Ten

One wonders about the value of a number that is not. We assume that it exists in its place of glory because we have ten fingers and use them to map the universe. But if you ask someone what the ten digits are, they often say, "0-1-2-3-4-5-6-7-8-9." Sometimes, they take their cue from the keyboard or keypad layout and say, "1-2-3-4-5-6-7-8-9-0" or "7-8-9-4-5-6-1-2-3-0" (this last is pretty rare, but I've seen people visualise it like that).

No ten, even though there are ten digits. It would probably be the same if we had some other counting system or number base. There would be some mystical power associated with having to punt our digits out of the directly enumerable. Wait, let me rephrase. There is some sense of mystical completeness about counting up to the number at which you no longer have digits to proceed beyond.

Toes? Well, I suppose they would lead to metric feet.

Nine

If eight is secure, the frame of (n-1)-ness in a 3D universe of experience, then nine is shifty. For we are decimate humans, bound to our handheld digital computers, the split-processing multi-tasking things at the ends of our wrists. We count on our fingers, and they do not often disappoint us.

But they are where the great power of the number nine lies. For the number nine is one less than the base, 9 = 10-1. And because of that, it is the seed of many interesting patterns that all rely on having fallen short of the glory of ten.

Some people marvel at this. I don't. I think it's more wonderful to see that 1/7 is 0.142857…. See? Six repeating digits gained by doing a reciprocal on seven.

But nine is nice; it is three by three, and the nearest thing we have to numinosity in the palm of our hands.

Eight

Why eight? The corners of a cube? The permutations of the trigram, that ancient binary oracle? The major points of the magnetic rose, encompassing? Or is eightness so revered because of our bilateral pseudo-symmetry?

It is possible to build up any kind of theology — any kind of conspiracy theory, numerology, arcanum — around any number. Or set of numbers, even. Oddly enough, it boils down to empiricism. The numbers we like the most are the numbers we like the most; there may be no other reason behind it but aesthetics.

But eight is a secure frame in a three-dimensional universe. We see it way too often.

2800

Always, the numbers. Somehow, mysterious numbers trigger thoughts as much as scents or symbols. When I see '60', it is as pungent to my mind as the scent of ammonia or the sight of a red circle.

Today, it is 2800.

Seven Subjects

If one is the loneliest number, seven must be blessed. But seven is an odd number in more ways than one.

Seven is not a handful, and neither is it two. Seven is not a crowd, but is two crowds with one left over. Seven is not eleven, but is its frequent rhyming partner.

And if you had to study seven subjects, which ones would you study? And would they thank you for it?

Algorithmic

At some stage in my life, I was trained to convert processes into algorithms. The great thing about this training is that it is of great utility in many other disciplines besides the one in which I learnt this.

Take for example the definition of a natural number. It is easy (although it might be tedious) to prove if a number is a natural number by using this algorithm (which is something I just came up with, but which I'm sure anyone can do likewise):

1. Accept a given real number, x.
2. Is the number zero? If so, the number is/was a natural number and you terminate.
3. Subtract 1. Is the number less than zero? If so, the number was not a natural number and you terminate.
4. Repeat step 3.

Of course, there are possibly more efficient ways of doing this, but this way is 100% effective. Note: some mathematicians don't treat zero as a natural number; if you're one of them, just change 'zero' in steps 2 and 3 to read '1' instead.

You can do this with all kinds of things for the sake of fun, profit, indulgence, curiosity or perversity. It helps you do things like mentally convert any kind of distribution to one that can be compared to a normal distribution, for example. It can even help you write the minutes of meetings before the meeting is carried out. Seriously. Used to do that all the time, they were that predictable...

May The Fours Be With You

Every time this date in the year comes round, I think apocalyptic thoughts. It's 4/4, that mystical time or timing, whether you are oriental or occidental, or purely accidental. The world divides into four ages, the apocalypse has four horseman, and the four gospels and their four evangelists are signified by four different beasts. There are four archangels, and four corners of the world and four cardinal directions and four elements of the material world.

