explain xkcd - User contributions [en]

3023: The Maritime Approximation

2024-12-12T00:05:53Z

AnnapolisKen: I'm not sure if "numerously noted" was some joke instead of "humorously noted" but I decided that clarity should be our watchword in editing.

{{comic
| number = 3023
| date = December 11, 2024
| title = The Maritime Approximation
| image = the_maritime_approximation_2x.png
| imagesize = 265x126px
| noexpand = true
| titletext = It works because a nautical mile is based on a degree of latitude, and the Earth (e) is a circle.
}}

==Explanation==
{{incomplete|Created by a SEMICIRCULAR SAILOR - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

MPH, or Miles Per Hour, and Knots are both units used to calculate the speed of vehicles. Miles per hour are typically used in the US for the speed of cars and other similar vehicles, while Knots are used by some sailors or pilots to describe the speed of ships or aircraft. Novice sailors or sailors who spend a lot of time on land may find it helpful to quickly convert between MPH and Knots. Usually, this is the form of 1 knot = 1.2 MPH, or 1 MPH = 0.87 knots, however Randall has humorously noticed that π MPH= e Knots. This is a coincidence{{Citation needed}} despite the claim of the title text, since even though Knots are based on nautical miles which are related to degrees of latitude (and thus to π, which is used to describe the circumference of a circle) miles per hour have no relation to either e or π. Randall has made similar observations of different dimensions that equal each other in the past in the past with comics such as [[687: Dimensional Analysis]], where he compares {{w|Plank Energy}}, the pressure at the earth's core, the gas mileage in a Prius, and the width of the English channel to Pi. In addition, in [[What If?]], he has compared the mass of Earth to be Pi "miliJupiters," or Pi times the mass of Jupiter divided by 1000, and noted that the volume of a cube with side lengths of one mile is roughly similar to the volume of a sphere with a radius of 1 kilometer.

The equality shown in this strip consists of several different parts:

# The mile per hour (mph) is a unit of speed common for motor vehicles in a few countries, such as the United States and United Kingdom.
# The knot is a unit of speed that is one nautical mile (1 852 m) per hour, used in nautical contexts.
# π is a number equal to the ratio of a circle's circumference to its diameter, about 3.14159.
# e is Euler's number, the base of the natural logarithm, about 2.71828.

π mph × (1609.344 meters/statute mile ÷ 1852 meters/nautical mile) ≈ 2.72996 knots. The result is only about 0.43% larger than ''e'' knots ≈ 2.71828 knots.

The joke is that it is not exact, but only correct to a certain percentage, unlike Euler's Identity, which is exact and that's what makes the latter truly remarkable. It isn't helped by the fact that it carries the implication that this neat, easy to remember identity is actual useful for sailors but indeed, being easy to remember is all it has going for it. Otherwise it doesn't make calculations any easier and is impossible to do without a calculator or paper, and doing it on paper is much harder than other conversions, given that pi and e are both irrational, and transcendental.

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

:[Equation inside a frame with a footnote:]
:π mph = ''e'' knots*
:<small>*Correct to <0.5%</small>

:[Caption below the panel:]
:The sailor's version of e<sup>iπ</sup>=−1

{{comic discussion}}

[[Category:Math]]

Talk:2971: Celestial Event

2024-08-15T14:05:34Z

AnnapolisKen: response

Unfortunately, this calculation doesn't account for the eventual end of total solar eclipses due to the tidal recession of the moon. [[Special:Contributions/172.69.246.142|172.69.246.142]] 05:31, 13 August 2024 (UTC)

:This is a great comment! Very much like something Randall would have written for title text. [[Special:Contributions/172.71.146.49|172.71.146.49]] 05:58, 13 August 2024 (UTC)
:: Agreed! Also, it seems like the article should have a footnote or separate section going full Randall, "Based only on the data given in this cartoon, what is the possible range of Randall Munroe's home location?" --[[User:AnnapolisKen|AnnapolisKen]] ([[User talk:AnnapolisKen|talk]]) 18:21, 13 August 2024 (UTC)
::: Speculating about people's addresses online is generally frowned upon, in court if nowhere else. [[Special:Contributions/172.68.14.183|172.68.14.183]] 00:50, 14 August 2024 (UTC)
:::: As in the original post, the humor in it is that the quest would be effectively useless, right? I mean probably the best data point would be that it's in an area where 17-year cicadas brood. I'm not sure any other data could narrow it down beyond that. --[[User:AnnapolisKen|AnnapolisKen]] ([[User talk:AnnapolisKen|talk]]) 14:05, 15 August 2024 (UTC)

