaning that the user would essentially need to balance on a single point. Also, most casters swivel, meaning that the balance point would move around under the rider's feet and make it even more difficult to balance. In addition, there's no apparent means of propulsion, which means the only way to move forward would be to either roll exclusively downhill, or use one foot to push off the ground. Either strategy would make retaining balance almost impossible. &lt;br /&gt;
&lt;br /&gt;
Multiple-wheeled vehicles greatly reduce the issue of balance simply by having multiple points of contact with the ground. The size of the wheels varies greatly; small, rigid wheels are generally suitable only for flat, smooth, rigid surfaces at relatively slow speeds, while vehicles expected to handle high speeds and varying road (and off-road) conditions will necessarily have larger wheels. &lt;br /&gt;
&lt;br /&gt;
The &amp;quot;monocaster&amp;quot; design offers no advantages and would be nearly unrideable, making it obvious why such a vehicle has never been seriously proposed. &lt;br /&gt;
&lt;br /&gt;
The title text extends the joke by listing the disadvantages mentioned above, but not providing a rebuttal. Instead it only attempts an emotional appeal by saying that the competitors are being mean and by commenting that Randall believed they were friends.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=wikitable&lt;br /&gt;
! scope=&amp;quot;col&amp;quot; | Vehicle&lt;br /&gt;
! scope=“col” | Number of wheels&lt;br /&gt;
! scope=“col” | Wheel Diameter&lt;br /&gt;
! scope=&amp;quot;col&amp;quot; | Explanation&lt;br /&gt;
|-&lt;br /&gt;
| 1920s Monowheel || 1 || 3 meters ||  A monowheel is a vehicle in which the rider sits inside a single, large, hollow wheel. Versions have existed which were hand- or pedal-cranked, but the &amp;quot;1920s&amp;quot; version portrayed here is apparently motor-driven. These vehicles have generally been seen as novelties, as their stability and practicality issues limit their usefulness for actual transport. &lt;br /&gt;
|-&lt;br /&gt;
| Unicycle || 1 || 45 centimeters ||  Probably the best known single-wheeled form of transport, a unicycle consists of a single wheel, usually driven directly by pedals, with a seat mounted on top. Due to their difficulty, they are most commonly used as novelties and for comic performances, more than as practical transport. &lt;br /&gt;
|-&lt;br /&gt;
| OneWheel || 1 || 20 centimeters ||  A one-wheeled electric skateboard in which the user stands on both sides of a large, central wheel. The design self-balances by increasing the velocity as the user leans forward. This allows balancing and speed control to operate in a single motion. &lt;br /&gt;
|-&lt;br /&gt;
| Bicycle || 2 || 45 centimeters ||  A two-wheeled, pedal-driven vehicle. The relatively simple, inexpensive and efficient design of these vehicles makes them practical for transport in a variety of situations. As a result, they've long been among the most popular and widely-produced vehicles in the world.&lt;br /&gt;
|-&lt;br /&gt;
| Scooter || 2 || 8 centimeters (*) || A two-wheeled vehicle driven either by pushing with a foot or by an electric motor or fuel-powered engine. Scooters are ridden both for recreation and as a form of transportation in cities.&lt;br /&gt;
|-&lt;br /&gt;
