On counting

Who is your favourite character from the Muppets?MissPiggy

Excluding Miss Piggy of course, because She is such a great hero and role model for us all, not to mention such a powerhouse amongst pigs, that I don’t think it would be fair to make the rest of us compete on the same playing field as Her.

Mine is The Count. I loved him from the first moment I saw him. There are so many things about him that are absolutely great. Like, he’s a vampire, yet he isn’t all that scary. He’s a really sharp dresser, with an intriguing, Bohemian-sounding (literally) Eastern European accent. He’s highly educated, loves organ music, and is always happy. He made capes cool long before Harry Potter came along.

Image result for the count muppet

And he counts. Everything. As character catchphrases go, they don’t get much better than “I love to count! Mwu ha hah.”

For me, he is a soul mate.

My relationship to counting is not so much one of love as addiction. I can’t help counting things. I feel a responsibility to the world, to make sure that things are adequately counted, so that it is known how many of them there are. That way, things will remain under control.

No doubt, that’s why they tell women in labour to count the seconds between contractions.

Now those of you that know me, and know how much I love maths, might think that this is just a manifestation of that general phenomenon. But it’s not. My love of maths is about depth, symmetry, harmony, aesthetics, the joy of finding a new pattern. Whereas my need to count is just a tic. I count steps when I’m jogging, magnets on a fridge, bricks on a wall. I do push ups on Tuesday and Saturday mornings just so that I can count them out loud in German – because that sounds so much more profound than counting them in English with an Australian accent. I count seconds between lightning and thunder, seconds of held breath when trying to dispel hiccups, and number of children in a class walking across the road on a school excursion.

In nothing is my need to count more apparent than in counting the storeys of multi-storey buildings. I put this down to growing up in Canberra in the seventies, when the only high-rise buildings in our known world were two office towers in Woden, of which I think one was about twenty storeys. Whenever I went there, I needed to count them again, just to make sure none of them had worn away or otherwise disappeared. It’s odd then that I no longer remember how many there were. I’m sure it was at least twenty, and not more than twenty-five, but I can’t tell you more than that. You’ll have to go and count them yourself.

Those high rise buildings symbolised sophistication, cosmopolitanism, urbanity, everything that Canberra then wasn’t. We even had a café owner that had to fight the council for years just to be allowed to have outdoor tables and chairs – something that must have been viewed suspiciously as Too European (meaning continental Europe, not Britain, which was Home) and in those days to be European was considered only one or two steps away from Communism.

But nevertheless, those Woden towers – so many storeys – my how grand! To a little boy, those big buildings in Woden were very exciting, although I never went inside one, and still haven’t.

When I got bigger, I sometimes got to visit Sydney then, ultimately, came to live there. I thought it was amazing how many tall buildings they had. There were several skyscrapers, the largest being the Australia Square tower with fifty storeys. That ruled the roost for more than a decade, to be eventually surpassed in 1977 by the MLC Centre with sixty storeys. Like a true country bumpkin, I would walk up to the tower, look at the ground floor, then slowly tilt my head back until my gaze reached the top – a tiny point in the sky, seeming so far away.

But I didn’t count the storeys. There was no point. You always lost track. Anyway, the really impressive thing was not these few skyscrapers, but that the average building in the CBD was at least four storeys high, often six or more. Coming from Canberra – a sea of one-storey bungalows – that was the real shock – that just ordinary street buildings could be so high. The fact that most of Sydney was a sea of boring bungalows just like Canberra didn’t seem to matter when you were in the CBD.

So I started counting. For every building I passed I had to start at the bottom and count until I got to the top – was it five, six or seven? No, wait, there’s a little penthouse, or a row of dormer windows just below the roof, so that’s eight. Unbelievable!