But most of all, there were four Beatles. And once in a while I dig up the old music and go on a magical mystery tour. It is with that in mind that I present to you the lyrics to one of the few songs that was ever written deliberately to both communicate and confuse. I also indulge in a little bit of Shakespearean taming; it was an intelligent and largely pleasing session I had this morning, with you-know-who-you-are. Enjoy.

I am He as You are He as You are Me
And We are all together
See how they run like pigs from a gun
See how they fly
I'm crying
Sitting on a cornflake
Waiting for the van to come
Corporation T-Shirt
Stupid Bloody Tuesday
Man, you been a naughty boy
You let your face grow long

Chorus:
I am the Eggman
They are the Eggmen
I am the Walrus
GOO GOO GA JOOB

Mr. City Policeman
Sitting pretty little policemen in a row
See how they fly
Like Lucy in the sky
See how they run
I'm Crying
I'm Crying
I'm Crying
I'm Crying
Yellow matter custard
Dripping from a dead dog's eye
Crabalocker fishwife
Pornographic Priestess
Boy, you've been a naughty girl
You let your knickers down

(Chorus)

Sitting in an English garden
Waiting for the sun
If the sun don't come
You'll get a tan from
Standing in the English Rain

(Chorus)

Expert Texpert
Choking smokers
Don't you think the Joker
Laughs at You?
Ho-Ho-Ho-Hee-Hee-Hee-Ha-Ha-HA!
See how they smile
Like pigs in a sty
See how they snide
I'm Crying
Semolina Pilchard
Climbing up the Eiffel Tower
Elementary Penguin
Singing Hare Krishna
Man you shoulda seen them
Kicking Edgar Allen Poe

(Chorus)

(Oompah, oompah stick in your jumper!
Everyone has one, everybody has one!)

If you listen carefully to the whole song, you'll hear a lot more random stuff and even a few lines from King Lear...

Gaming the System: A Brief Introduction

The rise of Atlantis has always been predicated on quantitative sorcery. The numeromancers and numerologists of the Thunderbolt Circle have always looked back to the time of the Gnome and his infamous 1954 thesis on 'How to Look Rich by the Standards of the World'.

Let me put it to you in simpler terms. It's not how much you own, or how much you have, or how much you can move, that necessarily makes you rich. It's how 'rich' is defined. So if you want your country to look rich, you ask around and see how people define 'rich'. Then you rig the outputs (not in the sense of 'bias the game', but more in the sense of 'setting the sails') so that the nation (or the game, or the ship) appears to be heading towards the right direction as far as 'rich' is defined.

This prestidigitation (also known as 'extremely fast number-management process'), if successful, will give rise to the impeccable claim that you are rich by any official measure. Whether you are rich or not in reality does not matter, since all that matters is what the numbers are supposed to say; all else is ineffable, immeasurable, beyond the terms of the discussion.

Let me put it to you in more relevant (to some of us) terms. Let's say your bank balance is US$500,000. You put the card into the machine and ask for a statement of account, and that is what is shown. But how do you know how much that money is? How do you know if you are rich? What if, unbeknownst to you, you have slipped into some sort of timewarp, and US$1,000,000 is actually the cost of a loaf of bread? Well, you'd have to ruefully remind yourself that half a loaf is better than none.

It's all about numbers, to some people.

But let's think about what happens when an education system begins to experience this sort of numerical subversion (or subvention, as some inventive people have called it).

In order to establish how good an education system you have, you decide that only quantitative measures are used. Even when you bring qualitative measures in, you use numerical rubrics and a final score expressed as some number. Worse, you require trend lines for everything, including the development of human virtue or social behaviour (for example, what percentage of the student population expresses confidence in the long-term prospects of your nation).

You decide to create an examination system that is vulnerable to the same prestidigitation. Everyone gets a number. The smaller, the number, the closer to Number One you are. The minimum magic number is 6. But if you are clever, this becomes 4, or 2, or zero. Or perhaps you make it the other way round; the higher the number, the more you've scored. If you get 45, that's the highest; if you get anything approaching 24 and below, time to start looking at the fine print.

The problem is of course that while numbers are good things to have in analysis, a lot of their relevance depends on two things: the assurance that the system is not being gamed in such a way that it fails to measure the quality of education (validity), and the assurance that everyone who does the same thing gets the same mark (reliability). If you look at these two things, you will realise that gaming the system — by doing things which are not educational but are number-manipulating or system-gaming — can give you marvelous results.

