Whenever my sons moan about maths, I give a lecture on the untold benefits of calculating probability. Almost nothing is as useful as being able to undertake a competent risk assessment and to recognise when the odds are stacked against you. I only fully realised how useless most people are at doing this during the covid pandemic, when many hugely over-estimated the risk posed to themselves and loved ones, despite the fact they weren’t old, overweight, or living with illnesses and disabilities. The UK’s foremost expert on risk, Professor David Spiegelhalter, even pointed out that a child’s chance of getting serious covid was less than their risk of being struck by lightning. Of course, when the risk factor is far higher (doing parkour, for example) you may choose to proceed in any case. Which is fine so long as you accept the chances of mishap, don’t embroil innocents in your venture and don’t blame others when things go tits-up. 

My interest in this is fuelled by the fact I come from a long line of gamblers. My dad had an account at the local bookies, but never staked more than he could afford to lose, as his own father had been so improvident. I tend to follow dad’s lead and only indulge in semi-cautious risk-taking, like my decision to have my second son at home, aged 40, following an emergency C-section for the first. Which may sound very high risk, but my independent midwife was incredibly experienced and I was far less anxious at home –  resulting in less cortisone in my system, which can impede birth. After chatting to assorted birth professionals, looking at the best available stats and checking a swift transfer to hospital was possible if things went wrong, we reckoned my risk of things going badly awry was around 1-in-350 at worst, 1-in-500 at best. No insurer would cover my midwife, so I had to sign a waiver. Which sounds drastic, but equestrians and mountaineers accept significant risk on a regular basis, believing it a fair exchange for embracing their passions.

Sailors accept dangers too, knowing there’s always a chance of freakish weather conditions, a risk that’s high in public consciousness following the tragic sinking of Mike Lynch’s super-yacht off Sicily. We all now know that even the most expensive craft can be capsized by a sudden typhoon. With six people still missing, the story has dominated the news – made even more headline-grabbing by the fact Lynch had only just been cleared of serious fraud charges in the US (relating to the sale of his company Autonomy to Hewlett-Packard in 2011). In fact, one newspaper headed an article on the court case with the words Lynch “was given 0.5% chance of acquittal”. Perhaps this is what makes the story so particularly gripping: he had beaten sky-high odds only to become the victim of a passingly rare disaster.

But what takes the tragedy to the realm of cinematic fiction is the fact that Lynch’s co-defendant in the trial, Stephen Chamberlain, was killed in the UK, hours earlier, in another freak accident – hit by a woman motorist in a village near Ely, while out running. 

If you think this rumination on tragedy is in poor taste, I totally agree. And yet I can’t stop thinking about it. I am just going to put this out there. Lynch clearly thought about probability and risk a LOT himself. His yacht was called The Bayesian after the “Bayesian Theorem” of probability, named for Thomas Bayes: an eighteenth-century Presbyterian minister and statistician). In mathematical notation the theorem runs: P(A\B) = (P(B\A)P(A))/P(B). Yup, this is above my maths pay grade too. But the excellent popular science writer Tom Chivers believes it to be the most important theorem in mathematics and published a book on the topic, Everything is Predictable, last year. I can’t possibly explain it as clearly as he does, but the simplest explanation I’ve found online is: tests are flawed because there’s a margin of error (think lateral flow tests) so “Bayes Theorem converts the results from your test into the real probability of the event.” Basically, the calculated probability of any given occurrence changes once you add extra background information. (Read Chivers’ book). 

This whole story now feels like an episode of Sherlock. What are the odds of the two main defendants in a vast fraud trial dying within twelve hours of one another? One on a yacht called Bayesian? And are those odds different if the deaths occur in places long associated with dodgy types, such as Sicily and the Fens? Yet there are no suspicious circumstances surrounding Chamberlain’s road accident, according to police. And the freak tornado conditions off Sicily were also indisputably real. I ended up emailing Booker-Prize winning novelist DBC Pierre, who is adept with risk and probability, as well as outlandish plots – do read his brilliant novella about gambling and maths, Big Snake Little Snake. He also happens to live in the Fens. 

Pierre told me: “It is the stuff of novels, to be freshly acquitted along with a partner in a ten-year fraud trial and then each be nailed in a one-in-a-million act of God on the same day. But even Putin couldn’t pull that off, especially the water spout.” I agree and yet I’m still haunted by the story. Random events such as these, that feel scripted, make me feel like abandoning maths and statistics altogether and returning to a more pagan view of the universe. In short, the cruel Fates are beyond all understanding. 

