explain xkcd - User contributions [en]

2319: Large Number Formats

2022-07-15T16:04:20Z

TheBlueRiolu:

{{comic
| number = 2319
| date = June 12, 2020
| title = Large Number Formats
| image = large number formats-2.png
| titletext = 10^13.4024: A person who has come back to numbers after a journey deep into some random theoretical field
}}

==Explanation==
This comic shows what the way you write large numbers says about you. Different people use different methods to express large numbers. And this comic claims it can tell something about you based on the way you format large numbers. In this way, the comic is similar in idea to [[977: Map Projections]], where it was your choice of map projections that could tell something about you.

See the [[#Table of types|table]] below for each of the 10 different ways to express large numbers, plus the 11th mentioned in the title text.

The number used as an example is the [https://www.wolframalpha.com/input/?i=Distance+to+Jupiter+in+inches approximate distance] from the planet {{w|Earth}} to the planet {{w|Jupiter}} as of the release day of the comic on June 12th 2020, in {{w|inch|inches}} (1 inch = 2.54 cm).

Two days after the release of the comic the following text could be found on [https://theskylive.com/jupiter-info Jupiter info] on [https://theskylive.com/ The Sky Live].
:The distance of Jupiter from Earth is currently 640,084,108 kilometers, equivalent to 4.278698 Astronomical Units. Light takes 35 minutes and 35.0908 seconds to travel from Jupiter and arrive on Earth.

64,008,410,800,000 cm / 2.54 cm/inches = 25,200,161,732,283 inches - much less than the number used in the comic. But Jupiter's distance to Earth changes quite quickly, and was decreasing at the time of the release of the comic.

According to a graph of the distance as a function of time on The Sky Live, the distance on the release day was 643.1 million km. This will give 25.3*1013 which the used number will round to.

The used number 25,259,974,097,204 is equivalent to 641.6 million km. On June 13th the distance is given as 641.7 million km in the graph on The Sky Live, very close to the number used. As this was the day after the release of this comic, it seems like [[Randall]] used a different distance than the exact one for the release day. He may have also used an average for June which would be 642 million km based on the average of the distance on June and July 1st.

==Table of types==
{| class="wikitable"
|-
! Number
! Type of person
! Notes
|-
| 25,259,974,097,204
| Normal Person
| This is the full number, 25259974097204, written out in the normal fashion, with commas to indicate powers of 1000. Although writing out the number in full is indeed a common action for normal people, the specific comma convention depicted here is only considered normal in the anglophone world; conventions for writing large numbers in full vary considerably across cultures. For example, in countries where the period is used as a {{w|decimal separator}} (including Europe outside the UK), one would write the number as 25.259.974.097.204 (or 25'259'974'097'204 in Switzerland, or 25 259 974 097 204 in Poland, France and Estonia). Under the {{w|Indian numbering system}}, this number would be written as 2,52,59,97,40,97,204 or “two nil, fifty-two kharab, fifty-nine arab, ninety-seven crore, forty lakh, ninety-seven thousand, two hundred and four.”
|-
| 25 Trillion
| Normal Person
| This is the number, rounded to trillions in the normal fashion.
|-
| 25 Billion
| Old British Person
| In current English usage, across the Anglophonic world with some hold-outs, the nth zillion means 10^(3n+3) as per the {{w|short scale}} system popularised by American influence in international trade, so a trillion means 10^12, as above. However, older British English use had the nth zillion meaning 10^(6n) (i.e. the simpler calculation of ''million^n''), so a billion meant 10^12. The change stems from a 1974 commitment by Harold Wilson, the Prime Minister of the UK at the time, to change from the {{w|long scale}} (previously often described as the British system) to the short one for all official purposes.

Though not instantly widely adopted for common usage, the mid-'70s could therefore be considered the key turning point between when an older or younger British person learns (as the change filters through the system at various stages of education) what their "Billion"s and "Trillion"s are supposed to represent.

