A Child's Guide to the Quantitative Sciences

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Mathematics is the study of surprising relationships between patterns. Almost nobody outside the subject can see why anyone would want to spend grown-up time on it.

The mathematician starts with some definitions, adds a few axioms, and then spends the next twenty years discovering consequences which were logically but obscurely present from the beginning. Occasionally it turns out that two completely different branches of mathematics are covertly describing the same structure. This is regarded as tremendously exciting, and quite properly so, by the twelve people capable of understanding it.

In the future no-one will understand it.

Physics is what happens when people rummage through this enormous mathematical warehouse and discover that some of the weirder items appear to describe actual phenomena.

Physicists are much less fussy than mathematicians about whether the machinery is actually legal. If an integral diverges, a function does not really exist, or an infinite quantity has to be subtracted from another infinite quantity to obtain the measured mass of an electron, the physicist just calculates to see what number comes out. If the answer agrees with experiment to eleven decimal places, this is normally regarded as ok. The mathematicians can tidy up afterwards (if they feel like it; the physicist does not care).

Chemistry begins where physics is too hard to use.

In principle, most chemists know perfectly well that everything they are doing is quantum mechanics. In practice, doing chemistry from quantum mechanics is like deriving the rules of chess from quantum chromodynamics. There may be no philosophical objection - but life will be over before you have got anywhere.

Chemists therefore employ a magnificent collection of approximations, heuristics, semi-empirical rules, diagrams, conventions and things which generally happen if you heat something for twenty minutes in the presence of a catalyst. Electrons are represented by dots. Bonds are represented by lines. Molecules actually have 'shapes' which are not quite the shapes shown in the book. Reactions proceed through mechanisms which are not little films of what the atoms are actually doing, but which are close enough to enable somebody to manufacture aspirin.

At intervals a physicist explains why one of these rules works; nobody cares.

Biology is chemistry complicated by the fact that human beings cannot bring themselves to believe that a cat is merely a complex series of chemical reactions at scale.

This is biology's permanent intellectual embarrassment. Every biologist knows that organisms consist entirely of ordinary matter obeying ordinary physical laws. Yet almost the entire vocabulary of biology suggests otherwise. Hearts are for pumping blood. Eyes are for seeing. Cells send signals.

Evolution by natural selection makes this language legitimate without requiring God, Aristotle or an élan vital to be hiding inside the mitochondria. Everyone plays lip service to it, even the media.

But there's a robust emotional resistance to the proposition that a living creature really is an immensely complicated chemical system. Tell someone that a crystal is molecules and they nod. Tell them that what they see in the mirror is molecules and they feel that biology has omitted something important.

Economics, by contrast, is largely common sense formalised for the benefit of people whose common sense stops working when the answer becomes politically or emotionally disagreeable. Not that those folk will pay any attention.

Most of its elementary propositions are almost insultingly obvious. People respond to incentives. If a product gets cheaper, people mostly want more of it. If you make an activity more expensive, they tend to do less of it. Resources used for one purpose cannot simultaneously be used for another. Somebody always eventually pays. You can't indefinitely distribute goods which nobody has produced.

None of this sounds like much of a science, and indeed much of it would not be necessary if human beings were better at following an argument through its second and third consequences.

Which unfortunately they are not.

And sociology? Tell me, how do you feel about that?

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Politics Advice to my Grandchildren

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A Letter to My Grandchildren When They Are Fifteen

When I was fifteen I listened to contemporary politicians, Wilson and Heath in the 1966 election, berating each other in morally heated terms. I wondered why there wasn't a clear right or wrong answer on these pressing policy matters. I wondered how to decide – what could be the methodology? – between the different parties' positions.

Unlike in the maths or physics I was studying, no one seemed to have a good theory.

Eventually – and after I learned some economics – I came to understand. Politics is not what it pretends to be: a search for correct answers as to how to run things (in the scientific sense). Not at all. It’s actually a system for distributing power between powerful people who represent conflicting interests, under conditions of uncertainty and limited knowledge - and varying degrees of competence, we might add.

Let’s listen to the economist Joseph Schumpeter (1883–1950): democracy is not the rule of “the people” discovering the common good. Instead it’s a competition between political groupings, usually organised as parties, for the right to govern (see Capitalism, Socialism and Democracy, 1942). Elections are not moments of truth or attempts to achieve generalised optimality; they are moments of selection. You are choosing only between elite teams representing diverse interest groups.

Finally, the tone of political debate begins to make sense. Each side is not calmly reasoning toward a shared conclusion. Each side is attempting to win by mobilising its supporters while undermining its opponents. Moral language is part of the toolkit, galvanising ‘us’ and demonising ‘them’.

Incidentally, this is why the famous GOAT, the ‘Government of All the Talents’ is a non-starter except in times of national emergency - when domestic factional struggles get to be put on hold.

The Machinery Beneath the Stage

It’s after the election when Public Choice Theory intervenes to provide the next layer of our education. It begins with a simple observation: the people inside political systems – politicians, civil servants, advisers – are not saints or neutral calculators. Like all human beings, they respond to the incentives available to them.