| {{w|Roller shoe}} || 2 || 1 centimeter (*) || Shoes with small wheels built into the back end of the soles, putting them underneath the wearer's heels (which is what the brand-name  &amp;quot;{{w|Heelys}}&amp;quot; is derived from). They allow the user access to wheeled movement by pushing off the ground and balancing on the slightly protuding wheels. They are not as fast or comfortable as a dedicated wheeled vehicle, their rolling action is limited to sufficiently flat surfaces and they are not as easy as regular shoes to simply walk in. However, such shoes allow for some degree of both walking ''and'' rolling without having to carry a separate wheeled vehicle, or necessarily having the baseline difficulty of other 'fuller' versions of wearable skates.&lt;br /&gt;
|-&lt;br /&gt;
| Tricycle || 3 || 20 centimeters || Appears to be a {{w|Big Wheel (tricycle)|&amp;quot;Big Wheel&amp;quot; type}} child's toy, which actually have smaller 'trailing wheels', rather than either {{w|Tricycle#Upright|upright}} or {{w|Tricycle#Recumbent|recumbent}} style cycles for adults which ''usually'' match the wheel-sizes of their bicycle equivalents.&lt;br /&gt;
|-&lt;br /&gt;
| Scooter (three-wheeled) || 3 || 3 centimeters (*) ||  Very similar to two-wheeled scooters (see above), but using two wheels in the front instead of three. This increases stability but makes the scooter less maneuverable. The modern 'tail-wheel' variant as shown (usually with lean-and-steer front wheels, rather than handlebar twisting) has superseded the traditional tricycle layout (closely paired rear wheels, single steerable front wheel) that was the more usual three-wheel version of children's scooters in the decades before the millenium. The steering geometries and ride behaviours of each type experience significantly different advantages and flaws, both also handling differently from the typical two-wheel version.&lt;br /&gt;
|-&lt;br /&gt;
| Monster Truck || 4 || 2.5 meters || Monster trucks are vehicles equipped with (usually four, but sometimes more) outsize wheels. They are almost always driven as part of events where specifically trained drivers use them to perform dangerous stunts and crush smaller vehicles. Because of their size, the danger to other vehicles, often very poor mileage, and design choices that can be in violation of local laws and regulations regarding motorized vehicles, monster trucks are generally illegal to drive on public roads and have to be transported in dedicated trailers, making them poor choices for transport where one has to leave private property.&lt;br /&gt;
|-&lt;br /&gt;
| Car || 4 || 50 centimeters || Cars are motorized vehicles designed to move one or more people and an amount of goods around fast. While almost all cars have four wheels (discounting reserve wheels), there are a few that have more than four (certain limousines) or fewer (the Reliant Robin only has one wheel in the front). Cars are more expensive than most options on the chart due to their higher cost, the use of fuel and maintenance requiring specialized knowledge (and sometimes replacement parts), they make up for this with their speed, access to (at least in most of the world) an extensive system of roads and refueling stations, the ability to move a number of people and goods, and the comfort of being in what is almost always an enclosed and air conditioned compartment. Because of the potential danger of an object of a car's size and speed, drivers are required to perform a test of their ability to both control the vehicle and be aware of other traffic to obtain a license to drive one. Cars are a common source of leisure, with interests ranging from driving them normally, driving them as part of a race, maintaining them or enjoying luxury cars.&lt;br /&gt;
