explain xkcd - User contributions [en]

2321: Low-Background Metal

2020-06-17T17:44:20Z

Jhtx: Added several categories

{{comic
| number = 2321
| date = June 17, 2020
| title = Low-Background Metal
| image = low_background_metal.png
| titletext = The only effect on the history books were a few confusing accounts of something called 'Greek fire.'
}}

==Explanation==
{{incomplete|Created by a TIME TRAVELER. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}
In this comic, Megan and Black Hat have invented time travel. Time travel is a common trope in Science Fiction, and such a discovery would be likely to change the world as we know it. However, Megan and Black Hat's machine requires the use of metal with little to no radiation, meaning currently available metals are too passively radioactive for safe use. Noting that the only way they can obtain this metal, which is presumably consumed upon use of the machine, is by salvaging it from ancient Roman ships, they use the machine to travel back in time to when the Roman Empire was at its height in order to sink its vessels and in turn create more Roman lead for them to use.

"Low-background metal" presumably refers to {{w|low-background steel}}, which was produced before atmospheric nuclear tests occurred and therefore does not incorporate {{w|radionuclides}} from the air used in its manufacture; physicists use it in experiments detecting radionuclides.

The title text refers to {{w|Greek fire}}, which was an incendiary weapon invented and employed by the Byzantine empire. It was a flammable liquid used in naval combat to set fire to enemy ships, but the details of its manufacture and deployment are vague. As it was a closely-guarded military secret, many of the details have been lost to time, and modern chemists have only been able to develop educated guesses of what it ''probably'' was. Randall proposes a rather outlandish alternative hypothesis: that all records of Greek fire were actually in reference to the modern weapons used by the time travelers.
==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[Megan, Black Hat and Cueball stand around a time machine on a table]
:Megan: Our time machine works.
:Megan: But we're almost out of low-background metal.
:Cueball: What's that?

:Megan: Modern metal is contaminated by fallout from nuclear testing, and lead also has natural radioactivity that fades over time.
:Megan: To shield sensitive equipment, physicists use lead from sunken Roman ships.
:Megan: But shipwreck lead is hard to find.

:Black Hat: How much do we have?
:Megan: Enough for one trip through time.
:Black Hat: ''Hmmm...''
:[The scene changes to the group having traveled through time. They are in a helicopter, with Megan piloting, Cueball as a passenger, and Black Hat firing a flamethrower at a Roman ship. The sailors on the ship are alarmed and attempting to escape. Two already-burning ships can also be seen, with one almost completely sunken.]
:Flamethrower: FWOOOSH

{{comic discussion}}

[[Category:Comics featuring Black Hat]]
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]
[[Category:Time travel]]

2319: Large Number Formats

2020-06-13T15:13:51Z

Jhtx:

{{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==
{{incomplete|Created by ABRAHAM LINCOLN. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}
This comic shows how different people express large numbers. This number in question is approximately the distance from the planet Earth to the planet Jupiter as of June 2020, in {{w|inch|inches}} (1 inch = 2.54 cm).

{| class="wikitable"
|-
! Number
! Type of person
! Notes
|-
| 25,259,974,097,204
| Normal Person
| This is the full number, written out in the normal fashion, with commas to indicate powers of 1000. Note that this convention is only considered normal in the Anglo-Saxon world; conventions for writing large numbers in full vary considerably across cultures. For example, in countries where the comma 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 25,25,997,40,97,204.
|-
| 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, an n-illion 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 an n-illion 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.

(The 1971 transition to decimalised currency may also date a person's experiences, but was a more comprehensive and immediate change for everyone who handled any money at all, in the UK, and thus was a more definite point of change apart from the extended survival of the "12 times table" being taught by rote in primary education, rather than ending at the 10s.)

