# Grace

What is grace? I think of it as a sort of beauty associated with movement. A dance can be graceful, but a symphony or a painting cannot. They have a different sort of beauty.

It can also refer to human interactions. When done tactfully and considerately, leaving nobody feeling awkward, or worse than they need to feel, they are graceful. Somebody that deals with others in a way that is unnecessarily rough and hurtful ‘lacks grace’.

I think there may be a connection between these two. I’ll think about that later. But for now let’s think about the grace of movement.

I am a huge fan of graceful movement. It doesn’t just have to be dance, which is often designed to be graceful. It can be found in the most unexpected places.

Since my third year of high school I have enjoyed physical activity and being fit. In my youth that included going in cycling and running races. In later high school I trained hard on my bicycle, and the fitness gained from this equipped me to win our annual school cross country race. That then put me into the team for the inter-school races for our region – the Southern Districts of New South Wales. I was at a Catholic school and I think we competed against the other catholic and non-government schools in that region.

I nearly always came third in these inter-school competitions. There was a boy from another Canberra school that came second. I think his name was David Rowe, but I am not sure. What I am completely sure of is that the winner was always Andrew Reardon, from Saint Patrick’s boarding school in Goulburn.

I didn’t see much of Andrew in those cross country races. Just a pair of heels disappearing into the distance as soon as the starting gun went off. If we were running on trails in the pine forest, as we often were, my only goal was to keep him in sight so I could follow his route and thereby avoid taking a wrong turn.

In summer we would have inter-school athletics. I was chosen to represent my school at the middle distance events, of which I usually chose the 1500m and 3000m races. Again I usually came third, but this time I got to see Andrew Reardon in action from closer quarters, and not just from behind. We often raced on lovely, smooth grass 300m tracks that belonged to the richer private schools. A 3000m race was ten laps, which was enough time for Andrew to get to being on the exact opposite side of the track from me – 150m ahead – so I could see him running from the side. And what a gorgeous sight it was! He seemed to just float over the ground in an effortless manner with a grace that words cannot describe. It felt like watching a gazelle or a cheetah in a David Attenborough film, except that cheetahs are sprinters and would probably keel over if asked to run further than 400m.

Any feelings of envy or competitive resentment just leached out of me, as I just felt so privileged to watch this graceful performance. One would say it was poetry in motion if it hadn’t been said a million times before. But the loss of my competitive urge didn’t make me slow down. Rather I increased my pace so that the distance between us didn’t get to more than half a lap and thereby degrade my view of this majestic performance. I imagine Andrew was just cruising at what was a comfortable pace for him, while I was gasping and spluttering. I expect he could easily have accelerated and lapped me quite soon had he a mind to do so. If so, it was a demonstration of the other sort of grace to not subject me to that humiliation. Noblesse oblige.

What was it about his running style that touched me so? I want to say rhythm and symmetry, but that has a connotation of mechanistic, and it was anything but mechanistic. Relaxation was another key aspect, and machines are not relaxed. Andrew looked like he was playing, or floating. It was like a Brandenburg Concerto in vision. You had to be there.

Thereafter I worked on making my own running style as relaxed, symmetric and rhythmic as I could. This wasn’t just vanity. I also believed that running that way would use less energy and allow me to run faster. Perhaps it worked a bit. I did get much faster over the next few years, and some people were even kind enough to say that I had a ‘nice running style’.

The last I saw of Andrew Reardon was in late 1980, when I saw him on telly, which was showing a NSW schools championship athletic meet at Hensley Field in Sydney, which was then a lovely, smooth grass track (now it’s synthetic). It was a 1500m event, which he won reasonably easily, I think in about 3:52. Watching it on telly, without being distracted by my own attempts to run, I could revel in the joy of this exhibition of perfect movement. It was great.

I sometimes wonder what became of Andrew Reardon. Did he become a farmer, as many of the boys at that rural college might have done, or did he move to the city and become a businessman? Did he grow a middle-age paunch as most men do (Oh no!), or did he keep himself trim? Does he still run?

Shortly thereafter I was struck by the running of another Andrew – this time the Australian representative Andrew Lloyd. I saw him on telly, I think running some national championship meet, at perhaps 5k or 10k. He too had a beautiful, relaxed style, seeming to glide along as if his feet weren’t even touching the ground. I remember he was wearing a cap, which runners would generally avoid as an encumbrance, and making it hard to dissipate heat. But it didn’t seem to trouble him. He looked so cool!

In my university days I trained sometimes with athletes at the Australian Institute of Sport, since that was in Canberra and so was I. So I got to see Andrew Lloyd up close while training, and to admire his easy style.

He was involved in a horrible road accident in the early 1980s in which his wife was killed and his elbow was smashed. When he recovered, his elbow was, if not fused, swollen and difficult to move, so his style became lopsided and a bit awkward. But he was still very fast. I think he won the City to Surf a few years after that.

Grace is not a pre-requisite for being a fast runner. Contemporary with Lloyd was Laurie Whitty, a runner with a famously ungainly style, but who won national championships and represented Australia. One of the most famous ever distance runners was the Czech Emil Zatopek, who apparently had a very ungainly style. There is not much film of him running because his heyday was in the fifties. Australia’s most prestigious 10k race is named after him because he won in the 1956 Melbourne olympics and apparently really liked Australia.

Have you noticed that the lululemon logo looks very similar to a capital Omega: Ω? It also looks a bit like the emblem on the Torres Strait islander flag.

In the early eighties I was heavily influenced by a book by Percy Cerutty, who coached a number of brilliant Australian distance runners, including Herb Elliott, who held the world 1500m and mile records and won the 1500m at the 1960 olympics in Rome. He advocated a very nature-based training regime, involving only natural foods – mostly raw – and running on sand hills, beaches and in forests rather than on athletic tracks. But the most memorable – to me – aspect of his philosophy was his claim that through too much soft living, adult humans had forgotten how to move naturally. So to learn how to run properly, and fast, we should watch how other animals do it.

Cerutty disdained symmetry. I don’t know what he would have thought of Andrew Reardon. Percy thought human running should have different modes like a horse – trot, canter and gallop, in order of increasing speed. While trotting is symmetric and may be suitable for marathons, cantering and galloping are not, and he thought they should be used for distances of 10k and shorter. I remember running on the beach when on summer holidays trying to imagine myself as a two-legged horse and transition from trot to canter and then to gallop as I sped up. It seemed to work but maybe it was all psychological. If you imagine yourself galloping then you feel fast and, to some extent, that makes you go faster.

I remember seeing some visiting African athletes jogging about in tracksuits on the training track in Canberra, while preparing for a race on the main track that was next door. They just looked so flexible and bouncy, as if every movement was joyful play. That was another manifestation of grace.

Enough about athletics. That is just one example of where grace can crop up unexpectedly. It is there in hurdling and high jump and pole vault as well as in running. Maybe we could even see it in shot put, but we might have to look a little harder.

