The City of God
Anne Hamilton
No, not the book by Augustine of Hippo but an essay on
- some super-chilled mathematics
- the spiritual legacy of the French Revolution
- what you can learn from medieval poetry
- the vision of Ezekiel, and
- why cricket is sure to be the sport of heaven
Mathematics is full of fascinating curiosities. One of these is the number 12345679 (note it has a missing 8). Multiply this number by 8 and it turns into 98765432. Cool, huh? Multiply it any multiple of 9, however, and it’s so cool, the icicles just about drip from the equations.
12345679 x 9 = 111111111
12345679 x 18 = 222222222
12345679 x 27 = 333333333
12345679 x 36 = 444444444
12345679 x 45 = 555555555
12345679 x 54 = 666666666
12345679 x 63 = 777777777
12345679 x 72 = 888888888
12345679 x 81 = 999999999
Now, take the very last number and multiply it by the very first number and we journey into seriously arctic territory:
12345679 x 999999999
= 111111111 x 111111111
= 12345678987654321
Impressively cool as this is, especially the last which is truly the alpha to omega of the number world, I’ve always thought of it as lovely but ultimately useless. I’ve used it to awe a few 12 year old boys in my time, but that always seemed to be the limit of its practicality. Until this week.
I was digging around in some medieval poetry when the number 12345679 turned up in a most peculiar fashion. Now those medieval poets knew a thing or two. And not just about rhyme and rhythm. Truth to tell, they knew very little about rhyme because in those days alliteration was a much bigger deal. They knew about maths, however. Indeed it was said that it was impossible to aspire to be a poet seven centuries ago unless you were a superb mathematician. Numerical literary style (also known as Biblical style or structural arithmetic metaphor) had been around since, well, not quite Adam was a boy but at least as far back as the time Ecclesiastes was being written. For well over two millennia poets regularly practised the technique. Milton (who wrote Paradise Lost) seems to have known about it — 'this little known tradition, not obvious, nor obtrusive, but retired' — although it is not clear if he ever used it.
Today, because the overlap between poets and mathematicians is not quite zero, but pretty close, the art of mathematical poetry seems almost arcane and critics often confuse it with numerology, whereas in fact the two are entirely different 1.
Now I won’t bore anyone with the details of the poem I was reading or the mathematics or the commentary, but you’re welcome to ask if interested. The mathematical theme, however, was the marriage of heaven and earth. In other words, the mathematics of heaven as it bears on the geometry of earth. A bit of a tall ask, you may think. How does a poet know what the mathematics of heaven is? By reading Ezekiel where the description of the City of Yahweh Shammah ('THE LORD IS THERE') is outlined in chapter 48.
The late Chinese politician, Chou En-Lai, was once asked by a reporter what he thought the effect of the French Revolution had been on history. His reply is legendary: 'It’s too early to tell.' In mathematics, however, it’s a different story: the effect of the French Revolution after two centuries is abundantly clear. It brought us the decimal system in measurement. We don’t have yards anymore, we have metres; we don’t have miles, we have kilometres; we don’t have acres, we have hectares. We now have a vastly simplified system, although the previous one has never really been completely overturned because it hasn’t quite been erased from people’s minds even after forty years of use in Australia. Fabric shops tend to be a preserve of inches and yards. Occasionally I’ve come across very young children who are more comfortable with inches than centimetres. And while the new system might be a massive simplification of the old, let me assure you it’s no easier to learn. In fact, for many students, it seems to be strangely harder. I have regularly tried to teach whole classes of sixteen year olds the metric measurement system but they still get confused by whether there are ten millimetres in a centimetre or a hundred.
The architects of the French Revolution were not, in fact, wanting to simplify an old and archaic system when they gave orders for the devising of a new measurement system. They were intent on taking God out of the picture — out of society, out of history, out of any sort of contention at all — indeed, even out of measurement itself. So instead of 12 inches in a foot and 3 feet in a yard and 1760 yards in a mile, everything became multiples of 10. They even tried to make a week of 10 days, but that didn’t last very long at all. It turned out the human body actually needs a rest every 7 days.
So these ardent atheists two centuries back were responsible for getting rid of the following system in which they believed there was some reference to God.
