Ten minutes into an episode of Netflix series Nobody Wants This, the two main characters are desperately, logically, trying to agree why their intense, love-at-first-sight connection will never work.
“I don’t believe in God,” she tries, so surely it would be impossible for a rabbi to date her? But this is not an insurmountable hurdle: “Baked into the Jewish experience is wrestling with what God is or isn’t, and not knowing,” the young religious leader replies.
This beautiful vignette mirrors part of the struggles within a new book, Orthogonal Thinking, by Johannesburg-based business-person and author David Buckham. It’s a mind-bending work, both straightforward and labyrinthine, pure and opaque, wondrous but sometimes so challenging as to be maddening.
Geometrically, orthogonality can be understood as perpendicular lines, initially divorced from one another, that eventually intersect at right angles. Thinking orthogonally, then, in simplified terms, implies the practice of ideating by connecting seemingly dispersed and independent spheres of knowledge.
But even the title of the book remains a giant question in the author’s mind. In the introduction he writes that he is unconvinced about his own understanding of orthogonal thinking, that “I can authentically say that this book is the shortest distance I know of between not knowing what orthogonal thinking is and having made some use of it in my life”.
Buckham has clearly searched for many things, but the one lying at the heart of all aspects of his intellectual, physical and spiritual quests — his life’s work, in a sense — is to discover meaning in the conundrum of uncertainty, this “not knowing”. What mystery of the universe underpins everything, including who and what we are as humankind and as individuals?
Extraordinarily, in 200 pages it manages to merge mathematics and literature, philosophy and sociology, travel and little-known snippets of history in the structure of a memoir. Quirkily, it includes childlike illustrations; some are odd distractions, but many hit the mark as mnemonics for the chapter’s key point and augment Buckham’s suggestion for us to become more childlike in recapturing our inquisitiveness, our marvel at life.
Which segues into the issue of mathematics, which ebbs and flows throughout the book. This could have resulted in an overly academic treatise, or a monograph that only touches more accessible spheres. But in Buckham’s hands even the pure or abstract maths sections maintain interest; the scribbled formulas — gobbledegook to this reader — lead quickly to a provocative point or a question that is then illuminated in a musing about his personal life, or a story of his travels, or an observation about the world.
So, reading about axioms, correlations, logarithms, regression analysis and vectors becomes a portal to a different plane — an orthogonality — of engaged, rewarding thinking.
Also, the brief histories of mathematical discoveries and the lives of genius mathematicians are fascinating. Carl Friedrich Gauss, for example, is known as the Prince of Mathematics because in his 1798 doctoral thesis, written when he was just 21, he proved certain critical aspects of arithmetical relationships, thereby synthesising the entire body of mathematics into a coherent numbers system or theory.
Actually, I prefer a simpler, more charming story to understand his genius: aged seven, as punishment for naughtiness, his teacher told him to add up all the numbers from one to 100. He cracked it in just seconds, realising immediately that moving inward from the beginning and end of the sequence, each two paired numbers (so, 1+100, 2+99 and so on) equals 101. Now it’s easy — try it yourself: how many pairs are there?
More or less in this graspable ambit, Buckham explains that 125 years ago another German mathematics genius, David Hilbert, presented 23 unsolved problems that would set the agenda for all future mathematical discoveries. Hilbert’s sixth problem, when (if ever) solved or proved, would define and explain the physics of the entire universe — infinity too — in a single equation, an overarching hypothetical framework subsequently called the Theory of Everything.
This link between mathematics, philosophy and the origins and laws of the universe is striking. Pinpointing this, “there is an incontestable, divine beauty in the pattern of numbers”, Buckham writes. Recalling the 1990s, for him a period of career achievements and rock-climbing mastery, he explains these were also “halcyon days” in terms of breakthroughs in the fields of theoretical and particle physics, especially in the quest to find the Higgs boson, the so-called God particle.
In a memorable passage that sparkles with his feelings of anticipation and deep emotions, he remembers believing at the time that “we were but a few years away from fundamentally understanding the universe” because the God particle will, in time, unlock the Theory of Everything.
This is heady stuff. But it doesn’t do justice to the book to mention only its abstractions and angles about the possible meaning of life. There are rich veins of other themes and topics, literature, in particular, the study of which Buckham embarked on after his maths degree. Here, rather than the befuddlement of maths, it kindles smiles of crisp and clear agreement, such as when he describes attempting to read James Joyce’s canonised Finnegan’s Wake, “which is, of course, completely unreadable, a literary experiment that does not even attempt to be grammatical”.
Indeed, the way Buckham conveys his love of the works of seminal writers is a highlight of Orthogonal Thinking. One notable passage quotes from a scene in Tom Stoppard’s absurdist play about free will and finding meaning, Rosencrantz and Guildenstern Are Dead. After 157 consecutive coin tosses all land on heads, says the Guildenstern character, “a weaker man might be pushed to examine his faith, if nothing else, at least in the law of probability”.
Coming towards the end of the book, this is strangely sad. All Buckham’s intellectual endeavours, his spiritual quest — and his orthogonal thinking — have been in vain. Will the perpendicular lines of his own life ever meet, he seems to ask, or are all the supposed systems, the structures of order, and the shapes of our beliefs that we as humankind would have wished for, and continue to hope for, subsumed within randomness?
Paradoxically, in his humility (“I would never come close to understanding even the tiniest percentage of knowledge that could be understood”) there remains a wistful yearning in which, he says, he is “almost happy”.
The book is open-ended enough for readers to reflect on much, and to prompt the pondering of their own stories and journeys. But I conclude that Orthogonal Thinking is ultimately a winding tale of a beautiful obsession about trying to discover and appreciate the wonder of life. In that sense the book is a pilgrimage — and a love story — the object of which is infinitely, divinely mysterious.
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