Anti-mathematics is the new, the 100% abstract, 100% logical, 100% lucid way… to describe transient reality.  And there are transient realities all around us, quite different from —actually much commoner than— the allegedly timeless realities onto which so much attention has, historically, been paid.

How did it come about that transient reality has been so comprehensively ignored and undervalued? Why did it take more than two millennia for mathematics to be put firmly in perspective —as simply one of two polar-different 100% abstract languages?

Our lives are, of course, streams of consciousness, and their transient nature is, equally obviously, of their essence. Our awarenesses are in a perpetual state of change… our sense of relative values changes, our feelings change, our moods change, our images change, our intentions, ideas and agendas change.  As an aeroplane can only stay in the sky by moving fast, so our joie de vivre —our awareness of being alive and conscious— can only carry meaning by moving forward.

And the most concentrated meanings we ever feel, or meet, have this transience at their centre.  So how can we properly and seriously focus onto the meaning of mathematics, the much-lauded language which valorises timelessness, the epitome of absent transience?

To the Classical Greeks mathematics was a remarkable, marvellous, rational language —quite unlike anything which had gone before. It was the metaphorical midwife which ushered-in the glorious age of Pericles, Socrates, Plato and Aristotle.  It highlighted pattern, principle, order, laws, stability, structure…sought-after emphases in an idyllic corner of the known world which was also, alas, prone to war, plunder and inter-city strife.

The Roman Empire —a subsequent ‘proto-Enlightenment’— was based on the lucidity of its Greek ‘Bible’, Euclid’s Elements. The Imperium Romanum was more brutal than the 18^thcentury, but equally rooted in blind faith in the kind of authority and regimentation which stems from maths.

So mathematics, left unchecked and unhindered by any opposing paradigm, was, we can now see, dangerously uncapped. It appeared —to crude opinion— to justify brutality.  It claimed a monopoly of rationality. It claimed to account, in principle, for everything. It claimed to be the language used by God when He created the universe. These bold, extravagant claims were widely believed, rarely, if ever, queried. There appeared to be not the slightest basis for a counter point of view.

Such a missing basis has, however, now arrived: anti-mathematics.

Anti-mathematics is crafted, like mathematics, out of pure abstraction.   Its building block —jumping random sequences—- is composed of blank tallies, like mathematics… Its standardised reliable objects are created by reification, like mathematics… It represents our best hope for future cultural stability and meaning.  It could, once it reaches the threshold of wide recognition, become the mainstay of our intellectual confidence, a renewer of cognitive health, a restorer of faith in reason.

But that Then is not Now. Today it is still at its earliest stage, and, being only a dimly-observed, embryo research programme —one carrying a heavy load of expectations—  it needs to be better understood.

Meaning counts. Meaning which encompasses a high degree of over-lapping and triangulation counts more than impoverished, patchy or threadbare meaning. It gives our lives their shape, their feel and confidence. But we are forever searching for richer meaning… meaning stretching beyond familiarity and standard norms… meaning which resonates, amplifies, exemplifies purpose, pride and intent.

It is a search which has historically suffered setbacks: meaning is not composed of Teflon, and it is not an open book.

The Garden of Eden is a mythic, traditional metaphor for a moment of  sudden meaning-loss, of broken confidence.

But around 1900 another historic sudden meaning-loss occurred. Two utterly incomprehensible problems appeared.  Physics was thrown into confusion by the sheer unbelievability of Michelson-Morley’s discovery of the relativity of light. And shortly afterwards the logic of sets, underlying mathematics also lost its credibility. Heidegger later called this sudden dimming of the light of reason ‘The End of the Enlightenment Project’.  A Door had Slammed: a previously taken-for-granted confidence in the power and rationality of the human mind had gone.

Ever since that dimming of the light, our search for meaning has been compromised —jinxed— by an unknown, unnamed, unfathomed block. So, instead of trying to make progress in understanding our two basic disciplines… what passes for “serious modern experience” has been sidetracked… distracted towards alternatives: in hedonism, IT gimmickry, in money, credit, travel, sports, exploring, climbing, building, fantasy,  convenience, comfort, lifestyle… etc.

Everything, it seems, but a renewed quest for the core meaning which has gone. Familiarity with these side tracks doesn’t compare with the feeling of peace of mind —which can only come from stabilising and renewing the deepest bases of our reasoning and meaning.

Now hope and help are, belatedly, on the way… but the mental damage caused by more than a hundred years of demoralisation won’t just disappear. Culture has diluted, judgment has weakened, solidarity has lost its nerve, and, to make matters worse —much worse— genuine (mind-growing) education has all-but disappeared.  We act as if nothing untoward has happened: but confidence-sapping “stuff” has happened… Previously unexpected lapses of competence, of sense and rigour are apt to surface. After a summer of too much heat, too little rain, savage floods, covid-19, war in Ukraine, rocketing prices, inflation, substance abuse, street crime and fraud… it takes an effort of stoic resolve to sustain our positivity and cheerfulness.

What’s to be done?

The first step is to apply the demystification of maths to mathematic education. Mathematics teaching can be transformed by switching to narrative maths, maths interpreted firmly as the Pathfinder for Progress. This is vital, because mathematics teaching is at the heart of the crisis in education.  And the crisis in education is at the heart of today’s gloomier-than-ever mood.

CHRISTOPHER ORMELL 1^st September 2022