Today is February 29th, which is a day that is usually added to our calendar once every four years (on years that are multiples of 4, such as 2004, 2008, 2012, and 2016). This is to correct for the fact that the number of days it takes the Earth to completely revolve once around the sun is slightly more than 365.
I'd like to elaborate on that word usually though, as not every fourth year is a leap year.
Mathematically speaking, it's more accurate to say that a true solar year is closer to 365.25 days than 365 days, as each year is longer than 365 days by almost 6 hours. This is almost a quarter of a day unaccounted for, which justifies the inclusion of an extra day every fourth year (because by then, four quarter-days have accumulated, equaling a full day). Repeating the four-year sequence of "365 days, 365 days, 365 days, 366 days" would be perfect if a solar year was exactly 365.25 days.
It's not though. As a result, a few additional (and much rarer) nuances are included in our calendar, so that we maintain synchronization over several centuries. It turns out that one solar year is slightly less than 365.25 days, which means that the additional leap day every fourth year is a slight overcorrection that needs to be adjusted from time to time.
The generally accepted length of a solar year, based on observation and calculation, has been averaged to be 365.2425 days. This means that two additional calendar rules are implemented to keep our calendars consistent:
1. Our calendar removes a leap year once every one hundred years on the century-year (e.g., the years 1700, 1800, and 1900 were not leap years; they did not have February 29ths). Unfortunately, this readjustment goes a bit too far in counterbalancing this issue, which leads to... 2. Our calendar puts back the leap year in every century-year that's a multiple of 400 (e.g., the year 2000 and the year 2400 will have February 29ths, despite the years 2100, 2200, and 2300 not having them).
These two additional corrections to our calendar combine to remove 3 leap years every 400 years (called a "leap cycle"). This means that we have 97 leap years- not 100 leap years- every 400 years. Here's the math for a leap cycle:
97 leap years = 97 * 366 days = 35,502 days 303 common years = 303 * 365 days = 110,595 days In a 400-year period: 35,502 + 110,595 = 146,097 days 146,097 days / 400 years = 365.2425, which is the precise average number of days we want to obtain for a solar year. (It's those extra 97 leap days spread throughout the 400-day leap cycle that adds the ".2425" correction that we need, which is 97/400.) Therefore, while individual leap years play an important part in the correction of our calendar, it's not until an entire 400-year leap cycle has completed that we're corrected to the accuracy and satisfaction of leading scientists and mathematicians.
Just a word of caution, however: "daily" still means "365 times per year" in most math or science contexts (especially in word problems and textbooks). It's never a bad thing to check with your teacher just to make sure, but you may want to reserve this fun math fact about leap year technicalities for dinner table conversations and social mixers.
If you'd like to listen to this leap year process explained by a fantastic astrophysicist with a dreamy voice, click here:
The funny thing is that the length of a day slowly changes. So the calendar will get more and more incorrect as the centuries pass. That is a problem somebody in the future will have to solve.
"With the current system, it’s not actually perfect. There’s an extra 0.000125 days being accumulated. Over course of 8,000 years, the calendar will lose a single day." Disregarding the changing day length.
On February 29 2016 23:36 Cascade wrote: Nice write-up! And what's the story with the leap seconds again?
Leap seconds are added to synchronize atomic clocks with the Earth's slowing rotation, so that one day really does equal a full Earth rotation (as accurately as possible). If the Earth's rotation slows a bit, then it'll take more seconds to complete the rotation; that's when leap seconds come in to play.
On March 01 2016 00:44 Yurie wrote: The funny thing is that the length of a day slowly changes. So the calendar will get more and more incorrect as the centuries pass. That is a problem somebody in the future will have to solve.
As of right now, these discrepancies are still very close together and are averaged together to give us that .2425 adjustment to correct for. Fortunately, adding in leap seconds and leap days does a great job of staying on top of this natural variation.
This completely ruins the notion of a year for me though, I think you need to stop fiddling with mathematics and start using rockets to speed up the Earth so that it does one full rotation* in 365 days exactly. Let's get practical.
On March 01 2016 01:51 Djzapz wrote: This completely ruins the notion of a year for me though, I think you need to stop fiddling with mathematics and start using rockets to speed up the Earth so that it does one full rotation in 365 days exactly. Let's get practical.
Instead of accelerating Earth's revolution, we could instead slow down Earth's rotation. Since that's already happening due to the presence of the moon, we just have to wait until we reach the correct ratio at which point we can strategically jettison the moon out of orbit.
On March 01 2016 01:51 Djzapz wrote: This completely ruins the notion of a year for me though, I think you need to stop fiddling with mathematics and start using rockets to speed up the Earth so that it does one full rotation in 365 days exactly. Let's get practical.
