explain xkcd - User contributions [en]

2646: Minkowski Space

2022-07-16T18:27:34Z

Buddhafool:

{{comic
| number = 2646
| date = July 15, 2022
| title = Minkowski Space
| image = minkowski_space.png
| titletext = My liege, we were able to follow the ship into Minkowski space, but now they've jumped to Hilbert space and they could honestly be anywhere.
}}

==Explanation==
{{incomplete|Created by A RELATIVISTIC QUANTUM STATE - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

In science fiction, {{w|faster than light travel}}, an impossibility with our current understanding of physics, is often explained away by having ships enter into some form of different realm, frequently termed "hyperspace", where (presumably) the laws of physics are different so as to allow such superphotonic travel to occur. Such an action is called "jumping".

In this comic, a spaceship is being chased by an enemy ship. The crew attempt to escape by jumping, since (if they were headed to hyperspace) it would allow them to escape their pursuer as quickly as possible, however instead of doing such, they opt to enter {{w|Minkowski space}}. Minkowski space, compared to conventional 3-D space, combines space and time together into one manifold (object), which is useful for some analyses of {{w|special relativity}}. Since it is practically identical to "normal" reality otherwise, shifting to Minkowski space is meaningless and offers no benefit compared to simply staying in normal space and flying as fast as possible at sublight speeds, providing the humor of the comic's absurdist joke.

The visual depiction of the spaceships skewed diagonally is based on the graphical {{w|Minkowski diagram}} representation of objects in Minkowski space, where the {{w|world line}} of matter is bounded inside its diagonal {{w|light cone}}.

The mention of distance depending on the observer's frame of reference refers to distances changing when measured in different {{w|inertial frame of reference|inertial frames of reference}}, a concept called the {{w|relativity of simultaneity}}. Here are [https://www.youtube.com/watch?v=asW78vToNLQ some videos] intended [https://www.youtube.com/watch?v=Xrqj88zQZJg to explain] that concept. The skewing depicted changes the distance between the spaceships in such a way that the tip of the pursuer comes closer to the pursued spaceship, but their centers move further apart. So the question of whether they have come closer is indeterminate for the reader of the comic.

The title text is a status report from someone in the pursuing spaceship to their leader (whom they call "my {{w|Homage (feudal)|liege}}.") They tell their superior that following the spaceship to Minkowski space was not a problem, but now they cannot find them after they jumped to Hilbert space, as they could now be anywhere. As in the [[2577:_Sea_Chase|Sea Chase]] comic, there was also more than one type of space to jump to here.

Whereas trying to hide in Minkowski space failed, it turned out that hiding in {{w|Hilbert space}} is much easier. This is because Hilbert spaces can have an infinite number of dimensions, and thus are much more complicated than four-dimensional Minkowski space. However, Hilbert space is used to describe mathematical objects such as functions of various parameters and complexity, not physical spatiotemporal reality, so it is very unusual for a physical object to be represented in Hilbert space. The reference to Hilbert space could also relate to the {{w|uncertainty principle}}, as quantum states can be represented as vectors in a Hilbert space.

==Transcript==
:[A spaceship is being pursued by another spaceship. Both ships have a black part in the front representing a window. They are the same size but different designs. The pursued spaceship to the right has two engines below and a big engine behind. The pursuing spaceship to the left has a V-shaped rear end, and what seems like two weapons on either side pointing forward. At least two persons inside the pursued spaceship are talking to each other, and their text comes out from two starburst on top and bottom of the spaceship.]
:Voice 1: The enemy ship is right behind us!
:Voice 2: Prepare to jump to Minkowski space on my mark.

:[Same setting, with star burst above only. The sound coming from the pursued spaceship is written inside a burst of small lines below the spaceship. Voice 2, by context, is the same as in panel 1.]
:Voice 2: Three... two... one... ''mark!''
:Click

:[Both spaceship are tilted upwards and becomes distorted so they become longer and thinner.]

:[The tilting increases and the distortion is now so pronounced that the spaceships are almost unrecognizable, almost just lines with structure. The distance between the tip of the pursuing spaceship and the pursued becomes shorter in the last two panels, but the distance between their center parts becomes larger. Up to three distinct voices are shown, here, which may include those seen in Panel 1 but with no clear relation.]
:Voice 3: Are they still getting closer?
:Voice 4: I can't tell.
:Voice 5: I think it depends on your frame of reference.