Grace seems important in Zen, although it doesn’t seem to be identified or named as such. In the Japanese tea ceremony, great importance is placed on the way one moves in preparing the tea, in serving it, and in how one drinks it. I love the way the cup is offered with both hands and a bow, and is received in the same way. This translates to the way that business cards are presented, and even how purchases are handed across in a shop. I try my best to remember to participate in such small but special rituals. When in doubt, use two hands and make a slight bow!

I have never mindfully raked pebbles as Zen monks sometimes do, but I imagine grace plays a role in that as well – watching the intricate patterns made by the pebbles as they are disturbed by the rake tines and then resettle in their wake.

I think if we look hard enough we can find grace in many things that move around us – humans, other animals, trees and bushes in the wind, even inanimate objects. I try to find this when I feel disheartened. It helps a bit.

I think again about the role of grace in human interaction. The grace is in the speech acts, in the words said, the tone in which they are said, and in accompanying gestures and facial expressions. I suppose all of these are movements. On a simple level, they are movements because speech comes from movement of body parts – lips, tongue, larynx, lungs – and of the intervening air that carries the sound waves. On a more abstract level, they are movements because they are expressed over time, and movement is defined in terms of time. They cannot be captured by a still picture – although a skilful snapshot can hint at it. Even more abstractly, they are movements of emotion – a communication of feeling from one being to another.

I would like to cite an example of a well-known graceful interaction, but my memory fails me (I imagine there are lots from Barack Obama. He is a very graceful person). Nevertheless, we all know what they are and have witnessed and valued them. They catch our attention particularly in difficult circumstances – when somebody turns aside aggression or insult, or rejects a crude suggestion, without aggression and without making anybody feel bad. When somebody finds a way to include somebody that is excluded by their difference, without making a big deal of it. When somebody finds a way to show solidarity and support for somebody that is grieving, without patronising them or putting them in a position where they are obliged to respond.

Then there is grace shown by somebody under extreme pressure – be it their own tragedy, anger, fear or anxiety. When they surprise us by expressing and taking care for things beyond themselves and their worries, despite all.

I don’t know whether it’s the same sort of grace. Classifications rarely matter anyway. But it seemed worth mentioning.

I resolve to try to be more graceful in my relations to other living beings, rather than just in how I run.

Andrew Kirk

Bondi Junction, August 2019

PS I just remembered cricket. I couldn’t send this off without mentioning the joy of watching a truly graceful batter. How they can deal with a heavy red projectile fired at them at up to 160 kph by a small, subtle flick of the wrists that sends the ball to the boundary for four runs. Watching really good batting is like watching a brilliant dance. It’s not for nothing that cricket enthusiasts, more than in any other sport I know, keep photos of their heros in action – in the execution or the aftermath of one of the wide variety of elegant shots available to them.

# Obviously, …

When it comes my turn to be king of the world I will ban the word ‘obviously’, together with its fellow travellers ‘clearly’ and ‘evidently’. My challenge to you, the other inhabitants of the kingdom of Earth, is this: find me a single example of a sentence that is improved by the use of the word ‘obviously’!

I assert that, not only is ‘obviously’ never an improvement to a sentence, but it usually degrades a sentence into which it is inserted and renders it foolish, pompous, or just plain false.

The first memory I have of encountering this rebarbative word is in mathematics lectures at university. It was the early 1980s. In those days lectures performed their proofs live on the black board with chalk – a difficult endeavour indeed. As soon as you saw that word on a board, you felt that if you couldn’t instantly see why that line followed logically from the line before, you must be very dim. If you hadn’t seen the connection by the time they finished writing the next line, you started to panic. The only solution was to accept the claim without challenge and try to keep up with what came next. There would be time that evening to go over your notes and try to work out why the claim was ‘obviously’ true.

Sometimes in the evening you could figure it out without difficulty. Sometimes you figured it out but it needed a page or so of closely written reasoning to justify it. Sometimes you couldn’t make it out at all. That’s when you had to summon your courage and challenge the lecturer about it before the next lecture. You’d sidle up to him and say ‘Sorry to bother you but I can’t see how you get line five. Can you please explain it?

In short, it was rarely obvious. Even when it was moderately obvious, there were other lines that were more obvious, for which the tag was not used.

I started to detect a pattern. The word was being used to cover for the fact that the lecturer couldn’t remember, off the top of their head, the justification for the line. By writing ‘obviously’ they made potential hecklers too worried about seeming dumb to challenge the claim on the spot. It was the Emperor’s New Clothes all over again. What was needed was the little boy to blurt out ‘But it’s not obvious at all. In fact I can’t even see it.

I forgive those lecturers, because what they were doing was very difficult. I would feel under a lot of pressure having to perform mathematical derivations on a blackboard in front of a specialist audience.

It is less forgivable when it occurs in text books. In many a mathematics or physics text book I have come across the prefix ‘obviously’ before a line that was the exact opposite. The authors of textbooks do not have the excuse that they have to come up with explanations on the spot, but they are nevertheless under time pressure because, unless a text is chosen as a key text for courses at many major schools or universities, it will not bring in much revenue, so extra time spent writing it makes it even harder to be profitable. Why spend hours deriving a proof of something you are fairly sure is true, but don’t remember why, when you can just write ‘obviously’ in half a second, and move on to the next line?

I don’t begrudge them saving that time, but there are more honest and helpful ways to do it. Other phrases that can be used are “It turns out that…” and “It can be shown that…”. These make it clear that what the author has written is not a full proof, and that the step over which they are glossing is not trivial. When I encounter those I don’t mind very much because they don’t contain the implicit challenge “If you can’t see why this line follows from the last one you must be stupid!”. The most generous excuse of all is “It is beyond the scope of this paper / text / chapter to prove X, so we will take it as read”. That way the reader knows that proof is long and difficult.

It is annoying when academics use the word ‘obviously’ in that way, but at least they use it in relation to a claim that is true. In political argument, that is not the case. People use ‘obviously’ to justify any claim, no matter how dubious, or sometimes just plain wrong. Examples abound, from politicians, shock jocks and reactionary newspaper columnists.

Obviously, decriminalising marijuana use would make the problem worse

Obviously, it makes no difference whether Australia reduces its greenhouse gas emissions, since ours only make up a small part of the world’s total

Obviously, what’s needed to solve our city’s traffic problems is to build bigger roads

Obviously, we have to be cruel to refugees, otherwise many more would come to our country”.

It’s used as an excuse to not even consider any evidence that may be available, to not even entertain rational discussion on a topic. It implies that anybody that does not accept the claim must be stupid or have dishonest intentions. It’s an attempt to shut down inquiry and discussion, lest that lead to an outcome against which the speaker has an entrenched prejudice.

Is anything ever obvious?

