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Imagine that humanity find out that their current date allegedly representing years A.D. is several years off.

The only unquestionable timestamped data on the physical state of the Universe (including the Earth itself) is 100–200 years old, but this data is on the cutting edge of our modern science. E.g., there may be astronomical catalogues, relative positions of tectonic plates, and so on. But only the data, without any timekeeping devices like atomic clocks.

Can that imaginary humanity restore the exact date A.D. using this data? What is the best possible resolution, assuming that the technology level is still equal to ours and that the timestamp resolution is ideal?

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    $\begingroup$ If you know the age of the universe to +-50 years you're doing pretty good for yourself. The current error on that measurement is on the order of 0.12 Billion years. $\endgroup$ – sphennings May 19 '17 at 23:27
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    $\begingroup$ why would they want to restore it, why would it even be a relevant date for them. Why more relevant than anything in their own history anyway. Calculating back would be easy enough, just don't see why anyone except a few academics would see a need. ALL the canned goods are PAST their expiry date, no need to doublecheck $\endgroup$ – Kilisi May 20 '17 at 1:34
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    $\begingroup$ Why would they care? As a matter of fact, the current A.D date is supposedly off by 4 years, but that doesn't appear to bother anyone. (Still less that no one can undisputably prove that the event it's based on even happened :-)) But if you have access to astronomical tables from any time in the last few centuries, and a decent telescope, you can figure the elapsed time between then and now from the position of the planets. $\endgroup$ – jamesqf May 20 '17 at 4:33
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    $\begingroup$ @jamesqf: The current AD (or CE) date is not off; the definition is that 1 AD = 754 AUC (years since the foundation of Rome). It's true that eventually chronologists found out that Yehoshua the Annointed could not have possibly been born in 1 AD, but then neither was Rome founded in 1 AUC (= 753 BC); and the first Olympic Games did not take place in the supposed year 1 of the first olympiad (=776 BC, by the definition of AUC which requires 1 AUC = year 4 of the 6th olympiad). $\endgroup$ – AlexP May 20 '17 at 10:12
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    $\begingroup$ @AlexP: I agree about CE, but A.D is by definition (Anno Domini = Year of Our Lord) based from that birth date. $\endgroup$ – jamesqf May 20 '17 at 17:12
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As explained in a comment by the original poster, the assumption is that at some time in the future there will be a break in chronology because people somehow regressed to the stone age or some other reason, and when they become civilized again they will have to search for a method to link their Future Modern Chronology with ours. For example, let's say that in 2117 an event happens which destroys human civilization, and that when people become civilized again they have a vague notion that they live somewhere around 2420 plus or minus 10 or 20 years.

Dendrochronology

Enter dendrochronology. Dendrochronology works by establishing a correspondence between the growth rings of trees. Today, in 2017, we have an unbroken chain of tree growth rings going back to the 5th or 6th millennium before the common era using oak trees (and possibly to even deeper time using a combination of species).

This does not help with precisely dating historical events, of course; but it would be very helpful for our confused descendants. All they have to do is to find a way to link their dendrochronology with ours; if we allow them the chance of finding some our dendrochronological records then bridging a gap of a few centuries will be easy.

But what if they don't find our dendrochronological records?

Astronomy

Enter astronomy. For example, in 1999 Romania put out very large number of 2000 lei polymer banknotes celebrating the solar eclipse of 11 august 1999. They looked like this:

2000 ROL, 1999, obverse

2000 ROL, 1999, reverse

Those are practically indestructible and there were very very many of them -- it was a very small denomination, 2000 Romanian lei of 1999 being about 0.05 Euros of 2017. The confused chronologists of the future need only to find one of those, and then they can easily compute when the eclipse took place. Note that the note helpfully says "11 August 1999" and "eclipsa totala" which, even if the Romanian language will be forgotten, is easy to translate as "total eclipse".

And even if they don't find one of those numerous and resilient notes they will certainly find some of our astronomical records.

In general

Some our records must survive, unless the gap is very large. Ours is a highly literate society, leaving behind an enourmous quantity of chronological records. If the gap between our chronology and the Future Modern Confused Chronology is of only a few centuries they will have little trouble linking the two.