Instead of accelerating Earth's revolution, we could instead slow down Earth's rotation. Since that's already happening due to the presence of the moon, we just have to wait until we reach the correct ratio at which point we can strategically jettison the moon out of orbit.
Good idea.
I want to point out that by "rotation around the sun" I did indeed mean revolution. Or something.
Before we "correct" this in our calendar. How do we know we have year 2016? Maybe we "forgot" a year at ~200.000 B.C or whenever. Do we have evidence that there were no calendar mistakes since human life?
On March 01 2016 06:03 Dingodile wrote: Before we "correct" this in our calendar. How do we know we have year 2016? Maybe we "forgot" a year at ~200.000 B.C or whenever. Do we have evidence that there were no calendar mistakes since human life?
Our current calendar- the Gregorian calendar- first started being used in 1582. Since then, advances in astronomy and other related sciences have allowed us to compute and implement the required "leap" corrections. As a result, it's not really an issue what happened before then, because we know where we are right now and how to adjust our calendar for the future.
On March 01 2016 06:03 Dingodile wrote: Before we "correct" this in our calendar. How do we know we have year 2016? Maybe we "forgot" a year at ~200.000 B.C or whenever. Do we have evidence that there were no calendar mistakes since human life?
The calendar year number is based on the birth of Jesus Christ since it is a Christian calendar at its base. Nobody knows if it is correct on where year -1 and 1 is.
On March 01 2016 06:03 Dingodile wrote: Before we "correct" this in our calendar. How do we know we have year 2016? Maybe we "forgot" a year at ~200.000 B.C or whenever. Do we have evidence that there were no calendar mistakes since human life?
Every calendar is a social construct, so who cares if we made a mistake
On March 01 2016 06:03 Dingodile wrote: Before we "correct" this in our calendar. How do we know we have year 2016? Maybe we "forgot" a year at ~200.000 B.C or whenever. Do we have evidence that there were no calendar mistakes since human life?
Every calendar is a social construct, so who cares if we made a mistake
I think Dingodile means as far as maintaining the level of reliability and accuracy that our calendar is supposed to maintain. If we say it's accurate, then we shouldn't be making unaccounted mistakes.
On March 01 2016 06:03 Dingodile wrote: Before we "correct" this in our calendar. How do we know we have year 2016? Maybe we "forgot" a year at ~200.000 B.C or whenever. Do we have evidence that there were no calendar mistakes since human life?
Every calendar is a social construct, so who cares if we made a mistake
I think Dingodile means as far as maintaining the level of reliability and accuracy that our calendar is supposed to maintain. If we say it's accurate, then we shouldn't be making unaccounted mistakes.
Yes, but if we made a mistake and we're in fact in 2017, no one knows it and everyone agrees that we're in 2016, thus the reality is that we're in 2016 and not in 2017. See where I'm going? d:
On March 01 2016 06:03 Dingodile wrote: Before we "correct" this in our calendar. How do we know we have year 2016? Maybe we "forgot" a year at ~200.000 B.C or whenever. Do we have evidence that there were no calendar mistakes since human life?
Every calendar is a social construct, so who cares if we made a mistake
I think Dingodile means as far as maintaining the level of reliability and accuracy that our calendar is supposed to maintain. If we say it's accurate, then we shouldn't be making unaccounted mistakes.
Yes, but if we made a mistake and we're in fact in 2017, no one knows it and everyone agrees that we're in 2016, thus the reality is that we're in 2016 and not in 2017. See where I'm going? d:
Well that's not "the reality". We're just misinformed lol. Facts are facts, regardless of whether or not we understand or believe them
To use a calendar analogy: Some people argue that 2001 is the start of the new millennium, not 2000. This is because our calendar starts at 1, not at 0, and so a millennium would be 1-1000 and then 1001-2000, meaning that 2001 would signify the beginning of the third millennium A.D. Similarly, 1901 would be the start of a new century, 2011 would be the start of a new decade, etc. As far as I'm aware, this is mathematically sound and the reality is that 2000 wasn't the beginning of a new millennium according to the beginning of our calendar/ A.D.. A lot of people thinking it was doesn't change that fact. However, most people see the changing of a digit (tens' digit, hundreds' digit, thousands' digit, etc.) as the visual factor that acknowledges a new millennium/ century/ decade, and so it's easier for people to recognize. I guess one way to reconcile this is to just pretend that the first decade A.D. had only 9 years, the first century A.D., had only 99 years, and the first millennium A.D. had only 999 years; this way, the later groups wouldn't be off. But whatever lol. It's not that important in the long run.