|-&lt;br /&gt;
| ATV || 4 || 20 centimeters (*) || ATVs or &amp;quot;all-terrain vehicles&amp;quot; are unenclosed, handlebar-steered vehicles designed for off-road riding. They have four, large, low-pressure tires and a robust suspension system to accommodate rough terrain. They generally aren't designed to carry passengers, and have limited cargo capacity, which limits their usefulness for regular transport. They're generally used either for recreation or for transport in areas without well-maintained roads. &lt;br /&gt;
|-&lt;br /&gt;
| Skateboard || 4 || 2 centimeters (*) || Skateboards consist of a single board with four, small rigid wheels attached. They are propelled by pushing off the ground with one foot (or by coasting downhill). They're commonly used for recreation and trick-riding, but can be used for short-distance transport where well-maintained and flat roads are available. &lt;br /&gt;
|-&lt;br /&gt;
| Three-Wheel Skates|| 6 || 4 centimeters (*) || Three-wheeled skates are a type of inline skate (shoes with a line of wheels affixed underneath the shoe) that differ from the more commonly used four wheeled inline skates by having three larger wheels. They are inexpensive and easy to maintain, but they require significant skill to use effectively and the user is reliant on smooth surfaces to skate around on. Another downside is that the wheels cannot be removed from the shoes, requiring the user to either carry an extra pair or have an extra pair at their destination.&lt;br /&gt;
|-&lt;br /&gt;
| Roller Skates|| 8 || 2 centimeters (*) || Roller skates are shoes with small wheels underneath them in a rectangular pattern. This makes roller skates much more stable than inline skates, allowing users to stand on them with more ease. Like inline skates they are cheap and low maintenance, but in order to move any significant distance without support they require a skilled user, smooth surfaces and the user needs backup shoes when taking them off (though there exist strap-on roller skates).&lt;br /&gt;
|-&lt;br /&gt;
| Semi-Trailer Truck (Articulated Lorry) || 10-18 || 1 meter || A semi-trailer truck is a motorized vehicle designed to pull trailers that can be easily decoupled from the truck itself. This allows the truck to switch trailers and move a different cargo without having to unload the trailer. The name in brackets that was used here (articulated lorry) is a name most commonly used in British English (or &amp;quot;artic&amp;quot;, for short), with articulation meaning that the truck can swivel at the point where the truck connects to the trailer. This allows for the truck to make much tighter turns than if it were one long vehicle, which is another advantage of this configuration, with typically more stability than with a {{w|Drawbar (haulage)|drawbar}} attachment. Trucks are designed to haul cargo for long distances, with the cargo in question being either too heavy or too large to carry with a smaller hopper, tanker, hard-/soft-sided container or flatbed placed entirely upon a single truck chassis. They are driven either by drivers employed by a transport company, or by self-employed individuals who haul cargo for a living. A specialized license is required to drive one, and because of their size (even without a trailer), trucks have more limitations on where they can drive and park than normal cars. Like cars, trucks are a source of leisure, but because of the higher cost to purchase, maintain and drive them, they are more often enjoyed for their aesthetics rather than actually driving them for leisure. There are events like races for trucks, and trucks can be given elaborate paint jobs to have them stand out.&lt;br /&gt;
