Monthly Archives: December 2011

365 words for drunk

I mentioned in my word tasting note for crapulous that I could do blog entries on words and phrases for “drunk” for a whole year. I don’t intend to do that, but I have decided to rise to the challenge and accumulate 365 words (and phrases) for “drunk”. I’m up to 263 351 362 so far (with the aid of several from other languages), and would like the assistance of my readers and their bibulous compatriots in making up the gap. Have a look at the list so far, and use the comments to add any I’ve missed.

And now you can have words for drunk on your shirt or mug! Buy the “drunk words” merchandise at Café Press – your handy reference for 302 ways of saying “drunk” in English!

Continue reading

Index, icon, symbol: a tale of abduction

Published in The Indexer 29:4 (December 2011)

In the semiotic theories of Charles Sanders Peirce, an index is a type of sign that signifies by having a direct connection to what it signifies – smoke is an index of fire, and a pointing finger is an index of what it indicates. The index is one of a trichotomy of sign types, the other two being the icon (which signifies by resemblance) and the symbol (which signifies by conventional association). Most semiotic constructions have elements of all three, and book indexes are no exception. The way signs are interpreted involves another trichotomy, of types of inference: abduction, deduction and induction. What readers take away from your index will depend on how you manage it – and your process of creating it – to optimize its indexicality, iconicity and symbolicity for optimal abduction. Continue reading

allure

The quote of the once-faddish computer-game dysfluent English “All your base are belong to us” that I used in yesterday’s note on merry led me to think about allure. Not because I was wondering what the allure is of such games but just because of the sonic resemblance of all your to allure.

Part of the allure of English, for people who like to play with language, is of course its inconsistencies. And allure figures among them. It makes me think of adult, not because allure is an adult thing – though it’s probably more often seen in reference to “adult” things – but because, just as adult is a word that may make you stop and think how you want to say it (“ADult? aDULT?”), so is allure.

The opening a is fairly unproblematic. Generally it’s said as a schwa, that mid-central reduced vowel we often use in English in unstressed positions; if we don’t want to reduce it, it will probably be said as /æ/ as in hat. But it’s the second syllable that brings in the variations. Mostly it depends on your dialect, but there are still options. And I think many a Canadian has used – or even puzzled over – several or all of them at one time or another. It’s all about the end of the word (after the /l/). Is it like “you” plus /r/, or like a clearly said “you’re”, or like “oo” in fool plus /r/, or like “u” in full plus /r/, or does the vowel fold into the following liquid so the second syllable is /lr/? And will it depend on the context and the price of the item in question? Will you say it differently between “I don’t understand the allure of Justin Bieber” and “Not needing a car is part of the allure of living downtown” and “Succumb to the timeless allure of this beautiful art”?

The pronunciation is indeed liquid – it is not quite fixed, but it always has those two liquid consonants, /l/ and /r/. And it has certain allure to its look. Those paired l’s add a tall, lean something, like pinstripes or the legs of a willowy miss or a champagne flute or… Well, parallels are available.

We have a few particular ways we like to use this word. We will use it when analyzing some thing: its allure, its central allure, its timeless allure, its exotic allure… Often we will talk about an aspect of something that is part of its allure. We will talk about something that has lost its allure; we will talk about trying to understand the allure of something. And a thing may often be said to hold a unique (or special, or considerable, or…) allure. When we account for the allure, we say it lies in something. As in The allure of English lies in its flexibility and inconsistency.

Which is to say that’s what draws us. We hunger for it (we being not everyone but the sort of person who reads this sort of thing). We return to it like the falcon to the falconer. After all, when you train a falcon, you feed it from an apparatus of thong and feathers called a lure (from Old French leurre, from a Germanic word for “bait”), and it learns to come to the lure; add a meaning “to” to lure and you get (with a doubling of the joining consonant) allure.

Which is fair enough. If you succumb to the allure of something – be it lovely scenery, a unique voice, a fashion magazine (called Allure, for instance), a cruise ship vacation (on the Allure of the Seas), or even just a pair of lovely eyes – you take the bait. And then all your base are belong to them.

merry

I arranged for the usual coffee bunch to meet at Starbucks this time. I did this solely for the enjoyment of provoking Margot with their latest seasonal campaign slogan. I succeeded.