Perhaps, but we need to very careful in suggesting that. What is obvious to one may not be at all obvious to another. A high-visibility yellow vest is obvious to normal-sighted people but not to the colour-blind. A person walking across a basketball court in a gorilla suit is not obvious to observers that have been tasked with counting the number of times each player passes the ball.

Further, beliefs in what is obvious are often founded on stereotypes that may be damaging. Is it obvious that boys are better at maths than girls, or that men cannot be trusted to care for other people’s children?

This leads me to wondering whether there is any sentence in which the word ‘obviously’ can play a useful role. I don’t apply the same challenge to ‘obvious’ because it can have observer-dependent roles, as in “It eventually became obvious to Shona that the doorman was not going to let her into the club”. Or we can use it to express relative obviousness, as in “Not wanting to mislay them, he left his keys in the most obvious position he could think of – in the middle of the empty kitchen bench”.

But “obviously”? That adverbial suffix ‘ly’ seems to strip from the adjective any ability to convey subtleties of degree. There seems to be no way of using it that does not imply that anybody who does not agree with the following proposition, and understand why it must be correct, is simply stupid.

No wonder it is used either as a tool of bullying or as a lazy attempt to escape the need to justify one’s claims.

Sometimes it occurs without intent, as a verbal tic. Like most verbal tics, it is rooted in the insecurity of the speaker. Although it sounds like it has an opposite meaning to other tics like ‘if that makes sense’ or ‘if you like’, it serves the same purpose in deflecting attention from the speaker’s insecurity – but in an offensive rather than a defensive way. In both cases the speaker hopes not to be challenged. With ‘if that makes sense’ the hope is that the humility it projects will discourage a listener from saying ‘that doesn’t sound right’, if only out of charity to the speaker. The ‘obviously’ is like the puffed-out frill of a lizard – a pretence at invulnerability intended to discourage attack: ‘Challenge me on this and you’ll end up looking foolish!’. Except that the intent is usually subconscious and, once one has used the phrase many times, it becomes reflexive, devoid of any meaning, or even of subconscious intent.

I vowed quite some time ago never to use the word, or any of its synonyms. I think I have managed to keep the vow. I hope I have. But I cannot be sure. One uses so many words in the course of a week, that it’s hard to keep track of them all.

If something is truly obvious to almost everybody, there should be no need to state that. It will be obvious that it is obvious. If, as is more often the case, it is far from obvious, it is foolish at best, and dishonest at worst, to imply that it is.

Andrew Kirk

Bondi Junction, April 2019

So I was riding to work, right? And I went around the corner on a shared path and came a little bit closer to a family of pedestrians than is ideal. I didn’t come very close, and wasn’t going fast. There was absolutely no danger, or even capacity to frighten, but you know, it’s best to give pedestrians a wide berth on a shared path, because it can be a bit scary when a bike comes near. At least I find it scary when a bike comes near me if I’m not ready for it.

Anyway, I sort of mumble something like ‘Sorry – a bit close’ as I go by and I just see this guy’s face – the father I reckon – looking at me calmly and waiting for me to pass.

My, what a patient guy, I think.

Then, because I can’t help imagining and catastrophising at the same time, I imagine what if he were like one of those alpha males that aggressively yells at anybody given the slightest opportunity, and he abused me? What would I say?

I thought, well I’d probably sheepishly mumble something like ‘Didn’t mean no harm mate’, which I didn’t, you know, and anyway I wasn’t that close, and it was a shared path.

But then it occurs to me that, in Australia ‘Mate’ is as often a challenge as it is an expression of fellow-feeling. Expressed with the right tone of voice at the beginning or end of a sentence, it often means ‘You stupid, quivering, pathetic excuse for a human being (that isn’t as manly as I am)’.

That would been almost the exact opposite of what I meant to convey to the man (who, let us remember, was patient and calm in real life). But that’s the trouble with the word ‘Mate’ here downunder.

Reactionary politicians love to talk about ‘mateship’ being a cornerstone of our culture, as if it’s a good thing. That’s weird. If it just means friendship then how is that specifically Australian? Don’t people in other countries have friends, and aren’t they kind and loyal to them as well? It makes as much sense to claim that as an Australian characteristic as it does for American nationalists to pretend they invented the concept of freedom.

No it means more, and yet less, than that. For a start it’s a specifically masculine term, even though they like to pretend it isn’t. Mateship is about drinking together in the pub until you can barely stand, and then not dobbing in your mate if, when he’s had a few too many, he drives a car, or belts his wife. There’s no room for women in mateship, and very little for non-Caucasians.

So I don’t like mateship, OK. I regard it as toxic, to use the word du jour. Nationalist zealots might say I go too far in my criticisms, but I say Yah, Boo, Sucks to them. Let’s stick with friendship, tolerance and compassion if we want to characterise how we aspire to relate to others.

I don’t like ‘Mate’, but I quite like ‘Comrade’. Partly because it seems so quaint and old fashioned. To me it conjures up Australian icons like Phillip Adams and Gough Whitlam. Round here it is redolent of a bygone age when brave, committed, idealistic (some might say deluded but I don’t think we’re in a position to judge) Australians believed in and worked for the Communist or Socialist dream that they saw as the only way to help the downtrodden, before Stalin, Mao, Ceaușescu and Pol Pot ruined it for us all.

Well they didn’t actually ruin it completely. They sullied it, and nobody wanted to touch it for a few decades. But now that we’re seeing the impact of über-capitalism around the world destroying cultures, livelihoods, employment and the environment, and face the prospect, with AI starting to take away all the jobs, of the world dividing into ten percent or less super-rich who own all the technology and the patents, and the rest are the unemployable, expendable poor…. Maybe now, it’s time to have another look at Comrade.

Now I understand that for people who lived in the Soviet bloc, the word Comrade may have the same horrible associations of aggression as Mate sometimes does in Australia. So maybe that’s not the right word. It would be OK here in Oz, but probably not in Russia (Tovarich) or Rostock (Kameradin / Kamerad).

I have another proposal though – Citizen.

I’ve been reading ‘The Gods Are Thirsty’ by Anatole France. It was written in early 19th century and is set in 1793, four years after the French Revolution and only months before the beginning of ‘the Terror’, the orgy of show trials and guillotinings led by Robespierre, in which 17,000 people were executed and another 10,000 died in prison.

That’s what people called each other after the French Revolution – Citizen (in French  they said Citoyenne for women and Citoyen for men). Just as they called each other Comrade after the Russian Revolution.

Like Comrade, Citizen seems to have a connotation of working together, of shared civic responsibilities, that Mate doesn’t have. I like that. It’s nice to work together, rather than alone.

Shall we call one another Citizen, then?

But wait, what about those 27,000 dead in the French Terror? Did Citizen become just another term of passive aggressive bravado and bullying in the 1790s, just as Mate can be in Australia and maybe Comrade was in the 1930s Soviet Union?

Oh bother! Maybe we can’t call each other Citizen either.