{{comic discussion}}

[[Category:Space]]
[[Category:Math]]
[[Category:Physics]]

2636: What If? 2 Countdown

2022-06-23T17:00:30Z

Buddhafool:

{{comic
| number = 2636
| date = June 22, 2022
| title = What If? 2 Countdown
| image = what_if_2_countdown.png
| titletext = If you don't end the 99 Bottles of Beer recursion at N=0 it just becomes The Other Song That Never Ends.
}}

==Explanation==
{{incomplete|Created by a BOT THAT IS WONDERING ABOUT THINGS - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
This comic takes the idea of {{w|Advent calendar}}s, and takes it to the extreme. It uses rather absurd and/or obscure ways to measure the amount of time until [[Randall]]'s new book ''What if? 2'' is released, with esoteric units or esoteric numbers. And often both.

Some concepts that appear several times throughout the calendar are:

* '''{{w|SI prefixes}}''', which can be applied to the beginning of a unit's name to multiply or divide the unit by powers of 10 or 1,000. This is standard for units like meters and grams, but is rarely applied to measurements of time.
* The '''{{w|Gettysburg Address}}''', a famous speech delivered by U.S. president Abraham Lincoln in 1863, where he began by referring to the signing of the Declaration of Independence taking place "four score and seven years ago". A score is a dated term for the number 20, so "four score and seven" is equivalent to 87.
* A '''dog year''' is traditionally considered to be one-seventh the length of a normal human year, since a dog's overall lifespan is roughly one-seventh of a typical human's. The comic applies this to other units of time, such as minutes and months, each of which is also one-seventh the length of the standard unit.
* Other comparative durations of time that are not normally or usefully applied to day-length multiples. At the top end, there is the age of the universe, at the other there is {{w|Planck_units#Planck_time|Planck-time}} – with entire durations of periods of human history and the time needed to watch popular TV/film franchises in-between – most of which require a non-trivial multiplier or divisor to bring them to the necessary scale required.
* A '''{{w|baker's dozen}}''' is 13, or one more than a normal dozen. Here, the "baker's" prefix can be applied to any unit by adding an extra one of its constituent parts, like an extra hour added to a day.
* '''{{w|Irrational numbers}}''' like {{w|pi}} (3.14159...), {{w|Euler's number}} or ''e'' (2.71828...), the {{w|golden ratio}} (1.61803...), and the {{w|square root of 2}} (1.41421...). These are all interesting numbers because of their mathematical properties, but very impractical to use as arbitrary measurements of time because they have an endless series of non-repeating decimal digits.
* The teenage dating game {{w|Seven minutes in heaven}}.
* Rotation and revolution periods of various planets and moons in the Solar System.

