The Amazing Mathematics of the World’s Most Watched Object, Princeton University Press, 2025, 130 p, including 4 p Credits, i p Preface, i p Translator’s Note. Translated from the French LA PETITE HISTOIRE DU BALLON DE FOOT, (Odile Jacob, 2023,) by Teresa Lavender Fagan.

The translator’s note at the beginning informs us the history of both names for the game played with the titular object is fascinating but she has chosen to call the game football rather than soccer (as is only proper.) There was only one lapse.

This book could almost have been designed for me A football fan (well, a fan of the Sons of the Rock, so arguably not football) with a scientific background and therefore a grounding in maths. How could a discussion of the mathematics surrounding the football not interest me? Nevertheless it wasn’t a book I sought out; indeed I was unaware of its existence until I unwrapped it as a birthday present.

Amazingly (to me at least, I discovered it in this book) the rules of football state about the construction of the ball only that it must be made of a suitable material – but without specifying what constitutes suitability! (It must also be spherical and lie within a certain circumference and weight range with internal pressure between 1.6 and 2.2 atmospheres at sea level.)

The book starts with the familiar Telstar ball, dating from the 1970 World Cup and containing twelve black pentagonal panels, twenty white hexagons and requiring ninety seams. It is impossible (despite the illustrations on UK road signs which indicate football grounds) to construct a sphere only from hexagons, or indeed solely from pentagons. In this regard the logo for the (so-called) Champions League is incorrect. The actual ball has five-pointed stars surrounding curved hexagons, three stars around each hexagon. The logo, in places, has four.

In terms of geometry the Telstar is in fact a truncated icosahedron (ie one with its points cut off) and then inflated to [near] sphericality. It is also extremely symmetrical, ensuring stability in flight, but the pattern for cutting out the panels is very complicated.

The balls for more recent World Cups are truncated versions of other Platonic solids. Teamgeist (2006) was a truncated octahedron, the Jabulani (2012) a truncated tetrahedron with eight panels which weren’t flat, the Brazuca (2014) a truncated cube! (Albeit that last had curved panels.) 2022’s Al Rihla was based on an icosidodecahedron.

So much for geometry. The other criterion considered here is drag. It is the interaction between drag and gravity that determines a football’s flight. Without drag the ball’s flight would be inherently unpredictable and, due to turbulence, slow down too quickly! The ninety seams on the Telstar ensured sufficient drag. The Jabulani’s fewer seams and relative smoothness made it seemingly erratic. (Drag reduces with smoothness.) French goalkeeper Hugo Loris called the Jabulani a catastrophe. More modern footballs like the Al Rihla, as a close-up photograph demonstrates, are dimpled (in a similar way to golf balls) so as to reduce drag.

This is an excellent book for those interested in both football and maths but I think its explanations, not to mention the copious illustrations and diagrams, are sufficiently clear to pose no barrier to the maths-phobic.

Pedant’s corner:- “The horizon is a straight line” (It isn’t; it’s actually slightly curved,) “the English government” (there is no such thing. [there is a UK government, though],) uses English plurals (rather than Greek) for the Platonic solids.

Thirty four Scottish books read this year; equally divided between female and male authors. Fiction, Poetry, Science Fiction, Fantasy, Non-fiction, Football. I have linked to my reviews if they have appeared here.

No Dominion  by Louise Welsh

Hieroglyphics by Anne Donovan

For the Good Times by David Keenan

Wild Geese by Nan Shepherd

Paper Cup by Karen Campbell

The Christmas Truce by Carol Ann Duffy

A Would-Be Saint by Robin Jenkins

Something Like Happy by John Burnside

The Mandelbaum Gate by Muriel Spark

The Dark Remains by William McIlvanney and Ian Rankin

Scotland’s Lost Clubs by Jeff Webb

The Oath Takers by Naomi Mitchison

Vinland by George Mckay Brown

Beethoven’s Assassins by Andrew Crumey

Chimera by Alice Thompson

Hester by Mrs Oliphant

Antimacassar City by Guy McCrone

The Marriage Portrait by Maggie O’Farrell

The Philistines by Guy McCrone

Fishnet by Kirstin Innes

A Gift From Nessus by William McIlvanney

Sea-Green Ribbons by Naomi Mitchison

Companion Piece by Ali Smith

Night Boat by Alan Spence

Europa Deep by Gary Gibson

Murder in the Merchant City by Angus McAllister

O Caledonia by Elspeth Barker

The Puritans by Guy McCrone

King Hereafter by Dorothy Dunnett

Escape From Hell by Hal Duncan

The Pearl-fishers by Robin Jenkins

The Bachelors by Muriel Spark

Klaus by Allan Massie

Early in Orcadia by Naomi Mitchison

No this is not a headline from a science-fictional Altered History.