What about ‘Friend’, then? That’s the sort of thing that wise old women and men call you in fantasy epics  when you meet them on the deserted, long and winding roads through the wildlands. Surely that’s good isn’t it? Could we call each other that?

It can sound a bit creepy, I know. Like a stranger trying to insinuate themselves into your confidence. But is that just the product of the modern cynical mind? If we said Friend and meant it, and when it was said to us we accepted it as being meant as a genuine, friendly salutation, would it work? I think it might.

Sadly, it does remind me of another revolution though. Or perhaps this was more of a coup than a revolution – the seizure of power by Julius Caesar and his proclaiming himself emperor.

You know: “Friends, Romans, countrymen, lend me your ears”.

Caesar was a fairly violent ruler – he invaded and slaughtered my ancestors for goodness sake! Everybody can find a story of colonisation and persecution of their ancestors if they go back far enough. But it only continues to mean anything if it’s recent enough to affect the memories or the life opportunities and prosperity of people whose ancestors were colonised and persecuted. And that’s not the case for me. Not even as regards the Norman invaders – bastards! And the even more recent English invaders of my Irish ancestors – double bastards! I know that some of my ancestors will have been colonisers of the other ancestors – the Romans, Angles, Saxons, Jutes, Vikings, Normans and English invaded and/or colonised the Britons, Anglo-Saxons and the Irish. But none of my current family were alive at the time of the persecutions, and my life opportunities have not been constrained by them, so I can’t complain.

What about Friend then? Does its association with Caesar and the aftermath of a coup make Friend yet another term that is tainted by association with brutishness?

Well now, I remember of a sudden that it was Shakespeare that wrote that bit about friends and ears, not Caesar. And in any case, Wikipedia tells me that it was Marc Antony, not Caesar, that uttered those words in the play.

So maybe Friend is OK.

Trouble is though, I don’t think I can quite carry it off. I am neither old enough nor wise enough to address people as Friend without appearing like a creep or a dangerous loon.

I think it will have to be Comrade after all. I’ll just be careful not to use it to address anybody that lived under Soviet oppression. And maybe I’ll make the odd switch to Citizen now and then when I want to sound sophisticated and cosmopolitan, provided I am sure there are no survivors of the Terror nearby to be offended by it.

Anything is better than Mate.

Perhaps Mate is okay as a non-sex-specific description of a life partner though, as in ‘puffins mate for life’, which is just so heart-warming, and how could anybody not love puffins? I’ve heard they are disgusting to eat, all oily, fishy and livery, like gelatinised cod liver oil. But that doesn’t worry me since I don’t eat any birds.

Andrew Kirk

Bondi Junction, December 2018

# And She shall reign for ever and ever

It’s a busy time, the end of choir practice. It’s 9:05pm and I haven’t had my dinner. I need to put away chairs, don my cycling safety gear, unlock the bike and whiz back home to look for something to eat. Busy, busy, busy. So one is distracted, right?

And I found myself singing that famous line from the Hallelujah chorus

and She shall reign for ever and ever

Why were you singing that, Andrew? I hear you ask.

Well the chorus had been the last thing we were practising and, you have to admit (if you’ve ever heard it) that it’s very catchy. No wonder that GF Handel was the Andrew Lloyd Webber of his day.

No, not that, you respond – I mean, why ‘She’? Don’t you know that the official lyric says ‘He’?

Well actually yes, I do know that, which is why I was a little surprised to find that my subconscious mind, after deciding to make me sing that song, had also decided to make me sing ‘She’. I don’t know why it did. I think it may be because there’s a lovely alliteration in ‘She shall….’ that you don’t get with ‘He’.

But then I thought to myself, as I strode in a purposeful and manly manner towards my bicycle, why not She? Where does it say that God has a sex, and that it is masculine?

Now I know what you’re thinking: the Bible and the Quran are both full of He this, He that, Father this and Lord the other. That’s true, but you ask any theologically sophisticated Christian or Muslim whether God has gonads and I’m pretty sure they’ll say ‘Of course not!’ God is much too big and impressive, not to mention invulnerable, to have a collection of soft, funny-looking, easily damaged organs dangling annoyingly between his legs.

I think there are two reasons why male pronouns and nouns are used to refer to God in the scriptures of Middle-Eastern religions (Christianity, Islam, Judaism), both of which are to do with cultural traditions and have no theological basis.

The first is that ancient Middle-Eastern cultures, like most all other old cultures, including English and American, are patriarchal and use masculine pronouns in all cases except where the person being referred to is definitely female. All sorts of interesting reasons for this can be discussed but, whatever the reason, we cannot doubt that that is the practice. In a sense, ‘He’ is just the way of saying ‘She or He’ in that language tradition. In the modern, progressive parts of the world, we are working to undo those traditions, because of their toxic effect on sexual equality. But that’s a modern phenomenon that occurred centuries after the King James bible, let alone the original versions written in the period 950BCE – 150CE (600-900CE for the Quran).

The second reason is more specific. In those patriarchal cultures, it was assumed that a figure of authority must be male. Yahweh / Allah was the ultimate Boss, so It was described as male, as the notion of a female boss would have just been too incomprehensible – and unacceptable – to consumers of the stories.

Neither of these reasons retain any validity in modern, Western society, so there is no reason to perpetuate the implicitation of masculinity that was adopted at the time of writing. In fact, there are good reasons to actively overturn that implication, as just another undesirable plank in the ugly edifice of male dominance.

There is one other reason that was suggested to me by a Roman Catholic friend, that is more concrete. That is that Jesus was a man. Let’s accept for now the biblical narrative that there was a single man called Jesus of Nazareth, on whom the gospel stories are based, and whose body housed the incarnate spirit of God. Then the worldly container for the spirit of God did indeed have an XY chromosomal pattern, testicles and a penis. But why should that make us think that the immaterial spirit that pre-existed that body, and survived it, also has those things. We are told that Jesus had a beard. Does that mean that the spirit also has a beard?

If God’s plan was to incarnate as a human and preach an important message, It had three options for a body in which to incarnate: as a man, as a woman, or as a human of indeterminate sex. In Palestine CE30, only one of them had any chance of success. Nobody would have taken a woman seriously, and someone of indeterminate sex would likely have been put to death as a perceived infraction of God’s laws. So the choice of Christ (the part of God’s spirit that is said to have incarnated as Jesus) to incarnate as a man was simply an expedient, and says nothing about the sex of Christ.

Christians pray to Christ – the spirit – rather than to Jesus, even though they may say Jesus because it sounds more friendly. Jesus was the incarnated man, and he only existed for about thirty years. It is Christ that the religion says is eternally in heaven, and to whom a Christian prays. And there is nothing to credibly suggest that Christ has a sex.

Are there any other reasons why God should have a sex?

Thinks.

I can’t think of any that aren’t completely silly. One that immediately comes to mind is that God is The Boss, and bosses are more often than not male (although personally I have been fortunate to have had at least as many female as male bosses in my work career, and there is no doubt about who wields the power in the reasonably-happy home I inhabit). We’ve already dealt with that.

