The Space Between Things

A life of John Venn, told in circles

(Factual scaffolding: Venn was born in Hull in 1834 and died in Cambridge in 1923; he worked at Gonville and Caius College, Cambridge; published The Logic of Chance in 1866; introduced what we now call Venn diagrams in his 1880 paper; resigned from the Anglican clergy in 1883; served as President of Caius from 1903 until his death; and he also designed a quirky cricket bowling machine in the early 1900s.)

PROLOGUE: The First Circle

There are men who spend their lives inside a single shape.

They learn its boundaries young—what fits, what does not. They inherit its rules like heirlooms: polished, worn, unquestioned. The circle is comforting because it is complete. It makes a small universe out of the mind.

John Venn’s first circle arrived with a gentle violence, as circles often do: not as prisons, but as promises.

The family line was thick with faith, with sermons and certainties stacked like books in a rectory. In Hull—wind off the water, salt on the windowpanes—his childhood felt like an argument conducted politely. The sky said one thing; the church said another; the world, unasked, said both.

He learned early that truth could be a room you entered in silence.

And he learned something else, too: that the mind wants to see what it believes.

Some boys traced ships. Some traced maps. John traced relations—this belonging to that, this inside that, this beside that, this crossing that, this refusing that. He did not yet have circles for them, not formally, but he had the hunger: to draw a world that would hold still long enough for meaning to be noticed.

He would spend a lifetime trying to draw the part that doesn’t hold still.

The space between things.

CIRCLE I: FAITH

Scene: The collar

He is ordained because the story has always moved in that direction, like water down a familiar ditch. He wears the collar and feels, for a time, that he has been fitted properly into the old set.

But there is a secret problem with inherited circles:

They are perfect only from the inside.

From the outside, every circle is a claim.

In the quiet hours—late, when the candles shrink and the mind becomes honest—John begins to notice a tenderness that feels like betrayal: he is still devoted, and yet he cannot pretend he doesn’t see the seams.

Logic is not his enemy. Logic is his conscience.

It arrives like an unwanted angel: not to destroy faith, but to ask what faith means when it is asked to account for itself.

He begins lecturing, begins teaching, begins living inside Cambridge, inside rooms where thought is treated as a sacrament. At Gonville and Caius College, the days are measured in bell tones, footsteps, and the peculiar hush of old stone that has heard too much to be surprised by anything.

Faith remains a circle.

But it starts to drift.

CIRCLE II: LOGIC

Scene: The book of chance

In 1866, he publishes The Logic of Chance.

The title sounds like a paradox even to sympathetic ears: logic—clean, exact, starched; chance—muddy, windblown, laughing. Yet Venn insists the world belongs to both. Not as enemies. As neighbors.

He writes about probability in a way that feels almost moral: not as superstition dressed in numbers, but as something grounded in what happens again and again. A kind of humility: you don’t get to declare the universe from a single anecdote. You count. You watch. You admit what you don’t know.

A colleague tells him—half compliment, half warning—that he is trying to make uncertainty respectable.

John smiles without meaning to. That is exactly it.

At night, he draws diagrams that aren’t yet diagrams, shapes that aren’t yet agreed upon, as if he’s trying to design a language the world can speak without lying.

And in those nights, a visitor begins to appear.

Not physically. Not even as a ghost.

As a presence in the margin.

A name.

Euler.

CIRCLE III: DOUBT

Scene: The rivalry that time allows

Leonhard Euler has been dead for decades—more than a century, in fact—but in John’s mind, Euler sits like an old portrait whose eyes follow you.

Euler had used curves to illustrate reasoning long before John—closed shapes as tidy little universes for syllogisms. In the history of logic, Euler’s circles had become a kind of shorthand for “obviousness.”

The trouble with obviousness is that it ages into arrogance.

John begins to feel—strangely, personally—that Euler’s circles are too confident. Too eager to show only what matters. Too willing to omit the embarrassing possibilities.

Euler’s method is elegant: it shows the relationships that actually obtain. (It refuses to clutter the page with what isn’t needed.) 

But John has a different temperament. He trusts what is possible—especially the possibility that the obvious picture is incomplete.

He speaks to Euler sometimes, silently, as if addressing a senior colleague whose work he both admires and resents:

“You draw the world as you wish it to behave.” 

“I will draw it as it can behave—every way it might.”

Euler, in John’s imagination, replies in a voice like polished brass:

“Then you will drown in your own thoroughness.”

John is not offended. He is frightened—because he suspects Euler is right.

And still, he keeps drawing.

Because thoroughness, in John’s mind, is not vanity.

It is mercy.

INTERSECTION: FAITH ∩ LOGIC

Scene: The resignation

By 1883, the drift becomes a break: he resigns from the clergy, concluding that Anglicanism cannot be reconciled with his philosophical beliefs.

This is not a conversion story. It is something quieter and more painful: the story of a man who cannot pretend that his mind belongs to his community as neatly as his body does.

He does not become a caricature—neither triumphant skeptic nor bitter apostate. He simply steps out of one circle and admits, with a kind of private grief, that he still loves what he cannot fully inhabit.

If you listen closely, you can hear the Venn diagram trying to be born here—not as a classroom tool, but as a personal theology:

I belong to you. 

