Those of you who have me on Facebook have already probably seen the news today: my book now has an ISBN and a rather attractive cover. Further good news today also, from the Press, in that it looks like the book will be out by November, as opposed to spring 2010 as I had feared. The price on Amazon is $87.83 which is a little higher than I had anticipated, but not actually too bad for a thick hardcover monograph. Huzzah!

Tags: numerals

Okay, readers, here is your opportunity to aid in the cause of Science! I am doing some preliminary research on how people read numbers in various contexts, focusing initially on phone numbers (North American format). This poll is designed to help me develop further research questions; I'm not using the results directly as data, so I'm not particularly concerned with the non-randomness of the sample. Of course, if you have any theoretical or practical insights, feel free to comment!

For each question, there are a number of possible readings of a specific phone number (the poll name). Answer each question in each poll according to the following scale:

1: Incorrect: This form is definitely incorrect and probably confusing
2: Marginal: This is a form that I would never use and might require clarification
3: Understandable: This is a form that I would clearly understand, but probably not use
4: Acceptable: This is a form that I might use, but not the most likely one
5: Preferred: This is the form that I would most likely use

The list of forms for each is not exhaustive but should (I think) cover most of the forms most people would be likely to use, plus some that they likely would not. But if it fails miserably, that will give me information also! You will have to submit each poll separately using the 'Submit Poll' button at the bottom of each.

Please link to this post and encourage others to take the poll; the more the merrier!

( Follow this link to the polls! )

Thank you very much for your participation!

Tags: language, numerals
Current Mood: accomplished

I just got an email from my publisher suggesting that I change the title. I already changed it (very modestly) once, from The Comparative History of Numerical Notation to A Comparative History of Numerical Notation. But now there has been a suggestion from the marketing department in favour of Numerical Notation: A Comparative History. I'm waaaaay too close to the situation to make a neutral decision, and I don't actually have a really strong preference, so as with all important decisions, let's leave it up to LJ-poll!

Poll #1335290 What should I call my book?
Open to: All, detailed results viewable to: All

What should I call my book?

Tags: numerals

The manuscript is off to the Press via Fedex, all 179,359 words of it. It may be drastically (and for me uncharacteristically) late, but it is Good and it is Done. Tonight, I celebrate with Julia! I've also been thinking about how to celebrate with all of you - maybe I can find a chatroom on Facebook or IRC where I just have everyone 'over' for a virtual shindig in the new year (bring your own booze to your own location).

Tags: numerals

In news from the burgeoning field of the anthropology of numbers, the Union Internationale de Pentathlon Moderne has decided that the pentathlon will now comprise only four distinct events, combining the shooting and running components into a single event. But this change in structure will not be accompanied by a change in nomenclature, sparking a barrage from the linguistic blogosphere, such as this Language Log post, discussing the change and the inevitable cries of etymological impurity. Now Bill Poser at LL has very sensibly pointed out that since the shooting and running event is a two-event sport (thus a biathlon), three events plus a biathlon is still five separate disciplines and the etymological issue is a non-starter.

These issues involving numerical prefixes are very obvious instances where we think that the etymology should correspond to reality. Of course if something involves the prefix penta-, it should involve five, right? Not so fast. This is really a special case of the logical fallacy known as the etymological fallacy: the notion that the current meaning of words ought to reflect their etymology. It rarely does, and there is no reason we should expect every language user to be a language historian.

The etymological fallacy in English is normally applied only to a particular set of words: scientific and technical vocabulary that form part of the Greek and Latin superstrate introduced into the language from the 16th century onward. Latin and Greek vocabulary is often seen to be logical, rational, and predictable, in contrast to wayward Anglo-Saxon and French elements in the modern English lexicon. It isn't true, as anyone who has studied classical languages for any period of time will attest. Rather, when borrowing and developing this aspect of the English lexicon, early modern wordsmiths borrowed fairly regular elements (predictable morphemes that could be combined with others), and left a lot of the complexity behind, leaving the illusion that Latin is a purely logical language.

I grant that if someone tried to redefine triskaidekaphobia as fear of the number 11, I might feel a bit put out. The semantic transparency of numerical prefixes contributes to the sensible notion that we should know what they mean unambiguously. But by that logic, we ought to insist that decimate be used to describe only the destruction of one-tenth of something (which earned the word a spot on the annual Banished Words List some years back). And don't even get me started on the debate between biannual and semiannual. In this case, the 'quinquemation' of the pentathlon doesn't bother me in the least.