“‘Let’s merry’? ‘Let’s merry’?!” She was frothing more than a cappuccino would.

“You’re not merrying,” I said. “It’s Christmas. Or advent, anyway. You should merry!”

“I’m not the merrying kind,” she said with some asperity.

“Don’t I know it,” said Daryl sotto voce. Margot was momentarily nonplussed and decided to blush.

“It is rather odd,” Jess said, blowing on her eggnog latte.

“I would have thought you would be defending it,” Margot said, regaining her voice. “Your precious verbing and all that. And no doubt there’s some historical usage of merry as a verb.”

“The latter is confirmed,” Daryl said, scrolling through the OED on his iPad. “Both transitive and intransitive. I merry you, you merry me, let’s merry.”

“Enough,” Margot said in a barely audible whisper, her skin colour increasingly Christmassy – red with shades of green.

Daryl continued, waving his hand at his iPad with an almost studied casualness. “Interestingly, merry has a lot of cognates in Indo-European languages, and most of them have something to do with brevity. Indeed, even Latin brevis is a related word: there’s a predictable transformation between /b/ and /m/ and between /w/ and /g/. It seem that pleasantry and mirth – that’s another related word, mirth – it seems they make the time pass more quickly.”

“Ironically,” Jess said, “getting short with people has rather the opposite effect.”

“But that’s all adjectival originally,” I said. “And it’s not really in current use as a verb.”

“The OED has intransitive use into the 20th century,” Daryl said. “Latest citation is from James Joyce. It’s figurative, mostly. ‘Warm sunshine merrying over the sea.’ The transitive use is cited up to 1961… Oh, but with up: ‘merry up their hearts’; ‘people merrying-up themselves’…”

“Oh, well that’s a bit different,” I said. “You can use quite a lot of words with up to make causative transitive verbs. ‘She prettied up her face and uglied up her attitude,’ for example. It’s a sort of modular formation. And for the intransitive, as a figurative usage, it’s less surprising. Again, ‘A warm sunset oranging on the horizon’ would not be such an odd figure.”

Margot seemed genuinely surprised. “So you really don’t like it,” she said to me.

“Didn’t say that,” I said. “I’m just accounting for its seeming odd. We don’t verb adjectives of state as much as we do adjectives of activity and nouns, I don’t think. Anyway, you’re going to have to get used to it.”

“It sounds like Chinglish,” Margot said. “Or Japlish. Like some packaging or some cheap Xbox game.”

“Starbucks say ‘All your base are belong to us,'” I said.

“But why not be merry or make merry?” Margot protested.

“Or even get merry,” Daryl mused apart as though to no one in particular. “‘We got merried on Christmas.'” He sipped his caramel brûlé latte and looked at not Margot.

“Would you really go with be merry?” I asked Margot, whose lower lip seemed to be shaking slightly. “Don’t you tell your English tutoring students to avoid forms of to be when they can? There’s a certain prejudice against them. Admittedly, many texts can be greatly improved by moving away from be- and noun-centred constructions and into action verbs. But sometimes it leads to rather forced results.”

Make merry is nice and active,” Jess said.

“It’s still two words,” I said. “There’s an idea that one-word verbs are better than compound predicates. Some people absolutely hate adverbs. Most verbs could of course be paraphrased as another verb plus an adverb, and there’s no reason in principle that a given verb-adverb combination couldn’t be expressed as a one-word verb if one existed. It just happens that many of them don’t have single words. And a single word is punchier. It occurs to me that make plus adjective, intransitive, tends to show up in phrases referring to intercourse: make love, make whoopee, makin’ bacon…

Merry, meanwhile, gets around quite a bit,” Daryl said, again with the iPad. “Merry and bright, merry-faced, merry-hearted, merry-lipped, merry-mouthed, merry-voiced, merry Monday, merry night, merry Christmas. The more the merrier. Two are merrier than one. ’Tis the season to merry, it seems. So let’s! Time’s a-wasting.”