I have lived in Sydney for more than half my life now, and worked in the CBD most days. But I still have to count any building with more than two floors. If it’s more than four then I feel a small surge of pride – like ‘that’s proper urban that is’.Paris_Hausmann

My family took me to Europe this last northern winter. We stayed on the fifth floor of an apartment building in Paris (that’s sixth floor for Americans). I think there were seven floors altogether – the top one being attic style with windows peeking out through the dark-grey, zinc roof. In Paris nearly all buildings are between six and eight storeys, because it was all knocked down and re-built in a period of about twenty years under central control, directed by Baron Hausmann. You’d think I could have relaxed knowing that all the buildings were of height seven, give or take one but NO, I had to count most of them that we walked past, just to make sure. After all, if I didn’t do it, what if nobody else did? Then it wouldn’t have been counted and where would we be?

Same thing in London. At least there’s a bit more variety in height there (don’t tell anyone, but sometimes I wonder whether the much-praised uniformity of Paris’s Hausmann streetscapes is just a little bit boring). And of course Liverpool.

Anyway, next time you are at a musical show and you just have to know how many chorus members there are, don’t be shy. Go ahead and count them. Then tell your companions after the show. They’ll be glad you did. Certainly the Count and I will.

Andrew Kirk

Bondi Junction, November 2018

Let’s all use the word ‘Interlocutor’ more often

Today is international polysyllablitis awareness day. I hope you can spread the word so that people will better understand this debilitating condition and try to support those that suffer from it.

Polysyllablitis is a communication disability that primarily affects people that read too many fancy books. The main symptom is a swollen vocabulary, leading to frequent difficulty in finding an acceptable word to express a concept they are trying to convey. Such difficulty typically manifests in uncomfortably long pauses mid-sentence, because the speaker was about to say that the proposed expedition to a nightclub would be ‘inimical to his health‘, but didn’t want people to think him a ponce for saying a fancy word like ‘inimical‘, yet the alternatives ‘it would make me feel bad‘ or ‘I’m tired‘ (average syllable count per word = 1.0) refused to present themselves to his desperately searching mind.

For this to happen just occasionally – say every couple of months – is manageable. Many people have such experiences. But people with really serious polysyllablitis (known as PSI to health and remedial vocabulary professionals) can suffer such attacks as often as several times a day. At such frequencies it can become terribly debilitating. Sorry, I mean it makes the person feel really bad.

Chronic sufferers have complained of persistent diffidence (meaning they often feel shy), disorientation (they feel dumb or lost), isolation (they feel lonely) and melancholy (they feel sad).

I have studied this phenomenon (sorry, I mean thing) for many years now. I think there is hope for the sufferers, as long as they don’t get excluded (shut out) from society. That’s why we need this awareness day. If people can keep a look out for others that may be suffering this malady (it makes them ill) they will be able to find ways to help them, reassure them (make them feel good) and put them on the road to rehabilitation (get better).

The best way to help these unfortunates (poor guys) is to include them in your conversations. When they say an unnecessarily fancy word, or get stuck mid-sentence with that look on their face that says they can’t remember the normal-people’s word for ‘lugubrious’*, the best thing to do is to gently correct them, remind them of the normal-person word while making clear that we still love and accept them. (*it’s ‘sad’). Studies have shown that these inclusionary strategies (being nice to them) are in most cases highly efficacious (they work).

However, in my years of study, there is one word for which I have simply never found a way of translating it into normal person speech, and that is the word ‘interlocutor‘ – being ‘the person with whom one is having a conversation‘. I have searched in vain for a simple alternative. The closest I’ve seen is ‘discussant’ but that has the dual problems that (1) it’s ugly and (2) I suspect it’s not a real word.

The next most reasonable alternative seems to be to replace the word with its definition ‘the person with whom one is having a conversation’. But that doesn’t really help much, as that ‘whom’ is bound to raise eyebrows, not to mention the monarchical ‘one’ (sorry – I mean like how the queen would speak). Plus inserting that long string of words into a sentence raises the risk of apparent poseur-ness because of the length of one’s sentences.

‘He’s always interrupting those with whom he is having conversation‘ just doesn’t have the pizazz of ‘He’s always interrupting his interlocutors‘.

I doubt Hemingway would approve.

It wouldn’t matter if it was a useless word, like that silly old ‘antidisestablishmentarianism’ that schoolboys used to quiz each other on, but nobody ever used in a genuine sentence. That was, until the Guinness Book of Records people wanted to get in on the act and invented ‘floccipausinihilipilification’, just so that people would buy their book to find out about the new record-breaking word.