(Crossposted to Glossographia)

Tags: language, numerals

Amateur (and professional) numerologists take note! Apparently, gas stations around the United States are running out of a vital commodity: the numeral 4. With gas prices in most parts of the US now higher than $4.00 a gallon for the first time, this essential grapheme is in shorter supply than the fossil fuels whose price it indicates, leading to chaos ... CHAOS ... well, okay, to hand-made numerals written on paper.

It all sounds like a parody from The Onion or a similar site, although the usual targets are vowels, not numerals:
Clinton Deploys Vowels to Bosnia
Vowel mining set to peak in 2012
'Wheel of Fortune' contestants hit hard as vowel prices skyrocket

But this is no parody (even if it is a fairly lighthearted piece). As a professional numbers guy, and someone interested in writing and literacy in contemporary society, this is fascinating to me. I hadn't thought about it before, but of course a gas station would need more 9s, and more of whatever the dollar amount is per gallon, but numeral packages come with equal numbers of each digit, creating a 'numeral gap' until more numerals can be rounded up and marshalled for the cause.

In Canada, a lot of stations switched from plastic numbers to electronic numerals around the time that gas prices hit $1.00 a litre, a level they hit first in 2005 during and after Hurricane Katrina, but during that time you could find paper 1s stuck up all over the place. There the problem was not a lack of the appropriate numeral, but a sort of mini-Y2K problem, with not enough digit spaces for the price. The principle may be different, but the workaround was the same.

Okay, so this is not exactly the most important consequence of higher gas prices - not even the numerically most significant. You definitely do see a cultural shock surrounding a new digit at the start of a price (after all, this is one of the reasons why prices end in .99, to avoid reaching the next dollar value). By now Canadians are more or less accustomed to gas over $1.00, and certainly Americans will adjust to $4.00 gas quickly enough - they had better, since $5.00 is just around the corner. It would be interesting to know whether a particular dollar value will correlate with a sudden shift (or rather, an increased rate of change) in consumer behaviour. Alas, probably not.

But won't anyone think of those poor unused excess 3s?

Tags: language, numerals

Stonehenge is never really out of the news; in fact, it's probably the archaeological site that enjoys the most media exposure. Even so, it has been in the news quite a lot lately, what with the recent report of work by Mike Parker Pearson's Stonehenge Riverside Project, which has given us radiocarbon dates from burials excavated in the 1920s, suggesting that the site was used for burials from around 3000 BCE, several centuries earlier than previously thought and really quite early in the British Neolithic.

I must insist, however, that Parker Pearson's theory that Stonehenge stood in contrast to the much larger timber circle at Durrington Walls, is plausible at best but completely unproven. Based on an ethnographic analogy resulting from some earlier fieldwork he did in Madagascar, Parker Pearson has sought to revive structuralist archaeology with his contention that the two British sites were conceptually binary opposites, the stone of Stonehenge representing permanence and ancestry, with wood representing transience and impermanence. Okay, so far so good (though still 'not proven'). However, he goes on to assert that stone is not only ancestral but also male, while wood is (quoting PP himself) "soft and squishy, like women and babies." (1) At which point my inclination is to get out a Walloping Cod and suggest that he keep his structuralism to himself until he has archaeological evidence for all this.

But lost amidst all this highly-funded work is a new book by Anthony Johnson, Solving Stonehenge: The Key to an Ancient Enigma(Thames and Hudson, 2008), offering clues to the mathematical abilities of the builders of the monument. I haven't read the book (which isn't published for another week) , but an article in the Independent suggests that the geometrical knowledge of the builders was more considerable than previously believed (by some). I hadn't heard of Johnson before (despite having a very strong research interest in the prehistory of mathematical thought, and a secondary interest in the archaeology of megaliths). He appears to be a doctoral candidate at Oxford working on geophysical techniques in archaeological survey, but has not published before on Neolithic mathematics. One does need to be cautious when dealing with topics in ancient science, which are particularly prone to attracting the attention of pseudoarchaeologists, but I don't think that's what's going on here.

How, then, do we evaluate what an ancient monument can tell us about the mathematical abilities of its creators? The most important finding that Johnson is suggesting, from my perspective, is that other than the well-known solar alignments of the monument, no significant astronomical knowledge was employed in the orientation of the site. Rather, it was in geometry, and the creation of complex polygons using 'rope-and-peg' technology (making arcs and lines on the landscape using physical means), that the Stonehenge builders excelled, creating, over 1000+ years of the site's history, a palimpsest of complex polygons among the various features of the site. By 'experimental archaeology' I take it that Johnson used this technique himself to show that using modest technology and a modicum of geometrical knowledge about the relationship between circles and squares, the monument's shapes could have been constructed precisely. This is fascinating stuff, and gets us away from Alexander Thom's 'megalithic yard' and Gerald Hawkins' 'Neolithic computer' theories, both of which start from the assumption that astronomy was the function of the site.

