How Concepts Become Possible: IV. When the Circle Breaks

A new conceptual possibility does not necessarily free us from the constraints of the old world.

Sometimes it does something more interesting.

It gives us a new place from which the old constraints can be tested.

This is what happened to Johannes Kepler.

Copernicus had moved the centre of the planetary system. But he had not abandoned the circle.

For Kepler, the circle was more than a convenient mathematical device. It belonged to a deeply established conception of cosmic order. The heavens were supposed to exhibit a perfection that terrestrial things did not possess. Perfect celestial motion meant uniform circular motion.

The circle was not merely a shape.

It was an expectation about what the heavens ought to be.

And then the observations refused to cooperate.

The inherited possibility

Kepler inherited a remarkable intellectual situation.

Copernicus had opened the possibility that the Earth moved around the Sun. Tycho Brahe had accumulated observations of planetary positions of unprecedented precision. Kepler had the mathematical resources with which to compare theory and observation.

But he also inherited assumptions.

The planets should move in circles.

Their motions should be uniform.

The heavens should display mathematical harmony.

These assumptions did not simply restrict what Kepler could think. They helped determine what he initially looked for.

This is an important feature of conceptual possibility.

The concepts that make one discovery possible can also make another discovery difficult.

An intellectual environment is not merely a collection of affordances. It is also a field of expectations.

Mars refuses the circle

Kepler's problem became particularly acute with Mars.

The observations available from Tycho Brahe were accurate enough that a circular orbit could not accommodate them satisfactorily.

The discrepancy was small by ordinary standards.

But it was too large for Kepler.

The famous story that he eventually found an ellipse after abandoning circular orbits can make the process seem deceptively straightforward. In reality, the route was tortuous.

He tried different circular constructions.

He explored combinations of circles.

He searched for geometrical arrangements that might preserve the traditional ideal while accommodating the observations.

Again and again, the data resisted.

The important point is not simply that Kepler made an error and then corrected it.

It is that the error belonged to the conceptual world in which he was working.

The circle was not an arbitrary guess.

It was what the prevailing conception of celestial order made plausible.

When constraint becomes destructive

This gives us a different role for evidence.

In our previous post, evidence helped a structure take shape.

Here, evidence does something more dramatic.

It destroys an affordance.

The observations do not tell Kepler, in any simple deductive sense, "use an ellipse."

They tell him that a whole family of possibilities he had regarded as privileged cannot survive.

The constraint works negatively before it works positively.

It closes a path.

And once that path is closed, other possibilities become visible.

This is a crucial feature of conceptual evolution.

A constraint can create possibility by removing an impossibility that had previously been taken for granted.

The breaking of the circle does not immediately reveal the ellipse.

First, the circle has to cease being sacred.

The ellipse was already available

There is an irony here.

The ellipse was not a newly invented mathematical object.

It had been known since ancient Greek mathematics.

The novelty was not the shape itself.

It was the role assigned to it.

An ellipse had been available as a mathematical possibility for centuries. What had not been available was the possibility that an ellipse could describe the fundamental motion of a planet.

This distinction is important.

A concept can exist in a culture without being available for a particular explanatory purpose.

The conceptual possibility of the ellipse was already present.

The astronomical possibility of the ellipse was not.

Kepler's achievement was therefore partly a matter of reassigning an existing possibility within a new relational structure.

That is conceptual evolution again: not necessarily creating a new element, but changing what an element can do within the system.

The two failures

There is something especially revealing about Kepler's persistence.

He was not simply looking for any curve that fitted the observations.

He was trying to preserve as much as possible of the inherited conception of celestial order.

This is why the ellipse is more than a successful curve-fitting exercise.

It emerges only after Kepler has discovered that the old conceptual structure cannot survive the evidence.

The process therefore has two distinct moments:

the failure of an established possibility,

followed by

the emergence of another possibility capable of taking its place.

The second depends upon the first.

This suggests that conceptual evolution is not always additive.

Sometimes progress requires the loss of a possibility.

An idea that once organised the world becomes an obstacle to seeing what the world can afford.

From circle to ellipse

Once Kepler accepts the ellipse, the planets acquire a new kind of intelligibility.

Their paths no longer have to conform to an ideal of perfect circular motion.

The deviation from circularity is not an imperfection to be explained away.

It is part of the structure itself.

The heavens become mathematically intelligible by becoming less like the heavens were supposed to be.

