<p>The concept of zero didn't reach western Europe until the 13th century. The concept of zero is a bit heretical (a thing that represents nothing???), but is arguably the most important concept in mathematics.</p>
<p><a href="https://en.wikipedia.org/wiki/Year_zero" rel="noreferrer">Astronomers and others</a> have inserted a year zero for quite some time, at least since Cassini, making proleptic astronomical dates prior to 1 AD be offset from the standard dating by one. Zero is such a useful concept that it is silly not to use it for ancient dates.</p>

CC BY-SA 4.0
2024-04-14T13:47:10.363Z
Note that BC (BCE) dates prior to 1 AD  (1 CE) are also proleptic. Peoples who lived a century before 1 AD did not know that 100 years in the future would result in an important event.
David Hammen
CC BY-SA 4.0
2024-04-15T04:16:35.603Z
https://en.wikipedia.org/wiki/Anno_Domini says "This [BC AD] dating system was devised in 525 by Dionysius Exiguus but was not widely used until the 9th century".
PM 2Ring
CC BY-SA 4.0
2024-04-15T09:15:18.943Z
Aren't the year numbers basically ordinal numbers rather than cardinals, same as for days and months? So, year 1 AD/CE is actually the 1st year after the epoch, and year 1 BC/BCE is the first year before the epoch. As the epoch is a point in time, there is no zeroth year. Of course, it is awkward for calculations, but everything with dates is.
Chieron
CC BY-SA 4.0
2024-04-15T16:06:10.557Z
@Chieron That's the point. The AD/BC system is ordinal; astronomical dates are not. The year in an astronomical date indicates the number of full years since (or before) the beginning of 1 BC.
Sneftel
CC BY-SA 4.0
2024-04-15T16:53:05.657Z
@Sneftel yes.. but that has nothing to do with the concept of zero. Even if the concept existed beforehand, the "traditional" year numbering might not have been different. This is misleading in the answer.
Chieron
CC BY-SA 4.0
2024-04-15T16:59:28.203Z
@Chieron I really don’t understand what point you’re trying to make.
Sneftel
CC BY-SA 4.0
2024-04-15T17:20:07.670Z
@Sneftel the answer starts with an irrelevant statement about zero. Years are traditionally named with ordinals, and possibly would have been so even after zero existed as a concept. Astronomers switched this to cardinals to simplify calculations with dates.
Chieron
CC BY-SA 4.0
2024-04-15T17:37:21.417Z
But… that’s the same thing the OP was saying. The meaningfulness of non-positive numbers in a system is equivalent to whether the numbering is ordinal or not.
Sneftel
CC BY-SA 4.0
2024-04-15T19:28:51.900Z
Zero is the most important concept in mathematics -- after 1 (paradoxically, if you want ;-) ).
Peter - Reinstate Monica
CC BY-SA 4.0
2024-04-16T20:11:31.607Z
I echo Chieron that the first paragraph seems irrelevant and it is also unsourced.
Rabbi Kaii
CC BY-SA 4.0
2024-04-16T21:44:04.093Z
I have a problem with the opening statement mostly because it is one of these "everybody knows that" myths that live on exactly through repetition like this. Which "concept of zero" are you talking about? The concept of an absence of quantity certainly did exist, there just was no accepted symbol for it. And it was not the zero *per se* that was popularized by Fibonacci in his 1202 "Liber Abaci", but the Hindu-Arabic numeral system as a whole. -- The stories of the "dark middle ages" arose in the Renaissance, when people desired to see themselves as "improved". They often lack substance.
DevSolar
CC BY-SA 4.0
2024-04-21T10:44:17.263Z
@DevSolar This is one of those things everyone should know. Fibonacci introduced the Hindu-Arabic numbering system to the west in 1202. That was the only numbering system invented by mankind that had a true zero. The Mayans came close, but there zero lacked some of the features of a true zero. A true zero, amongst other things enables the use of negative numbers. BTW, negative numbers were considered to not be numbers well after Fibonacci, hence the "negative" qualifier. Leibniz, one of the inventors of calculus, long viewed negative solutions as false solutions.
David Hammen
CC BY-SA 4.0
2024-04-21T11:49:37.877Z
The same goes for imaginary numbers, with the "imaginary" qualifier intentionally introduced as a derogatory term by Descartes in the 17th century. (This didn't work, much as derogating the concept of an expanding universe as the "Big Bang"; this term arose as an intentionally introduced derogation by opponents to the concept.) It wasn't until the 19th century that numbers were truly well understood.
David Hammen
CC BY-SA 4.0
2024-04-21T11:57:37.887Z
*Sigh* I understand that you are fascinated with Fibonacci's work, and I have no issue with that. But while he introduced a *sign* for zero, neither did he introduce the *concept* of the absence of quantity (that did exist well before), nor indeed did he introduce using it in calculations (that didn't happen until well into the 17th century). Fibonacci called the zero a *sign*, not a digit. That's the thing with these things "everyone should know".
DevSolar
CC BY-SA 4.0
2024-04-23T11:44:18.003Z
@DevSolar It took a couple of centuries after Fibonacci to fully accept the concept of a true zero. He did not develop that concept; that was India. Fibonacci merely introduced to the West what he had learned from the Islamic world when it was in its golden age. He did not develop the concept of negative numbers; that came much later. But regarding concepts in the West regarding numbers, Fibonacci was the starting place for doing it right. The West used Roman numerals prior to Fibonacci, which was not doing it right.
David Hammen
CC BY-SA 4.0
2024-04-14T12:05:32.973Z
2024-04-14T12:11:02.630Z
2024-04-14T12:11:02.630Z
David Hammen
<p>This is all explained on the home page All dates are astronomical dates.  These match CE (or <sub>AD</sub>) dates for positive values but differ by 1 for BCE dates.</p>
<blockquote>
<p>The Gregorian calendar is used for all dates from 1582 Oct 15 onwards. Before that date, the Julian calendar is used. For more information on this topic, see Calendar Dates. The Julian calendar does not include the year 0. Thus the year 1 BCE is followed by the year 1 CE (See: BCE/CE Dating Conventions ). This is awkward for arithmetic calculations. Years in this catalog are numbered astronomically and include the year 0. Historians should note there is a difference of one year between astronomical dates and BCE dates. Thus, the astronomical year 0 corresponds to 1 BCE, and astronomical year -1 corresponds to 2 BCE, etc..</p>
</blockquote>