My only major issue (prior to reading the book, which I'll have to do over the next few months) is Johnson's claim that "It shows the builders of Stonehenge had a sophisticated yet empirically derived knowledge of Pythagorean geometry 2000 years before Pythagoras", mostly because Pythagoras was essentially a fiction about whose work we know almost nothing, and because it suggests inappropriately to the untutored reader that in fact the Stonehenge builders had proven the Pythagorean theorem, which is not what is being claimed. It's not quite the same kind of error as asserting that sunflowers 'know' the Fibonacci sequence because their florets are arranged in such a pattern (okay ... no one actually claims that, as far as I know). The point is, though, that there is always a danger in inferring specific mathematical knowledge from the outcomes of processes such as the rope-and-peg technique. Similarly, while it is plausible that "this knowledge was regarded as a form of arcane wisdom or magic that conferred a privileged status on the elite who possessed it", we don't actually know who exactly controlled this knowledge (and how), whether in fact the engineers/surveyors/artisans involved were part of the (as-yet incipient) social elite at the site, whether that status changed at all over a millennium or more (almost certainly!), and whether in fact geometrical knowledge was perceived as 'magic' in any sense.

In my 'Prehistory of Language and Mind' seminar, I emphasize the real dangers in attempting to hermeneutically insert oneself into the minds of prehistoric individuals based on their material culture, a caution that is worth repeating here. This is particularly true in the case of megaliths, which archaeologists approach too often on the basis of intuition, faulty ethnographic analogies (I'm looking at you, Parker Pearson...) and wishful but unsupported thinking, as Jess Beck and I show in a forthcoming publication (2). All of which is fine when one is speculating idly, or creating one's own personalized or intuitive understanding of the past, but is pretty shoddy evidence-based scholarship. Accordingly, I'd insist that even Johnson's work (to which I am initially positively disposed, and whose use of experimental archaeology is a definite advantage here) needs to be treated with the utmost caution, due to the exceedingly high risk of erroneous interpretations of ancient scientific abilities.

(1) Caroline Alexander. 2008. If the stones could speak. National Geographic, June 2008, p. 50.
(2) Jess Beck and Stephen Chrisomalis. Landscape archaeology, paganism, and the interpretation of megaliths. Forthcoming in The Pomegranate.

ETA: Anthony Johnson himself has now commented on the post, noting that the quotation from the news article about Pythagoras does not actually reflect his words. The blog for his book can be found at Sarsen56.

Tags: anthropology, numerals

Last Sunday evening I was watching TV when an ad came on for the new movie, The Number 23, featuring Jim Carrey. Apparently the plot is that a man reads a book entitled 'The Number 23' and after doing so, begins discovering odd patterns and correlations between the book and his life, most of which involve that very number. I have to admit being vaguely intrigued; although most Jim Carrey movies are utter drek, I'm mildly fond of The Truman Show and quite liked Eternal Sunshine of the Spotless Mind.

Anyway, in what is almost certainly not a coincidence but rather a marketing ploy, the ad immediately following it was an ad for Dr. Pepper, whose new marketing campaign is advertising that it is an authentic blend of 23 flavors, with a tie-in hunt for 23 treasures.

The next morning, I went off to catch my bus when I happened to look across to the bus stop across the street, where I saw, in addition to the old sign for bus 102, a new (or at least new to me) sign for buses 102 ... and 23! Now, being a numbers guy, I was impressed that my attention could be so easily manipulated to see a pattern, much as the pattern of 1:11 and 11:11 that one can train oneself to see in all things, as with this guy here who emailed me over four years ago. This sort of cognitive illusion is really pervasive, but is particularly easily demonstrable with things like numbers. So, I thought, neat enough, but of course there was a rational explanation. Although it did lead me to wonder why I had never seen such a bus. When I got to work, I went on the Montreal bus system web site, only to learn...

There is no bus #23.

So, my sanity having taken a gut-shot, I became a little obsessed with figuring out what the heck was going on. I used it as an example of how pseudoscience makes coincidences seem patterned in my Pseudoarchaeology seminar on Wednesday, and my students were very impressed. I further pointed out that there were 23 students in attendance that day! By Thursday, a couple of them had reported weird 23 sightings in their lives. Heh heh ... warping the young. Is there anything more rewarding?

Finally, yesterday morning, I found the solution. Apparently there is a new seniors' shuttle-bus #23 that has been running during the daytimes since last year, and apparently they have only now gotten around to putting up the sign for this stop. Mystery solved.

