explain xkcd - User contributions [en]

2687: Division Notation

2022-10-20T09:07:23Z

162.158.166.73: /* Explanation */ paragraph

{{comic
| number = 2687
| date = October 19, 2022
| title = Division Notation
| image = division_notation_new_2x.png
| imagesize = 235x310px
| noexpand = true
| titletext = Science tip: Scientists hardly ever use the two-dot division sign, and when they do it often doesn't even mean division, but they still get REALLY mad when you repurpose it to write stuff like SALE! ALL SHOES 30÷ OFF!
}}

==Explanation==
{{incomplete|Created by a GROUP OF SCHOOLCHILDREN DIVIDED AMONGST THEMSELVES. Do NOT delete this tag too soon.}}

This comic pokes fun at some of the ways to write the {{w|Division (mathematics)|division}} operation in math. In this comic, Randall has used A as the dividend (the number being divided) and B as the divisor (the number that A is divided by). Division is the fourth simplest arithmetic operation in mathematics, after addition, subtraction, and multiplication.[https://plato.stanford.edu/entries/principia-mathematica/#PartIVRelaArit]

The first two of the seven notations shown are the {{w|division sign}} (÷) and the tableau used for {{w|short division}} and {{w|long division}} in beginning arithmetic. (Note: the short/long division tableau is only used in some countries, and there are [https://en.wikipedia.org/wiki/Long_division#Notation_in_non-English-speaking_countries different notations in the non-English speaking world]). These methods of division are often used by school children because the ÷ sign is what most people use when first learning division, and the short division tableau is usually the first algorithm learned for dividing arbitrary dividends, typically starting with the easier abbreviated short division form.

The expression on the third line, A/B, is the way division is usually written in software code. The 4 simple arithmetic operations in programming usually are +, -, *, /. This one was missing in the first version of the comic. This is most commonly seen in regular mathematics as it somewhat saves space, and is easy to type with the slash key. Additionally, it uses standard {{w|ASCII}} characters instead of extended charsets, which would have helped to establish its traditional usage.

The expression on the forth line, a/b, is how the division is usually written when typography costs are not in question, in fraction notation. The Unicode character sets provide some specific fractions such as ⅓ as well as some superscript and subscript characters, so someone familiar with it might use it to write fractions such as ²²⁄₇. But this is tedious and can't be used on more complex expressions, so it is rarely used in everyday life (the fraction A/B cannot be written this way; there is a superscript A, but no subscript B).

The fifth notation is the way division is written in science: dividend on top line and divided on bottom line. This is the closest format to how a {{w|Fraction|fraction}} would be written. It has the advantage of clearly separating the numerator and denominator when they are longer expressions, such as polynomials, without needing to add parentheses. This format is mostly used in written math, as it can't be typed without something like {{w|MathML}}, {{w|LaTeX}} or HTML tables.

The sixth notation uses a negative exponent. The exponent -1 is equivalent to reciprocation. It can be used to keep the entire expression on one line. Note that ab-1 is equal to a/b.

The final form of notation declares a function. The writer defines a new function, F, that takes in the parameters A and B, before listing out the function's definition (trailing off in increasingly smaller text). Randall warns the reader they should escape while they still can, because both the function itself and the math environment as a whole are going to get relatively tedious. Integer division can be defined in terms of multiplicative inequalities and the remainder, or modulo ('%' in Python), operator. This situation is likely to occur in abstract algebra, where one might have to define what "division" means for two elements of a mathematical object such as a group, ring, or magma. One example would be an object G, such that, for two elements A and B of G, "A divided by B" is defined as an element C such that CB=A, or alternatively as an element C such that BC=A. These definitions will differ if multiplication in G is not commutative. Furthermore, if such a C is not unique, the function F(A,B) will need to include a method to select a unique value for "A divided by B" for each A and B. Thus, the F(A,B) in the comic might not even refer to a uniquely defined operation, but simply to the property of a function F(A,B) that is a valid division operation on G, given some definition of division.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:Division notation
:A÷B
:B⟌A Schoolchild.
:A/B Software engineer.
:A⁄B Normal person or Unicode enthusiast.
:A over B Scientist.
:AB-1 Fancy scientist.
:F(A, B) such that F(G)= (text getting smaller) Oh no, run

