L.A.Times Reporter Might Have Messed up the Math — Will the Ancient Astronomers Come to the Rescue?


You won’t believe the revolutionary discoveries that modern astronomers have found, by carefully decoding old astronomical tablets written on tablets, in cuneiform, as long ago as 700 BC in modern-day Iraq!

You might not be surprised that a science reporter and various commentators reporting on the story – including myself – may have got the math wrong.

This is not just clickbait – the historical research was very dedicated and quite clever, and it shows that all the  years I’ve tried to to study and learn Arabic, astronomy, Babylonian, calculus, Chinese, French, geometry, Hebrew, Latin, mathematics, Russian, Spanish and Turkish might actually pay off one day, when I grow up! (*)

What’s the scoop?

In a nutshell: Researchers read and translated a bunch of ancient and more recent records of eclipses of the Sun and Moon, from cultures all over the world, over a period of 27 centuries. They compared those results  with what modern software and computers calculate they should be if you simply went backwards in time at a rate of precisely 24 hours per day. That meant studying lots of obscure records written in Chinese, Babylonian, Arabic, and Latin, as well as in modern languages.

The researchers were quite impressed at how accurate the Arab and Chinese records were, even though their instruments were much cruder than what we have today. (Obviously, no telescopes, no electric clocks, etc, etc…) The records from the Roman empire and early Mediaeval Europe, however, are apparently not nearly as good (200 BC – 600 AD) as the Chinese and Arab ones were.


After the invention of the telescope a bit over 400 years ago, records became much richer. For example, observers could record the time, to the second (or even better), when a star would get blocked out by the Moon and then eventually re-appear on the other side.

(David Dunham , though retired, is an expert on this.)

Bottom line, according to the newspaper reporter: If it’s noon right now, and you could somehow go back in time precisely twenty-five centuries ago to exactly where you are standing or sitting, then everybody else back then (about 500 BC) would see the time as the equivalent of 7 PM, because the earth is turning on its axis ever so slightly slower today.

Revolutionary, I told you! Not joking, not exaggerating either!

But wait a second – how much would that be slowing down per year? The article doesn’t spell it out, but 7 hours is 420 minutes, or 60*420 = 25200 seconds,. If we divide that by about 2500 years, you get 10 seconds per year!

Wait a second, that doesn’t sound right at all! These days, if the earth really got slower at a uniform rate of 10 seconds per year, many of our cheap quartz watches and clocks are so accurate that we would actually notice the difference!

Let’s go back. The LATimes reporter, Deborah Netburn, wrote:  “the amount of time it takes for Earth to complete a single rotation on its axis has slowed by 1.8 milliseconds per day over the course of a century” – which is not very clear.

A commenter on LATimes website, named “It is me Here” wrote:

The time discrepancy described as “It may not sound significant, but over the course of 2½ millenniums, that time discrepancy adds up to about 7 hours” is not 7 hours. Over 2500 years it amounts to: 1.8 (milliseconds) x 365 (days per year) x 2,500 (years) = 1,642,500 milliseconds, that equals 1,642 seconds that equals 27.38 minutes, not 7 hours.


Did you get that, and do you agree? If not, let’s go back a little further, to the  abstract of the original study report which says:

New compilations of records of ancient and medieval eclipses in the period 720 BC to AD 1600, and of lunar occultations of stars in AD 1600–2015, are analysed to investigate variations in the Earth’s rate of rotation. It is found that the rate of rotation departs from uniformity, such that the change in the length of the mean solar day (lod) increases at an average rate of +1.8 ms per century. This is significantly less than the rate predicted on the basis of tidal friction, which is +2.3 ms per century.

(my emphasis – gfb)


So, would we really be 7 hours slow if we went back?

Maybe, maybe not.

Let’s think about it differently:

Since 500 BC, it has been about 25 centuries. According to the study, every century the earth slows down by about 1.8 milliseconds, which isn’t very much. 25 * 18 milliseconds is 450 milliseconds, which is a bit less than half a second. So does that mean we have to add up all of those 1.8 milliseconds by 365 days

That’s not much at all.

(BTW, why does the earth get slower? One source of the slowing down is simply the friction of the ocean tides. If you’ve ever been to the ocean and paid attention, you know that the gravitational pull among the Sun, Earth and Moon raise and lower a WHOLE lot of water all over the world, twice a day. That takes a HUGE amount of energy and a lot of it is dissipated in friction, which slows things down. But there are others.)

But here is a different way of looking at it still, as a trapezoid: the left-hand parallel side is about one-half second shorter than 24 hours – the length of a day in during ancient Babylonian days. The right hand parallel side is exactly 24 hours long. In between, there are 2,500 elapsed years.

Let’s pretend that each of those years contains 365 days (let’s agree to ignore the effect of leap years for right now). If the shape were a rectangle, then that would mean that the earth had not slowed down at all, and if you went backwards in time from now by 2500 years it would be exactly the same date, same time.


Apparently, it’s not. The lost or extra time is the part I show in this next diagram:



That little pink section is a a long skinny triangle with its right hand end 1/2 second per day long, and the base is 2500 years long, or 912,500 days. The area of a triangle is 1/2 * base * height, and so we use 1/2 * 1/2 * 912,500 and get 228,125 seconds lost (the ‘days’ units cancel out), or about 3802 minutes, or 63 hours, 22 minutes, which is 2 days, 15 hours, and 22 minutes off.

Not sure if I’m right or not, but would appreciate comments.

Here is one of the figures from the paper:


(*) Note that I don’t claim to be fluent in all of them. Far from it! Guess in which of the languages ones I can reed perdy guud and which ones I can at least stumble a conversation in?


Published in: on December 8, 2016 at 4:39 pm  Comments (4)  

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4 CommentsLeave a comment

  1. hey – renewable wave energy – maybe future gens will look back at us and wonder why we were so slow in coming up with it! (Sorry – for the rest of your thesis, I’m not good at checking math…)


  2. French, Hebrew, Latin, Russian, and Spanish.


  3. French, Hebrew, Latin, Russian, and Spanish.


    • I can only mangle a few phrases in Russian and slowly decipher words. Can’t read it or speak it or understand it. Certainly cannot speak Latin, though I studied it for about six years in secondary school. But I can read Newton’s Latin fairly well.


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