CC BY-SA 4.0
2024-04-14T10:55:55.423Z
2024-04-14T10:55:55.423Z
James K
<p>I was looking through NASA’s Five Millennium Canon of Solar Eclipses, and I am really confused by the fact that there is a year -1, 0, and 1. I was always taught that there was no year 0, that we just <a href="https://science.howstuffworks.com/science-vs-myth/everyday-myths/time7.htm#:%7E:text=In%20the%20modern%20calendar%2C%20we,preceding%20it%20is%201%20B.C." rel="noreferrer">went from 1 B.C. to 1 A.D.</a>. However, NASA’s data clearly has a year 0.</p>
<p>In year -1, there are three eclipses, on February 5th (hybrid), July 31st (hybrid), and December 26th (partial). Year 0 also has three: June 20th (partial), July 19th (partial), and December 14th (annular). Finally, there are two eclipses in year 1: June 10th (total) and December 14th (annular). So clearly there is an extra year there where we typically do not have one. So, am I wrong to believe that SOME SORT of shifting is required? Year 0 either moves AD forward a year or BC behind a year. Am I crazy? Where does this year zero come from?</p>

CC BY-SA 4.0
2024-04-16T13:54:03.853Z
There are no negative numbers in BC either, it's 1 BC not -1 BC...
Jason Goemaat
CC BY-SA 4.0
2024-04-17T04:16:37.040Z
"there is a year -1, 0, and 1" --> just view all three as AD (or CE). It is the that year system extended back for earlier years.
chux
<the-sun><the-moon><earth><solar-eclipse>
Why is there a year 1 B.C., a year 0, and a year 1 A.D. in NASA’s Five Millennium Canon of Solar Eclipses?
Curious Layman
# Why is there a year 1 B.C., a year 0, and a year 1 A.D. in NASA’s Five Millennium Canon of Solar Eclipses?

(Asked by: username_0 on 2024-04-14)

I was looking through NASA’s Five Millennium Canon of Solar Eclipses, and I am really confused by the fact that there is a year -1, 0, and 1. I was always taught that there was no year 0, that we just [went from 1 B.C. to 1 A.D.](https://science.howstuffworks.com/science-vs-myth/everyday-myths/time7.htm#:%7E:text=In%20the%20modern%20calendar%2C%20we,preceding%20it%20is%201%20B.C.). However, NASA’s data clearly has a year 0.

In year -1, there are three eclipses, on February 5th (hybrid), July 31st (hybrid), and December 26th (partial). Year 0 also has three: June 20th (partial), July 19th (partial), and December 14th (annular). Finally, there are two eclipses in year 1: June 10th (total) and December 14th (annular). So clearly there is an extra year there where we typically do not have one. So, am I wrong to believe that SOME SORT of shifting is required? Year 0 either moves AD forward a year or BC behind a year. Am I crazy? Where does this year zero come from?

**Tags:** the-sun, the-moon, earth, solar-eclipse
> **Comments:**
> **username_1**: There are no negative numbers in BC either, it's 1 BC not -1 BC...  
> **username_2**: "there is a year -1, 0, and 1" --> just view all three as AD (or CE). It is the that year system extended back for earlier years.  

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## 2 answers

### Answer by username_10 on 2024-04-14. Score: 45 | Accepted answer

This is all explained on the home page All dates are astronomical dates. These match CE (or AD) dates for positive values but differ by 1 for BCE dates.

