Year Zero

[Agent Smith]

So in the back of me mind I'm trying to grasp the mathematical critique of our calendar, specifically the absence of year Zero. The calendar, I believe we're using the Gregorian/Julian calendar at present, starts with 1 AD and the year immediately before that is 1 BC i.e. there's no year \(\displaystyle 0\). Today, I came to some kinda quasirealization that years aren't lengths, despite the fact that they span 365.25 days, they're points and so there's got to be a \(\displaystyle 0\), just like an ordinary scale has a \(\displaystyle 0\) cm/inch mark.

My understanding is incomplete however. It's non liquet (not clear).

Inviting discussion/clarification/comments/etc.

P.S. I wonder if the Mayan/Hindu calendar has a year \(\displaystyle 0\).

 

[Dr.Peterson]

Today, I came to some kinda quasirealization that years aren't lengths, despite the fact that they span 365.25 days, they're points and so there's got to be a 0, just like an ordinary scale has a 0 cm/inch mark.

No, years are intervals. This is why we can't really have a year zero.

What specific point in the current year do you consider to be 2024?

On the other hand, astronomers use a different system in which time is measured from a 0 point, so they do talk about a "year zero" for the sake of calculations. I don't know what point in 1 BC they take to be the actual zero point; sources I find don't seem to go to that granularity.

 

[Agent Smith]

No, years are intervals. This is why we can't really have a year zero.

What specific point in the current year do you consider to be 2024?

On the other hand, astronomers use a different system in which time is measured from a 0 point, so they do talk about a "year zero" for the sake of calculations. I don't know what point in 1 BC they take to be the actual zero point; sources I find don't seem to go to that granularity.

Doesn't it mess up the calculations? How many years between 1 BC and 1 AD? \(\displaystyle 1 - (-1) = 2\)?

 

[Agent Smith]

Also @Dr.Peterson, it's complicated . When I'm asked to find [imath]2024 - 1973[/imath], am I computing the distance between \(\displaystyle 2\) POINTS or the difference between \(\displaystyle 2\) LENGTHS/INTERVALS?

 

[Dr.Peterson]

Doesn't it mess up the calculations? How many years between 1 BC and 1 AD? \(\displaystyle 1 - (-1) = 2\)?

That's why astronomers do what they do. (I doubt that you read the link.)

Also @Dr.Peterson, it's complicated . When I'm asked to find [imath]2024 - 1973[/imath], am I computing the distance between \(\displaystyle 2\) POINTS or the difference between \(\displaystyle 2\) LENGTHS/INTERVALS?

Yes, dealing with time is complicated.

You tell me: When you do that calculation, why are you doing it? What two points in time are you comparing? The same date in both years, or different dates? Or, what might it mean to subtract two entire years (as intervals)? Please actually think about it.

 

[blamocur]

On the other hand, astronomers use a different system in which time is measured from a 0 point, so they do talk about a "year zero" for the sake of calculations. I don't know what point in 1 BC they take to be the actual zero point; sources I find don't seem to go to that granularity.

Julian day is counted from 1/1/4713 BC.

 

[Agent Smith]

That's why astronomers do what they do. (I doubt that you read the link.)

Yes, dealing with time is complicated.

You tell me: When you do that calculation, why are you doing it? What two points in time are you comparing? The same date in both years, or different dates? Or, what might it mean to subtract two entire years (as intervals)? Please actually think about it.

It seems even considering time as an interval doesn't void the need for a \(\displaystyle 0\). \(\displaystyle 0\) is where you start to measure off \(\displaystyle 1\) year. So if the year is \(\displaystyle 1\) AD, the \(\displaystyle 0\) must be \(\displaystyle 0000\) hours 12/31/1 BC or 1/1/1 AD. Right? Can you comment please.

 

[Agent Smith]

Julian day is counted from 1/1/4713 BC.

Is that year zero?

 

[Dr.Peterson]

It seems even considering time as an interval doesn't void the need for a \(\displaystyle 0\). \(\displaystyle 0\) is where you start to measure off \(\displaystyle 1\) year. So if the year is \(\displaystyle 1\) AD, the \(\displaystyle 0\) must be \(\displaystyle 0000\) hours 12/31/1 BC or 1/1/1 AD. Right? Can you comment please.