{{comic discussion}}

[[Category:Math]]
[[Category:Science]]
[[Category:Programming]]
[[Category:Science tip]]

Talk:2687: Division Notation

2022-10-20T09:05:56Z

162.158.166.73: Ratio and metaphor operator :

Fun fact: In Poland, we don't write the long division like that; we just write A:B with the bar above. I was VERY confused the first time I saw that notation. [[Special:Contributions/172.70.246.235|172.70.246.235]] 21:03, 19 October 2022 (UTC)
:Unrelated to {{w|Polish notation}}, i presume? [[Special:Contributions/172.70.134.13|172.70.134.13]] 22:43, 19 October 2022 (UTC)Bumpf
:In German elementary school we learned the a:b notation. When we learned more complex divisions in secondary school it was with the "scientist" notation. And as I am a software engineer AND (presumably) a normal person I use in general the respective notations. [[User:Elektrizikekswerk|Elektrizikekswerk]] ([[User talk:Elektrizikekswerk|talk]]) 07:24, 20 October 2022 (UTC)

For me, the version on the xkcd website has an additional line ("A/B: Software Engineer") that's not on this site. I think the comic might have been updated. Is anyone else seeing that? [[User:JBYoshi|JBYoshi]] ([[User talk:JBYoshi|talk]]) 23:20, 19 October 2022 (UTC)
:Updated. [[User:Natg19|Natg19]] ([[User talk:Natg19|talk]]) 00:31, 20 October 2022 (UTC)

For the Unicode one, I think it’s a reference to ⁄ (U+2044, fraction slash) or characters like ½, ¼, etc. - [[User:Cherryblossom|Cherryblossom]] ([[User talk:Cherryblossom|talk]]) 00:24, 20 October 2022 (UTC)

Is it important to note that 1/2 auctocorrects to ½ in many text-based programs like Microsoft Word?--[[User:Theunlucky|Theunlucky]] ([[User talk:Theunlucky|talk]]) 02:32, 20 October 2022 (UTC)

It's possible to use fraction-style notation in LaTeX by using \frac, or am I missing something?--[[Special:Contributions/162.158.2.125|162.158.2.125]] 05:49, 20 October 2022 (UTC)

"the long division symbol is only used in some countries". Only English-speaking ones, to be more precise. Most of the countries of the world use a different notation. [[Special:Contributions/172.68.51.80|172.68.51.80]] 06:19, 20 October 2022 (UTC)

In the UK, the 'long division symbol' is nowadays often referred to (particularly with Primary classes, children aged 4 - 11) as the "Bus Stop Method". Because it looks like a UK bus shelter. [[User:MarquisOfCarrabass|MarquisOfCarrabass]] ([[User talk:MarquisOfCarrabass|talk]]) 07:07, 20 October 2022 (UTC)

As a Dutch primary schoolchild, I have used a÷b for calculations and "a over b" for fractions (e.g. ⅘).
For more difficult divisions, like what is 785/35, we used [https://nl.m.wikipedia.org/wiki/Staartdeling Staartdelingen] (nl), long division, of which the primary notation is 35/735\.
I think in early highschool we started using a over b for more complex calculations, "like (x+3) over 5 = 2, what is x". I had up to this XKCD never seen B⟌A, and would confuse it for what we use as square root symbol (√). [[User:IIVQ|IIVQ]] ([[User talk:IIVQ|talk]]) 07:16, 20 October 2022 (UTC)
:Come to think of it, it's kind of odd that we used ":" for division. Why are there this many different division notations anyway? Same for multiplication. There's x, *, ⋅, x but centered vertically, and concatenation (for letter variables)!
:: The : operator is for ratios, where a:b could be a/b or b/a, but also metaphors, where a:b::c:d means a is to be as c is to d. [[Special:Contributions/162.158.166.73|162.158.166.73]] 09:05, 20 October 2022 (UTC)

In Austria, school children are using the "scientist" notation from this comic. [[Special:Contributions/172.68.50.51|172.68.50.51]] 08:17, 20 October 2022 (UTC)
* Same thing in Russia [[Special:Contributions/172.71.98.97|172.71.98.97]] 08:46, 20 October 2022 (UTC)

