explain xkcd - User contributions [en]

2971: Celestial Event

2024-08-14T02:25:31Z

172.68.14.183:

{{comic
| number = 2971
| date = August 12, 2024
| title = Celestial Event
| image = celestial_event_2x.png
| imagesize = 471x300px
| noexpand = true
| titletext = If we can get a brood of 13-year cicadas going, we might have a chance at making this happen before the oceans evaporate under the expanding sun.
}}

==Explanation==
{{incomplete|Created by a CURSED SHOP THAT APPEARS EVERY FOUR POINT THREE BILLION YEARS - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

This comic was posted shortly after some people reported seeing the aurora in conjunction with the perseids meteor shower.<ref>https://www.msn.com/en-us/weather/topstories/the-2024-perseid-meteor-shower-and-northern-lights-overlapped-in-a-rare-cosmic-display-see-photos-of-the-dazzling-event/ar-AA1oJKKC</ref>. It lists several events that are considered special to be witnessed due to their rarity. Total solar eclipses, auroras and comet sightings are all rare events. This year, all three of these events happened in parts of the United States, where the author lives.

Although it might be, conceivably, possible to witness all three at once in a given location (in this case, the author's neighborhood), the odds stack up to make that occurrence extremely improbable. To boot, those events can only be observed with a clear sky (a 50:50 chance), so that too has to be accounted for in the calculation.

17-year {{w|Periodical cicadas|cicadas}} are also special in the sense that a brood will only emerge from the ground once every 17 years. Periodical cicadas recently became the object of media furor in 2024 as a 13-year brood and a 17-year happened to emerge together, an event that only happens once every 13x17 = 221 years. This caused a lot of noise and double the amount of dead cicadas after they had mated. Needless to say, having a cicada emergence co-occur with all those previously mentioned events would be extra rare, and thus extra special.

How rare, exactly, is the point of this calculation. The resulting product is the expected frequency that all of them would occur at the same time at that location. The value he calculates is once every 4.3 billion years. This is in the same ballpark as the current age of the Earth, about 4.5 billion years.

There are multiple inaccuracies in this type of calculation, although, given the extravagant nature of the proposed event and the unfeasible time scale, that hardly matters. Multiplying probabilities only works for random variables that are entirely independent. If nothing else, orbits are (luckily[maybe]
) not random.{{cn}} It also requires that all of the probabilities remain constant over time. In reality, cicadas will not exist for very long compared to the time scale, since Earth will become uninhabitable to complex life within a billion years' time and all life will be extinct within {{w|Future of Earth|4 billion years}}. Also, the moon is moving away from Earth, and total solar eclipses will cease to occur in about [https://www.space.com/37627-total-solar-eclipse-earth-moon-alignment-future.html 600 million years]. Luckily, this is not the time that you are ''always'' going to wait, merely the (usual) period between one occurance and the next. A person starting to wait at a random point in the cycle, and no knowing anything else, would ''on average'' only have to wait ''half'' the time. (If very lucky, it could happen tomorrow, as it hypothetically might have done a bit over four billion years ago; if unlucky, it would indeed be slightly more than four billion years, having most recently happened yesterday; if ''very'' unlucky, the frequencies are slightly less defined, do not actually align as expected for the next conclusion of the cycle and additional billions of years need to be waited until the next example when it 'might' indeed occur as anticipated. Finally, if '''extremely''' unlucky, you will never get a clear sky. Ever.

In order for the math to work out, some unit conversion is necessary. To solve "20 days / 11 years", one can consider 1 year = 365.24 days (a reasonable approximation that accounts for most leap years). For "2 months / 50 years" and "2 months / 17 years", the simplest way is to convert 1 year into 12 months. Unit cancelation works out, and you end up with a number in years that corresponds to the average amount of time between events when all those different things are happening at once. (the implied unit for eclipses is events per year, and that's the unit you get as a result, so the actual length of the eclipse doesn't influence the result much).

In the title text, Randall mentioned swapping 17-year cicada broods for 13-year ones, to have some chance at witnessing the proposed super-event before life on Earth becomes impossible. Massachusetts is near the northern limit of {{w|Periodical_cicadas|Magicicada}} distribution, and only one 17-year brood is established there (and not in Cambridge, MA). However, the introduction of a different brood could, with some help from global warming, be feasible.