“Then why make it pass more quickly,” Margot said quietly, eyes downward. She stood, pulled her coat around her. “A happy Christmas to you,” she said, looking at me and then at Jess. She glanced quickly at Daryl, then turned and hurried towards the door.

“Have a happy,” I said. She broke her stride for half a moment, her hands tensing perceptibly, but then passed through the door. I looked back to see Daryl stuffing his iPad in his bag and getting up.

“Gentlemen,” he said, nodding at me and Jess. He made towards the door.

Jess raised one eyebrow, and then lifted her cup in a toast towards him. “God rest you married,” she said, slightly indistinctly, as he exited.

“Yow know,” I said, relaxing back in my chair, “that conversation couldn’t have happened quite that way if we had British accents.”

“Where merry and marry are not homophones. Indeed.” She looked into her cup and saw residue encircling it. “Oh look. Starbucks has even given me a ring. I guess they really do want to merry.”

edentulous

Words are wonderful things. They can be quite delectable, giving you something to sink your teeth into or at least to roll around on your tongue; they can be bright, shiny toys, too. And sometimes that’s a problem. One has to be careful exactly where and how one uses spicy or shiny new words – you don’t toss a whole jar of a new spice into your stew (imagine doing that with cloves, for instance – gaaah), and you certainly don’t toss in a shiny new toy; you’d break a tooth.

A couple of aggravating factors in this issue are the frequent desire not simply to have fun but to sound impressive, and the fact that uncommon words tend not to have accretions of strong positive or negative values, so they look like good alternatives to some more common words.

So, when there is a particularly delicious and erudite-sounding word, even if it is really quite unfamiliar and frankly a bit ridiculous in context, it may be prone to appearing unexpectedly in place of something rather better known, especially under the digits of lexically edacious pseudo-didacts. An example is the little Canadian Press factoid box that showed up in newspapers on November 6: “QuickFacts about edentulous Canadians.”

What does edentulous mean? The article doesn’t tell you directly. The first sentence repeats it: “Many Canadians are edentulous but cannot afford workable false teeth.” The rest of the article is light statistics about Canadians with no natural teeth, plus some general toothcare-related factoids. So… you can figure readily that the dent refers to teeth, as it tends to. You may also reckon that the ul is the Latin diminutive, which shows up in assorted words such as capsule and macular. That leaves the e, and you may recall that e pluribus unum means “out of many, one”; it happens that edentulous is an adjective (as shown by the ous ending) that means “out of teeth” – because the teeth have gone out of you!

Of course, you could prefer to see Eden and some echo of Dracula, but Eden is where Eve met a snake and bit an apple, and snakes have fangs and it’s hard to bite an apple without teeth, and Dracula is surely not edentulous either. On the other hand, if it sounds more like eventual, that may be appropriate, depending on your standard of tooth care, especially if it’s rather sedentary.

The Oxford English Dictionary presents some nice quotes using this word. From a 1782 Essay on comparative anatomy by Alexander Monro, “The chin and nose of edentulous people are much nearer.” And in 1784 the Philosophical Transactions of the Royal Society of London noted that “Fishes… [are] apparently utter strangers to edentulous old age.”

Edentulous? Toothless, for heaven’s sake. But, now, is it apposite or ironic that edentulous is said without any direct involvement of the teeth – all done with the tip of the tongue on the alveolar ridge? And that, on the other hand, toothless requires the tongue to touch the teeth, as though checking to make sure they’re still there?

Thanks to Amy Toffelmire for directing my attention to this one.

bisphosphonate

The first thing to note about this word is that it is not biphosphonate. That opening syllable is bis, as in “again” in Latin. And what comes again? In this word, spho – not a real morpheme, but just a coincidental sequence. If bis repetitia non placent (repetitions don’t please), one might subject it to haplology and kill one spho to make bisphonate, which, ironically, would seem to mean “sounded twice” or “spoken twice”, as long as we allow the Latin bis to wed with the Greek phone without thinking it phony (a more classical Latin formation would use bi in place of bis, but that’s not our bis-ness here). We have to watch that our derivation is from ϕωνή phóné, “voice”, rather than ϕόνος phonos, “murder”, though… we wouldn’t want to kill it twice (if we killed both sphos we would end up with binate, which would seem to mean “born twice”, even more ironically, and where would we go from there?).