... or is it?

Tags: numerals, weird
Current Mood: busy

I would hate to take too much credit for the development (kids learn the darndest things in the darndest ways), but whatever the cause, Arthur is well on his way to counting. He recognizes all the Hindu-Arabic numerals from 1 to 9, as well as 0, and identifies them spontaneously (i.e. he started reading the phone number off the pizza box earlier this week). He still gets a little confused with 6 and 9, because he encounters them frequently in the form of his little styrofoam numbers (which of course he can carry around with him in whatever orientation he chooses). Of course, naming number symbols isn't much more than a parlor trick in and of itself - kids can recognize and name abstract shapes without having well-developed number concepts. But it was very neat to go through the baby shoe aisle at Wal-Mart yesterday and have him shouting out shoe sizes.

He is, nevertheless, well on the way towards ordination (enumerating objects starting with one). I've been counting on my fingers up to 3 for him for a long, long time (nearly since his birth, actually, although I certainly had no expectations from that exercise). Now if I say 'Let's count!' he'll often say 'one' and then pull on my index finger, and then we go through the numbers up to 5 at least. I think he gets a little confused when moving onto the other hand - even though he knows the number 'six', I suspect he's still a little baffled by Daddy putting up his finger on his other hand, and often says 'one' again (quite rationally, in fact). He can also ordinate verbally without an obvious referent - i.e., if I say 'one', he will sometimes say 'two', and we will carry on from there. At least, until he gets tired of it. He must think his dad is obsessed with numbers or something...

I was, however, aware that potentially he could have been associating the fingers with number words without having the capacity to enumerate other (non-finger) objects. Yesterday, in the bath, however, he confirmed spontaneously that this was not the case. He had two blocks in each hand. He looked at one block, said 'one' and then kissed it. Then he switched to the other hand, looked at a block and said 'two' and then kissed it. He repeated these steps with the other block in the first hand 'three' and finally the last block 'four'. This was without any prompting. Not bad for 18 months!

So, needless to say, I am inordinately pleased (pun intended). I am going to have to decide what to do about Roman numerals, and what to do about 'eleven', sooner than I had anticipated! Of course, there is still the problem of cardination (identifying the quantity of a set of objects, rather than just numbering them in sequence), but all things in their due course. Or possibly slightly earlier!

P.S. To any grandparents who may be reading this: I promise I am not warping the boy!

Tags: arthur, numerals

Well, here we are at 06/06/06. Time to put on Iron Maiden, wear my devil horns, and wait for the Apocalypse.

...

All right, while I'm waiting, let me refer you to this hilarious BBC article on the big day. Who knew there were so many splitters in the Satanist community? And I think we can all, regardless of race, religion, or nationality, agree to come together on this momentous occasion to celebrate the National Day of Slayer. Although why that site, along with so many other sources, seems to think that 06/06/06 only comes along once a millennium, is beyond me. And let's not forget poor old U.S. 491, a highway running through parts of the Southwest, and which formerly had the (mis)fortune to have been named U.S. 666. All ridiculously tongue-in-cheek, which is great. Not so the news story on CNN this morning talking about a mother whose labour was induced on Sunday in order to avoid her baby's due date today, with sound bites with the parents saying how glad they were their child wouldn't be (possibly) born on this fateful day, and otherwise CNNifying what should be an occasion for ridiculing superstition.

I haven't received any emails about the big day, which is a bit disappointing, I suppose, for a numbers guy, although I don't really have anything to say that hasn't been said many times before. The best academic reference is W.C. Watt's paper, '666' (Semiotica, 77(4), 1989, pp. 369-392) which talks about why Revelation 13:18 reads the way it does (KJV: "Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number [is] Six hundred threescore [and] six." and in particular why 666 (or perhaps 616, as it reads in the Oxyrhynchus papyri) might have been relevant to the author of the book. The answer is that no one knows for sure, but it may have to do either with the structure of the Greek-Hebrew alphabetic numerals or the fact that it is the sum of the Roman numerals in descending order from 500 to 1 (DCLXVI). It is not primarily a cryptological reference to the emperor Nero (the popular theory), because one really has to stretch the numerical values of the letters and play with things to get the math to add up. It may, however, have already been a numerologically significant number to which the name of Nero was later attached. Nero was certainly a favourite object of scorn of both Jews and Christians in the late first century A.D. Strangely enough, Watt's article is alphabetically the last in my database of sources on numerical notation, when sorted by title. Make of that what you will.

Tags: numerals, weird
Current Mood: devilish
Current Music: Iron Maiden / Number of the Beast