Please answer my question before asking more.

 

[Agent Smith]

That's why astronomers do what they do. (I doubt that you read the link.)

Yes, dealing with time is complicated.

You tell me: When you do that calculation, why are you doing it? What two points in time are you comparing? The same date in both years, or different dates? Or, what might it mean to subtract two entire years (as intervals)? Please actually think about it.

Sorry.

If given 2 dates, I compute how many days have elapsed and then divide that by 365.25 to check how many years that is (1 year = 365.25 days).

If given only years, e.g. 1973 and 1953, I simply find the difference and that tells me how many years have gone by.

The issue is with the latter. Permit me to remind you of how 2 years would've elapsed between 1 BC and 1 AD, when the fact is only 1 year has. Christ's birth year would have to be year zero. so that the math would square with facts.

 

[Agent Smith]

We're counting the years from the year of the Salvator Mundi's birth. So Christ's birth year should be \(\displaystyle 0\) AD and \(\displaystyle 1\) AD would be the [imath]1^{\text{st}}[/imath] year, counting from the year Christ was born, oui?

 

[blamocur]

Permit me to remind you of how 2 years would've elapsed between 1 BC and 1 AD

Why? Because you choose to interpret 1 BC = -1 AD ? Judging by your own post this is not a correct interpretation.

 

[Agent Smith]

Why? Because you choose to interpret 1 BC = -1 AD ? Judging by your own post this is not a correct interpretation.

What is the correct interpretation then? How do we make the transition from BC to AD?

\(\displaystyle 3 \text{BC} \to 2 \text{BC} \to 1 \text{BC} \to \text{????} \to 1 \text{AD} \to 2 \text{AD} \to 3 \text{AD}\)

 

[Dr.Peterson]

Sorry.

If given 2 dates, I compute how many days have elapsed and then divide that by 365.25 to check how many years that is (1 year = 365.25 days).

If given only years, e.g. 1973 and 1953, I simply find the difference and that tells me how many years have gone by.

The issue is with the latter. Permit me to remind you of how 2 years would've elapsed between 1 BC and 1 AD, when the fact is only 1 year has. Christ's birth year would have to be year zero. so that the math would square with facts.

No, that doesn't answer my question:

When I'm asked to find 2024−1973, am I computing the distance between 2 POINTS or the difference between 2 LENGTHS/INTERVALS?

You tell me: When you do that calculation, why are you doing it? What two points in time are you comparing? The same date in both years, or different dates? Or, what might it mean to subtract two entire years (as intervals)?

The answer is that if you subtract 2024 - 1973, you are finding the elapsed time between the same date in the two years (e.g. from July 1, 1973 to July 1, 2024), which is a perfectly reasonable thing to do, but needs to be thought about consciously. It is not the elapsed time between the two entire years.

In other words, subtraction does mean something despite the fact that a year represents any time within an interval.

For the larger question, here's something I wrote, pulling together old answers to related questions; the relevant part starts at "The Y0 problem". We touch on your points, which are not particularly original. (It's discussed in the link I gave you initially.) In the middle, I point out how inserting a year zero doesn't really fix anything.

 

[Agent Smith]

No, that doesn't answer my question:


The answer is that if you subtract 2024 - 1973, you are finding the elapsed time between the same date in the two years (e.g. from July 1, 1973 to July 1, 2024), which is a perfectly reasonable thing to do, but needs to be thought about consciously. It is not the elapsed time between the two entire years.

In other words, subtraction does mean something despite the fact that a year represents any time within an interval.

For the larger question, here's something I wrote, pulling together old answers to related questions; the relevant part starts at "The Y0 problem". We touch on your points, which are not particularly original. (It's discussed in the link I gave you initially.) In the middle, I point out how inserting a year zero doesn't really fix anything.

Gracias for your help. Should I go with the astronomers instead of the theologians on this? Suppose Jesus was born in 1973 . What would be the year 1975 in AD? 1975 - 1973 = 2 AD right? What would be the year 1971 in BC? 1973 - 1971 = 2 BC. So then 1972 is 1 BC then 1973 is 0 BC/AD, oui???

 

[blamocur]

What is the correct interpretation then? How do we make the transition from BC to AD?