This is a formal-looking word, suited to a bishop, posh, neat. It has many flavours peeking from its orthography: hints of shop, hops, pose, phone, hosp(ital), p(r)onate, tea, and a big bite enclosing a heart set on Sappho (with a spare h). And for those who seek bliss from phonetics, that pair of paired fricatives /sf/ and /sf/ make a sufficient bed as soft as sphagnum moss between the headboard of /b/ and the foot at /neIt/. This is a word with no bones in the heart of it.

It is also a word for something that works on the hearts of bones. Bisphosphonates are a class of drugs used to prevent bone loss. They are used to treat people with osteoporosis; they reduce the risk of bone fracture. How much they reduce it by depends on the specific drug, the fracture site, whether you’ve had a fracture before, and whether you figure by absolute risk or relative risk: they may claim as much as a 45% relative risk reduction but with a 2% absolute risk reduction. I’ll explain the difference. Say you had 100 people with osteoporosis, and without treatment 4 would get a certain fracture, and with the drug 2 would get a fracture. In such a case, the drug cuts the fracture rate in half, from 4 to 2 – a 50% relative risk reduction – but in absolute terms it reduces the risk by only 2%, and you would on average need to treat 50 people for just one to get any benefit. But the problem is you don’t know which one, so you treat all 50. And more than one of them will get the side effects.

If you think you get a taste of phosphorus from this word, you are right. Bisphosphonates are so named because they have tandem phosphonates, and a phosphonate is an assembly of a phosphorus atom, three oxygen atoms, and some other stuff. Binding the two phosphonates is a carbon atom, and also hanging off that are a couple of other chains of stuff; it’s those other chains that differentiate between the different bisphosphonates, just as if along with bisphosphonate we had some other words like trisphosphonation and tetrakisphosphonetics. (Of course we don’t; that’s just philosophical phonetics.) Bisphosphonates work like decoys – when enzymes come along to break down the bones (bones are constantly being broken down and replaced, and the problem is when the rates differ), they step in for the enzymes’ usual dancing partners and keep them from doing anything. It sounds a bit like a seductress in a spy novel stopping an assassin. Perhaps James Bond… I won’t say you only live twice, but a new lease on life is a step in that direction. For the 2% who benefit.

iniquity

It’s Messiah season again, which means the Toronto Mendelssohn Choir owns my evenings for the next week. Tonight was the rehearsal with choir and orchestra (tomorrow we do it with the soloists as well) and, of course, the conductor – Nicholas Kraemer this time. It will be good.

During the chorus “Surely He Hath Borne Our Griefs” Maestro Kraemer pointed out that the long note on “our” in “he was bruised for our iniquities” was resulting in loss of precision on the following word so he couldn’t quite hear the quit. Well, there it is: sometimes we don’t know when to quit.

Is that a fair perspective on iniquity as well – not knowing when, where, and whether to quit? Deadly sins have a way of being normal things taken to excess: gluttony is simply eating too much food, greed is just wanting too much, lust is letting one’s attractions go a bit far, and so on. So is unquittingness in the propinquity? Not quite, though there is something to it.

Iniquity is often associated with elastic morals – I might more readily say with liquid morals, with a deliquescence of morals (caused by moral turpentine?), or perhaps even a deliquium of the conscience. It is also associated with archaism – that is to say, it shows up in old texts, and in texts that wish to call forth an old and formal style with strong Biblical overtones. In modern English its most common collocation is den of iniquity, and we know what that is: to quote Star Wars, a “wretched hive of scum and villainy” – especially of those things considered grave moral transgressions, such as drinking, gambling, and fornication, and perhaps just incidentally theft and so on.