As well as 'traditionalist' British use, the long scale is widely used in the non-Anglophone world, in local language versions, though while the British system tended to infill n-and-a-half powers of the million with the term "thousand n-illion", the suffix "-illi''ard''", or equivalent, is often used for the thousands multiple directly atop the respective "-illion" point.
|-
|2.526×1013
|Scientist
|This number is formatted in {{w|scientific notation}}, using the exponent 1013.
|-
| 2.525997×1013
| Scientist trying to avoid rounding up
| Using as many decimal places as necessary until hitting a digit (0-4) that results in rounding down, even if it goes against the common scientific practice of reporting the correct amount of "significant figures". [[:File:large number formats.png|A previous version of the comic]] had a typo (the number was ''2.5997x1013''), but Randall updated the comic.
|-
| 2.526e13 or
2.526*10^13
| Software developer
| The first example is how the number would be expressed as a floating point number in scientific notation in [https://rosettacode.org/wiki/Literals/Floating_point most common programming languages]. The second example is a technically correct way of expressing the same thing in some programming languages in which exponentiation is indicated by the ^ operator. However writing it that way instead of the first way could be considered quirky, as it is written as an instruction to the computer to calculate the product of a number with 10 raised to power 13, instead of just writing the number (although in many situations the compiler or preprocessor would detect this and solve it correctly, making it functionally identical to the first case). A software developer might write it that way if they are a novice who is not familiar with the first notation, or they could simply have an personal preference that considers the second version easier to read. Perhaps an additional joke for the second version is that it is the standard scientific notation with the x for multiplication and superscript for raising to a power replaced with the notation used in many programming languages of * and ^, i.e., a software developer writing down a number in scientific notation, not necessarily while writing a program, would by habit write a * for multiplication and a ^ for exponentiation.
|-
| 25,259,973,541,888
| Software developer who forgot about floats
| The two most common computer {{w|Floating-point arithmetic|floating-point}} formats are the IEEE 754 {{w|Single-precision floating-point format|single-precision}} and {{w|Double-precision floating-point format|double-precision}} representations. These are ''binary'' floating-point formats, representing numbers as the quantity ''a'' × 2''e'', for some fractional number ''a'' and exponent ''e''. Both the values ''a'' and ''e'' have a fixed size in bits, and therefore a finite range. In single-precision, ''a'' and ''e'' have (effectively) 24 and 8 bits, respectively, while in double precision the effective sizes are 53 and 11 bits.

Fully representing the number 25,259,974,097,204 (in any format) requires at least 45 bits. Therefore this number cannot be represented exactly as a single-precision float. The closest possible representations are 0.717931628 × 245 and 0.717931688 × 245; these work out to 25,259,973,541,888 and 25,259,975,639,040, respectively. Of these, the one ending in 888 is considerably closer to the original, so is chosen due to {{w|rounding}}. (Naturally these numbers are represented internally in binary, not decimal; the actual representations, in {{w|hexadecimal}}, are <tt>0.b7ca5e</tt> × 2<tt></tt>2d and <tt>0.b7ca5f</tt> × 2<tt></tt>2d.)