Earth's oceans may evaporate in about one billion years<ref>https://www.sciencedaily.com/releases/2013/12/131216142310.htm</ref>. In order to beat that, we need to better our odds. Using 13-year cicadas in our calculations reduces the average interval between events to 3.29 billion years. We can lower that further by hoping that we'll have clear skies by then (who knows, we might get good enough at manipulating weather that we can *make* it happen). That gives us an average interval between events of about 1.6 billion years. Which means a larger than 50% chance that we'll get our special super-event to happen within a billion years, therefore beating ocean evaporation. Of course, cicadas may not last that long.[baseless conjecture] [trust the cicadas]

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:Approximate frequency in my area

:Active northern lights: 20 days per solar cycle

:A naked-eye "Great Comet": 2 months every 50 years

:Total eclipse: once every 350 years

:Clear skies: 50% of the time

:17-year cicada emergence: 2 months every 17 years

opening bracket

20 days over 11 years multiplied by

2 months over 50 years multiplied by

1 over 350 years multiplied by

one half multiplied by

2 months over 17 years

closing bracket to the power of -1

equals 4.3 billion years

:[Caption below the panel:]
:Every 4 billion years or so, my neighborhood gets to see a ''really'' spectacular show.

{{comic discussion}}

[[Category:Astronomy]]
[[Category:Solar eclipses]]
[[Category:Time]]
[[Category:Animals]]

Talk:2971: Celestial Event

2024-08-14T02:21:22Z

172.68.14.183:

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)

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?

: 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.
: 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.
: 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)

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)

Talk:2971: Celestial Event

2024-08-14T02:20:29Z

172.68.14.183:

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)

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?

: Ooh, great question. It turns out cicadas only emerge in warm weather, particularly in summer, and {{you can only see the northern lights in winter}}. 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.
: 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.
: 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)

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)

2971: Celestial Event

2024-08-14T02:13:48Z

172.68.14.183:

{{comic
| number = 2971
| date = August 12, 2024
| title = Celestial Event
| image = celestial_event_2x.png
| imagesize = 471x300px
| noexpand = true
| titletext = If we can get a brood of 13-year cicadas going, we might have a chance at making this happen before the oceans evaporate under the expanding sun.
}}

==Explanation==
{{incomplete|Created by a CURSED SHOP THAT APPEARS EVERY FOUR POINT THREE BILLION YEARS - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

This comic lists several events that are considered special to be witnessed due to their rarity. Total solar eclipses, auroras and comet sightings are all rare events. This year, all three of these events happened in parts of the United States, where the author lives. This comic was posted shortly after some people reported seeing the aurora in conjunction with the perseids meteor shower.<ref>https://www.msn.com/en-us/weather/topstories/the-2024-perseid-meteor-shower-and-northern-lights-overlapped-in-a-rare-cosmic-display-see-photos-of-the-dazzling-event/ar-AA1oJKKC</ref>

Although it might be, conceivably, possible to witness all three at once in a given location (in this case, the author's neighborhood), the odds stack up to make that occurrence extremely improbable. To boot, those events can only be observed with a clear sky (a 50:50 chance), so that too has to be accounted for in the calculation.

17-year {{w|Periodical cicadas|cicadas}} are also special in the sense that a brood will only emerge from the ground once every 17 years. Periodical cicadas recently became the object of media furor in 2024 as a 13-year brood and a 17-year happened to emerge together, an event that only happens once every 13x17 = 221 years. This caused a lot of noise and double the amount of dead cicadas after they had mated. Needless to say, having a cicada emergence co-occur with all those previously mentioned events would be extra rare, and thus extra special.

How rare, exactly, is the point of this calculation. The resulting product is the expected frequency that all of them would occur at the same time at that location. The value he calculates is once every 4.3 billion years. This is in the same ballpark as the current age of the Earth, about 4.5 billion years.

There are multiple inaccuracies in this type of calculation, although, given the extravagant nature of the proposed event and the unfeasible time scale, that hardly matters. Multiplying probabilities only works for random variables that are entirely independent. If nothing else, orbits are (luckily[maybe]
) not random.{{cn}} It also requires that all of the probabilities remain constant over time. In reality, cicadas will not exist for very long compared to the time scale, since Earth will become uninhabitable to complex life within a billion years' time and all life will be extinct within {{w|Future of Earth|4 billion years}}. Also, the moon is moving away from Earth, and total solar eclipses will cease to occur in about [https://www.space.com/37627-total-solar-eclipse-earth-moon-alignment-future.html 600 million years]. Luckily, this is not the time that you are ''always'' going to wait, merely the (usual) period between one occurance and the next. A person starting to wait at a random point in the cycle, and no knowing anything else, would ''on average'' only have to wait ''half'' the time. (If very lucky, it could happen tomorrow, as it hypothetically might have done a bit over four billion years ago; if unlucky, it would indeed be slightly more than four billion years, having most recently happened yesterday; if ''very'' unlucky, the frequencies are slightly less defined, do not actually align as expected for the next conclusion of the cycle and additional billions of years need to be waited until the next example when it 'might' indeed occur as anticipated. Finally, if '''extremely''' unlucky, you will never get a clear sky. Ever.