{| class="wikitable"
|-
! Days !! Date !! Units !! Exact value !! Explanation
|-
| 83 || Jun 22 || πe millidecades || 82.0304 days || π =~ 3.14159, e =~ 2.718, so πe is about 22.459. A millidecade is 1/1000 decade, or 1/100 year, or about 3.6525 days. Multiplying these results in 82.03 days. This is a play on Euler's identity, eiπ=-1, but raising pi to the power of e instead.
|-
| 82 || Jun 23 || 7 megaseconds || 81.0185 days || 7,000,000 seconds
|-
| 81 || Jun 24 || e lunar months || 80.27247 days || A lunar month =~ 29.53059 days, e =~ 2.718
|-
| 80 || Jun 25 || 60 rotations of Foucault's pendulum in Paris || 79.67 days || The Foucault's pendulum measures and/or proves earth's rotation. Possibly a reference to the Bogdanow brothers who used pointless circumlocutions with the Foucalt pendulum as tech babble in their fake dissertation
|-
| 79 || Jun 26 || 8 milligenerations || 78.84 days || A generation is in general 22-33 years, the mean is 27; so 8 * 0.001 (mili) * 365 (not accounting for leap years) * 27 =~ 78.84 days
|-
| 78 || Jun 27 || 777,777 dog minutes || 77.16 days|| A popular myth is that dogs age 7 times faster than humans, so 1 dog minute equals 1/7 human minutes.
|-
| 77 || Jun 28 || 7! episodes of ''Jeopardy!'' (skipping ads) || 77 days || 7!=7*6*…=5040 - The standard episode of ''Jeopardy'' is 22-26 minutes skipping ads - taking the lowest value you get 110880 minutes total which is the exact value needed.
|-
| 76 || Jun 29 || 5,000 repeats of ''99 Bottles of Beer'' || 76.3888... days || Each verse of {{w|99 Bottles of Beer}} is "''N'' bottles of beer on the wall, ''N'' bottles of beer. Take one down, pass it around, ''N-1'' bottles of beer on the wall." The entire song contains 99 verses. Randall apparently sings this rather slowly at around 72bpm, taking about 13 seconds per verse. Exact value inputs: 16 beats per verse * 99 verses = 1584 beats per song @ 72bpm = 4.5 verses per minute = 22 minutes per song = 65.454545... songs per day
|-
| 75 || Jun 30 || 5 baker's fortnights (15 days) || 75 days || A {{w|baker's dozen}} is a dozen (12) plus 1 extra item. Randall has generalized this to adding 1 to any unit. A fortnight is 2 weeks, so a baker's fortnight is 15 days. 5x15 is 75 days.
|-
| 74 || Jul 1 || √2 dog years || 73.79 days || See day 78 (Jun 27)
|-
| 73 || Jul 2 || π millivics (1/1000th of Queen Victoria's reign) || 72.966631 days || Queen Victoria ruled between 20 June 1837 and 22 January 1901 (23,226 days).
|-
| 72 || Jul 3 || 42 drives from NYC to LA (Google Maps estimate) || 71.75 days || According to Google Maps, the drive from New York City to Los Angeles via I-80 W (2789 miles or 4489 km) takes 41 hours.
|-
| 71 || Jul 4 || 1,000 viewings of ''Groundhog Day''|| 70.14 days|| Using 101-minute run time.
|-
| 70 || Jul 5 || 100,000 minutes || 69.44 days||
|-
| 69 || Jul 6 || 1/10th of Martian year || 68.70 Earth days || Martian sidereal and tropical years both round to 687.0 Earth days
|-
| 68 || Jul 7 || 1,234,567 sound-miles || || The speed of sound in air depends on the temperature. 15 °C or 59 °F gives the value 340 m/s and the travel time of 67.6349058 days.
|-
| 67 || Jul 8 || 2^π^e seconds ||5,766,073 seconds = 66.7 days || 2^(π^e)
|-
| 66 || Jul 9 || 2^16 beats (Swatch Internet Time) || 65.536 days || {{w|.beat}} is equal to 1/1000 day.
|-
| 65 || Jul 10 || 1,000 ISS orbits || || Each orbit of the ISS takes approximately 90 minutes.
|-
| 64 || Jul 11 || Five hundred twenty five thousand (base seven) Minutes|| 62.8833333333333 days || To convert from any number system to the decimal number system, the value of each digit is calculated as "value" * "base" ^ "position of the digit minus one" counting the position of the digit starting from the less significant side. The values of each digit are then added to get the value of the whole number. Base seven means the number only uses 7 digits (0-6). To represent 7 (base10) you would need the first two-digit number, which is 10 (base7). This gives: 5*7^5 + 2*7^4 + 5*7^3 + 0*7^2 + 0*7^1 + 0*7^0 = 90552 minutes. Also references the opening and recurring line "Five hundred twenty five thousand six hundred minutes" from {{w|Seasons of Love}}, a song from the musical ''Rent'' ("base seven" has the same rhythem as "six hundred").
