Flatland: A Journey of Many Dimensions (US edition) is a short book, but I read it very slowly. It’s less than 100 pages, and it took me six weeks, I think.

Perhaps if I had studied more than school-house geometry I would not have felt the need to spend so long pondering the perceptual consequences of living in two dimensions, as the characters in Flatland do.

Then again, there is the more frightening thought that I am in fact living a single dimensional existence without realising it. To understand how stupidly comic the book makes that idea seem you’ll have to get hold of a copy. It is a book that encourages humility in our understanding and yet aspiration to higher knowledge at one and the same time.

Written by Victorian London schoolmaster Edwin A. Abbott, Flatland was a mathematically-inspired parody of the restrictions (social, intellectual and philosophical) of the era. Abbott created an alternative two-dimensional world, expounded by geometrical observation and hand-drawn sketches to attack in allegory the conventional wisdoms of that hierarchical 19th century society.

But it barely takes any imagination to transpose the ideas into our own era. For it must ever be the case that a battle is going on within society between those who want to push our understanding upward, to challenge orthodoxy, and those whose economic benefit resides in the status quo. Quite literally these days our quantum friends ask us to consider many more dimensions than most of us have the faculty to conceive of.

The main protagonist and narrator of the story is A. Square, who is…a square; this makes him a professional man, or gentleman in Flatland. The middle classes are equilateral triangles, the lower classes isosceles. And in this world the women (ladies, you’ll not like this) are straight lines.

Remember, Abbott is describing a highly structured society. Social mobility in this world is generationally dependent. Deviations, if not correctable at birth, are extinguished. Squares beget pentagons, pentagons beget hexagons,etc etc. Regularity matters above all else.

The angularity of one’s body dictates not only your station in life but is also mirrored in your IQ; the pointier your angles the thicker you are. But Abbott’s protagonist from a middling station nevertheless demonstrates, through a combination of curiosity (his own and that of his hexagonal grandson) and through the revelation of a visitor from the higher plane, that there is a third dimension (and possibly more). He ends up challenging the established order held in place by his intellectual and geometrical superiors — the top-most of which are the priestly circles.

But this is more than just a reprint of Abbott’s text because the book is republished to accompany an animated movie(US DVD version). The narrative has been updated to account for a more contemporary sensibility and bring this geometrical allegory to life for a new generation, and one very easily turned off mathematics. So purists for the old story should get over themselves and help celebrate — if they were otherwise so inclined.

The movie was an instant hit with the two knackered chips off the old hack: one 13, the other eight. So if you are a secondary or junior school teacher tasked with enthusing children with the idea of maths and geometry in particular, there could be no better investment. And don’t worry about the women being lines; that liberal poster-child Martin Sheen plays Arthur Square in the film, and the precocious grandson, Hex, becomes a girl and is given voice by Kristen Bell.

The DVD extras also provide some great computer-generated animation that shows how three-dimensional shapes would be perceived in just two dimensions, and then, by the same logic, how higher dimensional objects might present themselves in our three-dimensional world.

And pay attention for the line in the trailer here: “Oh dude, you’re freakin’ me out!”, for that is the Line King talking.

What is particularly cute to my mind about the animated characters is that, while their outward form is two-dimensional, their insides are all revealed to be Mandelbrotian fractals. Now, there’s a truth we should all ponder.

Thanks to the movie’s animator Dano Johnson for providing the above on YouTube.

With it’s playful green and red cartoon dust jacket, Ed Smith‘s What Sport Tells Us About Life: Bradman’s Average, Zidane’s Kiss and Other Sporting Lessons (Penguin Books, £14.99) could easily be taken for a belated Christmas stocking-filler, destined for a long stay in the bathroom’s literature section. But it deserves to be taken seriously. As the inside cover says:

Sport is a condensed version of life — only it matters less and comes up with better statistics.”

I realised this myself some time ago, and periodically spend more time following sports science than business and finance. And it was one of the thematic reasons for starting the Knackered Hack in the first place, to explore what could be learned from sport in general and my own participation in it in particular, without being glib. The road to hell, as they say, is paved with good intentions…

Smith, who is captain of Middlesex County Cricket Club, offers up sport as an under-used analytical resource from which can be drawn a number of intellectual and practical lessons about education, business, politics, the study of history, etc. The book takes the form of a series of essays, each kicking off from one sporting theme and following where any beam of light is usefully shed.