I live in Denmark, and “÷” seems to be often used here for subtraction, instead of a minus sign! Got confused a few times. [[User:Nclm|nicolas]] ([[User talk:Nclm|talk]]) 08:52, 20 October 2022 (UTC)

; tableau
: tab·leau /ˌtaˈblō/ noun
::a group of models or motionless figures representing a scene from a story or from history; a tableau vivant. "in the first act the action is presented in a series of tableaux"
I don't think it means what the editor including it thinks it means. [[Special:Contributions/172.69.22.185|172.69.22.185]] 09:02, 20 October 2022 (UTC)

Talk:1515: Basketball Earth

2021-06-20T16:34:54Z

162.158.166.73: Rotation of the Earth

Apologies to the first editor, who made a snappier version of what I wrote. For the record, whilst fighting a dodgy internet connection I eventually ended up replacing the following...
Cueball is seen trying to explain the relative sizes of the earth and moon by comparing the earth to a basketball and the moon to what looks like a golf ball. This explanation is constantly thwarted by passerby interacting with the basketball while Cueball is explaining it.
For the title text, the answer is zero, since it is against basketball rules.
...with what I tried to keep short during my own writing from scratch. I also ommited several other concepts of my own thought: The fact that Blackhat must have used a very light-touch to ''only'' generate a megatsunami (albeit already unimaginably large, at Earthball's scale); The possibility of recursion (including something like the Men In Black 'cat collar' allusion); and that in the universe of the comic strip there is only ''one'' actual basketball (the Earthball itsself), although I like how we ''both'' had the idea that the basketballs upon Earthball would not have counted in a game of basketball with an Earthball-scaled hoop, due to quite obvious interpretations of the sport's regulations. [[Special:Contributions/141.101.98.67|141.101.98.67]] 05:11, 22 April 2015 (UTC)
:Oh yeah, and reversion is invited, if deemed preferable. As is amalgamation, and refinement and re-replacement by something even better, of course. As per the standard Wiki creed. Much as I am cringing at having upset the original contributor, I'm quite happy to be gazumped in turn. [[Special:Contributions/141.101.98.67|141.101.98.67]] 05:14, 22 April 2015 (UTC)
If you look at the third frame of the Blackhat sequence and compare it to the frames underneath, you can see that he didn't just touch the Earth or an ocean--he actually rotated it 90 degrees.[[Special:Contributions/108.162.221.115|108.162.221.115]] 09:38, 22 April 2015 (UTC)
:Well spotted! Edit that in! (Do it quickly with a pre-prepared edit. I kept getting hit by edit-conflicts, which I set about to resolve amicably without reversing anybody else's input; only to get hit by further edit-conflicts by the next person to come along and improve overlapping pieces, whom I also strived not to disregard.) [[Special:Contributions/141.101.98.67|141.101.98.67]] 09:57, 22 April 2015 (UTC)
::No he didn't. the Earth always rotates from the first panel to the next. So that it is in a different position when Black Hat touches it, to where it was the panel before does not imply that he rotated the Earth. If anything he only rotated it a few degrees, as it had already rotated most of those 90 degree from panel 1 to panel 2 before Black Hat reaches the Earth. As far as I can see there has not been any change to include this yet. So that is good. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 10:41, 22 April 2015 (UTC)

I really love this comic. It is great fun. Thanks Randall, happy Earth day. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 10:42, 22 April 2015 (UTC)

... a tennis ball an average 7.2 metres away, while the Sun would be 26 metres across and 2.8 km away. [[Special:Contributions/108.162.250.165|108.162.250.165]] 13:25, 22 April 2015 (UTC)

It's 13:23 right now, but the clock of explainxkcd.com says it's 13:37. [[Special:Contributions/108.162.221.201|108.162.221.201]] 13:37, 22 April 2015 (UTC)