Another is that God is portrayed as a Father. But again, the intent of this metaphor (metaphor because It’s not really a father – there is no divine sperm involved) is to convey that God has the same loving, guiding, protective relationship to us that a parent typically has to their child. The scripture writers just wrote Father rather than Mother or Parent because of the language conventions mentioned above.

Any more reasons? No, I’m afraid I can’t think of any.

On the other side, there are excellent theological reasons against attributing a sex to God.

According to 1 John 4:8, God is Love. Does love have a specific sex? No.

According to John 1:1 God is The Word. Do words have a sex? No.

According to the influential theologian Paul Tillich, God is the Undifferentiated Ground of Being. Do Grounds of Being have a sex (provided we don’t differentiate them!)? No.

According to St Thomas Aquinas, God is Pure Actuality. If we distill Actuality until it is pure, does it acquire a sex? No.

According to St Augustine, God is Goodness Itself. Does Goodness have a sex? No.

I can tell you don’t want me to go on, so I won’t.

Right, now that we’re all agreed that God has no sex, what are we going to do about the fact that nearly all the words written and spoken about God attribute masculinity to It?

This is my plan. Please listen carefully.

From now on, whether you believe in God or not, in every reference you make to God that is in a context where use of a sexed pronoun is natural, I want you to use the female form.

As you are all intelligent and attentive readers, you naturally understand that this is not because I think God has a sex and that sex is female. Rather it is that, even if this idea went viral, it would have no hope of balancing out the enormous number of references to God as male that are out there. So we’ll keep on at this until God references achieve sexual parity, and then we’ll think about what to do next. This is not, as Alan Jones or Donald Trump might claim, ‘playing with words’ or ‘political correctness gone mad’. It’s just using sensible language that recognises that women and men are equally human and equally capable of anything except for a very few sex-specific activities such as fertilising an ovum or gestating a baby human. It’s a step that subverts the subtle message that only a man can be a person of power and wisdom. It’s a small but meaningful step in the project of gradually dismantling millennia of male dominance and oppression. And who better to lead such a step than the religions that have historically been – and unfortunately in some cases still are – platforms for those that seek to perpetuate that dominance.

So, if you please, it’ll be:

‘Our Mother who art in Heaven….’, in The Dame’s Prayer.

‘And He shall reign for ever and ever….’

Jesus is the Son of Woman (note the preservation of the word Son for Jesus, on account of the real-life testicles on the body used for Christ’s incarnation).

‘And She looked down on Her creation, and saw that it was good’.

The hymns will need reworking too:

‘Hail Redeemer Queen divine’

‘Queen of Queens, and Dame of Dames’

Everything, except specific references to the body of Jesus of Nazareth, has to go, and be replaced by its feminine equivalent.

What nice, friendly, inclusive places churches will become when this is adopted. I would happily visit them and sing along to ‘God rest ye merry (gentle)women’ in a spirit of ecumenical solidarity.

I don’t want to pick unfairly on Middle-Eastern religions, even though, they being by far the most powerful ones, they can take it. So let’s pause to consider the others.

Non-Middle-Eastern religions seem to generally be less patriarchal than the Middle-Eastern ones. There are powerful goddesses in Indian, Egyptian, Native American, Norse, Greek and Roman religions. But in all cases the boss of the gods is male. Apparently there have been, through the twentieth century, groups of scholars that believed that ancient religions such as druidism worshipped an Earth Mother type deity as their main focus, but these beliefs have fallen into disfavour in academia, and start to look more like wishful thinking of survivors of the Peace and Love generation of the sixties, than historically accurate accounts. The only well-known religions – ancient or modern – in which the most powerful being is female are neopagan religions such as Wicca. Well good for them, I say. But they are a very small minority, and the male dominance of the other religions I mentioned at least lets the Middle-Eastern triumvirate that currently dominates the world off the hook a little.

But Andrew, you protest, you are not a practising Christian, or a Muslim, or a Jew, so why should you care what words they use to talk about their gods?

You make a fair point, dear reader. The religions towards which I feel the greatest affinity are Buddhism and Vedanta, neither of which have any connection with the Middle East. But although I am not a Christian, Christianity has a major effect on my daily life and the lives of those around me, through the enormous influence that Christian power-brokers have on our laws and social customs. So it is in my interest, and in the interest of anybody that wishes for a kinder society, for the average Christian, as well as the power hierarchies of the various Christian sects, to become more consultative and compassionate. I think the religion becoming less male-dominated and male-oriented would help in moving along the road towards that goal.

And the same applies to Judaism and Islam. While their influences are minor where I live, there are parts of the world where their influence is intense. The people living in those regions would greatly benefit from those religions shedding some of their patriarchal orientation, and where better to start than to stop pretending that God is a bloke.

Andrew Kirk

Bondi Junction, December 2017

# Thought Association

I was jogging on the beach, trying to think of something else because the last couple of days had been rather upsetting. I settled on thinking about an essay I am trying to write about The End of The World. Very soon I found that I had the REM song It’s the end of the world as we know it running through my head on repeat.

After a while I noticed somebody running along next to the concrete promenade, where the sand is softest because it is furthest from the water and almost never gets wet from the sea. The sand was pretty soft where I was, about halfway between the promenade and the water. But maybe it was softer over near that other guy. In any case, we’d had heaps of rain recently, so if water makes sand pack together harder, presumably where I was would be just as water-hardened as next to the promenade.

But then maybe seawater has a different effect. Perhaps it makes the sand stick together better than rainwater does. If so then the sand next to the promenade really would be softer, unless the sea ever gets up to there.

That led to me wondering about whether, in the wildest sorts of weather, the sea ever came all the way up to the concrete wall below the promenade (about fifty metres from the high tide mark).

Thinking of stormy weather made me think of the scene in the movie The French Lieutenant’s Woman where the female lead stands at the end of a long jetty in a storm, only a metre or two above the rough sea – a precarious position, deeply evocative.

That led me to wonder whether it is sexist to refer to the character as somebody’s ‘woman’, thereby seeming to suggest ownership. That led to my thinking about the reverse phrase ‘somebody’s man’, which led me to think of the Tammy Wynette song Stand by your man.

And without any conscious decision to do so, there I was, jogging along the beach, mentally humming Stand by your man instead of It’s the End of the World as we know it.

Thought association.

Andrew Kirk

Bondi Junction, April 2017

Featured Image is from the 1981 movie The French Lieutenant’s Woman, showing the jetty called ‘The Cobb’ at Lyme Regis UK.

# Anti-Trumping without Godwin

Hallelujah! I have found a solution to the most difficult dilemma faced by those of us on the anti-Fascist fringe of 21st-century politics. I am referring, of course, to the problem of how to accurately criticise the new US president without either falling foul of Godwin’s Law on the one hand, or understating the harm he is causing on the other.