Scotland’s football team really has qualified for a World Cup finals.

Scotland women, that is – a historic first for them. Congratulations to the team and management.

So we can now definitively say Scotland’s women are better than its men.

So Alan Gilzean, whom Jimmy Greaves said was the greatest foootballer he had ever played with, has gone.

I never saw him play in the flesh, his time in Scotland being before I started watching football regularly and he was in any case in a different division to Dumbarton but he was a byword for accomplishment.

Before his move down south to Tottenham Hotspur Gilzean played for a great Dundee team, so great it won the championship of Scotland in 1962 and a year later reached the semi-finals of the European Cup. That was, of course, in the time when other Scottish clubs could compete almost on a level playing field with the two Glasgow giants. That success came in a remarkable 17 years when Hibernian (1948, 1951, 1952,) Aberdeen (1955,) (Hearts 1958, 1960,) Dundee (1962) and Kilmarnock (1965) became Scottish Champions. An incredible sequence: between the wars only Motherwell, in 1932, had broken the monopoly of Rangers and Celtic on the League Championship and subsequently only Aberdeen (1984, 1985) and Dundee United (1983) have performed the feat.

The power of money and the lucrative nature of European competition for the big two brought all that to an end. We’re unlikely to see anything like it again.

I’ve strayed somewhat from the point.

Gilzean was a great player, one whose movement on the pitch (from televisual evidence) was deceptively effortless looking, he seemed to glide over the ground in that way that only accomplished players manage to achieve. His scoring record isn’t too mean either; 169 in 190 games for Dundee, 93 in 343 for Spurs, 1 in 3 for the Scottish League and 12 in 22 for Scotland.

Alan John Gilzean: 22/10/1938 – 8/7/2018. So it goes.

I was sad to hear of the death of Cyrille Regis, a stalwart of a West Bromwich Albion side which finished third in the English top division in the late 1970s and fourth a couple of years later. Imagine that happening now!

Prior to his career along with Laurie Cunningham and Brendan Batson (nicknamed the Three Degrees though that seems excessively patronising now) there had been few black players in the British game since its very early days.

Albert Johanesson of Leeds United and West Ham United’s Clyde Best were trail-blazers and the amount of racist abuse all these had to suffer doesn’t bear thinking about.

Regis and the other two degrees helped to show that players like them could, “do it on a wet Wednesday afternoon in Stoke.” Not that that should ever have been doubted.

Regis’s five caps for England is not a true reflection of his abilities and stands as an indicator of the difficulties he faced in forging a career in football.

Cyrille Regis: 9/2/1958 – 14/1/2018. So it goes.

An anthology of Scottish football fiction. Polygon, 2003, 191 p.

From Stuart Cosgrove’s foreword, with its tag of “Anybody who says he disnae like football is a lyin’ bastard,” – a quote from the final story – to that final tale this book is an examination in prose of Scotland’s contradictory love affair with the Beautiful Game – an affair at times not beautiful and not a game. The tendency of Scots to see anything and everything through the filter of football is evident from the contents.

This paperback edition contains additions (by Brian Hennigan and Bernard McLaverty) to the original hardback contents. Each story’s title page is illustrated by photographs taken by Paul Thorburn of different sets of goalposts from round Scotland. Occasional double page photos, overlaid with quotations from the stories, intersperse the book.

As is usual for anthologies and might be expected from the range of contributors the stories are varied in tone and style. The relevance of football to some of them is a bit dubious, though.

