Someone is Wrong on the Internet.

Many of the readers of this blog will probably recognise the title of this post, as the punch line to one of the best ever xkcd cartoons. Regular readers will also know that the Renaissance Mathematicus cannot resist stamping on people who post inanely inaccurate or downright wrong history of science claims, comments etc. on the Internet. This last pre-Christmas post brings two examples of such foolishness that crossed our path in recent times.

The first concerns a problem that turns up time and again, not only on the Internet but also in many books. It is the inability of lots of people to comprehend that there cannot be a year nil, year zero or whatever they choose to call it. (Have patience dear reader the reason will be explained soon). Even worse are the reasons that such people, in their ignorance, dream up to explain the absence of the, in their opinion, missing numberless year. I stumbled across a particularly juicy example on the BBC’s History Extra website last Thursday, in a post entitled, 10 of the most surprising numbers in history. Actually the whole post really deserves a good kicking but for now I will content myself with the authors surprising number, AD 0…  the date that never was. The entry is very short so I’ve included the whole of it below:

The AD years of the Christian calendar are counted from the year of Jesus Christ’s birth, and, as the number zero was then unknown to the west, Dionysius began his new Christian era as AD 1, not AD 0. [my emphasis]

While it is now the consensus that Jesus was probably born between 7 and 3 BC, Dionysius’s new calendar is now the most widely used in the world, while AD 0 is one of the most interesting numbers never to have seen the light of day.

The first time I read this sparking pearl of historical wisdom I experienced one of those extremely painful ‘head-desk’ moments; recovering from my shock and managing at least a semblance of a laugh at this stunning piece of inanity I decided to give it the Histsci Hulk treatment.

Before I explain why there cannot be a year zero, let us look briefly at why Dionysius Exiguus, or Dennis the Short, started his count of the years with AD 1. Dennis, he of little stature, was not trying to create the calendar we use today in everyday lives but was making his contribution to the history of computos, the art of calculating the date of Easter. Due to the fact that the date of Easter is based on the Jewish Pesach (that’s Passover) feast, which in turn is based on a lunar calendar and also the fact that the lunar month and the solar year are incommensurable (you cannot measure the one with the other), these calculations are anything but easy. In fact they caused the Catholic Church much heartbreak and despair over the centuries from its beginnings right down to the Gregorian calendar reform in 1582. In the early centuries of Christianity the various solution usually involved producing a table of the dates of the occurrence of Easter over a predetermined cycle of years that then theoretically repeats from the beginning without too much inaccuracy. Dennis the vertically challenged produced just such a table.

In the time of our little Dennis there wasn’t a calendar with a continuous count of years. It was common practice to number the years according to the reign of the current monarch, emperor, despot or whatever. So for example the year that we know as 47 BCE would have been the third year of the reign of Gaius Julius Caesar. For formal purposes this dating system actually survived for a very long time. I recently came across a reference to a court case at the English Kings Bench Court in the eighteenth century as taking place on 12 July ‘4Geo.III’, that is the fourth year of the reign of George III. In Dennis the Small’s time the old Easter table, he hoped to replace, was dated according to the years of the reign of the Emperor Diocletian (245-311, reigned 284-305). Diocletian had distinguished himself by being particularly nasty to the Christians so our dwarf like hero decided to base his cycle on the 525 532 years “since the incarnation of our Lord Jesus Christ”; quite how he arrived at 525 532 years is not really known. AD short (being short, Dennis liked short things) for Anno Domini Nostri Iesu Christi (“In the Year of Our Lord Jesus Christ”). It was only later, starting with the Venerable Bede’s History of the Church (Historia Ecclesiastica) that Dennis’ innovation began to be used for general dating or calendrical purposes. The idea of BC years or dates only came into use in Early Modern period.

We now turn to the apparently thorny problem as to why there cannot be a year zero in a calendrical dating system. People’s wish or desire to find the missing year zero is based on a confusion in their minds between cardinal and ordinal numbers. (In what follows the terms cardinal and ordinal are used in their common linguistic sense and not the more formal sense of mathematical set theory). Cardinal numbers, one, two, three … and so on are used to count the number of objects in a collection. If, for example, your collection is the cookie jar there can be zero or nil cookies if the jar is, sadly, empty. Ordinal numbers list the positions of objects in an ordered collection, first, second, third … and so on. It requires only a modicum of thought to realise that there cannot be a zeroeth object, if it doesn’t exist it doesn’t have a position in the collection.

This distinction between cardinal and ordinal numbers becomes confused when we talk about historical years. We refer to the year five hundred CE when in fact we should be saying the five hundredth year CE, as it is an ordinal and not a cardinal. Remember our little friend Dennis’ AD, Anno Domini Nostri Iesu Christi (“In the Year of Our Lord Jesus Christ”)! We are enumerating the members of an ordered set not counting the number of objects in a collection. Because this is the case there cannot be a zeroeth year. End of discussion!

That this error, and particularly the harebrained explanation for the supposedly missing year zero, should occur on any history website is bad enough but that it occurs on a BBC website, an organisation that used to be world renowned for its informational reliability is unforgivable. I say used to be because I don’t think it’s true any longer. I would be interested in who is responsible for the history content of the BBC’s web presence as it varies between sloppy as here and totally crap as witnessed here and discussed here and here.

My second example is just as bad in terms of its source coming as it does from the Windows to the Universe website Brought to you by the National Earth Science Teachers Association. You would think that such an educational body would take the trouble to make sure that the historical information that they provide and disseminate is accurate and correct. If you thought that, you would be wrong, as is amply demonstrated by their post on Hellenistic astronomer, Ptolemy.