In order for the math to work out, some unit conversion is necessary. To solve "20 days / 11 years", one can consider 1 year = 365.24 days (a reasonable approximation that accounts for most leap years). For "2 months / 50 years" and "2 months / 17 years", the simplest way is to convert 1 year into 12 months. Unit cancelation works out, and you end up with a number in years that corresponds to the average amount of time between events when all those different things are happening at once. (the implied unit for eclipses is events per year, and that's the unit you get as a result, so the actual length of the eclipse doesn't influence the result much).

In the title text, Randall mentioned swapping 17-year cicada broods for 13-year ones, to have some chance at witnessing the proposed super-event before life on Earth becomes impossible. Massachusetts is near the northern limit of {{w|Periodical_cicadas|Magicicada}} distribution, and only one 17-year brood is established there (and not in Cambridge, MA). However, the introduction of a different brood could, with some help from global warming, be feasible.

Earth's oceans may evaporate in about one billion years<ref>https://www.sciencedaily.com/releases/2013/12/131216142310.htm</ref>. In order to beat that, we need to better our odds. Using 13-year cicadas in our calculations reduces the average interval between events to 3.29 billion years. We can lower that further by hoping that we'll have clear skies by then (who knows, we might get good enough at manipulating weather that we can *make* it happen). That gives us an average interval between events of about 1.6 billion years. Which means a larger than 50% chance that we'll get our special super-event to happen within a billion years, therefore beating ocean evaporation. Of course, cicadas may not last that long.[baseless conjecture] [trust the cicadas]

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:Approximate frequency in my area

:Active northern lights: 20 days per solar cycle

:A naked-eye "Great Comet": 2 months every 50 years

:Total eclipse: once every 350 years

:Clear skies: 50% of the time

:17-year cicada emergence: 2 months every 17 years

opening bracket

20 days over 11 years multiplied by

2 months over 50 years multiplied by

1 over 350 years multiplied by

one half multiplied by

2 months over 17 years

closing bracket to the power of -1

equals 4.3 billion years

:[Caption below the panel:]
:Every 4 billion years or so, my neighborhood gets to see a ''really'' spectacular show.

{{comic discussion}}

[[Category:Astronomy]]
[[Category:Solar eclipses]]
[[Category:Time]]
[[Category:Animals]]

Talk:2971: Celestial Event

2024-08-14T00:50:35Z

172.68.14.183:

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)

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?

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.
: 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.
: 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)

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)

2971: Celestial Event

2024-08-13T22:59:39Z

172.68.14.183:

{{comic
| number = 2971
| date = August 12, 2024
| title = Celestial Event
| image = celestial_event_2x.png
| imagesize = 471x300px
| noexpand = true
| titletext = If we can get a brood of 13-year cicadas going, we might have a chance at making this happen before the oceans evaporate under the expanding sun.
}}

==Explanation==
{{incomplete|Created by a CURSED SHOP THAT APPEARS EVERY FOUR POINT THREE BILLION YEARS - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
[[Randall]] has often obsessed over celestial events he wishes to see, and here lists three of these in this comic, hence the title. Recently there have been two total {{w|solar eclipse}}s in the US (2017 and 2024), so that has been ticked off his bucket list. And there have been {{w|aurora|northern lights}} this year far down into the mainland US. So it is likely he has also seen those. Whether or not he has seen a {{w|comet}} visible to the naked eye is not known, but there have been some candidates in his lifetime.

The next two on the list are not celestial events, but the lack of cloud cover is relevant in order to see the first three. Finally, he mentions the emergence of 17-year {{w|Periodical cicadas|cicadas}} which occurred most recently in the midwestern US in 2024 and in the eastern US in 2021.