In many programming languages, the keyword to request a single-precision floating-point variable is <tt>float</tt>, while the keyword to request double-precision is <tt>double</tt>. It is an easy mistake to make to forget about the limited precision available with type <tt>float</tt>, especially since its name sounds like what you want for "floating point". (Had the programmer remembered to use type <tt>double</tt>, the number 25,259,974,097,204 could have been represented exactly (still in hexadecimal), as <tt>0.b7ca5e43c9a000</tt> × 2<tt></tt>2d.)
|-
| 1013
| Astronomer
| For extremely large distances, astronomers typically only care about orders of magnitude, e.g. whether a number is 1013, as opposed to 1012 or 1014. Randall often jokes about the lack of precision needed by astronomers, such as in [[2205: Types of Approximation]] where the astronomer-cosmologist is equally willing to make pi equal to one, or ten. The original number is rounded to the nearest power of ten.
|-
| {∅,{∅},{∅,{∅}},{∅,{∅},{...
| Set theorist
| The natural numbers can be constructed in a {{w|set theory}} in various ways. In the most common of these, the {{w|Natural_number#Von_Neumann_ordinals|Von Neumann ordinals}}, the natural numbers are defined recursively by letting 0 = ∅ (the {{w|empty set}}), and ''n'' + 1 = ''n'' ∪ {''n''}. So, every natural number ''n'' is the set of all natural numbers less than ''n'', and since 0 is defined as the empty set, all numbers are nested sets of empty sets. Note that writing out a number in this form requires an exponential number of characters - that is, ''n'' + 1 requires over twice the characters as ''n'' does to write out. Thus, this method could not be finished, as it would require more data to be stored than there is matter in the universe to store it.
|-
| 1,262,998,704,860 score and four
| Abraham Lincoln
| In the {{W|Gettysburg Address}}, Lincoln speaks the number "87" as "four score and seven" ("score" meaning "20"). Base-20 or {{w|vigesimal}} numeral systems are or have been used in pre-Columbian-American, African and many other cultures. In French it is used only for higher numbers (e.g. 92 = quatre-vingt-douze). In English it can appear in certain archaic and classic contexts, such as the King James translation of the Bible ("threescore years and ten" to be the life expectancy of a human according to Psalm 90:10). In these cases, a number is written in "score" (multiples of 20) plus a remainder. In this case 1,262,998,704,860 * 20 + 4 yields the exact number.
|-
| 10^13.4024 ''(title text)''
| A person who has come back to numbers after a journey deep into some random theoretical field
| In some fields of mathematics, especially those dealing with very {{w|large numbers}}, numbers are sometimes represented by raising ten (or some other convenient base) to an oddly precise power, to facilitate comparison of their magnitudes without filling up pages upon pages of digits. An example of this is {{w|Skewes's number}}, which is formally calculated to be ''e''''e''''e''79, but is more commonly approximated as 10101034. 13.4024 is a rounded version of the {{w|common logarithm}} of 25,259,974,097,204 (log10 25,259,974,097,204 = 13.4024329009); thus, this "format" is still mathematically correct, but uncommon. However, only by using many more digits will the result get close enough to be rounded to the original number 10^13.40243290087302 = 25,259,974,097,203.5, which would round up to the correct number. The number from the title text, 10^13.4024 = 25,258,060,548,319.6, differs from the original number by over a billion.
|}

==Transcript==
:[A panel only with text. At the top there is four lines of explanatory text. Below that are 2 columns with 5 rows of number formats. Each numerical format is in red, with black text explaining the format below it.]

:<big>What the way you write large numbers says about you</big>
:(Using the approximate current distance to Jupiter in inches as an example)

:25,259,974,097,204
:Normal person

:25 trillion
:Normal person

:25 billion
:Old British person

:2.526x1013
:Scientist

:2.525997x1013
:Scientist trying to avoid rounding up

:2.526e13 or 2.526*10^13
:Software developer

:25,259,973,541,888
:Software developer who forgot about floats

:1013
:Astronomer

:{∅,{∅},{∅,{∅}},{∅,{∅},{...
:Set theorist

:1,262,998,704,860 score and four
:Abraham Lincoln

{{comic discussion}}

[[Category:Comics with color]]
[[Category:Programming]]
[[Category:Math]]
[[Category:Astronomy]]
[[Category:Science]]
[[Category:Comics featuring politicians]]
[[Category:Comics edited after their publication]]

2080: Cohort and Age Effects

2022-07-03T17:22:39Z

TheBlueRiolu: changed to canon ages

{{comic
| number = 2080
| date = December 3, 2018
| title = Cohort and Age Effects
| image = cohort_and_age_effects.png
| titletext = Younger people get very few joint replacements, yet they're also getting more than older people did at the same age. This means you can choose between 'Why are millennials getting so (many/few) joint replacements?' depending on which trend fits your current argument better.
}}

==Explanation==
Another of [[Randall|Randall's]] [[238: Pet Peeve 114|many]] [[:Category:Pet Peeves|Pet Peeves]], this time it's statistics. It is the first in more than four years, since [[1368: One Of The]].