The number of wheels is for both the {{w|Tractor unit#Axles|truck}} and a {{w|Semi-trailer#Types|trailer}}, which can each differ vastly between vehicle configurations.  The truck in the comic has five ''obvious'' axle-sets (thus at least ten actual wheels): a single pair of front wheels, two pairs of trailer-bearing rear wheels and two pairs of wheels on the trailer itself. The drawing of the truck actually spans the axis range of three wheels (unlikely to be true, and the minimum for a tractor-trailer would normally be six) all the way up to 16, so it's not entirely clear which number (≥10) Randall intends this one to portray. Most of the other illustrations are roughly centered over the relevant number of wheels, but applying this to the truck implies six wheels, which is clearly wrong as illustrated.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(*) It seems that Randall has made some mistakes in regards to the wheel sizes, especially in the centimeter range of the diagram. Most of the vehicles have bigger wheels and the number would suggest hat he meant inches instead of centimeters. Alternatively, he may have mistakenly recorded the wheels' radius instead of its diameter, as intended.&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
{{incomplete transcript|Do NOT delete this tag too soon.}}&lt;br /&gt;
&lt;br /&gt;
:[A chart picturing many wheeled vehicles with a caption below the chart window. The vertical axis is labeled &amp;quot;Wheel Diameter&amp;quot;, logarithmic from 1cm to 5m. The horizontal axis is labeled &amp;quot;Number of wheels&amp;quot;, logarithmic from 1 to 16. From top left to bottom right, there is a person with a cap, seated in a circle, labeled &amp;quot;1920s monowheel&amp;quot;, a monster truck with a skull and a lightning bolt on the side, a lorry (truck), a Cueball on a unicycle moving back and forth, a Cueball on a bicycle, a car, a Cueball using a Onewheel, a Cueball on a child's &amp;quot;Big Wheel&amp;quot; tricycle, a Cueball on a quad, a Cueball standing on a scooter, a Cueball standing on a board with one small wheel bellow, circled and labeled with two question marks, a three-wheel scooter, a skater, a Cueball using three-wheel skates, labeled &amp;quot;three-wheel skates&amp;quot;, a Cueball crouching and using skates, and a small Cueball using shoes with wheels (Heelys) moving forward.]&lt;br /&gt;
:Caption:  My new monocaster board fills a key gap in the wheeled vehicle market.&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Charts]]&lt;br /&gt;
[[Category:Scatter plots]]&lt;br /&gt;
[[Category:Comics featuring Cueball]]&lt;br /&gt;
[[Category:Multiple Cueballs]]&lt;br /&gt;
[[Category:Characters with hats]]&lt;br /&gt;
[[Category:Skateboard]]&lt;/div&gt;</summary>
		<author><name>172.71.134.31</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=Talk:2870:_Love_Songs&amp;diff=331292</id>
		<title>Talk:2870: Love Songs</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=Talk:2870:_Love_Songs&amp;diff=331292"/>
				<updated>2023-12-21T18:46:10Z</updated>
		