Politicians seek re-election. Bureaucrats seek budget, stability, and expansion of their power and influence. Voters, for the most part, remain only lightly informed because people are busy, the effort required to master public policy is large, and the influence of any individual vote is small to negligible.

Meanwhile, smaller, organised groups – industrial cartels, unions, the professions – have strong incentives to lobby for policies that benefit them... and the power and focus to succeed in doing so.

The result is that government policy tends to reflect the pressure of organised minorities much more than the diffuse interests of the majority (noting that all governments wish to keep the masses politically atomised and quiescent, which is why Populism is deprecated as so dangerous).

This stance is accentuated when the dominant governing ideology is managerialism, with political leaders who pride themselves on lacking any overarching vision, but who are content to triangulate between interest groups, thinking their role is to compute some kind of political vector sum.

How Power Settles and Hardens

Mancur Olson became justifiably famous (The Rise and Decline of Nations: Economic Growth, Stagflation, and Social Rigidities, 1982) by observing that those elite fractions strong enough to gain real power do not merely exercise it ‘in the moment’; they institutionalise it. They construct legal frameworks, regulatory regimes, and administrative practices that lock in their advantages. What begins as a contingent victory becomes a durable structure.

Each such structure generates beneficiaries, and those beneficiaries organise to defend it. Over time, society accumulates a dense network of such layers incorporating protections, subsidies, rules and exceptional treatment. Each, in the moment, could be justified. Together they form a dense web that becomes increasingly resistant to change – a de facto veto network which locks-in a stagnant status quo.

So this is Olson’s central point: democratic societies tend to become sclerotic. Not because they suddenly become foolish, but because they become crowded with entrenched interests that resist the shock of the new. Reform is not blocked by ignorance so much as conscious, organised opposition.

Machiavelli saw this long before modern economics. He observed that “there is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things” (The Prince, 1532).

Those who benefit from the old order resist fiercely; those who might benefit from the (untried and embryonic) new are uncertain, hesitant, or divided. Reform is intrinsically hard, even when it is vitally necessary for the larger society.

Why Change Requires Shock

As the web of special interest groups unfolds over decades, the system slows. It becomes less adaptive, less efficient, more preoccupied with managing its own accumulated complexity; the barriers to change are thus constructed.

Significant reform so often requires a countervailing force of unusual magnitude: economic crisis, political upheaval, war, or the arrival of disruptive technologies that make old arrangements untenable. Olson noted that societies experiencing social collapse, such as Germany and Japan after 1945, often exhibited faster growth in the following decades, partly because entrenched interests had been dismantled in defeat.

Marx, in his own way, grasped part of this dynamic. He spoke of a tension between the “forces of production” and the “relations of production”. When the former advance beyond what the latter can accommodate, strain builds. Something must eventually give. Despite Marx’s legendary revolutionary optimism, it’s far from a quick process.

The Role of the Public

Where does this leave “the people”? Not as sovereign masters in the romantic sense, nor as mere dupes. Most people are busy with their own lives; rationally inattentive to national politics. They rely on heuristics: party labels, reputations, broad impressions of competence or trustworthiness. People become aware in broad outlines when the current set-up is stalled and on a road to nowhere; when their own hopes of fulfilment are being dashed.

Why You Will Not Find a Single “Right Answer”

At fifteen, I wanted a method that would tell me the correct policies, the ones I should support, just like a calculation produces a correct result.

It took me a good few years to comprehend that there are no such methods, because political questions are not of that kind. They always involve trade-offs with winners and losers and everyone fights and obfuscates for their advantage. There is no neutral vantage point from which all interests align, although all parties will pretend the opposite.

So don't look for purity in politics. You will not find it. Look instead for cui bono: who benefits, who pays, who is organised, who is left in the cold. Watch out for bad arguments: specious narratives which make you wonder how anyone could ever believe that - special interests, dressed up in the garb of universal idealism, often look like that.

Hopefully you will see more clearly than I did at your age. You will not be seduced by moral hectoring, self-satisfied self-righteousness. 

Instead, you may take quiet satisfaction in looking behind the curtain at those little men and women pulling the levers and pretending to be wizards.

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Parents Write to their Son...

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Dear Son,

We’ve been thinking about your children - our grandchildren - enrolled as they are in primary school, barely socialised, learning the basic skills of reading, writing and arithmetic. It used to be so easy, when society was stagnant and slow-moving, to take a view of their future development and prospects.

Develop character, we’d say, master literacy, read the canon, be numerate, follow your interests - musical, sporting, artistic, scientific in any combination - and gradually perfect your skills. Society, the economy, will offer you a niche: you’ll advance, find your place and with luck be happy and fulfilled.

How does that work when there are no more niches?

In economic terms, human workers are general purpose primates pressed into use to carry out industrial processes. Correctly, employers do not find that a very good solution. Whenever automation has delivered improved performance at a lower cost, employers move swiftly to remove said workers from the mix - and the economy grows faster.