We see a particular eye on the most delectable kind of flagrante delicto in Nathaniel Hawthorne’s Scarlet Letter: “A blessing on the righteous colony of the Massachusetts, where iniquity is dragged out into the sunshine! Come along, Madame Hester, and show your scarlet letter in the market-place!” We see it in Henry Fielding’s Tom Jones: “as the old woman shared in the profits arising from the iniquity of her daughter, she encouraged and protected her in it to the utmost of her power.” Oh, those three i’s in iniquity – are they candles on the dresser, are they the torches of the morally offended coming to smoke out the offenders? Or just the all-peeping eyes of the moral judges?

But concupiscence, favoured object of scorn for the gossips, is not the sole or original form of iniquity. (Nor is drug use or alcoholism, though both seem implied in many modern uses of den of iniquity.) Certainly we see theft and similar villainy covered by it; a good example is from Walter Scott’s Guy Mannering: “Glossin, though a bold and hardy man, felt his heart throb and his knees knock together, when he prepared to enter this den of secret iniquity, in order to hold conference with a felon, whom he justly accounted one of the most desperate and depraved of men.”

If we look back to the Bible (the King James Version, of course; we no longer use the word iniquity much, so it would be an odd choice for a modern translation), we see it used in many places as a general word for sin, for breaking the commandments of God, but if we are to find a specific kind of sin, then it is of the sort indicated in Psalm 53: “Have the workers of iniquity no knowledge, Who eat up my people as they eat bread, And call not upon God?” Yes, people who devour others, who have no care for others, who show no mercy and give no justice.

What is justice? Equity. Fairness. Indeed, not grabbing all you can. So iniquity is inequity? Well, I can tell you that inequity is just a more recent reflex of iniquity. The Latin root is æquus “even, just, fair”; from it we get equal and equity. In Latin the negative of æquus was iniquus, and from that came iniquitas, whence iniquity. But though we’ve had iniquity in the language since the 1300s, its meaning shifted enough towards sin and moral transgressions in general that it was not functioning so well for “lack of fairness”. So by the 1600s we had inequity as well, formed in English from equity.

Which ought to remind us that harm to others is a very important factor in this, and lack of concern for others – and glorification of grabbing all you can – is surely much higher on the list of iniquities than grabbing a bit on the side, as Hester Prynne was labelled for doing. The greatest modern dens of iniquity, in truth, tend to be boardrooms and corner offices at the tops of financial district towers, and the computer desks where they trade in equities.

cattery

My friend Alex Goykhman forwarded an ad to me offering a deal: “$49 for 7 Nights of Cattery at the Lonesome Kitty Cat Hotel ($140 value).”

To modestly modify an Amy Winehouse song: What kind of cattery is this?

Well, we can feel quite certain that it has to do with cats one way or another. Aside from its being the Lonesome Kitty Cat Hotel, the formation cattery is quite unlikely to come from any false cognate such as the cata in cataplectic, catabasis, catastrophe, and so on. And cat is cognate with words throughout European languages (even borrowed into the non-Indo-European language Finnish as katti, which I particularly like). It even shows up in Byzantine Greek as κάττος kattos (meaning we could justifiably have had cattophile and cattophobe rather than the more opaque ailurophile and ailurophobe). The best guess is that the etymon was in Ancient Egypt, but we – hey, look, a kitty!

Spy cat (Jaggie and the bench)

Now, where were we? Ah, yes. The issue with this word is twofold. First of all is the issue of the multiplicity of meanings of cat (as opposed to The Multiple Cat, which is the name of a musical group who made a CD that I happened to pick up in a bargain bit titled “territory” shall mean the universe). This is illustrated by the assertion that the Web has gradually transformed from a cathouse to a cathouse – i.e., the videos occupying most of it, the joke goes, have shifted from smutty to kittycat. (See thedailywh.at/2011/11/14/all-cats-all-the-time-of-the-day/ for an amusing extended riff on this.)