		<summary type="html">&lt;p&gt;172.71.134.31: Questioning whether data point for &amp;quot;Girlfriend&amp;quot; fit's Avril Lavigne's Song&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&amp;lt;!--Please sign your posts with ~~~~ and don't delete this text. New comments should be added at the bottom.--&amp;gt;&lt;br /&gt;
&lt;br /&gt;
I need to know which axis means “does the ‘me’ like them” because I fail to understand it.--[[Special:Contributions/172.71.134.164|172.71.134.164]] 23:53, 20 December 2023 (UTC)&lt;br /&gt;
:Pick a song you know that isn't near the (X=Y) line, and it should explain it.&lt;br /&gt;
:e.g. &amp;quot;That don't impress me much&amp;quot;, at centre-top. Clearly the other party is trying to impress (likes the 'me') but Shania is ambivalent in response (she doesn't actually love their being a rocket-scientist, nor hate it).&lt;br /&gt;
:&amp;quot;Killing me softly...&amp;quot; is from 'me' having love, whilst &amp;quot;You're so vain...&amp;quot; is actively insulting the other party (but indifference by the target ''could'' be the attitude).&lt;br /&gt;
:Though for X=Y items (e.g. &amp;quot;I will survive&amp;quot; - it's declared to be an unamicable but ultimately mutually-acceptable split) the way round of course doesn't matter. [[Special:Contributions/172.69.194.224|172.69.194.224]] 00:12, 21 December 2023 (UTC)&lt;br /&gt;
&lt;br /&gt;
I'm hoping &amp;quot;I Will Survive&amp;quot; isn't a reference to the Zootopia abortion comic. [[Special:Contributions/172.68.174.82|172.68.174.82]] 23:56, 20 December 2023 (UTC)&lt;br /&gt;
:Well, some of the (apparently obvious) references I didn't know. First thought about &amp;quot;Girlfriend&amp;quot; was the {{w|Girlfriend in a Coma (song)|The Smiths song}} ''almost'' of that name. (And it looks like there are almost thirty possible songs... not sure how many are covers of others... {{w|Girlfriend (disambiguation)#Songs|under that exact name}}.) Can I suggest that any possible songs that could be confused (but maybe not match the plotted position, being of a different story/tone) be recorded in a &amp;quot;Not to be confused with...&amp;quot; section? [[Special:Contributions/172.71.178.177|172.71.178.177]] 01:02, 21 December 2023 (UTC)&lt;br /&gt;
&lt;br /&gt;
not pictured: Jim Steinman songs, which spend most of their time out of the XY plane. [[Special:Contributions/172.69.214.109|172.69.214.109]] 00:14, 21 December 2023 (UTC)&lt;br /&gt;
&lt;br /&gt;
Gotta say, Perfect is a far better Ed Sheeran song than Shape of You&lt;br /&gt;
&lt;br /&gt;
The fault here is not so much with the axes or their interpretation as with the verb, &amp;quot;to love.&amp;quot; [http://www.lel.ed.ac.uk/~heycock/thurber-only.html Nothing can be done about the verb &amp;quot;to love.&amp;quot;] [[Special:Contributions/172.70.210.62|172.70.210.62]] 04:19, 21 December 2023 (UTC)&lt;br /&gt;
&lt;br /&gt;
(reads comic) (automatically sorts in all &amp;quot;Offspring&amp;quot; love songs) (thanks very much, xkcd, you got me again) [[Special:Contributions/172.71.160.124|172.71.160.124]] 09:24, 21 December 2023 (UTC)&lt;br /&gt;
&lt;br /&gt;
&amp;quot;Girlfriend&amp;quot; by Matthew Sweet doesn't remotely follow the narrative in the explanation, but could nevertheless be graphed as shown.[[User:Yorkshire Pudding|Yorkshire Pudding]] ([[User talk:Yorkshire Pudding|talk]]) 10:07, 21 December 2023 (UTC)&lt;br /&gt;
&lt;br /&gt;
Why is &amp;quot;I Will Always Love You&amp;quot; higher on the Y axis than the X axis?? The title and chorus seem genuine to me, and the rationale for breaking up is &amp;quot;I'm not what you need.&amp;quot; [[Special:Contributions/172.68.34.58|172.68.34.58]] 15:08, 21 December 2023 (UTC)&lt;br /&gt;