In case you don’t know, Godwin’s Law states that ‘As an online discussion grows longer, the probability of a comparison involving Hitler approaches 1‘, meaning somebody is bound to make the comparison sooner or later. The Corollary of this law is that, if you have to resort to comparing somebody to Hitler, you have lost the argument.

I try to assiduously observe this rule by never making that comparison myself, as a consequence of which the comparisons I make for the most unpleasant of the world’s leaders and policies cover a wide range of alternatives, starting with the perhaps too-obvious Stalin, running through Mao and Pol Pot, Augusto Pinochet, Vladimir Putin, Robert Mugabe and then, just for variety, taking in some serial killers like Fred and Rosemary West.

But the following tweet from some Trump toady, in response to the President summarily banning travellers from a range of countries with Muslim majority populations, causing heartbreak, despair and airport chaos, had me stumped. Here it is, from someone called Kellyanne Conway:

Get used to it. @POTUS is a man of action and impact.

It is just screaming for somebody to respond ‘So was <He with whom, out of deference to Mike Godwin, we will not make comparisons>’

The idea that being a person of action is a virtue, regardless of the morality of that action, is so gob-smackingly asinine that it is beyond parody (which leads to another, lesser-known, internet law: Poe’s Law, which says that it is impossible to tell the difference between a parody of the US fundamentalist right, and the real thing).

But how can one respond, without invoking that famous Austrian, and thereby implicitly losing the argument?

Fortunately, I have found the answer, and it is…………..

### Voldemort

Ta dah!!!!!!!!!!

That’s right, all you need say in reply to such thuggish ejaculations as Conway’s above is

So was Voldemort

There is even a scriptural basis for this comment. In ‘Harry Potter and the Philosopher’s Stone‘ the wand-maker Ollivander sells Harry his first wand, and is fascinated to find that the wand – which chose Harry, rather than Harry choosing it (don’t ask) – is the ‘brother’ (don’t ask about that either) of the wand that Ollivander had sold to Voldemort as his first wand, decades earlier. Ollivander says:

we must expect great things from you, Mr Potter …. After All, He Who Must Not Be Named did great things – terrible, yes, but great‘.

So there you are: when apparatchiks or groupies of the US government confuse – deliberately or otherwise – decisiveness with virtue, or power with goodness, you can now skewer their idiocy without impaling yourself on the spike of Godwin. Just remind them about Voldemort, and all the great, powerful things he did.

By the way, just as an aside, in the course of researching this painstakingly-researched and highly-detailed essay, the internet has made me aware that, contrary to my belief and that of most other people, apparently Mussolini didn’t make the trains run on time.

Post Script: Just prior to posting this I searched for images of Voldemort to decorate it. To my bemusement, I found that many of them have the new president’s face photo-shopped over that of Voldemort, and there was even an article explaining why he really is Voldemort. I also came across reports of Joanne Rowling’s tweets about Trump and Voldemort, saying facetiously that the comparison was unfair to Voldemort. Well, bother! I had previously been aware of those tweets, but had utterly forgotten them. Apparently my subconscious hadn’t though. Well, never mind. If something’s worth saying, perhaps some things are worth saying more than once, by different people, as long as they don’t deliberately copy. I’ll put a nice, unphoto-shopped photo of He Who Must Not Be Named  on this anyway, and I hope you’ll forgive my subconscious plagiarism.

# Hypotheticals, counterfactuals and probability

This essay considers the notion of events occurring that we do not know to either have occurred, or to be almost certain to occur in the future. Imagination of such events is everywhere in everyday speech, but we rarely stop to consider what we mean by it, or what effect imagining such things has on us.

It is dotted with numbered questions, so it can be used as a basis for a discussion.

## Counterfactuals

A counterfactual is where we imagine something happening that we know did not happen.

This is fertile ground for fiction. Philip K Dick’s acclaimed novel ‘The Man in the High Castle’, written in 1962, depicts events in a world in which the Axis powers won World War II, and the USA has been divided into parts occupied by Japan and Germany. The movie ‘Sliding Doors’ is another well-known example, that imagines what ‘might have happened’ if Gwyneth Paltrow’s hadn’t missed a train by a second as the sliding doors closed in front of her..

When something terrible happens, many people torment themselves by considering what would have happened if they, or somebody else, had done something differently:

• What if I had been breathing out rather than in when the airborne polio germ floated by? (from Alan Marshall’s ‘I can jump puddles’)
• If she hadn’t missed her flight and had to catch the next one (doomed to crash), she’d still be alive now.
• What would life have been like if I hadn’t broken up with Sylvie / Serge?

We can also consider counterfactuals where the outcome would have been worse than what really happened, such as ‘What would my life have been like if I hadn’t met that inspirational person that helped me kick my heroin habit‘. But for some reason – so it appears to me – most counterfactuals that we entertain are where the real events are worse than the imagined ones. We could call these ‘regretful counterfactuals‘ and the other ones ‘thankful counterfactuals‘.

Then there are the really illogical-seeming ones, like the not-uncommon musing: ‘Who would I be [or what would I be like] if my parents were somebody else?‘ which makes about as much sense as ‘what would black look like if it were a lightish colour?

Here are some questions:

1. why do we entertain counterfactuals? What, if any, benefits are there from considering regretful counterfactuals? What about thankful ones?
2. given that for many counterfactuals, consideration of them just makes us feel bad, could we avoid entertaining them, or is it too instinctive an urge to be avoidable?
3. Do counterfactuals have any meaning? Given that Alan Marshall did breathe in, and did contract polio, what does it mean to ask ‘If he had been breathing out instead, would he have become a top-level athlete rather than an author?‘ Are we in that case talking about a person – real or imaginary – other than Alan Marshall, since part of what made him who he is, was his polio?

That last question can lead in some very odd directions. My pragmatic approach is that counterfactuals are made-up stories about an imaginary universe that is very similar to this one, but in which slightly different things happen. Just as we make up stories about non-existent lands, princesses and far away galaxies, we can make up stories about imaginary worlds that are very similar to this one except in a handful of crucial respects.

Some philosophers insist that counterfactuals are not about imaginary people and worlds but about the real people we know. My objection to that is that, for example, the Marshall counterfactual cannot be about the Alan Marshall, because he had polio. It can only be about an imaginary boy whose life was almost identical to Marshall’s up the point when the real one contracted polio. My opponents (who would include Saul Kripke, that we mention later) would counter that polio is not what defines Alan Marshall, that it is an ‘inessential’ aka ‘accidental’ property of that person, and changing it would not change his being that person. Which begs the question of what, if any, properties are essential, such that changing them would make the subject a different person. Old Aristotle believed that objects, including people, have essential and inessential properties, and wrote reams about that. In the Middle Ages Thomas Aquinas picked up on that and wrote many more reams about it. The ‘essential properties’ of an object are called its ‘essence’, and believing in such things is called ‘Essentialism’. That is how certain RC theologians are able to claim that an object that looks, feels, smells, sounds, tastes and behaves like a small, round, white wafer is actually the body of Jesus of Nazareth – apparently because, although every property we can discern is that of a wafer, the ‘essential’ properties (which we cannot perceive) are those of Jesus, thus its essence is that of Jesus. I tried for years to make sense of that and believe it, but all it succeeded in doing was giving me a headache and making me sad. For me, essentialism is bunk.