An extra special celestial event would be to see all the three first things at the same time during a 17-year cicada event. Northern lights and a comet can only be seen during the night, except during a total solar eclipse where they could be visible for the few minutes of totality. (However, it rarely gets really dark during totality, and it is so short that night vision cannot be achieved before the totality is over.)

This joke of the comic comes from Randall multiplying the fraction of time that these selected classes of events occur over a particular location on the Earth's surface, in this case, {{w|Cambridge, Massachusetts}}, where the cartoonist was living when this comic was published. The resulting product is the expected frequency that all of them would occur at the same time at that location. The value he calculates is once every 4.3 billion years. This is in the same ballpark as the current age of the Earth, about 4.5 billion years.

The calculation itself is not going to be accurate, which is likely part of the joke. Multiplying probabilities only works for random variables that are entirely independent. If nothing else, orbits are (luckily{{citation needed}}) not random.{{cn}} It also requires that all of the probabilities remain constant over time. In reality, cicadas will not exist for very long compared to the time scale, since Earth will become uninhabitable to complex life within a billion years' time and all life will be extinct within {{w|Future of Earth|4 billion years}}. Also, the moon is moving away from Earth, and total solar eclipses will cease to occur in about [https://www.space.com/37627-total-solar-eclipse-earth-moon-alignment-future.html 600 million years]. Luckily, this is not the time that you are ''always'' going to wait, merely the (usual) period between one occurance and the next. A person starting to wait at a random point in the cycle, and no knowing anything else, would ''on average'' only have to wait ''half'' the time. (If very lucky, it could happen tomorrow, as it hypothetically might have done a bit over four billion years ago; if unlucky, it would indeed be slightly more than four billion years, having most recently happened yesterday; if ''very'' unlucky, the frequencies are slightly less defined, do not actually align as expected for the next conclusion of the cycle and additional billions of years need to be waited until the next example when it 'might' indeed occur as anticipated. Finally, if '''extremely''' unlucky, you will never get a clear sky. Ever.

Conversion of "days" and "months" to fractional years, required for conservation of units in the equation, is ambiguous as presented due to the leap year phenomenon and the inconsistent number of days in a month. Differing values for these fractional years yield a range of frequency solutions between 4.2 and 4.4 billion years. If the value for days in a year is given as 365.25 (the mean value for all years, ignoring infrequent additional 'leap year' corrections), as in the first term of the equation ((20/365.25)/11), and the mean value for days in two months is given as 60.9 as in the second term ((60.9/365.25)/50), the result is 4.2995 *10^9 years. On top of that, the length of the day {{w|Earth's rotation#Ancient observations|may change significantly}} (and also, potentially, {{w|Stability of the Solar System|the year}}), which would conceivably change the observable frequencies (and thus the length and offset of the compounded frequency of coincidence) quite a lot over the lifetime of the 'now'-calculated interval of recurrance.

In the title text, Randall mentioned 13-year cicadas. Massachusetts is near the northern limit of {{w|Periodical_cicadas|Magicicada}} distribution, and only one 17-year brood is established there (and not in Cambridge, MA). In other parts of the US, a 13-year brood and a 17-year brood emerged during 2024, an event that only happens once every 13x17 = 221 years. This caused a lot of noise and double the amount of dead cicadas after they had mated. Randall wondered whether it would be possible to get a brood of 13 year cicadas started near his home. In that case he could replace 13 with 17 in the calculation. Then, he hopes to achieve his "really spectacular show" before Earth's oceans evaporate. However, 4.3 billion years x13/17 is still more than 3 billion years.{{citation needed}} The oceans will not last that long, and given the merely 40 million year history of the genus Magicicada and its relatives, neither will the periodical cicadas.[baseless conjecture]

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:Approximate frequency in my area

:Active northern lights: 20 days per solar cycle

:A naked-eye "Great Comet": 2 months every 50 years

:Total eclipse: once every 350 years

:Clear skies: 50% of the time

:17-year cicada emergence: 2 months every 17 years

opening bracket

20 days over 11 years multiplied by

2 months over 50 years multiplied by

1 over 350 years multiplied by

one half multiplied by

2 months over 17 years

closing bracket to the power of -1

equals 4.3 billion years

:[Caption below the panel:]
:Every 4 billion years or so, my neighborhood gets to see a ''really'' spectacular show.

{{comic discussion}}

[[Category:Astronomy]]
[[Category:Solar eclipses]]
[[Category:Time]]
[[Category:Animals]]