> The Gregorian calendar is used for all dates from 1582 Oct 15 onwards. Before that date, the Julian calendar is used. For more information on this topic, see Calendar Dates. The Julian calendar does not include the year 0. Thus the year 1 BCE is followed by the year 1 CE (See: BCE/CE Dating Conventions ). This is awkward for arithmetic calculations. Years in this catalog are numbered astronomically and include the year 0. Historians should note there is a difference of one year between astronomical dates and BCE dates. Thus, the astronomical year 0 corresponds to 1 BCE, and astronomical year -1 corresponds to 2 BCE, etc..


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### Answer by username_3 on 2024-04-14. Score: 6

The concept of zero didn't reach western Europe until the 13th century. The concept of zero is a bit heretical (a thing that represents nothing???), but is arguably the most important concept in mathematics.

[Astronomers and others](https://en.wikipedia.org/wiki/Year_zero) have inserted a year zero for quite some time, at least since Cassini, making proleptic astronomical dates prior to 1 AD be offset from the standard dating by one. Zero is such a useful concept that it is silly not to use it for ancient dates.

> **Comments:**
> **username_3**: Note that BC (BCE) dates prior to 1 AD  (1 CE) are also proleptic. Peoples who lived a century before 1 AD did not know that 100 years in the future would result in an important event.  
> **username_4**: https://en.wikipedia.org/wiki/Anno_Domini says "This [BC AD] dating system was devised in 525 by Dionysius Exiguus but was not widely used until the 9th century".  
> **username_5**: Aren't the year numbers basically ordinal numbers rather than cardinals, same as for days and months? So, year 1 AD/CE is actually the 1st year after the epoch, and year 1 BC/BCE is the first year before the epoch. As the epoch is a point in time, there is no zeroth year. Of course, it is awkward for calculations, but everything with dates is.  
> **username_6**: @Chieron That's the point. The AD/BC system is ordinal; astronomical dates are not. The year in an astronomical date indicates the number of full years since (or before) the beginning of 1 BC.  
> **username_5**: @Sneftel yes.. but that has nothing to do with the concept of zero. Even if the concept existed beforehand, the "traditional" year numbering might not have been different. This is misleading in the answer.  
> **username_6**: @Chieron I really don’t understand what point you’re trying to make.  
> **username_5**: @Sneftel the answer starts with an irrelevant statement about zero. Years are traditionally named with ordinals, and possibly would have been so even after zero existed as a concept. Astronomers switched this to cardinals to simplify calculations with dates.  
> **username_6**: But… that’s the same thing the OP was saying. The meaningfulness of non-positive numbers in a system is equivalent to whether the numbering is ordinal or not.  
> **username_7**: Zero is the most important concept in mathematics -- after 1 (paradoxically, if you want ;-) ).  
> **username_8**: I echo Chieron that the first paragraph seems irrelevant and it is also unsourced.  
> **username_9**: I have a problem with the opening statement mostly because it is one of these "everybody knows that" myths that live on exactly through repetition like this. Which "concept of zero" are you talking about? The concept of an absence of quantity certainly did exist, there just was no accepted symbol for it. And it was not the zero *per se* that was popularized by Fibonacci in his 1202 "Liber Abaci", but the Hindu-Arabic numeral system as a whole. -- The stories of the "dark middle ages" arose in the Renaissance, when people desired to see themselves as "improved". They often lack substance.  
> **username_3**: @DevSolar This is one of those things everyone should know. Fibonacci introduced the Hindu-Arabic numbering system to the west in 1202. That was the only numbering system invented by mankind that had a true zero. The Mayans came close, but there zero lacked some of the features of a true zero. A true zero, amongst other things enables the use of negative numbers. BTW, negative numbers were considered to not be numbers well after Fibonacci, hence the "negative" qualifier. Leibniz, one of the inventors of calculus, long viewed negative solutions as false solutions.  
> **username_3**: The same goes for imaginary numbers, with the "imaginary" qualifier intentionally introduced as a derogatory term by Descartes in the 17th century. (This didn't work, much as derogating the concept of an expanding universe as the "Big Bang"; this term arose as an intentionally introduced derogation by opponents to the concept.) It wasn't until the 19th century that numbers were truly well understood.  
> **username_9**: *Sigh* I understand that you are fascinated with Fibonacci's work, and I have no issue with that. But while he introduced a *sign* for zero, neither did he introduce the *concept* of the absence of quantity (that did exist well before), nor indeed did he introduce using it in calculations (that didn't happen until well into the 17th century). Fibonacci called the zero a *sign*, not a digit. That's the thing with these things "everyone should know".  
> **username_3**: @DevSolar It took a couple of centuries after Fibonacci to fully accept the concept of a true zero. He did not develop that concept; that was India. Fibonacci merely introduced to the West what he had learned from the Islamic world when it was in its golden age. He did not develop the concept of negative numbers; that came much later. But regarding concepts in the West regarding numbers, Fibonacci was the starting place for doing it right. The West used Roman numerals prior to Fibonacci, which was not doing it right.  

---