Of course if you want a long word that’s actually used by proper people, it’s supercalifragilisticexpialidocious, which at 34 letters is longer than either of those non-words to boot. Plus it’s used by Mary Poppins, who is cool and not anything like a social reject that got her head stuck in a dictionary, so it must be OK.

But, unlike antidisestablishmentarianism, interlocutor is not a useless word. How can one talk about conversations one had yesterday without using it? More importantly, how can one give counselling and therapy to PSI sufferers if one cannot tell them useful things like ‘try to use the same words that your interlocutors use‘? The word is simply too useful to discard. I find myself needing to use it at least seven times per day on average. I’d be lost without it.

I can only see one way out of this conundrum (tricky thing). That is to make interlocutor an honorary normal person’s word. We could do that by all making an effort to use it at least once a day. Then before long it would seem as normal as ‘but’. There are precedents for this. Normal people use the pentasyllabic ‘qualification’ when talking about who might get into the finals in the footy, and the quadrasyllabic ‘ceremony’ when talking about who earns the right to humiliate themselves in the next round of a reality TV show. So I think, If we all make an effort, we can create some space for ‘interlocutor’ in normal people’s language.

I leave you today with these two requests:

  1. Please keep an eye out for PSI sufferers, and try to be kind to them (and help them to get better); and
  2. Try to use interlocutor as often as is consistent with common decency.

Just remember, no matter how strange and scary they seem, every PSI sufferer is somebody’s son or daughter.

Andrew Kirk

Bondi Junction, October 2016

Why mathematics is like plumbing

Mathematics is a bit like plumbing, don’t you think?

Not that I’ve ever done any proper plumbing. Electrical work I can manage, having paid careful attention when doing electricity in our high school physics classes. But plumbing is another matter altogether. Getting those joints water-tight requires just a bit more dexterity than I can manage.

That’s why it’s like maths. It’s those joints that are the problem. Let me explain.

Often in maths, when one is trying to prove some important result, one creates a series of theorems that build on one another to reach the final conclusion. If a proven result along the way is substantial enough – say if it takes more than half a page to prove – we call it a ‘theorem’, otherwise we call it a ‘lemma’. But a lemma is really just another theorem, only a bit smaller than usual.

Now a theorem is something that reads like this:

IF <bunch of premises> is true THEN <conclusion> is true.

Mathematicians try to make their premises as few and weak as possible, and their conclusion as strong as possible. For instance, we could prove a theorem that

IF x=2 THEN x2>0

This theorem is true, and easy to prove. But we can either make the conclusion stronger (ie more specific), turning it into say x2=4, or we can make the premises weaker, turning them into say ‘x is a real number’. We can’t do both however. We could, if we wanted, make the premises weaker and the conclusion stronger, but not by as much as what we just did. We could prove the theorem:

IF x>1 THEN x2>1

Now our premise is weaker (less specific) than before, and our conclusion is stronger (more specific) than before.

How this is like plumbing is as follows. Say we want to prove theorem D and, to do that we need to first prove theorems A, B and C. This might be because we need A to prove B, B to prove C and then C to prove D. So the conclusion of A becomes a premise for B, the conclusion of B becomes a premise for C and so on.

Now unless D is very easy to prove (eg like proving IF x=2 THEN x2>0), we won’t have much room for manouevre. If we make the premises of D too weak then we won’t be able to prove the conclusion, which is our ultimate goal. On the other hand, if we make the premises of D too strong we won’t be able to satisfy them with the conclusion of C.

This is like connecting a series of pipes (got you! And just in time. You thought I’d never get around to the plumbing didn’t you?). Each theorem is a pipe. Each pipe is a straight cylinder except that, at its inflow end, it flares out like a trumpet bell and, at its outflow end, it narrows. This enables pipes of the same diameter to snugly fit together. The end of each pipe has to fit inside the end of the pipe immediately downstream from it if the fit is to be tight enough to avoid a leak.