It's a bit like parents who insist on helping their kids with homework projects which are graded. You're not measuring the child's ability, but something else (the ability of the child to con the parents into doing it, the pressure society exerts on parents to do unethical things, etc). And if you build the whole edifice on it, the edification is not real.

SG Wages

I was watching a phenomenon last night. There was a young man, certainly not an investment broker but with the sort of income and tastes that you might associate with one. He was dressed in a blue outfit, not his usual one, and looked rather harassed, as if he had come home one day to find that all his leather shoes had turned to sandals.

Out of idle curiosity, I decided to see if my memories of his chosen sporting environment were correct. Yes, indeed; this young man named 'SG' was paid approximately £120,000 a week; which works out to about £17,300 a day. It is a mindboggling figure. If you were to type it into the little Google window and convert it to SG dollars, that would be about SGD 40,000 a day.

It put me in mind of a certain unsavoury incident that SG was involved in. Apparently, he was accused of participation in the sort of thing young men get up to when soused, and carted off to the local nick. The amount of income SG would have earned for 3 days in jail would have been 120,000 in SG dollars, just for sitting at Her Majesty's convenience for a while. I'm sure his fellow detainees would have been in awe.

These days, it seems that the wages of being a good ball-kicker are far greater than anything a conventional education might bring. That said, watching SG perform in his chosen colours, or even in his away kit (which makes him look as if he is from the other team in town), is an education all of its own. He is a great sportsman, even on a reasonably bad day; and in mitigation, there are about ten other sportsmen in his field who are paid more than he is throughout the world.

The Power of Number

I came home yesterday and promptly fell asleep. It's been a gruelling three days or so, at the Temple of the Red Queen's Race. Let me digress a bit before I continue.

=====

I don't know why people give such awful names to places. I have in mind two specific names: 'Cineleisure' and 'Leisuredrome'. I shall now enlarge on this digression etymologically.

'Cineleisure' is a sort of reverse-portmanteau-abomination-construct. It is a contraction, I think, of 'cinema' + 'leisure'. 'Cinema' comes from the Greek kinema ('movement') and hence 'cine' comes from Greek kinein ('to move'), while 'leisure' is related to 'lease', 'license', and other words which imply a relaxation of control. 'Cineleisure' means something like 'a loss of control over one's movement', and even in modern English, it should mean something like 'moving while not really bothering to move'.

'Leisuredrome' is just as bad. The Greek dromos means 'a running track' or 'a race course'. This of course is something like a reversed version of 'Cineleisure'. It probably means 'a place to run around recklessly'. I seem to remember that it had a skating rink in it, so I suppose that might have been part of the idea.

The Red Queen's Race is, of course, a concept taken from Lewis Carroll. The Red Queen had to keep running just to stay in the same place; it's somewhat related to the concept of Red Tape, which is created to keep people in the same place despite running around a lot.

=====

Digression over, let me just say why I was so sleepy when I got home. I've had to use my brain a lot, and the food supplied was simple and extremely good. I had a sublime pastrami-on-onion-rye sandwich, a wonderfully thin apple tart with fresh vanilla ice-cream, and a host of other treats, all washed down with delicious caffeine sources. All this makes one sleepy in a pleasant sort of way.

The upshot of the whole experience was that I am now a certified provider of 'digital literacy' and 'technology infused learning'. This amuses me a lot, although I am happy to have obtained the certification; I've always felt that 'digital literacy' should mean 'the ability to talk by using one's fingers'.

But what really hit me in the head this afternoon was the thought that if not for an accident (or incident) of number, we would be ten years faster in adopting many good practices. What I'm referring to is the phenomenon known as 'Y2K' or 'the year 2000'.

The year 2000 AD was the last year of the second millennium (which ran from 1001 to 2000, just as the first one ran from 1 to 1000). A lot of people had invested into the memetic package known as 'the 21st century', in which all things were supposed to be different and the future was supposed to have arrived.