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.
|-
|2.526x1013
|Scientist
|This number is formatted in {{w|scientific notation}}, using the exponent 1013.
|-
| 2.525997x1013
| 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". 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
| Computer code cannot typically use the superscripts or other types of rich text formatting, so the exponent is indicated with the {{w|caret}}. "e13" is {{w|Scientific notation#E notation|(scientific) E notation}} for the expression "10 raised to the power of 13".
|-
| 25,259,973,541,888
| Software developer who forgot about floats
| This is the number after being converted to the limited precision of a {{w|32-bit floating point|32-bit float}}.
|-
| 1013
| Astronomer
| For extremely large distances, astronomers typically only care about orders of magnitude, i.e. 1013, not 1012 or 1014. Randall often jokes about the lack of precision needed by astronomers, such as in xkcd #[[2205]] 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
| In {{w|Zermelo–Fraenkel set theory}}, 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.
|-
| 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"). This style of speaking numbers comes from {{w|French language#Numerals|French}}, and can appear in certain formal contexts, such as the King James Bible ("threescore years and ten" said to be the life expectancy of a human). The original number is rewritten in "score" (multiples of 20) plus a remainder (four).
|-
| 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 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.
|}

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[A panel only with text. At the top there is four lines of explanatory text. Below that there are 5 rows of number formats. There are 2 columns in each row. Each numerical format is in red, with black text explaining the format below it.]

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

:[First row:]
:25,259,974,097,204
:Normal person
:25 trillion
:Normal person

:[Second row:]
:25 billion
:Old British person
:2.526x1013
:Scientist

:[Third row:]
:2.525997x1013
:Scientist trying to avoid rounding up
:2.526e13 or 2.526*10^13
:Software developer

:[Fourth row:]
:25,259,973,541,888
:Software developer who forgot about floats
:1013
:Astronomer

:[Fifth row:]
:{∅,{∅},{∅,{∅}},{∅,{∅},{...
: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]]

2319: Large Number Formats

2020-06-13T03:44:48Z

Jhtx: /* Explanation */ Changed the set theory from zeros to empty sets. Those are clearly empty sets, because none of the zeros in the comic have crosses through them. Also the set theoretic definition of the natural numbers is nested sets of empty sets.

{{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==
{{incomplete|Created by ABRAHAM LINCOLN. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}
This comic shows how different people express large numbers. This number in question is approximately the distance to the planet Jupiter in inches (1 inch = 2.54 cm).

{| class="wikitable"
|-
! Number
! Type of person
! Notes
|-
| 25,259,974,097,204
| Normal Person
| This is the full number, written out in the normal fashion, with commas to indicate powers of 1000. Note that this convention is only considered normal in the western world; conventions for writing large numbers in full vary considerably across cultures. For example, under the {{w|Indian numbering system}}, this number would be written as 25,25,997,40,97,204.
|-
| 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, an n-illion 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 an n-illion 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.

(The 1971 transition to decimalised currency may also date a person's experiences, but was a more comprehensive and immediate change for everyone who handled any money at all, in the UK, and thus was a more definite point of change apart from the extended survival of the "12 times table" being taught by rote in primary education, rather than ending at the 10s.)

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.
|-
|2.526x1013
|Scientist
|This number is formatted in {{w|scientific notation}}, using the exponent 1013.
|-
| 2.525997x1013
| 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". 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
| Software code cannot use the 1013 format, so the exponent is represented as "e13" or "*10^13".
|-
| 25,259,973,541,888
| Software developer who forgot about floats
| This is the number after being converted to the limited precision of a {{w|32-bit floating point|32-bit float}}.
|-
| 1013
| Astronomer
| For extremely large distances, astronomers typically only care about orders of magnitude, i.e. 1013, not 1012 or 1014. Randall often jokes about the lack of precision needed by astronomers, such as in that one xkcd (#[[2205]]) 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
|
|-
| 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"). The original number is rewritten in "score" (multiples of 20) plus a remainder (four).
|-
| 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 the {{w|common logarithm}} of 25,259,974,097,204 (log10 25,259,974,097,204 = 13.4024329009), thus this "format" is mathematically correctly, but not commonly, used.
|}

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[A panel only with text. At the top there is four lines of explanatory text. Below that there are 5 rows of number formats. There are 2 columns in each row. Each numerical format is in red, with black text explaining the format below it.]

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

:[First row:]
:25,259,974,097,204
:Normal person
:25 trillion
:Normal person

:[Second row:]
:25 billion
:Old British person
:2.526x1013
:Scientist

:[Third row:]
:2.525997x1013
:Scientist trying to avoid rounding up
:2.526e13 or 2.526*10^13
:Software developer

:[Fourth row:]
:25,259,973,541,888
:Software developer who forgot about floats
:1013
:Astronomer

:[Fifth row:]
:{0,{0},{0,{0}},{0,{0},{...
: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]]