Are all of these events really statistically independent or are e.g. active northern lights and cicada mergence more or less likely to happen at the same time of the year? {{unsigned ip|172.68.194.201|06:15, 13 August 2024}}

: Ooh, great question. It turns out cicadas only emerge in warm weather, particularly in summer, and <s>you can only see the northern lights in winter</s>. That's bad news for us, our superevent might never happen. [[Special:Contributions/172.69.90.3|172.69.90.3]] 01:03, 14 August 2024 (UTC) — edit: oops, I got it wrong. It turns out you can see them all year round. They're actually happening right now in some parts of the US.

This comic was published the same night that saw both the Perseids meteor shower and an unusually strong northern lights. Strangely, the omission of meteor showers in Randall's account of Celestial Events suggests that this is a coincidence. [[User:Mumiemonstret|Mumiemonstret]] ([[User talk:Mumiemonstret|talk]]) 11:43, 13 August 2024 (UTC)

One eclipse every 350 years is not "1/350" - that would imply the eclipse lasted the whole year. The numerator unit should be a minute or so, vastly changing the result. {{unsigned ip|172.70.39.114|13:16, 13 August 2024}}
: Actually, thanks to unit cancelation, Randall's math checks out. I really really feel that it shouldn't, but it does. It's 1/350 years because what you're calculating is "once every X years". It doesn't actually matter how long an eclipse lasts, so long as it's a sufficiently small amount of time so as to be treated as a single point in time. "When that point in time happens, how frequently will those other things be happening?". You can give that answer in days, years, or whatever other unit of time you prefer. Since we're giving it in years, the number we need is "how often (am eclipse occurs) each year" - [[Special:Contributions/172.68.14.185|172.68.14.185]] 23:32, 13 August 2024 (UTC)
:: Yes, I came back to correct myself on this after more reflection. The implied unit is Event and this is the only such non-dimentionless factor. {{unsigned ip|108.162.245.186|23:40, 13 August 2024}}
: Tru dat, as are the comments regarding changes over time in eclipse parameters and the effects of time approximations. However, if we let "4 minutes" be the mean time of totality for an eclipse, and insert that term (for the record, 7.6E-06) for "1" in "1/350", the equation's solution becomes 4E+14, orders of magnitude greater than the age of the universe and, IIRC, well into its projected "heat death". The joke appears to reside in the proximity of Randall's solution to the commonly-accepted age of the Earth, making the solution "just possible". More "accurate" solutions would not be funny, and we would not have seen this comic.[[Special:Contributions/162.158.41.227|162.158.41.227]] 17:11, 13 August 2024 (UTC)
::In the "1/350years", I took it to mean that the unitless "1" represented a day (within which an eclipse occurs, and across this period would also extend the various other conditions). By treating all other unit-laden values as correctly converted to the number in the term of days (and back-converted to the 'more convenient' billions of years for the result), it probably ...not that I did the mathematics to check this... comes out as Randall suggests.
::If, indeed, the length of an (average, as of Earth's current configuration) eclipse, and all other values were understood as proxies for the "number of eclipse-lengths" (except for the uncloudy sky fraction, which is always a unitless half through cancelling out) then you might end up with a result that's different. But the way to check this is to accept the answer (in billions of years) and all the others with time-lengths (respectively) and work out the rough united-length of the "1" by to identify what unit would best fit that. But I leave that to whoever ''really'' wants to dive that deep into it, as the next logical step beyond mere attempted pedantry. [[Special:Contributions/172.68.205.164|172.68.205.164]] 20:22, 13 August 2024 (UTC)
: Every other 2 billion years, on days when it's cloudy or raining, the neighborhood ''doesn't'' get to see the spectacular show. [[Special:Contributions/162.158.154.98|162.158.154.98]] 19:19, 13 August 2024 (UTC)
::So just like the olympic games: They happen every 4 years, while also every 4 years, but offset by 2, there are the olympic winter games... --[[User:Lupo|Lupo]] ([[User talk:Lupo|talk]]) 05:43, 15 August 2024 (UTC)