Simply because of this cultural illusion fostered by the calendar, people waited till the year 2000 (when the first digit of the year designation changed) or 2001 (especially after Clarke and Kubrick's 2001: A Space Odyssey) to do new stuff. A lot of the new stuff came out in the late 1980s or the 1990s, but many people didn't bother with it, because they were subconsciously awaiting the new millennium. That is why a former superior of mine claimed Apple was dead and refused to do anything useful with IT until 2001, for example.

Because of the power of number (or at least, the terrible illusion this calendar case engendered), we wasted a decade or more.

Ordinal v Cardinal

The other day I was chatting with a hummingbird. Said hummingbird asked, "What's the difference between 'ordinal' and 'cardinal'?"

I was tempted to reply in the manner of my immediate male ancestor, "The former comes mostly in black, the latter comes mostly in red — like in roulette, you know. The zero is both black and red and hence is neither ordinal nor cardinal, or could be both."

Fortunately for the hummingbird, I chose to give a less spurious and more serious reply.

'Ordinal' comes from Latin ordo, a sequence or progression (hence, 'order'). 'Cardinal' comes from Latin cardo, a hinge (and hence, a critical point). Ordinals are therefore things which depend on sequence and do not stand on their own, while cardinals are things that stand on their own.

For example, 'first', 'second', and 'third' are ordinals which are linked to the cardinals 'one', 'two' and 'three' respectively. If you think of 'one', 'two' and 'three' as 'counting numbers', then they are being thought of in an ordinal sense, since they are being thought of as part of a counting sequence. But if you think of them as 'integers', then they are being thought of in a cardinal sense, since an integer is literally 'intact', 'whole' or 'untouched' (with a secondary sense of 'standing upright and alone').

Here is where we find the idea of 'extraordinary' — something which is beyond or outside the normal order or sequence of things. Related to the same root is 'coordination' — having sequences of events that are related to each other.

But beware of false etymologies: 'cardinal' has nothing to do with 'cardiological', despite the common association with the colour red. The latter comes from the Greek kardia, which means 'heart'.

Celebrationic

I was just reflecting, in my endless peregrinations over the Periodic Table, that it is fitting to see the elements that have the honour of being #10, #25, #50, #60, #75 and #100 – all the numbers we like to celebrate in major anniversaries.

#10 is of course neon, the 'new one' as its name means in Greek. When ionised hot, it glows red. How cheerful and symbolic of good fortune!

#25 is manganese, that oddly unappealing neighbour of iron, found in nodules and probably best known for its oxo-salt compound, the ferocious potassium permanganate.

#50 is tin, and not gold; that seems like a sterling reminder of how the hand can deceive the eye.

#60 is neodymium, the 'new twin' – one of those elements nobody ever remembers.

#75 is rhenium, for once a truly valuable metal – it is probably the rarest metal that can be used in engineering and metalwork.

#100 is fermium, named for Enrico Fermi – a rare talent, this; his name is found in an element, a class of subatomic particles, and a rather famous laboratory.

Oh very well, you've caught me out. I was just being idle and entertaining myself again.

The Archangel Of The Perverse

I have known for a very long time what the 'imp of the perverse' is. The term crops up in a short story by Edgar Allan Poe, and is a figure of speech that describes a self-destructive impulse in which one does what one should specifically not do.

But just this other day, a wingman raises the term 'The Archangel of the Perverse'. Neither he nor I could imagine whence it came, and so I did some digging. It isn't to be googled (although I imagine it soon will be). But I do find the two words in distant and uneasy relationship in the very short epistle to St Jude (patron saint of lost causes), in the New Testament, and the Old Testament book of Numbers.

In the former book, the canonical Bible's sole archangel, Michael, is inspired to rebuke Satan in a paragraph that seems to imply that there is only one Archangel, and if Satan ever was one, he is one no longer. In the latter book, the Angel of the Lord stops Balaam the false prophet and arraigns him for animal abuse ('Wherefore hast thou smitten thine ass these three times?' says the King James Version), making it clear that whatever Balaam's intended course of action, it is perverse.

It would seem that the commonality between the two passages is one of self-destructive behaviour, in both cases rebuked by the highest of divinely-aligned powers. Michael, the power who is said to oversee Israel's historical course, must surely have his hands full in these dark days.