On March 01 2016 06:03 Dingodile wrote: Before we "correct" this in our calendar. How do we know we have year 2016? Maybe we "forgot" a year at ~200.000 B.C or whenever. Do we have evidence that there were no calendar mistakes since human life?
Every calendar is a social construct, so who cares if we made a mistake
I think Dingodile means as far as maintaining the level of reliability and accuracy that our calendar is supposed to maintain. If we say it's accurate, then we shouldn't be making unaccounted mistakes.
Yes, but if we made a mistake and we're in fact in 2017, no one knows it and everyone agrees that we're in 2016, thus the reality is that we're in 2016 and not in 2017. See where I'm going? d:
Well that's not "the reality". We're just misinformed lol. Facts are facts, regardless of whether or not we understand or believe them
To use a calendar analogy: Some people argue that 2001 is the start of the new millennium, not 2000. This is because our calendar starts at 1, not at 0, and so a millennium would be 1-1000 and then 1001-2000, meaning that 2001 would signify the beginning of the third millennium A.D. Similarly, 1901 would be the start of a new century, 2011 would be the start of a new decade, etc. As far as I'm aware, this is mathematically sound and the reality is that 2000 wasn't the beginning of a new millennium according to the beginning of our calendar/ A.D.. A lot of people thinking it was doesn't change that fact. However, most people see the changing of a digit (tens' digit, hundreds' digit, thousands' digit, etc.) as the visual factor that acknowledges a new millennium/ century/ decade, and so it's easier for people to recognize. I guess one way to reconcile this is to just pretend that the first decade A.D. had only 9 years, the first century A.D., had only 99 years, and the first millennium A.D. had only 999 years; this way, the later groups wouldn't be off. But whatever lol. It's not that important in the long run.
On March 01 2016 06:03 Dingodile wrote: Before we "correct" this in our calendar. How do we know we have year 2016? Maybe we "forgot" a year at ~200.000 B.C or whenever. Do we have evidence that there were no calendar mistakes since human life?
Every calendar is a social construct, so who cares if we made a mistake
I think Dingodile means as far as maintaining the level of reliability and accuracy that our calendar is supposed to maintain. If we say it's accurate, then we shouldn't be making unaccounted mistakes.
Yes, but if we made a mistake and we're in fact in 2017, no one knows it and everyone agrees that we're in 2016, thus the reality is that we're in 2016 and not in 2017. See where I'm going? d:
Well that's not "the reality". We're just misinformed lol. Facts are facts, regardless of whether or not we understand or believe them
To use a calendar analogy: Some people argue that 2001 is the start of the new millennium, not 2000. This is because our calendar starts at 1, not at 0, and so a millennium would be 1-1000 and then 1001-2000, meaning that 2001 would signify the beginning of the third millennium A.D. Similarly, 1901 would be the start of a new century, 2011 would be the start of a new decade, etc. As far as I'm aware, this is mathematically sound and the reality is that 2000 wasn't the beginning of a new millennium according to the beginning of our calendar/ A.D.. A lot of people thinking it was doesn't change that fact. However, most people see the changing of a digit (tens' digit, hundreds' digit, thousands' digit, etc.) as the visual factor that acknowledges a new millennium/ century/ decade, and so it's easier for people to recognize. I guess one way to reconcile this is to just pretend that the first decade A.D. had only 9 years, the first century A.D., had only 99 years, and the first millennium A.D. had only 999 years; this way, the later groups wouldn't be off. But whatever lol. It's not that important in the long run.
So you do not believe that perception is reality?
I don't wish to have a semantics argument between truth and Truth right now
On March 01 2016 06:03 Dingodile wrote: Before we "correct" this in our calendar. How do we know we have year 2016? Maybe we "forgot" a year at ~200.000 B.C or whenever. Do we have evidence that there were no calendar mistakes since human life?
Every calendar is a social construct, so who cares if we made a mistake
I think Dingodile means as far as maintaining the level of reliability and accuracy that our calendar is supposed to maintain. If we say it's accurate, then we shouldn't be making unaccounted mistakes.