Second is the ery ending. There are different kinds of words that end in ery, as illustrated by just the set of words ending in ttery: lottery, battery, buttery, cattery, chattery, cluttery, flattery, fluttery, God-wottery, guttery, hattery, hottery, littery, lottery, mattery, muttery, nattery, nitwittery, nuttery, plottery, polyglottery, pottery, rattery, rettery, ruttery, scattery, shattery, skittery, slattery, slottery, sluttery, smattery, spluttery, sputtery, stuttery, tattery, tittery, tottery, twittery. Some are adjectives formed on words ending in er; we can rule that out in this case, as there is no catter for something to be like. Some are mass objects referring to a kind of thing, such as pottery; others are mass objects referring to some more abstract thing that is pervasive in some context, such as polyglottery and God-wottery; others are mass objects referring to a condition or state of being, such as sluttery; and some are referring to a place where things are made and/or kept, such as hattery.

So here’s the thing: cattery, according to dictionary definitions, and as shown in general use even still if you search it on the web, is a word for a place where cats are raised and/or housed. So, yes, it’s a cathouse, but the kind where actual cats sleep – the Lonesome Kitty Cat Hotel is a lodging in Toronto for cats for when their owners are away. (Now, think for a moment: $49 for 7 days for the other kind of cathouse? Or even $140? Really?) But in that case it would be 7 nights of a cattery, no? Where’s that indefinite article? Its absence makes the word a mass object: the ad appears to promise 7 days of kitty-catness, or of being surrounded by or playing with cats, or something similar – no need to catalogue all possible nuances.

I must admit, 7 days of that kind of cattery would be quite appealing – if only I weren’t allergic. Let me tell you, the thought of seven days free of allergy and playing with kittens honestly brings tears to my eyes, I would enjoy it so much. But you can’t always get what you want. Just as the word cattery is double-crossed in the middle, tt, I have been double-crossed by nature.

So it goes. But cats are all around us, and their action in inaction and inaction in action is the way of the play of the world. For the multiplicity of cats, territory shall indeed mean the universe: we are in a cattery of cattery, all of us from the bottom of the gutter to Cat Deeley and Kim Cattrall; all is a fractal of cat fur. Just as your tongue, in saying cattery, reaches quickly like a paw from under the couch to pull in a bit of string or food, all things are subject to the subtle little paw of the cosmic cat, catching at the catenary from catabasis to catacomb, catalyzing all from cataract to cataclysm, alternately cataskeuastic and catastrophic. But I don’t wish to be catachrestic. I will simply say that the world is cattery, seven times a cattery, seven times seven – which is 49, which is how much it would cost for week of cattery.

I was going to end with that, but, given the season, I will tack on a poem I wrote almost exactly 20 years ago:

Cassandra the Cat

Cassandra the cat sits smugly, placidly purring;
outside, a violent winter storm is brewing.
Cassandra wants none of that; she’ll stay by the fire
and enjoy guests who give the odd drop of egg nog to her.

Cassandra goes vaulting off the top of the couch,
scampering under the chair of a startled guest,
and, after a whirlwind tour of the house,
comes back to the fire and quickly returns to rest.

Cassandra is master of all that she surveys;
that small plate of cakes could be hers, if she wanted,
but no, she won’t bother to get up off her duff –
she’s just finished eating, so she’s not even tempted.

Cassandra, in later evening, covers the heat vents,
and, purring, prowls the hallways and the stairs
searching for hitherto unforeseeable e-vents
and mice and spiders to catch all unawares.

Cassandra the cat, you furry door-mat, you owner of home and hearth,
you never pause to realize your net equivalent dollar worth,
but content you lie by fireside and sit on the laps and lick the cups of specially invited guests,
never believing that you could be freezing in cold and snow with nowhere to go in a darkened alley on a hungry belly, if it weren’t for your magnanimous hosts!

Cassandra the cat twitches her tail, looks up
with one eye, smiles, purrs and returns to her nap.

fractal

Romanesco broccoli, whole

This week I ate the most beautiful vegetable I have ever seen.