The opener is The Thing About Brazil by Alan Spence. On a trip to Brazil, Andrew remembers his dad and their visits to Ibrox, takes in a Flamengo-Palmeiras game at the Maracanã and, later, has his own moment of football glory on Ipanema beach.
In A Belfast Memory by Bernard McLaverty a Belfast man remembers the time that “Charlie Tully called” and the discussion that ensued on the shameful demise of Belfast Celtic.
Linda Cracknell’s The Match is only incidentally about football. A woman is taking a holiday in the Carribean on her own since her husband wouldn’t miss a vital European match. (It could have been any obsession really but I suppose football is the most plausible.)
In This Is My Story, This Is My Song by Laura Hird some Hearts-supporting friends gather for the funeral of one of their number, killed in a van crash. Supporting Hearts is the biggest thing in the lives all of them.
Iain Maloney’s Football Scarves and Richard Kimble tells of a boy’s experience of his first match – a Cup Final – interspersed with his Dad’s reminiscences of how the ending of the TV show The Fugitive, gripping much of the nation at the time, was announced over the tannoy at a night game.
The Hand of God Squad by Gordon Legge is the tale of two (moderate) drinking pals, the hotels they drink in, the Englishman who first of all befriends them then joins in their trips away with the Tartan Army (complete with kilts.) All tied up with the sad end to the qualifying campaign for the 2002 World Cup.
In The Cherrypicker by Jim Carruthers the narrator’s grandfather was a Cherrypicker, so he is slightly disappointed both that no-one famous turned up at the old man’s funeral and at the absence of missives from Liverpool in his effects. Years later, on seeing Glenbuck, he cannot credit the team’s name.
Nae Cunt Said Anyhin by Andrew C Ferguson is narrated in a very broad Fife Scots. It is the story of Tam Johnston and the gift of sublime football talent the fairies passed on to him; a gift almost useless because Tam likes the drink too much (“George Best oan a budget”) and even though he gets to play for Scotland they’re “so shite even Tam cannae make a difference. Couldnae score on Loveboat.”
Billy Cornwall’s Jesus Saves has Wee Davy thrust into a game against older heavier boys, where he imagines himself as Kenny Dalglish.
Heatherstone’s Question by Des Dillon is another not really about football, even if two neighbours in Galloway do support different halves of the Old Firm. Rather, it is about neighbourliness, and reticence.
Alan Bissett’s A Minute’s Silence charts the friendship and rivalry between two boys that sours when they attend different schools and start to support different teams (you know the two.) About sectarianism and how it is not engrained, but learned.
In Denise Mina’s The Bigot a criminal has scheduled the divvy-up from a job for the day of an Old-Firm game. Again, the football content here is really incidental. Revenge, it seems, is a dish best served not only cold but well-planned.
Sufisticated Football by Suhayl Saadi has a man “lying in the cells at the dark bottom of the Old Partick Police Station” being visited by the ghost of Allegro Akbar, a celebrated football coach. Illuminated with words from Urdu and Arabic – ghosht = meat = the ball, pyar = love, and ishq = perfection (as in Zidane, Hampden, 15^th May 2002) – illustrating the philosophy of football.
The Tomintoul Deliverance by Brian Hennigan is the humorous story of how Loch Muick triumphed over the ancient enemy Athletico Tomintoul – despite not having played them for years and a season spent losing heavily to the likes of Dynamo Fochabers and Sporting Kilwhinnie (not to mention Unsporting Kilwhinnie) – mainly through managerial exhortation by cliché. A flavour of the tone is given by the sentence, “It was at times reminiscent of the film Zulu, particularly when the Tomintoul attack set fire to the thatched roof of our goal.”
The Last Man in Scotland Who Doesn’t Like Football by Colin Clark tells the story of “Pasty” Hastie, who doesn’t like football so got a hard time at school. The affliction goes on to haunt his adult life.

Pedant’s corner:- non sequitar (sequitur,) sprung (sprang,) its (it’s,) Billy McNeil (Billy McNeill,) “Better tae have to hoopsthough eh?” (the hoops makes more sense,) Queens Park (Queen’s Park,) “Where’s the excitement I that?” (in that, surely?) Thursday through the Saturday (that “through” is USian usage,) what we what we, was was, students’s, allen key (Allan key,) “’And you’ll have you got yourselves kitted out?’” epitomy (epitome,) gets the heads shaved (get,) Robert Prosineski (that’s how it’s pronounced but it’s spelled Prosinecki,) a missing quotation mark, were (where,) alter x 2 (altar – both times,) a few slice of bread (slices,) one and other (one another,) wanes (weans,) Ranger’s (Rangers’,) sliver shelving units (silver?) ranger top (Rangers top,) sleak (sleek,) viscose (viscous,) threw (thrown,) soccer (soccer!!!!) miniscule (minuscule,) deosil (usually deasil,) snuck (sneaked,) nine items or less (ought to be fewer, of course, but it’s a straight quote from a supermarket sign,) a question mark after what wasn’t a question, lead (led.)