1. Can you make any sense of Essentialism? If so can you help those of us who can’t, to understand it?

I can’t help but muse that maybe thankful counterfactuals have some practical value, as they can enable us to put our current sorrows into perspective. They are a very real way of Operationalizing (I know, right?) what Garrison Keillor suggests is the Minnesotan state motto – ‘It could be worse‘.

Maybe regretful counterfactuals sometimes have a role too, when they encourage us to learn from our mistakes and be more careful in the future. But they are of no use in the three examples given above. What are we going to learn from them: Never breathe in? Never fly on an aeroplane? Never break up with a romantic partner (no matter how unsuitable the match turns out to be)?

If we do something that leads to somebody else suffering harm, considering the regretful counterfactual can be useful. If I hadn’t done that, they wouldn’t be so sad. How can I make it up to them? I know, I’ll do such-and-such. That won’t fix it completely, but it’s all I can think of and at least it’ll make them feel somewhat better.

But once we’ve done all we can along those lines, the counterfactual has outlived its usefulness and is best dismissed. Otherwise we end up punishing ourselves with pointless guilt, which benefits nobody. Yet we so often do this anyway, perhaps because we can’t help it, as speculated in question 2.

I am completely useless at banishing guilt. But the techniques I have, feeble as they are, revolve around reminding myself that the universe is as it is, and cannot be otherwise. The past cannot be changed. If I had not done that hurtful thing I would not have been who I am, and the universe would be a different one, not this one. I am sorry I did it, and will do my best to make restitution, and to avoid causing harm in that way again. But the counterfactual of my not doing it is just an imaginary story about a different universe, that is (once I’ve covered the restitution and self-improvement aspects) of no use to anybody, and not even a good story. Better to read about Harry Potter’s imaginary universe instead.

This universe-could-not-have-been-otherwise approach is currently working moderately well in helping me cope with the recent Fascist ascendancy in the US. There are so many ‘if only…’ situations we could torture ourselves with: ‘If only the Democrats had picked Bernie Sanders’, ‘If only Ms Clinton hadn’t made the offhand comment about the basket of deplorables’, ‘If only the Republicans had picked John Kasich’. Those ‘If only’s are about a different universe, not this one. They could not happen in this universe, because in this universe they didn’t happen.

Counterfactuals also come into Quantum Mechanics. Arguably the most profound and shocking finding of quantum mechanics is Bell’s Theorem which, together with the results of a series of experiments that physicists did after the theorem was published, implies that either influences can travel faster than light – which appears to destroy the theory of relativity that is the basis of much modern physics – or Counterfactual Definiteness is not true. Counterfactual Definiteness states that we can validly and meaningfully reason about what would have been the result if, in a given experiment, a scientist had made a different type of measurement from the one she actually made – eg if she had pointed a particular measuring device in a different direction. Many find it ridiculous that we cannot validly consider what would have happened in such an alternative experiment, but that (or the seemingly equally ridiculous alternative of faster-than-light influences) is what Bell’s Theorem tells us, and the maths has been checked exhaustively.

## Hypotheticals

A counterfactual deals with the case where something happens that we know did not happen. What about when we don’t know? I use the word hypothetical or possibility to refer to where we consider events which we do not know whether or not they occur in the history of the universe. These events may be past or future:

• a past hypothetical is that Lee Harvey Oswald shot JFK from the book depository window. Some people believe he did. Others think the shot came from the ‘grassy knoll’.
• a future hypothetical is that the USA will have a trade war against China

What do we mean when we say those events are ‘possible’ or, putting it differently, that they ‘could have happened‘ (for past hypotheticals) or that they ‘could happen‘ (for future hypotheticals)? I suggest that we are simply indicating our lack of knowledge. That is, we are saying that we cannot be certain whether, in a theoretical Complete History of the Earth, written by omniscient aliens after the Earth has been engulfed by the Sun and vaporised, those events would be included.

Some people would insist that the future type is different from the past type – that while a past hypothetical is indeed just about a lack of knowledge about what actually happened, a future hypothetical is about something more fundamental and concrete than just knowledge. This leads me to ask:

1. Does saying that a certain event is ‘possible’ in the future indicate anything more than a lack of certainty on the part of the speaker as to whether it will occur? If so, what?

I incline to the view that it indicates nothing other than the speaker’s current the state of knowledge. What some people find uncomfortable about that is that it makes the notion of possibility depend on who is speaking. For a medieval peasant it is impossible that an enormous metal device could fly. For a 21st century person it is not only possible but commonplace. As Arthur C Clarke said ‘Any sufficiently advanced technology is indistinguishable from magic.’ To us, mind-reading is impossible, but maybe in five hundred years we will be able to buy a device at the chemist for five dollars that reads people’s minds by measuring the electrical fields emitted by their brain.

Under this view, the notion of possibility is mind-dependent. What would a mind-independent notion of possibility be?

There is a whole branch of philosophy called ‘Modal Logic’, and an associated theory of language – from the brilliant logician Saul Kripke – that is based on the notion that possibility means something deep and fundamental that is not just about knowledge, or minds. To me the whole thing seems as meaningful as debates over how many angels can dance on the head of a pin, but maybe one day I will meet somebody that can demonstrate a meaning to such word games.

Sometimes counterfactuals sound like past possibilities. That happens when we say that something which didn’t happen, could have happened. Marlon Brando’s character Terry in ‘On the Waterfront‘ complains ‘I coulda been a contender … instead of a bum, which is what I am‘. As I said above, I don’t think it makes literal sense to say it could have happened, since it didn’t. But if we didn’t know whether it had happened or not, we wouldn’t have been surprised to find out that it did happen. So in a sense we are saying that a person in the past, prior to when the event did or didn’t occur, evaluating it from that perspective, would regard it as possible. Brando’s Terry was saying that, back in the early days of his boxing career, he would not have been at all surprised if he had become a star. But he didn’t, and now it was too late.

## What would happen / have happened next?

With both counterfactuals and hypotheticals, we often ask whether some other thing would have happened if the first thing had happened differently from how it did. For instance:

• [counterfactual] If the FBI director had not announced an inquiry into Hilary Clinton’s emails days before the 2016 US presidential election, would she have won?
• [past hypothetical] If Henry V really did give a stirring speech like the ‘band of brothers’ one in Shakespeare’s play, exhorting his men to fight just for the glory of having represented England, God and Henry, were any of the men cynical about his asking them to risk death just in order to increase Henry’s personal power?
• [future hypothetical] If Australia’s Turnbull government continues with its current anti-environment policies, will it be trounced at the next election?