Yes, but if we made a mistake and we're in fact in 2017, no one knows it and everyone agrees that we're in 2016, thus the reality is that we're in 2016 and not in 2017. See where I'm going? d:
Well that's not "the reality". We're just misinformed lol. Facts are facts, regardless of whether or not we understand or believe them
To use a calendar analogy: Some people argue that 2001 is the start of the new millennium, not 2000. This is because our calendar starts at 1, not at 0, and so a millennium would be 1-1000 and then 1001-2000, meaning that 2001 would signify the beginning of the third millennium A.D. Similarly, 1901 would be the start of a new century, 2011 would be the start of a new decade, etc. As far as I'm aware, this is mathematically sound and the reality is that 2000 wasn't the beginning of a new millennium according to the beginning of our calendar/ A.D.. A lot of people thinking it was doesn't change that fact. However, most people see the changing of a digit (tens' digit, hundreds' digit, thousands' digit, etc.) as the visual factor that acknowledges a new millennium/ century/ decade, and so it's easier for people to recognize. I guess one way to reconcile this is to just pretend that the first decade A.D. had only 9 years, the first century A.D., had only 99 years, and the first millennium A.D. had only 999 years; this way, the later groups wouldn't be off. But whatever lol. It's not that important in the long run.
So you do not believe that perception is reality?
I don't wish to have a semantics argument between truth and Truth right now
I can understand that a mathematician is not amused by semantics, so I'll respect that (;
On March 01 2016 06:03 Dingodile wrote: Before we "correct" this in our calendar. How do we know we have year 2016? Maybe we "forgot" a year at ~200.000 B.C or whenever. Do we have evidence that there were no calendar mistakes since human life?
Every calendar is a social construct, so who cares if we made a mistake
I think Dingodile means as far as maintaining the level of reliability and accuracy that our calendar is supposed to maintain. If we say it's accurate, then we shouldn't be making unaccounted mistakes.
Yes, but if we made a mistake and we're in fact in 2017, no one knows it and everyone agrees that we're in 2016, thus the reality is that we're in 2016 and not in 2017. See where I'm going? d:
Well that's not "the reality". We're just misinformed lol. Facts are facts, regardless of whether or not we understand or believe them
To use a calendar analogy: Some people argue that 2001 is the start of the new millennium, not 2000. This is because our calendar starts at 1, not at 0, and so a millennium would be 1-1000 and then 1001-2000, meaning that 2001 would signify the beginning of the third millennium A.D. Similarly, 1901 would be the start of a new century, 2011 would be the start of a new decade, etc. As far as I'm aware, this is mathematically sound and the reality is that 2000 wasn't the beginning of a new millennium according to the beginning of our calendar/ A.D.. A lot of people thinking it was doesn't change that fact. However, most people see the changing of a digit (tens' digit, hundreds' digit, thousands' digit, etc.) as the visual factor that acknowledges a new millennium/ century/ decade, and so it's easier for people to recognize. I guess one way to reconcile this is to just pretend that the first decade A.D. had only 9 years, the first century A.D., had only 99 years, and the first millennium A.D. had only 999 years; this way, the later groups wouldn't be off. But whatever lol. It's not that important in the long run.
I don't understand what you guys mean with "actually 2017". We are pretty certain that we have kept track of the years since the calendar was introduced in 1500-whatever I think? So whatever happened before that doesn't matter, they defined that year to be the year 1500-whatever in that calendar, so that is accurate by definition. Then they based that on the birth of Jesus, which may have been off by a bit, but that doesn't change the fact that they defined that year to be what it is.
On March 01 2016 06:03 Dingodile wrote: Before we "correct" this in our calendar. How do we know we have year 2016? Maybe we "forgot" a year at ~200.000 B.C or whenever. Do we have evidence that there were no calendar mistakes since human life?
Every calendar is a social construct, so who cares if we made a mistake
I think Dingodile means as far as maintaining the level of reliability and accuracy that our calendar is supposed to maintain. If we say it's accurate, then we shouldn't be making unaccounted mistakes.
Yes, but if we made a mistake and we're in fact in 2017, no one knows it and everyone agrees that we're in 2016, thus the reality is that we're in 2016 and not in 2017. See where I'm going? d:
Well that's not "the reality". We're just misinformed lol. Facts are facts, regardless of whether or not we understand or believe them
To use a calendar analogy: Some people argue that 2001 is the start of the new millennium, not 2000. This is because our calendar starts at 1, not at 0, and so a millennium would be 1-1000 and then 1001-2000, meaning that 2001 would signify the beginning of the third millennium A.D. Similarly, 1901 would be the start of a new century, 2011 would be the start of a new decade, etc. As far as I'm aware, this is mathematically sound and the reality is that 2000 wasn't the beginning of a new millennium according to the beginning of our calendar/ A.D.. A lot of people thinking it was doesn't change that fact. However, most people see the changing of a digit (tens' digit, hundreds' digit, thousands' digit, etc.) as the visual factor that acknowledges a new millennium/ century/ decade, and so it's easier for people to recognize. I guess one way to reconcile this is to just pretend that the first decade A.D. had only 9 years, the first century A.D., had only 99 years, and the first millennium A.D. had only 999 years; this way, the later groups wouldn't be off. But whatever lol. It's not that important in the long run.