&lt;br /&gt;
I love the way this came out. Mad props to everyone who worked on the table summaries. Were LLMs employed? [[User:Liv2splain|Liv2splain]] ([[User talk:Liv2splain|talk]]) 18:31, 21 December 2023 (UTC)&lt;br /&gt;
&lt;br /&gt;
In my opinion the Y-Axis of &amp;quot;Girlfriend&amp;quot; does not fit Avril Lavigne's &amp;quot;Girlfriend&amp;quot;, it should be closer to &amp;quot;Yes&amp;quot; than to &amp;quot;No&amp;quot;. The lyrics include &amp;quot;I see the way you look at me [...] I know you talk about me all the time again and again&amp;quot;.&lt;br /&gt;
If the video counts: The guy ends up without his girlfriend (red-haired Avril) and seems to always enjoy the company and a kiss of black-haired Avril. The video ends with him and blond-haired Avril disappearing into a bathroom stall. Whomever you see as the &amp;quot;I&amp;quot; in the song, black-haired or blond-haired Avril, he seems sorta interested in both, so a &amp;quot;Yes&amp;quot;. [[Special:Contributions/172.71.134.31|172.71.134.31]] 18:46, 21 December 2023 (UTC)&lt;/div&gt;</summary>
		<author><name>172.71.134.31</name></author>	</entry>

	<entry>
		<id>https://www.explainxkcd.com/wiki/index.php?title=2835:_Factorial_Numbers&amp;diff=324650</id>
		<title>2835: Factorial Numbers</title>
		<link rel="alternate" type="text/html" href="https://www.explainxkcd.com/wiki/index.php?title=2835:_Factorial_Numbers&amp;diff=324650"/>
				<updated>2023-09-30T14:25:19Z</updated>
		
		<summary type="html">&lt;p&gt;172.71.134.31: Undo revision 324649 by 162.158.203.165 (talk) Still incomplete. (I've got things to add, when I've got time,. And surely others have, well within 24 hours of starting.)&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{comic&lt;br /&gt;
| number    = 2835&lt;br /&gt;
| date      = September 29, 2023&lt;br /&gt;
| title     = Factorial Numbers&lt;br /&gt;
| image     = factorial_numbers_2x.png&lt;br /&gt;
| imagesize = 628x481px&lt;br /&gt;
| noexpand  = true&lt;br /&gt;
| 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.&lt;br /&gt;
}}&lt;br /&gt;
&lt;br /&gt;
==Explanation==&lt;br /&gt;
{{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.}}&lt;br /&gt;
&lt;br /&gt;
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.&lt;br /&gt;
&lt;br /&gt;
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.&lt;br /&gt;
&lt;br /&gt;
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. &lt;br /&gt;
&lt;br /&gt;
In a &amp;quot;factorial base,&amp;quot; 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.&lt;br /&gt;
&lt;br /&gt;
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 &amp;quot;base 4&amp;quot; because it uses the digits 0 to 3. &lt;br /&gt;
&lt;br /&gt;
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 &amp;quot;illegal.&amp;quot; Randall believes that would make the largest &amp;quot;legal&amp;quot; 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 &amp;quot;about 3.6 million&amp;quot;). 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.&lt;br /&gt;
&lt;br /&gt;
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]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For completion of the examples shown in the panel, the numbers up to 200 in this variable base are:&lt;br /&gt;
&lt;br /&gt;
1=1&lt;br /&gt;
2=10&lt;br /&gt;
3=11&lt;br /&gt;
4=20&lt;br /&gt;
5=21&lt;br /&gt;
6=100&lt;br /&gt;