Up to now, automation has been coarse-grained. The lathe is a productivity amplifier, but it needs an operator, as well as stuff moved from here to there in the workplace. The economists said, with justice, that the bad jobs were automated - but new and more interesting ones were then created. Largely true up to now.

The combination of ‘Artificial General Intelligence’ (AGI) combined with mass-produced humanoid robotics replaces those human-powered gaps in automation with exemplary artificial workers: fine-grained automation. Employers in diverse sectors of the economy will ask themselves: why do I need to hire any human workers at all?

They could be right. And where does that leave our grandchildren?

2005 was the last year human beings were able to beat the best computer chess engines. Yet still the human championships proceed, we still have great players, people still care. The Tour de France still attracts millions of spectators, despite the fact that anyone on a motorcycle can easily defeat the greatest of road-racing champions on the steepest incline.

A paradox? People empathise with those facing challenges and predicaments. We feel the pain, applaud the courage and identify with the key personalities. We are social creatures and the so-competent machines are not included in the circle of ‘us’.

The philosopher Immanuel Kant strikingly emphasised that a person should always be treated as an end in themselves, never merely as a means to an end. In such an ethics our liberation from the mandatory workforce is a chance to be free, to be our true selves - provided we have the resources to exercise that freedom.

How should we prepare our grandchildren for such a benign future? It’s not a new problem: the elite have always considered themselves to be in that situation. Their answer is the foundation of elite schooling: the well-rounded individual, versed in the arts and sciences, with practical as well as theoretical skills, steeped in the best of our culture, prepared to advance it through their own creative effort. There’s even a latin tag.

But for everyone to be an aristocrat, the goods produced by the economy must be distributed equitably. We've all seen fiction where the discarded unemployed litter the shanty-towns which surround the gleaming metropolis of the elite - those who own the economy and appropriate its proceeds.

Our grandchildren should be politically-aware, and be prepared to join with their peers in preventing such a dystopia. It won’t be easy; there is no reason at all to anticipate the end of politics, of states, of aggression, of war - even if machine systems are doing almost all of the strategy, tactics and actual fighting.

So in summary, I suggest a broad education in whatever direction the children wish to go, to prepare themselves to properly interface with the almost science-fictional automation environment in which they will be embedded, and so that they will be able to leverage it to fulfill their potential: to be ends in themselves.

Best Wishes,

Clare and Nigel.

Nothing worse than elderly relatives bearing advice

Hi fellow comrades-in-arms for justice,

Let me introduce myself. I'm a student, a radical and passionate for change. I despise the tired establishment of this country which only ever presides over failure. Everything’s broken; nothing gets fixed; I'm terminally bored.

And that's why I’m wired for action.

Get outta the way, Grandpa!

Speaking of that, my dad gave me a copy of a letter my granddad wrote to me years ago - before he died. It was kept for me until I was eighteen! How condescending is that? I hate all that advice from beyond the grave stuff.

So here's an extract of what I have to put up with - just hear the pompous pontification, the smug condescension!

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“... It is the destiny of teens and twenty-something's to yearn for a cause, to join a movement of like-minded people fighting for a better future for all, as they see it. The activist tribe is intoxicating: self-righteous events follow one from other; there is no shortage of parties and romantic partners. Loneliness is banished, life is collective, active, exciting and seldom boring.

“The cause is seldom analysed too closely or too seriously. Christianity once promised Salvation and Heaven-on-Earth; Marxism promised a radical equality, the end of oppression, the unlocking of all the forces of progress; climate activism fights clear enemies to save a biosphere fit for all the people.

“But it takes years of immersion in the esoteric doctrines of the cause before its objectives, strategies and tactics can be properly understood and deployed. Rebuttals which are compelling rely upon complex analyses spanning several disciplines with which you will not, at this stage of your life, be familiar. During your period of apprenticeship you will be emotionally committed to the movement, chained to the induction process … and immune from outside criticism which you will find either tribal nonsense or too sophisticated for easy comprehension.

“And here is a meta-critique to which you are also immune.

“It is in the nature of young people, particularly those in somewhat elite institutions such as the universities, to believe they are owed a pathway to future success. In advanced economies, however, the pyramid is steep - and narrow at the top. Few aspirants will make it, and those few will generally owe their success to their family connections (in a very few cases, outstanding talent may hack it).

“The struggle therefore is bogus. It cannot deliver you what is promised. The Kingdom of God on Earth will not happen; the Communist Revolution will require an evolution to a world utterly different from your own; the Green movement's strategy is utterly decoupled from actually solving the problems it purports to address.

“So enjoy the struggle while you remain starry-eyed. Then enjoy it in retrospect as a fulfilling coming-of-age. Unless you were born with silver spoon in mouth (you were not!) - or you get very lucky indeed - you will need to readjust your objectives as you leave your twenties. We live in a complex society: hopefully you didn't trash your studies, your CV or your reputation in ways that prevent you from finding a life trajectory which really does work for you in future.

“Have fun - I wish you well...”

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Easy for him to dump all over us, isn't it. He's dead.