If the gap extends over several millenia so that the remains of our civilization are reduced to a few sherds of pottery, then they won't be able to link the chronologies very precisely. They will find themselves in the same situation as we are today with respect to historical events in the deep antiquity, where the difference between the "long chronology" (which puts the start of the reign of king Hammurabi of Babylon in 1848 BCE) and the "short chronology" (which puts the same historical event in 1728 BCE) is of about 120 years. (For the curious, the difference is due to us having only one astronomical record from that period, the Venus tablet, and there are four possible dates for the observations recorded by those ancient astronomers.)

For a gap of many millennia all bets are off. Our chronology is uncertain at the level of centuries for events in the first half of the 2nd millennium BCE; for even older events the uncertainty is even greater; and for events older than the 4th millennium BCE we don't even attempt to establish a chronology -- we say that they happened in pre-history and consider ourselves lucky if we can date them plus or minus one or ten or a hundred thousand years.

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  • $\begingroup$ A wonderful novelty in doing astronomical research by following the money. Polymer bank notes were invented by Australia. This is an excellent use of them. Your bank notes look as beautiful as ours. Plus one. $\endgroup$ – a4android May 20 '17 at 0:21
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    $\begingroup$ +1, great idea. Dendro in combo with ice cores and /or Earth cores can precisely date environmental events; it is how we date the KT boundary, but can also determine past temperatures, volcanic eruptions, even past precipitation, past flooding and past oxygen levels. If the old records include info about such things in the past few hundred years, we can tie the written records of such events to the tree rings and core samples. $\endgroup$ – Amadeus May 20 '17 at 10:16
  • $\begingroup$ @Amadeus: But we don't know the date of the K-T boundary all that precisely. Recent reports date it within a mere 0.25% or 40,000 years: berkeley.edu/news/media/releases/2008/04/24_argondating.shtml (Though oddly enough, we know the time of year it happened, just not which particular year.) $\endgroup$ – jamesqf May 20 '17 at 17:18
  • $\begingroup$ @jamesqf: Perhaps a bad example or a good one: For the OP, within 1/4 of 1% in a few hundred years is within half a year. So perhaps not the exact date, but still pretty close. $\endgroup$ – Amadeus May 20 '17 at 18:09
  • $\begingroup$ Add seasonal sediments to your list. $\endgroup$ – JDługosz May 20 '17 at 21:06
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Check a clock. It may be that a clock will still be running. The interested parties could check the time and date. The Clock of the Long Now is designed expressly with this purpose. The idea is that this clock will keep time for 10,000 years, and so presumably date and year also.

https://en.wikipedia.org/wiki/Clock_of_the_Long_Now

I am a little disappointed that they are somewhat vague about how the Clock of the Long Now will be powered if no-one comes to lift the pendulum. It seems obvious to me that such a clock should be powered by changes in barometric pressure, as is the case for the Atmos Clock and similar. As close to a perpetual motion machine as you are going to get.

I had thought there might be a clock at the Doomsday Seed Vault in Svalbard, Norway, having recently learned of the existence of this vault when it was in the news. If someone learns it is there and decides to make the trip to get some seeds it would be nice if they could check the time and date when they get there. I do not find explicit mention of a clock on the Vault website. I like very much, though, how Doomsday Vault-looking it is.

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Given accurate astronomical records, you can establish an accurate date by calculating planetary positions. (Start from your recorded base position and date, and calculate what date that gives you when you get to their current positions. Since planetary orbital periods aren't exact multiples of each other, the positions won't repeat over any practical time span.

You can also look at things like the orbits of Jupiter's moons, which change positions relatively rapidly, and should allow for finer resolution checks.

For cross checks, there's also the proper motion of stars, typically around 0.1 arcsecond per year, up to 10.25 arcseconds/year (see http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit1/motions.html),

and also the precession of the equinoxes - a gradual wobble of the earth's axis which shifts the celestial pole (the axis the stars appear to rotate around as a result of the earth's rotation) in around a 26000 year cycle (see https://en.wikipedia.org/wiki/Axial_precession). While it's a long cycle, it affects star positions enough that star charts / listed positions have to be updated regularly - they're usually quoted for a particular reference date (epoch), which tends to be updated every few decades (It's a straightforward calculation to transform values for the current date (Though you'd want to add in any shify due to proper motion).

Add in solar eclipses, as mentioned by AlexP, and working out the date should be fairly straightforward.

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