7=101&lt;br /&gt;
8=110&lt;br /&gt;
9=111&lt;br /&gt;
10=120&lt;br /&gt;
11=121&lt;br /&gt;
12=200&lt;br /&gt;
13=201&lt;br /&gt;
14=210&lt;br /&gt;
15=211&lt;br /&gt;
16=220&lt;br /&gt;
17=221&lt;br /&gt;
18=300&lt;br /&gt;
19=301&lt;br /&gt;
20=310&lt;br /&gt;
21=311&lt;br /&gt;
22=320&lt;br /&gt;
23=321&lt;br /&gt;
24=1000&lt;br /&gt;
25=1001&lt;br /&gt;
26=1010&lt;br /&gt;
27=1011&lt;br /&gt;
28=1020&lt;br /&gt;
29=1021&lt;br /&gt;
30=1100&lt;br /&gt;
31=1101&lt;br /&gt;
32=1110&lt;br /&gt;
33=1111&lt;br /&gt;
34=1120&lt;br /&gt;
35=1121&lt;br /&gt;
36=1200&lt;br /&gt;
37=1201&lt;br /&gt;
38=1210&lt;br /&gt;
39=1211&lt;br /&gt;
40=1220&lt;br /&gt;
41=1221&lt;br /&gt;
42=1300&lt;br /&gt;
43=1301&lt;br /&gt;
44=1310&lt;br /&gt;
45=1311&lt;br /&gt;
46=1320&lt;br /&gt;
47=1321&lt;br /&gt;
48=2000&lt;br /&gt;
49=2001&lt;br /&gt;
50=2010&lt;br /&gt;
51=2011&lt;br /&gt;
52=2020&lt;br /&gt;
53=2021&lt;br /&gt;
54=2100&lt;br /&gt;
55=2101&lt;br /&gt;
56=2110&lt;br /&gt;
57=2111&lt;br /&gt;
58=2120&lt;br /&gt;
59=2121&lt;br /&gt;
60=2200&lt;br /&gt;
61=2201&lt;br /&gt;
62=2210&lt;br /&gt;
63=2211&lt;br /&gt;
64=2220&lt;br /&gt;
65=2221&lt;br /&gt;
66=2300&lt;br /&gt;
67=2301&lt;br /&gt;
68=2310&lt;br /&gt;
69=2311&lt;br /&gt;
70=2320&lt;br /&gt;
71=2321&lt;br /&gt;
72=3000&lt;br /&gt;
73=3001&lt;br /&gt;
74=3010&lt;br /&gt;
75=3011&lt;br /&gt;
76=3020&lt;br /&gt;
77=3021&lt;br /&gt;
78=3100&lt;br /&gt;
79=3101&lt;br /&gt;
80=3110&lt;br /&gt;
81=3111&lt;br /&gt;
82=3120&lt;br /&gt;
83=3121&lt;br /&gt;
84=3200&lt;br /&gt;
85=3201&lt;br /&gt;
86=3210&lt;br /&gt;
87=3211&lt;br /&gt;
88=3220&lt;br /&gt;
89=3221&lt;br /&gt;
90=3300&lt;br /&gt;
91=3301&lt;br /&gt;
92=3310&lt;br /&gt;
93=3311&lt;br /&gt;
94=3320&lt;br /&gt;
95=3321&lt;br /&gt;
96=4000&lt;br /&gt;
97=4001&lt;br /&gt;
98=4010&lt;br /&gt;
99=4011&lt;br /&gt;
100=4020&lt;br /&gt;
101=4021&lt;br /&gt;
102=4100&lt;br /&gt;
103=4101&lt;br /&gt;
104=4110&lt;br /&gt;
105=4111&lt;br /&gt;
106=4120&lt;br /&gt;
107=4121&lt;br /&gt;
108=4200&lt;br /&gt;
109=4201&lt;br /&gt;
110=4210&lt;br /&gt;
111=4211&lt;br /&gt;
112=4220&lt;br /&gt;
113=4221&lt;br /&gt;
114=4300&lt;br /&gt;
115=4301&lt;br /&gt;
116=4310&lt;br /&gt;
117=4311&lt;br /&gt;
118=4320&lt;br /&gt;
119=4321&lt;br /&gt;
120=10000&lt;br /&gt;
121=10001&lt;br /&gt;
122=10010&lt;br /&gt;
123=10011&lt;br /&gt;
124=10020&lt;br /&gt;
125=10021&lt;br /&gt;
126=10100&lt;br /&gt;
127=10101&lt;br /&gt;
128=10110&lt;br /&gt;
129=10111&lt;br /&gt;
130=10120&lt;br /&gt;
131=10121&lt;br /&gt;
132=10200&lt;br /&gt;
133=10201&lt;br /&gt;
134=10210&lt;br /&gt;
135=10211&lt;br /&gt;
136=10220&lt;br /&gt;
137=10221&lt;br /&gt;
138=10300&lt;br /&gt;
139=10301&lt;br /&gt;
140=10310&lt;br /&gt;
141=10311&lt;br /&gt;
142=10320&lt;br /&gt;
143=10321&lt;br /&gt;
144=11000&lt;br /&gt;
145=11001&lt;br /&gt;
146=11010&lt;br /&gt;
147=11011&lt;br /&gt;
148=11020&lt;br /&gt;
149=11021&lt;br /&gt;
150=11100&lt;br /&gt;
151=11101&lt;br /&gt;
152=11110&lt;br /&gt;
153=11111&lt;br /&gt;
154=11120&lt;br /&gt;
155=11121&lt;br /&gt;
156=11200&lt;br /&gt;
157=11201&lt;br /&gt;
158=11210&lt;br /&gt;
159=11211&lt;br /&gt;
160=11220&lt;br /&gt;
161=11221&lt;br /&gt;
162=11300&lt;br /&gt;
163=11301&lt;br /&gt;
164=11310&lt;br /&gt;
165=11311&lt;br /&gt;
166=11320&lt;br /&gt;
167=11321&lt;br /&gt;
168=12000&lt;br /&gt;
169=12001&lt;br /&gt;
170=12010&lt;br /&gt;
171=12011&lt;br /&gt;
172=12020&lt;br /&gt;
173=12021&lt;br /&gt;
174=12100&lt;br /&gt;
175=12101&lt;br /&gt;