"{{w|Millennials}}" are the generation of Westerners who were born between the early 1980s and the late 1990s, whereas {{w|baby boomers}} are the generation born during the "baby boom", a period of high birth rates from the late 1940s to early 1960s. A common headline on news websites is "Millennials are killing the X industry" where X is a product whose sales have dropped in recent years, such as [https://ezplaytoys.com/pages/products jungle gyms for kids]. One of the most famous is the {{w|diamond industry}}, where a combination of the {{w|wage gap}}, stigma over {{w|Blood diamond|conflict diamonds}}, increased knowledge of ([https://what-if.xkcd.com/108/ in Randall's words]) {{w|De Beers antitrust litigation|"complicated gemstone market"}} and less desire to get married early has seen millennials buying less diamond jewelry than previous generations.

Randall spoofs this idea. In the comic, [[Cueball]], as a [[:Category:News anchor|news anchor]], presents a heading which opens his story by asking if millennials are killing the industry of surgical {{w|Joint replacement|joint replacements}}, illustrating it with numbers of joint replacement procedures among millennials compared to baby boomers. The joke is that millennials are simply too young for most of them to need joint replacements (which are usually used to treat senile {{w|osteoarthritis}}), so most people will see that so there really isn't a news story here. Randall is using this example to highlight that this kind of story is ridiculous. Millennials will likely need joint replacements in the future as they get older, potentially keeping sales of joint replacements at close to their current rate.

A '''{{w|cohort effect}}''' is a cultural difference between generations (such as buying fewer diamonds), whereas an '''age effect''' is one that is simply related to getting older (such as getting arthritis). Joint replacement rates are an age effect, but the newscast is presenting them as if they were a cohort effect. (More correctly, the table rows would be labelled e.g. “people aged 53–72” and “people aged 17–36”.)

The title text points out that although numbers of millennials receiving joint replacements are low, they are higher than the numbers of baby boomers who received them ''at the same age''—i.e. in their 20s—due to advances in medical diagnosis and technology in the last 50 years, as well as (in some countries at least) better access to healthcare. This statistic can be used to create a headline which is the reverse of the one in the comic, namely "millennials are getting more joint replacements than ever". Randall notes that you could therefore use either headline to back up your argument, depending on the agenda you are trying to present.

==Transcript==
:[Cueball as a news anchor is sitting at a desk with hands folded in front of him on the table.]
:Cueball: Tonight: Are Millennials killing the joint replacement industry?

:[To the left of Cueball is a presentation which includes a two by two table with a header above the table. Each of the two rows and columns are labeled, with rows entitled 'Baby Boomers' and 'Millennials', and columns entitled 'Knee' and 'Hip']

:;Operation rate per 100,000
::;Baby Boomers:
:::'''Knee:''' 720
:::'''Hip:''' 390
::;Millennials:
:::'''Knee:''' 1
:::'''Hip:''' 3

:[Caption below the panel:]
:Stats Pet Peeve: People mixing up cohort effects and age effects.

==Trivia==
*In the original title text there were two mistakes which were soon corrected. Here is the original title text with the removed word in <s>strike through</s> and the final version with the added word in '''bold''':
**Younger people get very few joint replacements, yet they're also getting more than older people did at the same age. This means you can choose between 'Why are millennials <s>are</s> getting so (many/few) joint replacements?' depending '''on''' which trend fits your current argument better.

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Pet Peeves]]
[[Category:News anchor]]
[[Category:Charts]]
[[Category:Statistics]]

2381: The True Name of the Bear

2022-05-21T16:20:14Z

TheBlueRiolu: Undo revision 273380 by CRLF (talk) you'we not foowing anyone

{{comic
| number = 2381
| date = November 4, 2020
| title = The True Name of the Bear
| image = the_true_name_of_the_bear.png
| titletext = Thank you to Gretchen McCulloch for fielding this question, and sorry that as a result the world's foremost internet linguist has been devoured by the brown one. She will be missed.
}}

==Explanation==
The Canadian Internet linguist {{w|Gretchen McCulloch}} [https://twitter.com/gretchenamcc/status/1113195661275611137 tweeted] about [https://www.charlierussellbears.com/LinguisticArchaeology.html the theory] that the word for bear became taboo in some branches of Indo-European languages - notably the Germanic one - and it was replaced by euphemisms. In the Germanic branch, the euphemism may have been "the brown one," and thus the modern word "bear" (derived from Germanic "beran") would more literally translate into the color "brown" rather than the animal.