Smith takes in some of the old chestnuts such as: are our sporting heroes what they used to be? (the golden age hypothesis says no) or are our sportsmen and women getting perpetually better? (evolutionary theory says yes); is sport too commercial? — you’ve heard these discussed in the pub no doubt. He also covers some remarkable new ground for me, making some startling and insightful connections.

Before we get into cricket v baseball, as Smith himself explores, know that Smith understands both games well, and bigs up baseball as a crucible for pithy life observation, just as obsessive fans would claim. And he critiques the Moneyball strategy of the Oakland As from a player’s perspective. He also reveals baseball to be most likely a French invention, overtaking cricket for popularity in the Civil War (American of course) because of rough pitches, and then being gamed by some 19th century spin doctor called A. G. Spalding, who touted it that baseball championed the egalitarian, in contrast to the effeteness of cricket. Yes, he was just trying to sell more gear. And it worked. Despite the fact that cricket had enjoyed wide social acceptance in the US earlier in the century, it fell into terminal decline as a national pastime.

I’m no expert on Schumpeter’s oeuvre — though I’ve lived through one or two creative destruction episodes. But after 87 pages of What Sport Tells Us, all I could think of was Schumpeter, Schumpeter, Schumpeter. Smith elaborates on the fluctuating fortunes of sport, not just in terms of games and spectacle. He shows how at an industry (and at a national cultural) level the individual sporting disciplines are so rich themselves in creative destruction, confounding the stereotypes that fans, commentators and team owners all too frequently apply. On page 88, Smith finally drops the great man’s name. For the reader like me it was a back-of-the-net moment, as they say in soccer. Well-scored, Ed! When Penguin offered me the book for review, I hadn’t expected to find a discussion of how the free market has worked its invisible magic to raise the salaries of “left tackles” in American football. These hulks go unwatched on the field of play because all eyes follow the star quarter-back; but their presence determines whether the star player makes the goal or ends up face down in the mud. It all made sense to me. Schumpeter, he the man!

Someone should get Russ Roberts at EconTalk to interview Smith for a podcast. Smith is a broadcaster himself, having fronted a BBC programme called Peak Performance, which is sadly no longer in their online archive. In Roberts’ podcast with Schumpeter biographer Thomas McCraw, he highlights that when we observe an economic phenomenon like income inequality, the dominance of particular corporations (or, I’d suggest, the current credit crunch) we tend to see only the present snapshot in time; we miss the continuum. This can be both positive and negative. Bad news and bad money can drive out the good. But, Smith shows us that in the larger sweep of sporting history as well, so much of the hand-wringing of the short run is misplaced.

He also despatches sporting cliches all over the ground like loose bowling. He sends the concept of professionalism for six, hits a homerun against the notion of talent’s primacy, but saves his best shot for the role of luck and our contradictory and mistaken attitude to how it operates both in games, and also how it influences entire career paths.

Believing that ‘you can be whatever you want to be’, on the other hand, is actually a rather easy doctrine. (At least until you realize the idea has led you up the garden path.) The fallacy that desire and determination hold the keys to all success appeals to the inner adolescent in us that cannot bear the thought of hard work going to waste. I try, ergo I succeed; the world is just, so I will prevail; there is a fair distribution of justice, so I will be lauded. Such a shame that it isn’t true.

Of course, that logic is not reversible. Sitting around waiting for luck to come your way is as misguided as thinking that good things always come to those who ‘want it enough.’ The truth is that determination and desire are necessary but not sufficient. We have to try like crazy; we have to retain a relentless sense of determination; we have to make sacrifices and take the road less travelled. And yet still there are no guarantees. Even after all that, we may come up empty-handed. That is the bleak but unavoidable logic of anyone who has deep ambitions.”

But before we get too depressed by the potential tragedy of it all, he has a whole chapter celebrating the need to retain a sense of amateur love for the game, but not in the long out-dated Corinthian notion. Quoting Simon Barnes, quoting Brazilian World Cup Coach Felipe Scolari:-

Scolari said: ‘My priority is to ensure that players feel more amateur than professional. Thirty to forty years ago, the effort was the other way. Now there is so much professionalism, we have to revert to urging players to like the game, love it, do it with joy.’