The inflow end represents the theorem’s premises. The stronger the premises, the narrower the inlet, and the stronger the conclusion the narrower the outlet. Now what happens if we make the premises of pipe D too strong? Then the downstream end (conclusions) of pipe C may not be able to fit inside the premise end of pipe D. If that happens then we need to narrow pipe C, which means making its premises stronger – hence a narrower inlet. That may then create a problem with fitting B into C, and so on. So if we are too ambitious in what we are trying to prove at D, that can create problems all the way back up the stream so that our premises at A are so narrow and restrictive as to make the whole combined theorem of no practical use (because the premises at A will hardly ever be satisfied). The theorem might only apply to left-handed, bearded Scottish taxidermists whose first and last names both begin with ‘X’.

Or, starting at the upstream end, if we start with premises that are too weak – non-specific – at A, our whole series of pipes will have to be so wide that the eventual conclusion at A will be as generalised as an astrologer’s forecast (‘Today will be a good day for working hard and believing in yourself!’). How can I relate this diffuse outcome to plumbing? Hmm, well if the pipe is too wide at the outlet then perhaps there won’t be enough pressure. Yes that’s it, no pressure. It would be like trying to water the garden with a big drainage pipe instead of a hose.

What one finds oneself doing then, as one tries to make the connection from A all the way to D, is going back and forth, loosening a premise here, tightening a conclusion there, then finding that with the premise we just loosened, the conclusion coming out of that pipe is too loose (wide) to fit into the next pipe so we tighten the premise again or alternatively look at the following pipe to see if we can get away with loosening the premises for that.

And now for one last bit that is completely unrelated, except that it also is like plumbing. Recently I’ve been working on something called Homology Theory, which is what you need to be able to tell the difference between a sphere and a donut. This discipline uses techniques of algebra to identify differences between different shapes. It often makes use of chains of things called modules, connected by functions, which are like arrows leading from one module to another. It’s a bit like how you can make a model of a molecule using plasticine for the atoms and straws for the chemical bonds (the modules are the plasticine and the functions are the straws, except it’s important to remember that the functions have a direction, as if water were flowing through the straw). An important part of a function going out of a module is something called the ‘Kernel’, which is a bit like the nucleus of the atom. Each function in a sense ‘projects’ the module from which it starts onto the module at which it ends, and the projection it makes is called the ‘Image’ of the function, which will be part or all of the target module. We call a chain of functions and modules ‘Exact’ if the image of the function coming in is identical to the Kernel of the function going out. Most chains are not Exact, but when a chain is Exact we can prove all sorts of useful things.

So this is more plumbing. If the pipe/straw (function) coming into a joint (module) is too wide (has too big an Image) it won’t fit the Kernel of the pipe/straw (function) going out. Then the liquid will spill out, we’ll have a big mess and we’ll never be able to tell our donuts from our spheres, let alone our circles and Klein Bottles. But if it all fits neatly, we’ll have an Exact Sequence, there’ll be no spillage, and we’ll be able to prove all sorts of useful things without needing a change of clothes.

I’m rather pleased with how many different metaphors I managed to mix together in that last couple of paragraphs. It leaves ‘to take arms against a sea of troubles’ far behind. I think the clarity may have suffered somewhat as a consequence though. Never mind.

Andrew Kirk

Bondi Junction, December 2014

On mending socks

How fine it is to mend things.

There is a real satisfaction in tinkering with a faulty object, examining it, taking it apart, finding the source of a problem and then coming up with a way to fix it. The satisfaction comes partly from the intellectual stimulation of trying to solve a puzzle, and the pleasure in successfully solving it. Then there is the pleasure in learning something new about the world. Once I fixed a metronome and was delighted at what I learned about the ingenious clockwork mechanisms that were concealed within the case.  I like to think of those creative and resourceful engineers and craftspeople that had remarkable ideas like putting a little doodad here that would tip the whirligig there on every third revolution, which would, via a series of additional baroque interactions, make a little bell chime.

What a brave new world it is, that has such people in it!

But the most important source of satisfaction from mending things is its contribution to sustainability. Every broken toaster, metronome or lamp shade mended is one less piece of rotten landfill and one more set of valuable resources saved to be used for another five or more years.