This is a profound conceptual reversal.

The old conception treated mathematical perfection as a criterion for astronomical truth.

Kepler discovers that empirical adequacy can require abandoning the inherited conception of perfection.

The world does not have to conform to our preferred mathematics.

Our mathematics has to become capable of conforming to the world.

Yet this should not be understood as the triumph of raw observation over theory.

Kepler did not simply look at Mars and see an ellipse.

The ellipse became visible as a possibility because of a highly developed mathematical and astronomical conceptual environment.

Observation supplied constraint.

Mathematics supplied possibilities.

The discovery occurred in the relation between them.

Possibility is relational

This brings us to a deeper point.

An ellipse is not inherently an explanation of planetary motion.

Its significance depends upon the relations in which it is placed.

In one conceptual environment, it is a geometrical figure.

In another, it becomes the orbit of a planet.

The physical world has not changed.

What has changed is the space of relations through which the figure can function as an explanation.

This is why it is misleading to think of conceptual possibilities as if they were objects stored in a warehouse waiting to be retrieved.

The possibility of the ellipse was available for centuries.

The possibility of planetary elliptical motion required a different relational configuration.

Conceptual possibility is therefore not simply about what can be imagined.

It concerns what can become intelligibly related.

Kepler and the limits of inevitability

Was Kepler's discovery inevitable?

Perhaps, eventually, the increasingly precise observations would have forced someone to abandon circular orbits.

But that is not the same as saying that the ellipse was inevitable.

The observations constrained the available possibilities.

They did not dictate the conceptual route by which the constraints would be understood.

Kepler's mathematical commitments, his ideas about harmony, his willingness to preserve and then abandon inherited assumptions, and his particular persistence all mattered.

Another thinker might have produced a different mathematical representation.

Another might have regarded the discrepancies as observational error.

Another might have modified a different part of the system.

The evidence narrowed the field.

It did not plough the field by itself.

From Copernicus to Kepler

The relation between Copernicus and Kepler now becomes especially revealing.

Copernicus changed the centre.

Kepler changed the shape.

The first opened a new conceptual space by questioning a supposedly necessary relation.

The second explored that space under increasingly severe empirical constraint.

Copernicus made it possible to ask whether the Earth might move.

Kepler discovered that, once it did, the planets need not move in circles.

The second discovery depended upon the first.

And this is another feature of conceptual evolution:

A new possibility can create the conditions under which another possibility becomes necessary to consider.

Possibilities can therefore be generative.

They do not merely occupy an intellectual field.

They alter the field for whatever comes next.

When the circle breaks

Kepler gives us another mode by which concepts become possible.

Darwin showed us convergence: an idea can emerge independently when an intellectual environment strongly affords it.

Watson and Crick showed us constraint: a structure can emerge as multiple forms of evidence become mutually intelligible.

Copernicus showed us recentring: a new possibility can arise when an apparently necessary relation is made contingent.

Kepler shows us constraint through failure.

A conceptual possibility may become visible only after an inherited possibility has been shown unable to survive.

The ellipse was not discovered because someone suddenly imagined a strange new shape.

It became possible because the circle could no longer bear the weight placed upon it.

Sometimes the world does not tell us what to think.

It tells us what we can no longer think.

And that may be enough to change the course of thought.

How Concepts Become Possible: III. When the Centre Moves

Sometimes a new possibility appears because the evidence has accumulated until a particular structure becomes compelling.

Sometimes something stranger happens.

The evidence remains much the same, but someone changes the place from which it is understood.

The Copernican revolution is a particularly revealing example.

It is often told as the discovery that the Earth moves around the Sun rather than the Sun around the Earth. But that formulation makes the achievement sound like the discovery of a new astronomical fact.

Copernicus did something more subtle.

He moved the centre.

The world before Copernicus

By the sixteenth century, the Ptolemaic astronomical system was already extraordinarily sophisticated.

It was capable of representing the apparent movements of the planets with considerable mathematical precision. Its complexity had grown, but complexity is not the same thing as failure.

The problem was therefore not simply that observations had become impossible to explain.

There was another problem.

The existing astronomical system had made the Earth the fixed centre of a universe whose celestial motions were organised around it. Copernicus wondered whether this arrangement was necessary.

What if it wasn't?

What if the apparent motion of the heavens was partly a consequence of the Earth's own motion?