|-
| 63 || Jul 12 || 10^50 Planck times || 62.38 days || 10^50 x 5.39 x 10^-44 seconds
|-
| 62 || Jul 13 || 4,000 episodes of ''The Office'' (skipping ads)|| 62.5 days || The Office was originally a BBC show which had no commercial breaks, but Randall is obviously more familiar with the US version. {{w|The_Office_(American_TV_series)}} This US "half-hour" comedy format contains 22.5 minutes of content (including title sequence) and 7.5 minutes of ads. 
|-
| 61 || Jul 14 || Four Score and Seven Kilominutes || 60.4166 days || 87 * 1000 minutes
|-
| 60 || Jul 15 || 2 Lunar Months || || There are a number of different ways to define the {{w|lunar month}}. The most common is the synodic month, because it relates to the phases of the moon, and it's a bit more than 29.5 days.
|-
| 59 || Jul 16 || Half a Day on Venus || || A Venus synodic day is 116 days 18 hours.
|-
| 58 || Jul 17 || 5 megaseconds || 57.8704 days || 5,000,000 seconds
|-
| 57 || Jul 18 || 30 MicroLits (1/1,000,000th of the time since the invention of literature) || 4681-4763 years x 10^-6 || Randall is stating that "literature" was invented approximately 2700 BCE. This is consistent with the earliest surviving coherent Sumerian texts, but the earliest proto-writing likely developed at least 500 years earlier {{w|History_of_writing}}
|-
| 56 || Jul 19 || 1,000 viewings of ''Run Lola Run'' || 55.556 days || Using a run time of 80 minutes
|-
| 55 || Jul 20 || One Million Sound-Miles || || The speed of sound in air depends on the temperature. 15 °C or 59 °F gives the value 340 m/s and the travel time of 54.7843137 days.
|-
| 54 || Jul 21 || 30 Ionian Months || 53.0741 days || Orbital period of Io around Jupiter is 1.769137786 days
|-
| 53 || Jul 22 || One Dog Year || 52.18 days || See day 78 (Jun 27)
|-
| 52 || Jul 23 || 60 Viewings of ''Star Wars Episodes I-IX'' || 51.75 days || According to [[https://dorksideoftheforce.com/2021/05/04/how-long-to-watch-every-star-wars-movie/ Fansided]] the combined running times are 20 hours 42 minutes.
|-
| 51 || Jul 24 || 1/ 100,000,000,000th of the Universe's age || || The universe is estimated to be about 13.8 billion years old.
|-
| 50 || Jul 25 || 5 milli-Generations || 49.3 days || See day 79 (Jun 26)
|-
| 49 || Jul 26 || 10,000 Games of ''7 minutes in Heaven'' or 7 games of ''10,000 minutes in Heaven'' || 48.61 days || 70,000 minutes. 10,000 minutes in Heaven is almost a week of making out.
|-
| 48 || Jul 27 || φ^e^π minutes || 47.6164 days || 68,567.57 minutes
|-
| 47 || Jul 28 || 4 megaseconds || 46.2963 days || 4,000,000 seconds
|-
| 46 || Jul 29 || 2^16 minutes || 45.5111 days || 65,536 minutes
|-
| 45 || Jul 30 || e^e^e seconds || 44.1467 days || 3,814,279.10 seconds
|-
| 44 || Jul 31 || π fortnights|| 43.98 days || 3.14159 * 14 days
|-
| 43 || Aug 1 || One Devil's spacewalk (666 orbits of the ISS) || || See day 65 (Jul 10). 666 is the {{w|number of the beast}}.
|-
| 42 || Aug 2 || 1 kilowatt-hour per watt || 41⅔ days || 1000 hours
|-
| 41 || Aug 3 || e^π Ionian months || 40.9390 days || Orbital period of Io around Jupiter is 1.769137786 days
|-
| 40 || Aug 4 || 30 rotations of Foucault's pendulum in Paris || 39.8357 days || Refer to Day 80 (Jun 25)
|-
| 39 || Aug 5 || e fortnights || 38.0559 days ||2.71828 * 14 days
|-
| 38 || Aug 6 || π^π baker's days (25 hours) || 37.98 days || See day 75 (Jun 30)
|-
| 37 || Aug 7 || One deciyear || 36.525 days || One tenth of one year
|-
| 36 || Aug 8 || 7! milliweeks || 35.28 days || 5040 × 0.001 weeks
|-
| 35 || Aug 9 || 100,000 plays of the ''Jeopardy!'' "Think" music || 34.72 days || ''Think'' is the music played while the contestants try to answer the Final Jeopardy question; it takes 30 seconds.
|-
| 34 || Aug 10 || 1000 BasketBall Games (Game Time) || 33.33 days || using the NBA game time of four 12 minute quarters, 1000 * 4 * 12 minutes = 48000 minutes
|-
| 33 || Aug 11 || 777 hours || 32.375 days ||
|-
| 32 || Aug 12 ||one millilincoln (1/1000 of fourscore and seven years) || 31.78 days || {{w|Abraham Lincoln}}'s {{w|Gettysburg Address}} begins with the famous phrase "Four score and seven years ago". 1 score = 20 years