The Indoeuropean root for bear is *rkto-, which has been inferred from modern languages that still use a word derived from it. In the comic, McCulloch applies {{w|Sound change|sound shifting}} laws to it to guess how it would have evolved in English had it not been superseded, but saying it seems to actually summon a bear.

Interestingly enough, the hypothesized word “arth” is the same as the Welsh and Cornish for the word “bear.” Welsh belongs to the Celtic language family, which is one of the Indo-European branches that still uses a word derived from *rkto-, as do the Italic (Romance), Greek and Indo-Aryan (Sanskrit) branches, while Germanic, Slavic and Baltic branches abandoned it for different euphemisms. Another Indo-European language where the word for bear is very close to this extrapolation is Armenian, where it's written [https://en.wiktionary.org/wiki/արջ արջ] and pronounced “artch”. The comic does not explain why speakers of Welsh, Cornish, Italic, Greek, Indo-Aryan, and Armenian languages do not summon a bear every time they refer to one.

Use of true names appears to be [[1013: Wake Up Sheeple|highly effective in the xkcd universe, rather like a fairy tale]], and it is also {{tvtropes|IKnowYourTrueName|a common trope}} elsewhere. Some say a true name contains clear meaning of who someone or something really is.

In [[2421: Tower of Babel]] a linguist that resembles Gretchen from this comic appears. Since that story takes place in biblical time, it is not Gretchen, but obviously this is how linguists look in xkcd from now on.

==Transcript==
:[Megan walks in front the left, looking down at her phone. Cueball and Ponytail are standing next to each other.]
:Megan: Wow - according to the internet, we don't know the true name of the bear.
:Cueball: What?

:[Gretchen McCulloch, drawn with short, curly hair, comes on-panel from the right.]
:Megan: Apparently there was a superstition that saying its name would summon it. "Bear" and "bruin" mean "the brown one." Its actual name has been lost.
:Cueball: Wow.
:Ponytail: Gretchen, is this for real?

:[Zoom-in on Gretchen.]
:Gretchen: Well, sort of
:Gretchen: The Proto-Indo-European root was *rkto-
:Gretchen: It was lost in the Germanic languages like English, but survived elsewhere, e.g. Greek "arktos" and Latin "ursus"

:[Back to the second panel, with Megan holding her phone down, Ponytail with her hands in the air, and Gretchen with her hand on her chin.]
:Megan: So could we figure out what the word would have been in English?
:Gretchen: Hmm. I mean, we'll never know, but given Germanic sound shifts, a reasonable guess might be "arth"?
:Ponytail: ''No!!''

:[The panel zooms in again to Gretchen.]
:Ponytail (off-panel): ''Stop! AAAAA!''
:Gretchen: What??
:Ponytail (off-panel): Don't ''say'' it!

:[Ponytail is holding her palms out. Megan is no longer in the panel.]
:Ponytail: What have you ''done''?
:Off-panel noise: <big>'''''ROAR'''''</big>
:Gretchen: Oh
:Gretchen: Oh no

== Trivia ==
The last comic strip that ended with the words "Oh no" was [[2314: Carcinization]], which also featured an unfortunate occurrence involving an animal as its punchline when Cueball spontaneously transformed into a crab.

{{comic discussion}}

[[Category:Comics featuring Megan]]
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Ponytail]]
[[Category:Comics featuring real people]]
[[Category:Language]]
[[Category:Animals]]

614: Woodpecker

2022-05-20T22:01:49Z

TheBlueRiolu: Undo revision 271116 by Explain xkcd server admin (talk)

{{comic
| number = 614
| date = July 24, 2009
| title = Woodpecker
| image = woodpecker.png
| titletext = If you don't have an extension cord I can get that for you too. Because we're friends! Right?
}}

==Explanation==
[[Beret Guy]] observes a {{w|woodpecker}}. A woodpecker is a type of bird known for using its bill to bore holes into trees to get access to and eat the insects living inside. [[Megan]] notes that the bird hatched approximately a year ago. Beret Guy seems touched by this fact, and attempts to explain to the woodpecker that it is the woodpecker's birthday.