If we assume 9,000,000 basketballs sold every year ([http://bbs.clutchfans.net/showthread.php?t=82227 bbs.ClutchFans.net]), one basketball lasts about 10,000 bounces ([http://www.sotruefacts.com/rule/770 SoTrueFacts.com]), and there's between 2,500 and 3,000 bounces per game ([http://www.answers.com/Q/What_is_the_average_lifespan_of_a_basketball_in_bounces_in_National_Basketball_Association_play Answers.com]) we can extrapolate that on average a basketball doesn't live for more than a year, and the number of basketballs sold replace those which have lifed-out. Let's build in a 10% slush factor and say there 10m basketballs produced in the world last year. Let's further say that there's an extra 1m basketballs sold every year which don't get regular use and are in some kid's room and those have been accumulating for about ten years (different kids get basketballs every year which end up in their bedrooms). Dunking a basketball gives two points, and at 20 million basketballs, that gives 40 million points – and a safe bet you're going to make it to the playoffs that year. [[User:Jarod997|Jarod997]] ([[User talk:Jarod997|talk]]) 13:51, 22 April 2015 (UTC)

Is it possible that the megatsunami is actually caused by the gravity of the scale Moon (it being way too close to the scale Earth)? This is a major problem that most children's books (or adult's books or websites) have. They scale the planets/moons/stars but not the distance. As the comment above, to get normal tides, the tennis ball should be 7.2m away at this scale. --[[User:Gravitron|Gravitron]] ([[User talk:Gravitron|talk]]) 14:06, 22 April 2015 (UTC)

I find it interesting that Randall makes the same mistake a lot of people make reguarding the distance between the earth and moon at that scale. I was watching Veritasium (https://www.youtube.com/watch?v=Bz9D6xba9Og) on Youtube a while back and the guy there was asking people how far away a tennis ball sized moon would be from a basketball sized Earth. Most people made the distance way too small, very similar to how far away they appear in the comic. In reality they would be something like 10 times that distance. Usually Randall is more accurate than this. [[Special:Contributions/108.162.221.171|108.162.221.171]] 14:09, 22 April 2015 (UTC)Agent0013
:Unless he was simply trying to compare the relative sizes. It's possible after that he would get in to the relative distance between the two - but good point. [[User:Jarod997|Jarod997]] ([[User talk:Jarod997|talk]]) 14:12, 22 April 2015 (UTC)
::It seemingly got lost when trying to resolve edits, but I'd calculated and intended to add that (for the size of a baseball, so a tennis ball would slightly different) 110 Moonball diameters separation between the two. Of course no human has (personally) seen that from a proper perspective, i.e. far enough away to get both bodies in the same convenient vision at the same time whilst off to the side. (Even the Apollo astronauts only got to look at one over the top of the other, at various times, or by panning between the two whilst in the midst of their trans-lunar trajectories.) But there's surely been a space probe or two with a suitable imager been tasked towards such a shot whilst off mostly perpendicular to the Earth-Moon and a decent distance away to get both in the same shot without distortion... [[Special:Contributions/141.101.98.67|141.101.98.67]] 17:52, 22 April 2015 (UTC)

I don't agree with the claim (at a couple points in the article) that *all* life would be extinguished by any of these manipulations. 2-4 may kill off most or all macroscopic life, but microbes would survive all of them (unless Megan has bleach in that sports bottle). If 3 or 4 shattered the earth, that might extinguish all microbes, but even that I doubt. The only case I can imagine would be if 3 or 4 caused it to spiral into the sun. [[User:Djbrasier|Djbrasier]] ([[User talk:Djbrasier|talk]]) 14:10, 22 April 2015 (UTC)

Title text might be reference to HHGTG: “
Ford Prefect: I read of one planet in the seventh dimension got used as a ball in a game of intergalactic bar billiards. Got potted straight into a black hole, killed ten billion people.
Arthur Dent: Madness. Total madness.
Ford Prefect: Yeah. Only scored thirty points too. ”[[Special:Contributions/198.41.241.91|198.41.241.91]] 14:23, 22 April 2015 (UTC)

-----

I admit that I'm super-confused by the structure of the comic. The explanation here describes possible consequences for the actions, but as depicted, only the first has any "real world" effect. I too would expect the water bottle to cause a deluge, but it doesn't seem to. What's going on? [[User:Mattdm|Mattdm]] ([[User talk:Mattdm|talk]]) 15:40, 22 April 2015 (UTC)

-----

The hoop in panel 16 seems too high, unless both Cueball and Megan are under 5 feet tall. --[[User:PsyMar|PsyMar]] ([[User talk:PsyMar|talk]]) 17:11, 22 April 2015 (UTC)
:It could be perspective...[[User:17jiangz1|17jiangz1]] ([[User talk:17jiangz1|talk]]) 12:58, 23 April 2015 (UTC)