12 lines = 1 inch
12 inches = 1 foot (=144 lines)
3 feet = 1 yard
22 yards = 1 chain
10 chains = 1 furlong (= 40 poles)
8 furlongs = 1 mile (=1760 yards)
An acre, described by experts as the ‘most intriguing’ of ancient measures, is defined as a rectangular area 1 chain in width by 1 furlong in length. A chain is the length of a cricket pitch: so an acre is a cricket pitch wide by 10 cricket pitches long!
Now, despite knowing the fact that the metric system was essentially anti-Christian in inspiration, it never really occurred to me that the French were attacking anything of true significance. Sure those numbers—3, 10, 12, 22, 40, 144 and 1760—had a traditional association with Christianity, but so what? They were messy and complicated and apparently random. Until the day before yesterday, it didn’t occur to me for an instant that there isn’t anything at all haphazard about them and that they are not the result of cobbling together different systems from all over, but are carefully and wonderfully thought out. At some time during the Dark Ages, someone unknown chose them to reflect not only the important recurring numbers in Scripture but designed them so that that seemingly bizarre measurement, the acre, mirrored Ezekiel’s vision of the City of God.
No hints as to what 3 and 12 symbolised. The other numbers aren’t all as easy as those two: 22 is the number of letters in the Hebrew alphabet (and in medieval times 22 was considered to be the number of different types of things God created at the beginning of Genesis, thus is signified ‘completeness in
creation’), 40 is the number of years the Israelites wandered in the wilderness and the number of days Jesus spent in the desert, 144 links to the 144000 elect in the book of Revelation, but where does 1760 come from? It’s quite simple. Medieval people believed that a cubit was 17.6 inches. And they understood the City of God in Ezekiel’s vision to have been built of cubits. In fact, the acre seems to have been designed precisely so that 100 of them would equal the area of that City.
In Ezekiel’s vision, the City of God is 18000 cubits in perimeter. Since it’s a square, this means each side is 4500 cubits. 4500 cubits at 17.6 inches per cubit is 79200 inches (or 6600 feet or 2200 yards or 100 chains). In other words it’s 100 cricket pitches long by 100 cricket pitches wide. It’s precisely 100 acres.
The suburbs of the City extend another 250 cubits north, south, east and west. This means that the City including suburbs is a square of side 5000 cubits. Now here’s the power of mathematics: it doesn’t matter whether medieval people were right or wrong about the cubit being 17.6 inches. If you’re looking for a ratio, it’s not necessary to know the size of the cubit. The ratio I’m looking for is the area of the City with suburbs compared to the City without suburbs. Drum roll, please. It’s: 1.2345679, that curious number missing an 8 which when multiplied by 999999999 produces the alpha to omega of the number world.
So, hidden in the numbers of the City of God seen by Ezekiel, there’s an image of completeness in creation—a completeness in new creation, actually—which medieval people tried to symbolise in the way they measured their fields and commons and greens.
You know, I’ve never heard anyone yearn for a few hectares of their own, but I still hear people wax nostalgic about the possibility of owning an acre or two. Perhaps that’s not simply semantics: perhaps it’s a deep sense, deeper than we know, of a yearning for the coming of the kingdom of God.
Today, all that’s left of the pre-decimal system of measurement is a cricket pitch with its 22 yards reflecting an ancient numerical symbol of completeness in creation. I have to admit that I’m not the world’s biggest fan of cricket; still, much as I hate to suggest it, I’m starting to suspect that cricket must be the game that angels play when they have a weekend off.
(c) Anne Hamilton
who teaches maths, reads medieval poetry & isn’t the least bit apologetic that this article is exactly 1717 words long.
Footnotes
1. To give an example: many people say 8 is the ‘number of Jesus’ or the ‘dominical number’ because, by assigning number values to letters in Greek, Lord Jesus Christ adds to 888. To me, this is Gnostic numerology. (If it worked in Hebrew too, that might be different. But it doesn’t.) Perhaps this is cultural bias on my part and I’m too influenced by rationalism, but if I have to make a mistake, I prefer to err towards science than Gnosticism. If there is a ‘number of Jesus’, it’s probably 17, though I don’t know why (but I suspect it’s something to do with fulfilling and shattering the Law). Whatever it is, 17 is clearly important through the New Testament. There are 17 references to ‘father’ in the Sermon on the Mount, 17 things that Paul tells us cannot separate from the love of God, 17 different groups of people who witnessed the events of Pentecost, 17 references to joy in Philippians (not 16, as usually stated—16 are based on chara and 1 on kauchaomai, the latter positioned to create a 3:1 ratio.)