Beret Guy leaves a present by the foot of the tree where the woodpecker is nesting. The woodpecker opens the present which turns out to be a power drill, a mechanical tool that is used to bore holes into wood, much quicker than a bird normally could. Not that this would be of much use to the bird, as the bird has no electricity{{Citation needed}} and so no means of powering the drill, let alone {{w|opposable thumbs}}{{Citation needed}} with which to operate the drill. In spite of this, the woodpecker has not only unwrapped the present; it has apparently accepted it, and flies off with it.

The title text appears to be Beret Guy talking to the bird still, pointing out that he can get the bird an extension cord to operate the drill because, in his mind, they are friends. In actuality, the bird may or may not care about the drill or Beret Guy. An extension cord, also, would not do much good as the bird would still have no electricity, and if it did have a source of electricity and was able to use the drill, it wouldn't be able to fly further than the length of the extension cord, which isn't far for a bird. This could be a reference to [[509: Induced Current]].

==Transcript==
:[Megan and Beret Guy are standing on a deck.]
:Beret Guy: A Woodpecker!
:''pop pop pop''
:Megan: Yup.
:[Woodpecker knocking against a tree.]
:Megan: He hatched about this time last year.
:''pop pop pop pop''
:[Megan leave the frame, leaving Beret Guy on the deck alone.]
:Beret Guy: ...Woodpecker?
:Beret Guy...It's your Birthday!
:Beret Guy: Did you know?
:Beret Guy: Did nobody tell you?
:[Beret Guy leaves the frame, changes to the tree base.]
:[Beret Guy brings a gift and places it at the tree trunk.]
:[The woodpecker comes down and opens the gift.]
:[The woodpecker flies away holding onto the cord of a power drill.]

==Trivia==
*A T-shirt based on this comic is available in the [https://store.xkcd.com/products/woodpecker xkcd store].

{{comic discussion}}
[[Category:Comics featuring Megan]]
[[Category:Comics featuring Beret Guy]]
[[Category:Comics with xkcd store products]]

859: (

2022-05-20T22:00:09Z

TheBlueRiolu: Undo revision 270630 by Explain xkcd server admin (talk)

{{comic
| number = 859
| date = February 11, 2011
| title = (
| image = (.png
| titletext = Brains aside, I wonder how many poorly-written xkcd.com-parsing scripts will break on this title (or ;;"'<nowiki/>'{<<[' this mouseover text."
}}

== Explanation ==

In programming, punctuation is often used to mark sections of code. Paired punctuation marks must always be matched up with a corresponding closing mark, otherwise a so-called {{w|syntax error}} occurs. The programming language {{w|Lisp_(programming_language)|Lisp}} (also featured in [[224: Lisp]] is known for large numbers of nested/paired parentheses. Even in literary works intended only for human consumption, the absence of a matching closing parenthesis as appears in this sentence or other "balanced" punctuation sets creates a mental expectation of eventual closure and completion that remains unfulfilled even long after the unmatched mark is encountered.

There is also reference to [[312: With Apologies to Robert Frost]] which could contain the missing parentheses.

It can also be interpreted as a {{w|metaphor}}, which compares the reader with a Lisp {{w|Interpreter (Computing)|interpreter}}. The interpreter looks for the parenthesis until the end of the file, where it eventually halts, and prints out the error. The comic claims that if you read an unmatched parenthesis, you will look for it for the rest of the day too.

It also refers to an awkward feeling when you see something out of place in a piece of literary text (like unmatched parentheses, spellying error or a randomly-plac,ed comma..

Finally, in some countries (Russia in particular) they use just parentheses instead of text smileys so that :) turns into ) and :( becomes (. Hence Russians can magically resist the unresolved tension of the comic but may feel a bit sad instead as a side effect.

The title text refers to the same issue as already highlighted in [[327: Exploits of a Mom]]: if your scripts trust external input, you sometimes will be surprised. At the time of this comic, there were quite a few websites that would grab the xkcd comic three times a week and publish them on their own site. This comic likely broke at least some of the websites because of either the unmatched brace or the extra unmatched markup that is in the title text.

==Transcript==
:[Caption inside an oblong panel:]
:(An unmatched left parenthesis creates an unresolved tension that will stay with you all day.

{{comic discussion}}
[[Category:Programming]]