Happy Earth Day everyone. Today is the day we regret everything we do to the earth, and the next is the day we forget all that. [[User:YourLifeisaLie|The Goyim speaks]] ([[User talk:YourLifeisaLie|talk]]) 17:59, 22 April 2015 (UTC)
:I just noticed that if [[1511]] (Spice Girl) had had been released on the following Friday, i.e. the slot actually given to comic 1513 (Code Quality), it would have coincided with Victoria "Posh Spice" Beckham's 41st birthday. So, that would probably not have been an intentional direct reference, but ''soooo'' close to ending up being an accidental one. While I'm happy to go along with Earth Day as a deliberate reference... it makes you think, eh? (Although I'd be happy if people thought about Earth Day itself more than the synchronicity. It's a good cause, and pause for thought.) [[Special:Contributions/141.101.98.67|141.101.98.67]] 19:55, 22 April 2015 (UTC)

Why the whole paragraph about it being a baseball? We have no indication of what it is, so why not just say "if it's a tennis ball..." [[Special:Contributions/173.245.50.107|173.245.50.107]] 18:35, 22 April 2015 (UTC)
:Might be my fault. I assumed it was a basketball/baseball comparison in my original endeavour, and this has persisted through other edits, even after the rather logical "...a tennis ball's proportions". Over-compensated for Randall being Leftpondian, probably, even though I've never played Baseball myself (only Rounders). [[Special:Contributions/141.101.98.67|141.101.98.67]] 19:55, 22 April 2015 (UTC)

The title is almost certainly a reference to the movie "Battlefield Earth" [[Special:Contributions/199.27.133.109|199.27.133.109]] 23:57, 22 April 2015 (UTC)

The points acquired for simultaneously dunking all basketballs in existence, or further out -- EVER made, would be at most 2 points (0 if any of the Referees deemed this an illegal/foreign object or an attempt at cheating). Introducing more basketballs onto the court would not result in more points being scored. Furthermore, the basketball earth, while 'containing' all other basketballs, is still itself a single object.{{unsigned|Dulock}}

Does anybody else find it odd that black hat is actually the one causing the LEAST destruction?[[Special:Contributions/199.27.130.228|199.27.130.228]] 03:09, 23 April 2015 (UTC)
:Except, in a way, he is causing the most harm. Scenario 2, 3, and 4 do cause everyone to die, but they would be relatively quick, and what black hat does has painful consequences. The megatsunami would cause huge-scale devastation, worst near the sea he poked, but still bad. This would, among other things, require major rebuilding efforts and include crop failures, leading to famines and the like. In addition, it would have scientists trying to explain it, which would lead to confusion, something black hat likes causing. [[Special:Contributions/162.158.2.138|162.158.2.138]] 07:04, 25 March 2016 (UTC)

A useful comparison from the Canadian comedy troupe, "The Frantics": "If we could shrink the sun to the size of a basketball, and the earth to the size of a pea . . . ''we'd be magic!''" {{unsigned ip|173.245.56.173}}

Just re-reading old pages...this discussion reminds me of one of my favourite pieces of public art. In Melbourne Australia, there's a scale model of the solar system along the beach. The sun is a ball around 2m across, mercury is pea sized and around 50m away (dimensions approx, long time since I've visited) and the rest scaled to match. Pluto (old sculpture) is around 5kms away, and a tiny speck on its plinth. And not far away from the sun is Alpha Centauri, apparently to scale if you walk the other way around the earth...[[Special:Contributions/108.162.250.35|108.162.250.35]] 14:41, 19 June 2018 (UTC)

It looks like in the Black Hat part, the Earth is actually skewing in its rotation (it starts out in the first panel with the Americas and Africa, the second panel looks like it's skewed about 45 degrees counter-clockwise, and the third panel definitely looks like Earth has rotated on what would be its side to our standard North Pole-oriented map a whole 90 degrees and therefore, Black Hat's hand (or the tip of his arm as stick figures are often thus undetailed) has landed on Antarctica. Of course, the physical damage to the polar ice cap and its subsequent dispersal into the Southern Ocean would definitely affect sea levels, but a tsunami striking any heavily-populated coastal town is out of the question.