[Barnes continues] This is not romantic twaddle. It is a fact that the more important something gets, the harder it is to do it well. We can all walk along the kerbstone in safety, but if the drop were not six inches but six miles, how then would we walk? Football matters too much; it matters to the players too much. As a result, the mattering gets in the way of the playing.”

In Smith’s own words:-

All professional sportsmen battle with their fears and anxieties. And by no means do they always conquer them. We live on the brink of disappointment, of failure, of being dropped, of getting sacked, of retreating back into civilian life with our dreams unfulfilled. That is the parlous state in which most sportsmen usually find themselves. All of us have experienced downward spirals of anxiety and introspection – I am losing form, my place is in jeopardy, my career could be in danger. Often you deny the problem, which secretly increases your anxiety – you are scared of admitting your fears even to yourself – and your form worsens still further.

He continues:-

Remove the obstacles to playing well. Anxiety is one of the obstacles. Worrying is one of the obstacles. Failing to focus simply and only on the job in hand is one of the obstacles [...] Dreading failure is one of the obstacles. Now you are thinking like a player again that is usually a beginning of a return to form.

The exposure to failure that really loving your sport entails is painful. The following paragraph(s) sang out particularly plaintively to the Knackered ears:

Trying desperately hard and not getting what you want is decent summary of what almost all sportsmen go through. The more deeply you compete and the greater the quality of your caring (to lift a line from Larkin), the more it hurts when you lose, or fail, or fall short. Each time a competitor taps into the essence of his personality in an attempt to win a sports match, he takes a risk. The risk is that he will get no reward — in the sense of a win or a personal triumph — for exposing himself to that degree of psychological rawness. It is easy to resent having tried so hard in the first place.

On the other hand, being too disengaged isn’t the answer, as the next paragraph elaborates:-

If it didn’t get us anywhere today, why should I bother to care so deeply next time? One answer is that being prepared and able to experience such deep emotions, and being exposed to that degree of disappointment, is a privilege not open to many. It doesn’t feel like a privilege at the time. It feels like hell. But it makes for a life more fully lived. After ten years playing professional sport, I have come to the startling conclusion that a big part of me actually enjoys caring about sport, even when that caring expresses itself as pain at losing. I wouldn’t rather life was more pallid. It sometimes reminds me that I am not wasting my time — and protects me a little from the resigned emptiness we all dread in sport.”

So don’t be put off from ordering a copy from Amazon.uk or Amazon.ca to steal a march on any US publication plans that Penguin has. He is good on this stuff, you know. He read History at Cambridge, and because he is younger than me, has been more exposed to counter-factualism, which he uses quite devastatingly to examine some rather controversial sporting triumphs, like England’s unexpected win in the 2005 Ashes cricket series against Australia.

And to show that someone has already deftly combined sport and philosophy, a re-run of one of my favourites. Schumpeter didn’t make the team on this occasion, but then… that was the story of his life.

A three part interview with Nassim Taleb can be found here.

It is very tempting to declare that The Black Swan(subtitled The Impact of the Highly Improbable) by Nassim Nicholas Taleb is the most important book of the century so far. I might say this for the bibliography alone. But the flaw in such a statement, which the book makes clear, is that I could not possibly know this without having read all the books that have been published to date. Even more challenging is the fact that, even if I were an accomplished speed reader, I would not be able to inwardly digest all the unpublished works, which are legion. This raises the problem of the “unknown unknowns”, an expression coined by Taleb and (in)famously adopted by Donald Rumsfeld, but from which Taleb understandably prefers to distance himself.

Black swans can be positive or negative, a blockbuster book like Harry Potter or a stock market crash. They are defined as rare events with an extreme impact, which are only retrospectively predictable. That last bit is crucial. Overestimating one’s own knowledge (what Taleb describes as “epistemic arrogance”) is central to our inability to handle and anticipate black swan events. Whether it is 9/11 or Virginia Tech, we retrofit a narrative to tell ourselves that someone should have seen it coming because we ourselves could not have been that stupid. And yet, we are no better prepared for the next one.

Why call these things “black swans”? It was Karl Popper’s notion that no amount of sightings of white swans can prove that all swans are white. It is falsifiable with just one observation of a black swan. Just because you have not seen it before does not mean it can’t or won’t exist. Continue reading ‘black swans and icebergs’