There are competing factors with regard to the eclipse. Obviously total eclipses don't last for an entire year {{cn}}, but in the distant past when the Moon was significantly closer, they occurred much more frequently than once every 350 years. Far enough back, the moon was significantly larger in the sky and orbited much more rapidly making total solar eclipses a much more common event (even if nobody with eyes was around to see). Using constants for probabilities when things have significant variation is tricky. [[User:Galeindfal|Galeindfal]] ([[User talk:Galeindfal|talk]]) 14:26, 13 August 2024 (UTC)
:I just added (without having seen the above comment) something that deals with that. Actually, that and the way that the 'beat frequency' may ''just'' fail to create an all-effect maximum due to it not being a strictly repeating frequency (if you have an eclipse on one date, with a "1 event in 350 years" calculation for your location/latitude, it doesn't preclude more than one per 350 years or two separated by vastly more than 350 years - though still likely to get "N+1" eclipses over any given 350xN year period for higher Ns).
:If it's a combinatorial experience of fully periodic frquencies (such as with [[1331: Frequency]] then you can be precise over the beat-frequency, but any statistical perturbation can make a 'full hit' into a 'not-fully hit' event quite easily. At its simplest, though the chances of any given day (or useful fraction of a day) of being clear-skied may be 50%, it's not as simple to say "yesterday was cloudy, tomorrow will be clear", or vice-versa. Perhaps slightly more useful to say that than "the year just gone had no clouds, so this year will be full of them" or imagining that every second you could glance up and see "clouds...", "no clouds...", "clouds...", "no clouds...". The meteorological 'calculations' would never be anywhere near as simple as even the (future-trends modified) far-future predictability of the astronomical effects. The biologist might be able to be reasonably sure that the season-locked emergence of a given cicada brood will actually continue to satisfy ''their'' contribution to the calculation for much longer than the weatherman might (though they'd have to admit to the high probability that an ecological upset would flat out end any chances before any of the other forecasts become too hazy to rely upon).
:So the changing of frequencies over the time of the 9calculated) meta-beat's recurrance will make for an compoundedly-chaotic 'actual' meta-beat (assuming it ever completes). This includes the possibility that it actually re-meshes its individual occurances into an actually far more frequent coincidence (two consecutive cicada emergences could end up ''both'' being accompanied by all the other requirements). Depends how much you take at face-value, rather than as a rough and ready 'approximation' for fun-and-non-profit... [[Special:Contributions/172.68.205.164|172.68.205.164]] 20:22, 13 August 2024 (UTC)

The adjustment due to leap years is far dwarfed by the approximate nature of "20 days" and "2 months" in some of the events. [[User:Barmar|Barmar]] ([[User talk:Barmar|talk]]) 15:06, 13 August 2024 (UTC)

Don't know how it could be calculated in, but there's a fundamental conflict between the solar eclipse and aurora borealis. Solar eclipses are only visible during the day {{cn}}, but the aurorae aren't symmetrical around the poles and drag further equator-ward on the night side of the planet. So the occurrences of Northern lights that would reach to Boston latitudes on the *day side* of the planet so as to be visible during a solar eclipse would be much, much rarer (closer to Carrington-event rarity, currently pitched at once every 100 to 1000 years instead of the 11 Randall used, but even then it'd have to be a particularly strong event). [[Special:Contributions/172.70.230.142|172.70.230.142]] 13:34, 14 August 2024 (UTC)

If he had included all these events happening on a Tuesday or a Thursday then we're getting close to 1 every 14 billion years. A time which everyone's neighbourhoods had a really big show. [[User:Kev|Kev]] ([[User talk:Kev|talk]]) 02:36, 15 August 2024 (UTC)

Someone has to say it. The explanation is so long and convoluted that it serves substantially more to confuse than to explain. Someone please edit it mercilessly. [[Special:Contributions/172.69.33.62|172.69.33.62]] 05:14, 15 August 2024 (UTC)
:I bit the bullet. I'm sure I left some important stuff out, but more sure I deleted more unimportant stuff. [[Special:Contributions/172.71.146.211|172.71.146.211]] 06:24, 15 August 2024 (UTC)

Talk:2971: Celestial Event

2024-08-13T18:21:13Z

AnnapolisKen: Added an idea for using the data in the cartoon to comically estimate the bounds of Randall Munroe's likely home location.