176=12110&lt;br /&gt;
177=12111&lt;br /&gt;
178=12120&lt;br /&gt;
179=12121&lt;br /&gt;
180=12200&lt;br /&gt;
181=12201&lt;br /&gt;
182=12210&lt;br /&gt;
183=12211&lt;br /&gt;
184=12220&lt;br /&gt;
185=12221&lt;br /&gt;
186=12300&lt;br /&gt;
187=12301&lt;br /&gt;
188=12310&lt;br /&gt;
189=12311&lt;br /&gt;
190=12320&lt;br /&gt;
191=12321&lt;br /&gt;
192=13000&lt;br /&gt;
193=13001&lt;br /&gt;
194=13010&lt;br /&gt;
195=13011&lt;br /&gt;
196=13020&lt;br /&gt;
197=13021&lt;br /&gt;
198=13100&lt;br /&gt;
199=13101&lt;br /&gt;
200=13110&lt;br /&gt;
&lt;br /&gt;
Note the apparent gap at 24 (4!) and 120 (5!) - apparent for those of us who are used to decimal numbers.&lt;br /&gt;
&lt;br /&gt;
==Transcript==&lt;br /&gt;
{{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}}&lt;br /&gt;
:[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.]&lt;br /&gt;
:[Poster:]&lt;br /&gt;
&lt;br /&gt;
:Variable-base Factoradic™ numbers&lt;br /&gt;
:{|&lt;br /&gt;
|Base 7||Base 6||Base 5||Base 4||Base 3||Base 2&lt;br /&gt;
|-&lt;br /&gt;
|3||5||3||0||1||1&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
:Left side&lt;br /&gt;
&lt;br /&gt;
:{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Base 10||Factoradic&lt;br /&gt;
|-&lt;br /&gt;
|1||1&lt;br /&gt;
|-&lt;br /&gt;
|2||10&lt;br /&gt;
|-&lt;br /&gt;
|3||11&lt;br /&gt;
|-&lt;br /&gt;
|4||20&lt;br /&gt;
|-&lt;br /&gt;
|5||21&lt;br /&gt;
|-&lt;br /&gt;
|6||100&lt;br /&gt;
|-&lt;br /&gt;
|7||101&lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
|21||311&lt;br /&gt;
|-&lt;br /&gt;
|22||320&lt;br /&gt;
|-&lt;br /&gt;
|23||321&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
:Right side&lt;br /&gt;
&lt;br /&gt;
:{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|Base 10||Factoradic&lt;br /&gt;
|-&lt;br /&gt;
|24||1,000&lt;br /&gt;
|-&lt;br /&gt;
|25||1,001&lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
|5,038||654,320&lt;br /&gt;
|-&lt;br /&gt;
|5,039||654,321&lt;br /&gt;
|-&lt;br /&gt;
|5,040||1,000,000&lt;br /&gt;
|-&lt;br /&gt;
| &lt;br /&gt;
|-&lt;br /&gt;
|999,998||266,251,210&lt;br /&gt;
|-&lt;br /&gt;
|999,999||266,251,211&lt;br /&gt;
|-&lt;br /&gt;
|1,000,000||266,251,220&lt;br /&gt;
|-&lt;br /&gt;
|1,000,001||266,251,221&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
:[Cueball:] Small numbers like seven or nineteen shouldn't use big numerals like &amp;quot;7&amp;quot; or &amp;quot;9&amp;quot;.&lt;br /&gt;
:[Cueball:] I mean, &amp;quot;9&amp;quot; is the biggest numeral we have! It should be reserved for '''''big''''' numbers.&lt;br /&gt;
:[Cueball:] Small numbers should be written with small numerals like &amp;quot;1&amp;quot; or &amp;quot;2&amp;quot;.&lt;br /&gt;
:[Cueball:] That's why my variable-base system uses...Hey! No, listen!&lt;br /&gt;
:[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.&lt;br /&gt;
&lt;br /&gt;
{{comic discussion}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Comics featuring Cueball]]&lt;br /&gt;
[[Category:Characters with hats]]&lt;br /&gt;
[[Category:Math]]&lt;br /&gt;
[[Category:Self-reference]] &amp;lt;!-- Comic number encoded in image 'example' --&amp;gt;&lt;br /&gt;
[[Category:Comics featuring Ponytail]] &amp;lt;!-- Hatted 'security officer' --&amp;gt;&lt;br /&gt;
[[Category:Multiple Cueballs]] &amp;lt;!-- If including otherwise cueball-like hatted 'security officer' of no other distinction --&amp;gt;&lt;/div&gt;</summary>
		<author><name>172.71.134.31</name></author>	</entry>

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