I do not belong to you. 

I belong to something that overlaps you.

Truth is not always a clean separation. Sometimes it is a shared region both sides deny.

INTERSECTION: LOGIC ∩ DOUBT

Scene: 1880 — The paper

In July 1880, he publishes the work that will outlive the rest: “On the Diagrammatic and Mechanical Representation of Propositions and Reasonings.”

He does not present it like a revolution. He presents it like a man tidying a room everyone has been living in too long.

Euler’s approach, he argues (with restrained English politeness that still cuts), is not general enough. It works—until it doesn’t. It illustrates some logical forms, but not all; it is guided by intuition, not a complete method.

So John does something that seems simple until you try to do it:

He draws circles not to show only the relationships that occur, but to show every possible relationship that could occur—including the empty, awkward regions no one wants to admit exist.

Two sets? You get four regions. 

Three sets? Eight. 

Every new circle doubles the demands of honesty.

Euler’s ghost chuckles in the margin: “See?” 

John answers by drawing the empty space anyway.

Because the empty space matters.

It is where falsehood is caught. 

It is where exceptions confess. 

It is where the mind stops flattering itself.

His circles are not merely shapes. They are an ethic:

Don’t just show what supports your conclusion. Show what could defeat it.

INTERSECTION: FAITH ∩ DOUBT

Scene: The moral sciences

In Cambridge, he teaches logic and the philosophy of science as part of what was then called “moral science.”

“Moral” here does not mean sermons. It means the human question: how does a mind decide what to believe?

John’s students arrive thinking logic is a tool for winning arguments. John tries to show them that logic is a tool for losing arguments gracefully—losing them when they deserve to be lost.

He does not mock certainty. He respects it. But he respects it the way you respect a strong drink: you treat it carefully because it can make you stupid.

Sometimes, when he is alone, he wonders whether his diagrams are prayers in disguise:

Not asking God for answers.

Asking the mind for humility.

CENTER: FAITH ∩ LOGIC ∩ DOUBT

Scene: The machine

Late in life, he builds something that seems—at first glance—like a joke:

A cricket bowling machine: wood and string and clever mechanics, a device that can bowl balls in a way that unsettles real batters.

People tell the story as trivia: “Did you know the Venn diagram guy also built a bowling contraption?”

But there’s a deeper continuity.

To build a machine that bowls like a human, you have to model the overlap of things humans rarely separate cleanly:

Force ∩ timing ∩ spin. 

Physics ∩ craft ∩ play. 

Precision ∩ unpredictability.

The machine is not a detour from his life’s work.

It is his life’s work wearing a grin.

He has spent decades drawing the world’s invisible regions. Now he builds a device that makes an invisible region visible on a field: the strange space where a ball obeys rules and still surprises you.

Euler’s ghost, oddly softened now, says:

“You could have been only a theorist.”

John tightens a knot, adjusts a spindle, watches the arm swing, and answers without words:

“And missed the joy of proving it with wood.”

THE LAST CIRCLE: LEGACY

Scene: President, old man, quiet rooms

From 1903 until his death, he serves as President of Caius. The position is dignified; the days are slow; the rooms are familiar in the way a long marriage is familiar—comforting, sometimes suffocating, always real.

Outside the college, the world becomes louder: modernity arriving with engines, cables, newspapers, war-winds, new certainties, new lies.

Inside, John becomes increasingly interested in histories—of the college, of families, of how human lives form lineages the way ideas do. 

Everything, when you look long enough, becomes a question of sets.

What belongs to what? 

What inherits what? 

What overlaps without admitting it?

Time itself starts to look like a diagram.

EPILOGUE: The Diagram Labeled “John Venn”

On an April day in 1923, he dies in Cambridge.

It is tempting to end there, neatly, like a textbook does.

But John would not approve of neat endings.

So imagine, instead, a final scene—quiet, almost impossible to witness.

A desk. A page. A pen held by an older hand that has done this a thousand times and still finds it mysterious.

He draws two circles.

The left is labeled:

JOHN VENN

The right is labeled:

HUMANITY

He hesitates.

He thinks of his childhood faith and his adult resignation. 

He thinks of chance measured honestly. 

He thinks of Euler’s elegant omissions and his own stubborn insistence on the empty regions. 

He thinks of wood and string and the ridiculous beauty of a ball that spins like a thought.

Then he draws the overlap.

Inside that shared region he writes, very small:

THE SPACE BETWEEN THINGS

He stares at it.

And for a moment, the diagram does what he always wanted diagrams to do:

It tells the truth without needing to argue.

Because the left circle will soon be empty.

But the overlap—the way he taught minds to be honest about belonging—remains, passed hand to hand, classroom to classroom, argument to argument, long after the man himself has stepped out of the set.

Somewhere, faintly, Euler laughs—not cruelly now, but like an old rival finally admitting admiration.

And John, who never needed to win the rivalry anyway, leaves behind the most human shape of all:

Two circles, imperfectly drawn,

holding—between them—

a region where we can finally say,

without shame,

that we are complicated,

that we overlap,

and that the truth is often found

not in the borders,

but in the shared, unclaimed middle.