When I was eight years old, I came home with a bloody nose and cried to my mother about being bullied. For context, this was in an outback town in Australia in the 1970s, and the kid who punched me went on to serve time for crimes far more serious. Instead of marching in to see the headmistress, Mum bought me and my brother boxing gloves and got us to practise fighting each other. Her message was clear enough. Whatever the rights or wrongs of the situation, the world is a harsh place and there are times we have to stand up for ourselves. Luckily though, when push next came to shove, I didn’t have to find my inner Muhammad Ali. An even tougher boy, this one with a moral compass, intervened and made clear there’d be no intimidation on his watch.

Since World War II the American-led West has seen itself in such a role: a defender of democracy and freedom not shy in stepping in to protect the less powerful from oppression. But its record is patchy at best. The highlights have been when it has acted through multilateral organisations – NATO’s umbrella over Europe, and the UN’s peacekeeping efforts in dozens of countries from Guatemala to Tajikistan, El Salvador to Lebanon. The low points have been conflicts like the Iraq War launched in 2003, where America and its closest allies acted unilaterally and ran roughshod over the very international frameworks and principles they were so instrumental in establishing.

This week’s announcement that Germany intends to radically reduce its support for Ukraine is just the latest sign that the collective West is now incapable of stepping in decisively to stop bullies on the global stage. It comes on top of our utter failure to restrain Israel from perpetrating the mass slaughter of innocents in Gaza, and perhaps to prevent a much wider conflict from erupting across the Middle East. On Monday, while the US busied itself in more peace talks, the UN declared that Israeli strikes against the Palestinians are now “relentless”. With more than 80 per cent of Gaza’s infrastructure destroyed, its people have no choice but to try and survive among the wreckage. The UN itself is powerless to intervene and can offer little more than words. Back in Ukraine, despite the country’s pluck in pushing back against Putin’s Russia with a surprise incursion into Kursk Oblast, the German move – if implemented – means their longer-term chances against a much more powerful aggressor have become even less likely. Ukraine has shown it is more than willing to stand up for itself, but inconsistent and limited western support means it has mostly been fighting with one hand behind its back. In all likelihood, history will judge that we gave them just enough rope to hang themselves.

Geopolitics is a complex business, and schoolyard tales offer little practical guidance on dealing with bullies armed with nukes and with no qualms over the deaths of thousands. But they can at least provide a ready reckoner as to whether the West is still in possession of a moral compass. In both Ukraine and Gaza we’ve shown we’re no longer willing to step into the ring to save others. God help us then when the day comes that we need to take the gloves off and save ourselves.

The saying, “it’s a dog’s life”, originated in the seventeenth century, when London’s streets were full of mistreated curs, but there’s plenty of literary, pictorial and archaeological evidence to show that dogs have also been treasured family members since they were first domesticated in prehistoric times, and even, for some devoted owners, “man’s best friend”.

One such is Mark Rowlands, a professor of philosophy who believes a dog’s life should be held up as an example to humans because they have a greater capacity for enjoying life than we do, not being crippled by our capacity for existential self-reflection. The Happiness of Dogs explores his observations of training, raising and observing his own beloved hounds, in an affable tone that’s part philosophy, part self-help and part enjoyable anecdote, but ultimately a paean to dogs and what we can learn from them. 

He writes lyrically of the canine joy involved in leaping across a meadow or chasing after ducks, pointing out that dogs exhibit ecstatic delight when repeating the same daily routines, whereas Sisyphean everyday repetitions wear us humans down. He wants to upend the Socratean idea – which underpins our modern, therapy-rich culture – that “the unexamined life is not worth living”. On the contrary, it’s the continual self-questioning that makes us miserable, he suggests, whereas dogs are better able to live in the moment. 

“Dogs generally don’t do self-examination… We think this makes us better than them… I suspect it is the other way around,” he claims. Dogs aren’t “riddled with questions” and therefore don’t suffer doubts. He describes a dog’s nature as “a granite slab of essence”, whereas his own feels attenuated by self-interpretation, becoming “insubstantial, diaphanous… gossamer thin”.

Rowlands’ observations of a dog’s life are often droll, yet his reverence for their simplicity of thinking can feel in itself simplistic and his arguments get a tad circular and repetitive. I got distracted by wondering why so many men, in particular, consider their dog to be their best friend. Is it because the dog is faithful no matter what his owner does? (Hitler’s dogs were famously devoted to him), or because dogs are far easier to please than wives? (instead of “Frailty, thy name is Woman”, it could be “Friendship, thy name is Fido”.)

Rowlands didn’t convert me to his thesis that “the unexamined life is most worth living”, but he’s persuasive about dogs’ infectious delight in nature. That seems a more realistic basis for his philosophical proposition: “If you want to know the meaning of life, get a dog.”

The Happiness of Dogs is out on 12 September