1. What exactly do these questions mean?

The first relates to something that we know did not happen and the other two relate to what is currently unknowable.

My opinion is that, like with counterfactuals, they are about making up stories. In the US election case we are imagining a story in which certain events in the election were different, and we are free, within the bounds of the constraints imposed by what we know of the laws of nature, to imagine what happened next. Perhaps in the story Ms Clinton wins. Perhaps she then goes on to become the most beloved and successful president the country has ever had, overseeing a resurgence of employment, creativity, and brotherly and sisterly love never before encountered. Or perhaps she declares martial law, suspends the constitution and becomes dictator for life, building coliseums around the country where Christians and men are regularly fed to lions. Within the bounds of the laws of nature we are free to make up whatever story we like.

The same goes for the past hypothetical of Henry’s speech. We can imagine the men swooning in awe and devotion, murmuring Amen after every sentence, or we can imagine them rolling their eyes and making bawdy, cynical quips to one another – but nevertheless eventually going in to battle because otherwise they won’t be paid and their families will starve.

However, the future hypothetical seems to be about more than a made-up story. If the first thing happens – continued anti-environmentalism – then we will definitely know after the next election whether the second thing has also happened. At that point it becomes a matter of fact rather than imagination.

To which I say, so what? Until it happens, or else it becomes clear that it will not happen, it is a matter of future possibilities and can be covered by any of the scientifically-valid imaginative scenarios we can dream up. It is only if the scientific constraint massively narrows down those scenarios that it has significance. If, for instance, we could be sure that any government that fails to make a credible attempt to protect the environment will be booted out office, our future possibility would become a certainty: If the government doesn’t change its track then it will be ejected. But in politics nothing is ever that certain. Other issues come up and change the agenda, scandals happen, natural and man-made disasters, personal retirements and deaths of key politicians. At best we can talk about whether maintaining the anti-environment stance makes it more probable that the government will lose office. Which leads on to the next thorny issue.

## Probability

Probability, aka chance, aka risk, aka likelihood and many other synonyms and partial synonyms, is a word that most people feel they know what it means, but nobody can explain what that is.

What do we mean when we say that the probability of a tossed coin giving heads is 0.5? Introductory probability courses often explain this by saying that if we did a very large number of tosses we would expect about half of them to be heads. But if we ask what ‘expect’ means we find ourselves stuck in a circular definition. Why? Because what we ‘expect’ is what we consider most ‘likely’, which is the outcome that has the highest ‘probability’. We cannot define ‘probability’ without first defining ‘expect’, and we cannot define ‘expect’ without first defining ‘probability’ or one of its synonyms.

We could try to escape by saying that what we ‘expect’ is what we think will happen, only that would be wrong. The word ‘will’ is too definite here, implying certainty. When we say we expect a die will roll a number less than five, we are not saying that we are certain that will be the case. If it were, and we rolled the die one hundred times in succession, we would have that expectation before each roll, so we would be certain that no fives or sixes occurred in the hundred rolls. Yet the probability of getting no fives or sixes in a hundred rolls is about two in a billion billion, which is not very likely at all. We could dispense with the ‘certainty’ and instead say that we think a one, two, three or four is the ‘most probable’ outcome for the next roll. But then we’re back in the vicious circle, as we need to know what ‘probable’ means.

1. What does ‘expected’ mean?

There is a formal mathematical definition of probability, that removes all vagueness from a mathematical point of view, and enables us to get on with any calculation, however complex. Essentially it says that ‘probability’ is any scheme for assigning a number between 0 and 1 to every imaginable outcome (note how I carefully avoid using the word ‘possible’ here), in such a way that the sum of the numbers for all the different imaginable outcomes is 1.

But that definition tells us nothing about how we assign numbers to outcomes. It would be just as valid to assign 0.9 to heads and 0.1 to tails as it would to assign 0.5 to both of them. Indeed, advanced probability of the kind used in pricing financial instruments involves using more than one different scheme at the same time, which assign different numbers (probabilities) to the same outcome.

This brings us no closer to understanding why we assign 0.5 to heads.

Another approach is to say that we divide up the set of all potential outcomes as finely as we can, so that every outcome is equally likely. Then if the number of ‘equally likely’ outcomes is N, we assign the probability 1/N to each one.

That seems great until we ask what ‘equally likely’ means, and then realise (with a sickening thud) that ‘equally likely’ means ‘has the same probability as’, which means we’re stuck in a circular definition again.

1. What does ‘equally likely’ mean?

After much running around in metaphorical circles, I have come to the tentative conclusion that ‘likely’ is a concept that is fundamental to how we interpret the world, so fundamental that it transcends language. It cannot be defined. There are other words like this, but not many. Most words are defined in terms of other words, but in order to avoid the whole system becoming circular, there must be some words that are taken as understood without definition – language has to start somewhere. Other examples might be ‘feel’, ‘think’ and ‘happy’. We assume that others know what is meant by each of these words, or a synonym thereof, and if they don’t then communication is simply impossible on any subject that touches on the concept.

Or perhaps ‘likely’ and ‘expect’ may be best related to a (perhaps) more fundamental concept, which is that of ‘confidence’, and its almost-antonym ‘surprise’. Something is ‘likely’ if we are confident – but not necessarily certain – that it will happen, which is that we would be somewhat surprised – but not necessarily dumbfounded – if it did not happen. I think the twin notions of confidence and surprise may be fundamental because even weeks-old babies seem to understand surprise. The game of peek-a-boo relies on it entirely.

Once we have these concepts, I think we may be able to bootstrap the entire probability project. The six imaginable dice roll numbers will be equally likely if we would be very surprised if out of six million rolls, any of the numbers occurred more than two million times, or not at all.

There are various frameworks for assigning probabilities to events that are discussed by philosophers thinking about probability. The most popular are

• the Frequentist framework, which bases the probability of an event on the number of times it has been observed to occur in the past;
• the Bayesian approach, which starts with an intuitively sensed prior probability, and then adjusts to take account of subsequent observations that using Bayes’ Law; and
• the Symmetry approach, which argues that events that are similar to one another via some symmetry should have the same probability.

It would make this essay much too long to go into any of these in greater detail. But none of them lay out a complete method. I suspect they all have a role to play in how we intuitively sense probabilities of certain simple events. But I feel that there is still some fundamental, unanalysable concept of confidence vs surprise that is needed to cover the gaps left by the large vague areas in each framework.

Here is one last question to consider:

1. A surgeon tells a parent that their three-year old daughter, who is in a coma with internal abdominal bleeding following a car accident, has a 98% chance of a successful outcome of the operation, with complete recovery of health. In the light of the above discussion, it seems that nobody can explain what that 98% means. Yet despite the lack of any explicable meaning, the parent is so relieved that they dissolve in tears. Why?

Andrew Kirk

Bondi Junction, January 2017