\(\displaystyle 3 \text{BC} \to 2 \text{BC} \to 1 \text{BC} \to \text{????} \to 1 \text{AD} \to 2 \text{AD} \to 3 \text{AD}\)

Just remove the question marks

 

[Dr.Peterson]

Gracias for your help. Should I go with the astronomers instead of the theologians on this? Suppose Jesus was born in 1973 . What would be the year 1975 in AD? 1975 - 1973 = 2 AD right? What would be the year 1971 in BC? 1973 - 1971 = 2 BC. So then 1972 is 1 BC then 1973 is 0 BC/AD, oui???

It's not about astronomy or theology, but about history and language. But it's all explained in the various links I've provided, so I'm not inclined to keep arguing with you when you don't seem to be paying attention.

The basic meaning of AD and BC is "after" and "before"; this terminology doesn't allow for zero.

Actually, it's a little more interesting than that (as mentioned in my article), because AD doesn't mean "after" something, but "the year of the Lord", so that AD 1 means "the first year of the Lord" (Anno Domini 1). Similarly, 1 CE means "the first year of the Common Era".

Suppose you were born in 1973, and because you are so important, we decided to name years starting then. Then 1973 would be "the first year of Smith", and 1975 would be "the third year of Smith". And 1972 would be "the first year before Smith".

But since we know about negative numbers now, we probably wouldn't create the new system using those ancient forms; we might instead say that 1973 is "Smith year 0", 1975 is "Smith year 2", and 1972 is "Smith year -1".

This is the point: The ancient system of naming years is what it is; it doesn't match up with math, so we have to make one small adjustment when we use it to calculate. If we were inventing it anew, we wouldn't do the same thing, but changing the existing system would have to mean replacing it (as astronomers have done away with "BC"). When using the old system, you do what the old system requires.

 

[Agent Smith]

It's not about astronomy or theology, but about history and language. But it's all explained in the various links I've provided, so I'm not inclined to keep arguing with you when you don't seem to be paying attention.

The basic meaning of AD and BC is "after" and "before"; this terminology doesn't allow for zero.

Actually, it's a little more interesting than that (as mentioned in my article), because AD doesn't mean "after" something, but "the year of the Lord", so that AD 1 means "the first year of the Lord" (Anno Domini 1). Similarly, 1 CE means "the first year of the Common Era".

Suppose you were born in 1973, and because you are so important, we decided to name years starting then. Then 1973 would be "the first year of Smith", and 1975 would be "the third year of Smith". And 1972 would be "the first year before Smith".

But since we know about negative numbers now, we probably wouldn't create the new system using those ancient forms; we might instead say that 1973 is "Smith year 0", 1975 is "Smith year 2", and 1972 is "Smith year -1".

This is the point: The ancient system of naming years is what it is; it doesn't match up with math, so we have to make one small adjustment when we use it to calculate. If we were inventing it anew, we wouldn't do the same thing, but changing the existing system would have to mean replacing it (as astronomers have done away with "BC"). When using the old system, you do what the old system requires.

First off, apologies if I haven't kept my side of the bargain in this exchange of what I consider vital knowledge. The mathematical issue here is cogito of immense importance (\(\displaystyle 0\) is missing from the number system and, despite its awkwardness, the significance of [imath]0[/imath] is a well-established fact; we could perhaps call it the gift of the Ganges ).

Methinks, the problem boils down to how modern math (with "knowledge" of \(\displaystyle 0\) a negative numbers) parses Dionysius Exiguus' calendar. The critical question is how many years have passed between \(\displaystyle 1\) BC and \(\displaystyle 1\) AD? Dionysius would obviously answer \(\displaystyle 1\) year. However when we superpose Dionysius' calendar on the number line as we know it, we have a problem. \(\displaystyle 1\) BC is \(\displaystyle -1\) and \(\displaystyle 1\) AD is \(\displaystyle +1\). An astronomer would compute the years between the \(\displaystyle 1\) AD and \(\displaystyle 1\) BC as \(\displaystyle |+1 - (-1)| = 2\) years. As the astute comedian Eddie Izzard says in one of his routines, "one of these is wrong!" If we have a year \(\displaystyle 0\), the problem is solved.