The football legend who has died today had a name that needed no further explanation. He was part of that legendary Real Madrid side that captivated the football followers of Glasgow and Scotland at the European Cup Final of 1960 – played at Hampden Park. di Stéfano scored a hat-trick.

I was too young to be aware of it at the time but the folk memory was promulgated and persists. Such was the effect of that display of what football could be that the names of the forward line still trip off the tongue with no need for googling. Canario, Del Sol, di Stéfano, Puskas and Gento. Mind you, I see film of that game now and think, “Where was the marking?”

One curiosity is that I believe the Eintracht Frankfurt team that formed the opposition that day were all amateurs – as was German football as a whole.

di Stéfano may be unique in having played international football for three different countries, his native Argentina, Colombia, where he played league football for a while, and Spain for whom he was naturalised in 1956. That was the type of scenario that I thought had been resolved by FIFA with its rules on eligibility but in the recent World Cup one of the commentators remarked that Kevin-Prince Boateng who played for Ghana in the tournament had previously played for Germany (but not, it seems, for the senior side.)

The World Cup was one stage that di Stéfano did not grace, for various reasons, but his thirteen national titles (two in Argentina, three in Colombia and no less than eight in Spain) and five European Cups – not to mention his scoring record – speak for themselves.

Alfredo Stéfano di Stéfano Laulhé: 4/7/1926 – 7/7/2014. So it goes.

So. Gordon Strachan.

Not much of a surprise there.

Can he turn things round though?

With over five SPL clubs now having said they’ll vote against a team bearing the word Rangers at least somewhere in its new name being in their division next season it now seems that the Newco will have to apply to the SFL for a place.

The thought that they might be in Division 1 next season fills me with foreboding. If Dundee take their place in the SPL it would mean that Dumbarton’s first league game in Div 1 for 16 years will not then be at Dens Park (thus incidentally depriving me of the opportunity to walk to the game from my son’s flat) and may be at Ibrox – in which case I’ll not be going.

Any precedent here is surely Gretna, who when they were relegated from the SPL while in administration were immediately demoted to Div 3. But the Newco will not quite have been relegated, they will have been expelled.

Moreover they are a NEW club and ought to apply for the vacancy which will (due to shuffling within the leagues as before – Airdrie Utd you win again!) be in Div 3, not Div 1.

I fear though that some SFL clubs may vote for short term financial gain over sporting integrity despite the fact that the original Rangers were part of the process of shafting the rest of Scottish football (probably hoping it would wither on the vine) when the SPL was set up. The SFL clubs, though, have not withered but rather have managed to keep themselves alive and financially viable – certainly in Divs 2 and 3 – unlike their supposed betters.

This open letter to the SFL was written by a Raith Rovers fan and puts the case very well.

My feeling is that the misdemeanours of Rangers have been so grievous that a mere one division demotion is no sanction at all: any other club could then play fast and loose financially and expect to get away with it with as little to pay. I am even coming round to the notion that Newco Rangers ought not to be admitted even to Div 3 (they do not meet the entry criterion of having three years’ accounts for a start.) Scottish football will find its level without them – and become steadily more competitive as Celtic will not have a partner with which to bully the rest. If this means fans of Rangers are lost to the Scottish game so be it. The smaller clubs don’t depend on them anyway.

Europa League (sic) Semi-final, first leg. Estádio José Alvalade, Lisbon, 19/4/12.

Not paint drying.

(Again, though, I only watched the second half.)

This was an object lesson on how a near miss can spur a team on and how an equalising goal changes a game. At 0-1 down Sporting looked out of it. At 1-1 they dominated, and scored another.

Should be interesting in Bilbao next week.

I see the other Europa League(sic) semi-final finished 2-4. That can’t have been boring either.