Ptolemy was a Greek astronomer who lived between 85-165 A.D. He put together his own ideas with those of Aristotle and Hipparchus and formed the geocentric theory. This theory states that the Earth was at the center of the universe and all other heavenly bodies circled it, a model which held for 1400 years until the time of Copernicus.

Ptolemy is also famous for his work in geography. He was the first person to use longitude and latitude lines to identify places on the face of the Earth.

We don’t actually know when Ptolemaeus (Ptolemy) lived, the usual way used to present his life is ‘fl. 150 CE’, where fl. means flourished. If you give dates for birth and death they should given as circa or c. To write them as above, 85–165 A.D. implies we know his exact dates of birth and death, we don’t! This is a trivial, but for historians, important point.

More important is the factual error in the second sentence: He … formed the geocentric theory. The geocentric theory had existed in Greek astronomy and cosmology for at least seven hundred years before Ptolemaeus wrote his Syntaxis Mathematiké (the Almagest). Ptolemaeus produced the most sophisticated mathematical model of the geocentric theory in antiquity but he didn’t form it. Those seven hundred years are not inconsequential (go back seven hundred years from now and you’ll be in 1314!) but represent seven hundred years of developments in cosmology and mathematical astronomy.

The last sentence contains an even worse error for teachers of the earth sciences. Ptolemaeus did indeed write a very important and highly influential geography book, his Geographike Hyphegesis. However he was not “the first person to use longitude and latitude lines”. We cannot be one hundred per cent who did in fact first use longitude and latitude lines but this innovation in cartography is usually attributed to a much earlier Alexandrian geographer, Eratosthenes, who lived about three hundred and fifty years before Ptolemaeus.

This is an example of truly terrible history of science brought to you by an organisation that says this about itself, “The National Earth Science Teachers Association is a nonprofit 501(c)(3) educational organization, founded in 1985, whose mission is to facilitate and advance excellence in Earth and Space Science education” [my emphasis]. I don’t know about you but my definition of excellence is somewhat other.



Filed under History of Astronomy, History of Cartography, History of science, Myths of Science

19 responses to “Someone is Wrong on the Internet.

  1. Unlike AD 0, IQ 0 does exist.

  2. > It requires only a modicum of thought to realise that there cannot be a zeroeth object…

    Apart from the Zeroth Law of Thermodynamics, obviously:

    (Nice post, by the way. I myself have been guilty of poking fun at Dennis the Vertically Challenged’s apparent gaff. I shall exercise more care in future.)

    • However, the ordinals for the laws of thermodymics are truly screwed up, with the 2nd law discovered(*) first, the first law 2nd, and the 0th and 3rd law after that (the 0th law coming last of all if we go by explicit statement).

      (*) that is, if we credit Carnot, as is usual, although he didn’t state it explicitly in its modern form.

    • Michael Weiss

      Then, there’s the (-1)st dimensional reduced homology group of the empty set….

      (See Hatcher, Algebraic Topology, p.170.

  3. Educational and entertaining 🙂

  4. guthrie

    Regrettably the BBC also manages to garble science, as you can see in this recent article:

  5. Regnal years were used in legislation into the 20th century I think, and may still appear in some ultra- formal things

  6. Jeb

    What struck me reading this was I know the social, political and cultural importance of this subject well, particularly as it plays out in early medieval Britain, but I know next to nothing about the actual knowledge, math, and astronomy part, as I studied history.

  7. Baerista

    I’m always happy to see chronology discussed on this blog. Just a quick correction: Dionysius Exiguus was referring to the 532rd year, not the 525th. AD 525 was merely the year in which he drew up his table.

  8. I have to disagree with your statements about why there “cannot” be a year 0. There easily could be; we simply would need to declare there would be one, as is done with Julian day number. Obviously the result would work better mathematically. We could make a dating system that starts with year 1, then year 2, then year 73, followed by year 4; it would be stupid and nobody would use it, but it would be well-defined. In a less silly example, you could start at 2 rather than 1. Year numbers do not have to correspond to ordinal numbers in the way you specify.

    Similarly, ordinals more generally need not start at one! The ordinal numbers as used in set theory don’t, they start at 0. There, the correspondence between finite cardinals and finite ordinals works by having n be the number of ordinals less than n, rather than less than or equal to it — thus 3 counts {0, 1, 2} rather than {1, 2, 3}. More generally, zero-indexing is used in lots of other contexts (e.g. programming). Sometimes you really do want to start with 1, but starting with 0 works better frequently enough that it’s the default in a number of contexts.

    And regardless of where you start, dates extend both backwards and forwards, and anyone today would extend it backwards by putting 0 before 1, and then -1 before that, etc.

    I don’t know whether or not Dennis the Short, or Bede, or the inventors of BC knew about the notion of zero as a number; doing it the way they did certainly doesn’t require being ignorant of zero entirely. And whether you start from 1 or 0 really makes little difference so long as you’re only counting forward; it’s the inventors of BC who caused the problem. But anyone today would have made the system two-sided from the start and included 0, because we know enough to see that the result is cleaner mathematically. And it seems to me to make perfect sense to say that Dennis the Short started with 1 because it’s the obvious way; zero-indexing, though useful, is a non-obvious concept that had to be invented. If he’d known about it, he still wouldn’t necessarily have used it, just as many people now don’t, but 1-indexing wasn’t forced on him mathematically.

    Apologies if I’m misreading you and saying obvious things, but you really seem to be claiming that there cannot be a year or ordinal 0. Tell that to the astronomers and the set theorists!

  9. Pingback: Astronomy Vs Cosmology | Astronomy News

  10. Pingback: Whewell’s Gazette: Vol. #27 | Whewell's Ghost

  11. I remember having a hard time arguing that the turn of the millennium ought to have been celebrated with the beginning of 2001 instead of 2000 😉

  12. Pingback: Year Zero | Diagonal Argument

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