I was shopping at Golden Orchard, the organic greengrocer in St. Lawrence Market where I buy my fruits and vegetables, and I saw, on the shelf, something labelled Romanesco broccoli. I couldn’t believe what I was seeing. Instead of the usual bumpy shape of broccoli, this had cones that were perfect spirals of cones that were perfect spirals of cones that were perfect spirals of cones that were… I had to have it, this fractal broccoli, this fractali, this fraccoli, this… beautiful vegetable.

I was, in a way, sad to break it apart and steam it, but that’s what it was there for: if I had left it untouched, it would have wilted and lost its beauty anyway. Steamed, it was delicious, sweet, mild, more like cauliflower in flavour – which is right enough, as it turns out actually to be more of a cauliflower, although the difference between broccoli and cauliflower is not as clear-cut as you might think.

But this is not a vegetable tasting note. I am here to talk about the word that described this vegetable’s form, a word I have already used: fractal. The odds are fairly good that you have encountered this word before, and as likely as not you have some image in your head of swirling geometric shapes that are emblematic of the beauty of mathematics in some ineffable way. They have perhaps a fragile beauty in their tracery, or perhaps a spectacular one; you may see them as evidence of craft or as something quite the opposite; or you may see them as infractions of your sense of order, causing you to rack your brain to the point of fracture. Your taste of this word will follow.

But the concept of the fractal is something other than what most people think it is, and at root involves an elegant simplicity. Ah, yes, another term mathematicians love – elegant. Ordinary people think of silver and china and linen and formal wear; mathematicians think of power in simplicity.

Fractal comes from the Latin fractus, broken. This may seem odd for things that appear to be very complex but entirely connected. But what they are is breakable: break one into smaller parts and you will have smaller parts that look like a whole breakable into smaller parts. It is self-similar recursivity: it contains a replica of itself, which contains a replica of itself, and so on. It’s the hall of mirrors.

I’m reminded of the Apple Lisa computer – the computer (a precursor to the Macintosh that did not meet with great success) was actually named after Steve Jobs’s illegitimate daughter, but the marketing explanation was that it stood for local integrated systems architecture. Now, you might think that that is somehow a definition for recursivity, but what I’m coming to is that the in-joke among the engineers working on the computer was that it stood for Lisa: invented stupid acronym. The first word of Lisa: invented stupid acronym is of course Lisa, which stands for Lisa: invented stupid acronym, and so on.

Some other examples of self-similar recursivity are in order. An easy one is Russian dolls: inside each one is a smaller one, and so on; in the world of math, unhampered by the limits of materials, these could continue all the way down to the infinitely small, and even at the infinitely small be just like the original size, with an infinity of nested smaller parts. This is what those swirling geometric shapes do: at whatever magnification, you see something much like the original, a shape having smaller echoes of the shape that have smaller echoes of the shape and so on. You see this in the Romanesco broccoli.

Romanesco broccoli, ready for steaming

Adding the dimension of time, you can even see it in humans. A girl is born, grows, becomes a woman; then she grows a child within her, which is born, grows, becomes an adult; and so on. And in the greater web of life, what we eat feeds the future, as it has been fed by the past. Is each generation less than the previous? No – with infinite recursive self-similarity, the idea of absolute scale is meaningless. To quote Walt Whitman’s Song of Myself,

Before I was born out of my mother generations guided me,
My embryo has never been torpid, nothing could overlay it.

For it the nebula cohered to an orb,
The long slow strata piled to rest it on,
Vast vegetables gave it sustenance,
Monstrous sauroids transported it in their mouths and deposited it
with care.

All forces have been steadily employ’d to complete and delight me,
Now on this spot I stand with my robust soul.

Something else that bumps up against the limits of meaning is how many dimensions a fractal has. Consider one of those fractal illustrations you see. It’s made of a line with curves and angles. If you zoom in on the curves and angles, each one has the same curves and angles within it, but smaller. And so on. Now, this shape is just a line, so it has no area; in math, a line is simply one-dimensional with no thickness, only length. But say you try to measure its length. You might look and see what appears to be a measurable bit of line with curves. But inside each curve is a smaller curve that adds some more length, and inside each smaller curve is a smaller one that adds a little more length, and so on to the infinity of smallness. While material limitations prevent something like a vegetable from actually continuing to infinite smallness, an abstract line of this sort has no such limitation, and within each curve is an infinity of smaller curves, meaning that the line has infinite length, and every segment of it has infinite length. In one dimension it is too full; in two, it is too empty.