Quality control in manufacturing is almost non-existent these days, except for products where faults can cause serious safety hazards. It is much cheaper for a manufacturer to dispense with quality control and simply replace any faulty items returned by customers than to maintain an expensive quality management process in their factory. Why do your own quality control when you can get your customers to do it for you, at no cost?

The consequence of this is that an older, mended object is often better quality than a new replacement, because the older item may have been made in a factory that paid more attention to quality.

My abilities at fixing things are very constrained though, and venture hardly at all into the domain of Soft Things. I can, only just, sew a button on a shirt. It will usually stay on for a while, but it’s not a pretty sight. But beyond buttons I am at sea. That is not generally a problem because my partner is highly skilled with soft things, so between the two of us we manage to take care of most feasible mending.

But there is one terrible exception to the portfolio of challenges with which we can cope, and that is the rehabilitation of socks. What I wonder is ‘Why does nobody darn socks any more?’.

Now I am not asking that as a curmudgeon hankering after the days of his youth, when he could barely walk about for risk of getting stuck by the needle of one of the innumerable sock darners with which he was surrounded. No, my youth was in the post-sock-darning era. My mother was an avid mender of all sorts of garments. Some of my school clothes were more patch than original material. But I can’t recall her repairing a sock (Perhaps she did and I have forgotten).

I know there was a sock-darning era, because I have read many times in books of people performing this wondrous act, but it seems to have pre-dated my life.

The art seems to be long gone, yet it seems to be so useful, that one wonders why it has gone.

Let me be perfectly frank about this: I own many, many pairs of socks. So when it comes to things sock-related, I modestly consider myself to be something of an expert. And I have noticed a tendency of some of my socks to develop holes at the end of the big toe. I stubbornly wear those socks for a while, hole and all, but usually end up having to give up and throw them away under the weight of protestations from my family at the shame it brings them to have a father or partner walking around with holes in his socks.

Think how proud they would be instead, if passers-by could all see that my socks had been mended, perhaps with a striking splotch of scarlet thread on the end that darned over the hole. What a grand world that would be, in which people had access to sock darning services, whether from talented friends and family, or from hired artisans.

I don’t know why the art of sock darning disappeared. Some suggest it is that the types of materials used to make modern socks make darning difficult and unreliable. But I blame children’s story books. Let me give one example. Doubtless there are many others.

The other morning I was doing reading assistance with children at the local primary school. The story that my charge chose to read was ‘The Hole in the King’s Socks’. It tells the story of a king that has a hole in the toe of one sock, and gets a cold toe. He seeks advice from all his courtiers as to how he should remedy this, and none of the remedies (eg stuffing it with leaves, as the Royal Gardener suggests) work.

In the end, the Queen suggests to the king that he knit himself some new socks. He rapidly learns to knit, makes some socks, puts them on, and they all live happily ever after, with warm toes.

It is nice that it encourages learning new skills but other than that, this story is wrong on so many levels!

Firstly, why does he need to make two new socks when only one is damaged? We can see from the illustrations that the new socks are identical in colour and pattern to the old, so there is no problem of mismatch (not that that would be sufficient reason to throw away a perfectly good sock anyway).

But more importantly, if he can learn to knit a sock, why can he not learn to darn, and simply darn the hole? That would use only a tiny fraction of the wool needed to make a whole new sock. Yet that option was not even considered. Presumably both the old socks – the pristine one and the only-slightly-damaged one – were consigned to landfill.

I ask you, what sort of message is this sending our children? “If something is faulty, just throw it away and get a new one”. Whether you make it or buy it makes no real difference. The resources used in the manufacture of the old thing are still wasted.

As you would expect, I gave my young, impressionable reader a moving homily on the foolishness of the king in throwing away his socks, and how we should always seek to mend rather than replace. I am not sure if it had any effect. She seemed more interested in trying to balance her pencil on its end while tipping her chair backwards. But one tries to plant the seeds of wisdom, you know. One never knows when they might take root and grow.