So you do not believe that perception is reality?
I don't wish to have a semantics argument between truth and Truth right now
I can understand that a mathematician is not amused by semantics, so I'll respect that (;
On March 01 2016 06:03 Dingodile wrote: Before we "correct" this in our calendar. How do we know we have year 2016? Maybe we "forgot" a year at ~200.000 B.C or whenever. Do we have evidence that there were no calendar mistakes since human life?
Every calendar is a social construct, so who cares if we made a mistake
I think Dingodile means as far as maintaining the level of reliability and accuracy that our calendar is supposed to maintain. If we say it's accurate, then we shouldn't be making unaccounted mistakes.
Yes, but if we made a mistake and we're in fact in 2017, no one knows it and everyone agrees that we're in 2016, thus the reality is that we're in 2016 and not in 2017. See where I'm going? d:
Well that's not "the reality". We're just misinformed lol. Facts are facts, regardless of whether or not we understand or believe them
To use a calendar analogy: Some people argue that 2001 is the start of the new millennium, not 2000. This is because our calendar starts at 1, not at 0, and so a millennium would be 1-1000 and then 1001-2000, meaning that 2001 would signify the beginning of the third millennium A.D. Similarly, 1901 would be the start of a new century, 2011 would be the start of a new decade, etc. As far as I'm aware, this is mathematically sound and the reality is that 2000 wasn't the beginning of a new millennium according to the beginning of our calendar/ A.D.. A lot of people thinking it was doesn't change that fact. However, most people see the changing of a digit (tens' digit, hundreds' digit, thousands' digit, etc.) as the visual factor that acknowledges a new millennium/ century/ decade, and so it's easier for people to recognize. I guess one way to reconcile this is to just pretend that the first decade A.D. had only 9 years, the first century A.D., had only 99 years, and the first millennium A.D. had only 999 years; this way, the later groups wouldn't be off. But whatever lol. It's not that important in the long run.
I don't understand what you guys mean with "actually 2017". We are pretty certain that we have kept track of the years since the calendar was introduced in 1500-whatever I think? So whatever happened before that doesn't matter, they defined that year to be the year 1500-whatever in that calendar, so that is accurate by definition. Then they based that on the birth of Jesus, which may have been off by a bit, but that doesn't change the fact that they defined that year to be what it is.
a decade has ten years, not nine, century = 100 years, but there is a difference. Century uses the time frame from 01 to 100 like 01.01.1701 - 31.12.1800 (18th century) decade uses 0 - 9 such as 01.01.1930 - 31.12.1939 (1930s)
I'm not disagreeing with you on what a decade or century or millennium is, but if you go far enough back to the beginning of A.D., at some point one has to concede that one decade/ century/ millennium has either 9 or 99 or 999 years, not the correct 10 or 100 or 1000 (although all the others have the correct number of years). And that's because there's no Year 0. There's no 0 A.D.
To get to the 2000s as a millennium (2000-2999), you need to have had the 1000s as a millennium (1000-1999). Before that was only 999 years in A.D. though... 1-999, not 0-999. The first millennium A.D. wasn't a millennium; it was 999 years. Same goes with how the first decade A.D. is 1-9 (not 0-9), and the first century A.D. was 1-99 (not 0-99). If you pick any decade or century A.D. and work backwards (counting by tens or hundreds), you'll see that the first decade or century has one fewer year in it. We don't really care about the misnomer of saying first decade/ century A.D., but it's mathematically true.
On March 02 2016 23:22 B-royal wrote: Are there any far reaching consequences of letting our calendar get out of sync with the earth's revolution around the sun?
Besides just having a winter when our calendar says it's summer?
In other words, would there be any consequences on normal life or for physicists, astronomers,...
Having winter when the calendar says summer is the only effect. Which yes, would give consequences for astronomers (physicists probably less so) that can see some objects better in summer/winter when the earth is on the right side of the sun. Astronomers almost for sure would adopt their own proper calendar.
Otherwise... yeah kindof big cultural changes with holidays, when people travel where, xmas beach and so on. WHich in turn would affect companies that are related to those things. But well, no otherwise I don't see any major affects, apart from the inconvenience.. I mean... let's face it, people wouild just start using a new calendar that is synced. They start talking about 3 months after midwinter and so on.
So all in all, it'd be mainly inconvenient and stupid. Possibly some costs involved as by-product of the inconvenience, and the scientific community would almost for sure adopt their own more logical standard. So like the imperial units in other words.
EPT