If the idea that a fractal could have zero area but infinite length doesn’t make sense to you, then good. It shouldn’t. It means we’re not measuring it the right way. Consider: if you ask about the area of a line or the volume of a square, you get zero, because you’re measuring it using too many dimensions. But if you try to get the measure the volume of a cube using two-dimensional squares, or the area of a square using one-dimensional lines, you will get infinity, because a square has no thickness in the third dimension, and a line has no thickness in the second. So one dimension is not enough dimensions in which to measure the fractal line, but two is too many. It actually exists with fractional dimensionality: 1.25, 1.33, 1.5… depending on the specific pattern.

It also stands to reason that my beautiful Romanesco broccoli, which is a three-dimensional object, represents (imperfectly, because of physical limitations) a shape that has more than three dimensions, and less than four.

I will stop there before I fracture the heads of any of my readers, but if you are intrigued by this, I recommend Yale University’s site on fractal geometry, which gives very clear and friendly explanations without dumping too much on you at once. A warning, though: to pursue a topic, you will find that you click a link, and that page has subtopics so you click on a link, and that page has subtopics so you click on a link…

Which brings me to the point that the World Wide Web, with its hyperlinks in hyperlinks in hyperlinks, is also, in its way, fractal. That’s right. You are reading this on a fractal that exists (by the calculation of J.S. Kim et al., arXiv:cond-mat/0605324v1) in 4.1 dimensions.

And you, too, of course, are part of a fractal. Like Walt Whitman, you are large, you contain multitudes, just as you and Walt are contained within the same fractal web in time, in the fractal folds of time. And you say, with Whitman,

The past and present wilt – I have fill’d them, emptied them.
And proceed to fill my next fold of the future.

solfatara

I’ve just come home from singing in the Toronto Mendelssohn Choir’s annual Festival of Carols. I really do love (most) Christmas music; it has such nice associations for me, of course, but the sounds are to my taste too. A good choir can make the harmonies so beautiful and clear, from crisply quiet to erupting with force. And it’s especially something when the organ blasts in – like a volcano, a cracking good Krakatoa of sound. So much air displaced! So many people moved! Such divine afflatus!

On the way to tonight’s performance, I happened to see, in a magazine I was reading, the word solfatara. Now, isn’t that a musical-sounding word? Sol, fa, like two notes (G and F), and tara as in taralala and ta-ra-ra-boom-dee-ay and so on. But I knew from the context that the note emitted by a solfatara is a steady one, often low, not always so pleasant, and don’t expect the smells of Christmas pudding and turkey and pine trees and so on. A solfatara displaces a lot of gas, but it’s not the CO2 of exhaling choristers. In place of divine afflatus we have chthonic – Stygian – flatulence. Miasma.

Yes, alas. A solfatara is a fumarole – a volcanic vent – that emits sulphurous gas. The G and F of sol-fa here may as well stand for gas and, uh, flatulence. Somehow I feel the word is too nice – perhaps if we rearranged it to something like asolfarta or something like that. But that would obscure the origin. You can probably spot sulphur in solfa; the word is Neapolitan Italian from Latin sulpha terra, “sulphur land”. It’s actually the name of a specific volcanic crater near Naples; from Solfatara we get the generic solfatara, just as from Geysir in Iceland we get the generic geyser.

That makes it rather more difficult to link to a Christmas concert. I might try to connect it to a reading done during the concert: “The Little Match Girl” used matches, which have sulphur… Bit of a reach, though. I can’t do “Gift of the Magma” – solfataras don’t erupt magma anyway. They just blow off steam, vent, produce noxious gases… Not a very Christmassy attitude, though common enough among those stuck in shopping malls. But that can be quite disconcerting. Better to welcome in the crisp, fresh air and the falalalalas.