In the past couple of decades we have seen a renaissance of previously unfashionable crafts such as knitting, quilting and crochet. Is it too much to hope that the craft of darning socks will also make a comeback? If I can only live long enough to see that, then I think I will truly be able to die happy.

Andrew Kirk

Bondi Junction, July 2014



The Inadvertent Whistling test

Much to my surprise, I found myself whistling a little snatch from a Monteverdi madrigal the other day.

The reason this surprised me is that I don’t really ‘get’ Monteverdi. I bought a CD of his madrigals a while back, to try to learn to appreciate his music, but it never really caught on. I decided I must be too much of a modernist, too caught up in the rebellious works of 18th century radicals like JS Bach to pay attention to an old-fashioned 16th century fuddy-duddy like Monteverdi. The songs never seemed to me to have proper ‘tunes’, instead just wobbling around in what seemed a rather scruffy series of notes that lacked any harmonic or rhythmic structure I could recognise.

So I gave up. I had to concede that I’m probably just not deep enough, or maybe not artistic enough, to understand Monteverdi.

But then came the magic of Windows Media Player’s Shuffle setting. I have installed my classical music collection on the hard drive of my work computer so I can listen to it while I work. I never know what it will play next (well, actually sometimes I can guess, because Microsoft’s pseudo-random number generator is a bit too pseudo and not enough random – lift your game, Mr Gates!).

The player has 2,296 classical tracks to pick from, but some of them are quite short, so you often hear the same thing a couple of times within a few days. Last Tuesday the computer decided to play a Monteverdi madrigal just before I went home. I had completely forgotten about it by the time I packed up and got into the lift but then, blow me down if I didn’t suddenly realise I was whistling it to myself. Maybe a series of pseudo-random exposures to his songs, unnoticed by me as I was hard at work regulating financial institutions and investigating mathematical models, had taught my subconscious mind to appreciate his finer points. Was I becoming a Renaissance sophisticate at last?

As soon as I get time, I plan to go and listen all the way through my Monteverdi album, to see if I can enjoy the whole thing now.

This pleasant little experience called to mind other occasions when I have found myself whistling unexpected things. There have been tunes from film scores, lots from stage musicals, even some Kylie Minogue and once a Smiths song. And of course, lots from those old German favourites: Beethoven, Bach and Kraftwerk. It made me think that perhaps that is the real test of whether a piece of music is any good. If it can sneak its way into your subconscious and embed itself there, emerging unexpectedly as an involuntary whistle or hum, it must have something going for it.

If this test has anything to it, it will be particularly useful to help me form opinions about ‘young people’s music’. It seems impossible to form an objective opinion about songs that are played nonstop by one’s teenage children, especially when most of the children’s conversation seems to be about how famous the singer is, how much they would love to be famous, and how they met somebody who once met somebody who said they had met one of Ed Sheehan’s roadies. It’s hard not to be naturally prejudiced against anyone that is the subject of such quasi-religious adulation.

But the subconscious mind doesn’t seem bothered by that sort of thing. I have found myself whistling a song by The One Directions, even though I have suspicions that they may be a Boy Band – a species of artistic ensemble that I thought went out with Milli Vanilli. I have also sometimes been known to whistle songs by Taylor Smith, even though I suspect that she is in league with Satan. How else could she possibly be so pretty, blonde, fluffy-haired, slim, tall, popular with girls and boys, and very, very, very rich? This is corroborated by the fact that, according to her songs, all of her romantic relationships seem to end within a few weeks in an alarming tragicomic farce of acrimony, deceit and recrimination, and it is well known that that that is one of God’s favourite punishments for those who defect to the opposition.

I am also tremendously comforted that I have never, to my knowledge, whistled a note of anything by Jackson Bieber. I once almost hummed an F sharp that I think he used in one of his ‘songs’ (it was from ‘Baby, Baby, Baby’ if I remember correctly, although I may not be reporting those lyrics exactly accurately), as I was humming my way towards the climax of Richard Strauss’s ethereally beautiful ‘Beim schlafengehen’. But I realised just in time and managed to skip over it.  I don’t think anybody noticed.

Andrew Kirk

Bondi Junction, February 2014