|-
| 31 || Aug 13 || 1,000 episodes of ''60 Minutes'' (skipping ads) || ||
|-
| 30 || Aug 14 || All of ''Star Trek'', consecutively || ||
|-
| 29 || Aug 15 || 777,777 nanocenturies || 28.4077 days || 777,777 × 10-9 × 102 years
|-
| 28 || Aug 16 || One sidereal lunar month || || The moon returns to a similar position relative to the fixed stars (sidereal month) in 27.3 days
|-
| 27 || Aug 17 || 6 dog months || 26.1 days || See day 78 (Jun 27)
|-
| 26 || Aug 18 || π^π kilominutes || 25.3209 days || 36,462.16 minutes
|-
| 25 || Aug 19 || 7 games of 7! minutes in Heaven || 24.5 days || 7 x 5040 minutes. See also day 49 (Jul 26).
|-
| 24 || Aug 20 || 50 viewings of the extended ''Lord of the Rings'' trilogy || ||
|-
| 23 || Aug 21 || A drive from NYC to LA where you keep remembering new things you forgot and have to go back 6 times || || See day 72 (Jul 3)
|-
| 22 || Aug 22 || ''It's a Small World'' sung at 1/10,000th speed || || {{w|It's a Small World}} is the song that plays continuously at the attraction of the same name at various {{w|Disney}} theme parks.
|-
| 21 || Aug 23 || 500 hours || 20.8333 days ||
|-
| 20 || Aug 24 || √2 fortnights || 19.7990 days || 1.4142 × 14 days
|-
| 19 || Aug 25 || Time it would take Vanessa Carlton to walk 1,000 miles|| || {{w|Vanessa Carlton}} is an American singer, and {{w|A Thousand Miles}} is her most successful song. Randall estimates her walking speed at about 2.2 miles/hour.
|-
| 18 || Aug 26 || 100,000 breaths || .26 min/breath || Normal respiratory rate for adults is typically 12-20 breaths per minute. Randall may have a health problem or be a practitioner of "slow breathing".
|-
| 17 || Aug 27 || √2 megaseconds || 16.3682 days || 1.4142 × 1,000,000 seconds
|-
| 16 || Aug 28 || π^π^π πcoseconds || 15.5112 days || 1.3402 × 1018 picoseconds (i.e., 10-12 seconds), or 1.3402 megaseconds
|-
| 15 || Aug 29 || One baker's fortnight (15 days) || 15 days || See day 75 (Jun 30)
|-
| 14 || Aug 30 || One baker's dozen (13) baker's days (25 hours) || 13.5416 days || 325 hours; see day 75 (Jun 30)
|-
| 13 || Aug 31 || 300 hours || 12.5 days ||
|-
| 12 || Sep 1 || One million seconds || 11.57 days ||
|-
| 11 || Sep 2 || One nonstop bike ride from NYC to LA || 10.54 days || Google maps estimates the trip at 253 hours
|-
| 10 || Sep 3 || 1/1,000th of a generation || 9.86 days || See day 79 (Jun 26)
|-
| 9 || Sep 4 || 777,777 seconds || 9.002 days ||
|-
| 8 || Sep 5 || 100 viewings of ''Groundhog Day'' || 7.014 days || Based on a running time of 101 minutes
|-
| 7 || Sep 6 || 100 games of ''Lincoln Kissing'' (Fourscore and seven minutes in Heaven) || 6.04 days || 8,700 minutes
|-
| 6 || Sep 7 || One pico-Universe-lifetime || || See Day 51 (Jul 24)
|-
| 5 || Sep 8 || The ''Baby Shark'' chorus for a family of 50,000 sharks || ||
|-
| 4 || Sep 9 || One centiyear || 3.6525 days ||
|-
| 3 || Sep 10 || Cyndi Lauper's ''Time After Time'' played 1,000 times || 2.79 days || Based on a length of 4 minutes, 1 second
|-
| 2 || Sep 11 || ''Speed'' (1994) played at one frame per second || 1.933 days || {{w|Speed_(1994_film)}} has runtime of 116 minutes = 6,960 seconds = 167,040 film frames at standard frame rate of 24 frames/second
|-
| 1 || Sep 12 || F(99) where F(N) means Sing all the verses of ''N Bottles of Beer On the wall'' followed by F(N-1) || || Each iteration contains ''N'' verses. ''N + N-1 + N-2 ... + 1'' equals ''N * (N+1) / 2'', so 99 recursions = 4950 verses. Using the same 13-second (72bpm) rate as Jun 29, this is close to 18 hours.
|-
| 0 || Sep 13 || ''What If? 2'' Release day || ||
|}

The title text refers to the recursive time period on Sep 12. If you don't stop when you reach N=0 bottles, the repetition never ends, so that time interval beecomes infinite. He likens it to {{w|The Song That Never Ends}}, another repetitive children's song, which is specifically intended to go on forever. The difference is that the Beer song has a natural stopping point at 0, while ''The Song That Never Ends'' is completely repetitive.

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

{{comic discussion}}