This is a very different kind of question from asking which curve best fits a set of observations.

It asks:

What if the frame within which the observations are organised is not privileged?

A change of centre

The striking thing about heliocentrism is that it does not initially add a new observation.

The planets still appear in the sky as they did before.

The observations available to Copernicus do not suddenly change when the Earth is moved from the centre.

What changes is the relational organisation of those observations.

The retrograde motion of Mars, for example, can be understood differently if the Earth is itself moving around the Sun. What had appeared to be a peculiar motion of another planet can become an effect of the changing relation between two moving bodies.

The phenomenon has not changed.

The relation through which it is understood has changed.

This is a recurring feature of conceptual transformation.

A thing that appears anomalous within one conceptual arrangement can become ordinary within another.

The anomaly was never necessarily a property of the thing itself.

It may have belonged to the relation between the phenomenon and the framework used to construe it.

But was heliocentrism forced by the evidence?

Not in any simple sense.

This is what makes Copernicus especially interesting.

The astronomical observations available in his time did not uniquely establish heliocentrism. Indeed, the Ptolemaic system could represent the apparent motions of the planets.

Nor did Copernicus immediately provide the decisive physical explanation that would later make the new system compelling.

His system still retained many inherited assumptions about circular motion and uniformity.

So the Copernican revolution cannot simply be described as the inevitable consequence of better observations.

The conceptual possibility came first.

Copernicus made it possible to ask:

What would astronomy look like if the Earth were not the centre?

That question reorganised the space of possible explanations.

Possibility before proof

This gives us an important addition to our emerging account.

With Darwin, the intellectual environment increasingly afforded a particular explanatory possibility.

With DNA, a network of empirical constraints helped select a structure.

With Copernicus, a new possibility emerged because an apparently fixed relation was made variable.

The Earth did not have to be the centre.

Once that became thinkable, a whole collection of astronomical relations could be reorganised.

This is an important characteristic of conceptual possibility.

Sometimes what prevents us from seeing a possibility is not a lack of information.

It is the assumption that some relation is necessary when it is only customary.

The centre may be moved.

The boundary may be moved.

The distinction between two categories may be questioned.

The hierarchy may be inverted.

A conceptual revolution can begin with a very small question:

Does this really have to be here?

The cost of moving the centre

But moving the centre is not free.

A conceptual framework is not merely a collection of propositions. It is a network of mutually supporting relations.

Change one relation and others begin to move.

If the Earth moves, what happens to falling objects?

Why don't we feel the motion?

What holds the planets in their paths?

Why does the sky appear to move?

What becomes of the traditional distinction between terrestrial and celestial motion?

Copernicus could change the astronomical centre without immediately answering all these questions.

That is part of the nature of conceptual innovation.

A new possibility does not have to arrive with a complete theory.

Sometimes its first achievement is simply to make a different set of questions possible.

Kepler will inherit the possibility

This is why the Copernican revolution cannot be understood in isolation.

Once the Earth has been displaced from the centre, the astronomical problem changes.

Johannes Kepler inherits Tycho Brahe's exceptionally precise observations and asks how planetary motion can be represented within the new framework.

The answer will not be what he expects.

The planets do not move in perfect circles.

They move in ellipses.

Here the mode of conceptual evolution changes again.

Copernicus opened a possibility by moving the centre.

Kepler will discover a structure through constraint.

The new conceptual space makes a new question possible; the evidence then begins to reshape the possibilities within it.

This is why conceptual evolution is rarely a sequence of isolated flashes of genius.

A possibility opened by one thinker can become the affordance for another thinker's discovery.

The second discovery may in turn make the first intelligible in ways its originator could not have anticipated.

A centre is more than a location

There is also something deeper in the idea of the centre.

A centre is not merely a point in space.

It is a way of organising relations.

To call something the centre is to specify how other things are related to it.

The Earth-centred cosmos therefore did more than place the Earth in a particular location. It organised the conceptual relations among Earth, heaven, motion and observation.

Moving the centre changed those relations.

This helps explain why conceptual change can be so disruptive even when the empirical objects remain the same.

The stars do not move differently because Copernicus changes his model.

The planets do not suddenly acquire new trajectories.

What changes is the relational structure through which their movements become intelligible.

And once that structure changes, the world appears differently.

The possibility of another world

There is therefore something almost paradoxical about conceptual discovery.

A new concept can reveal possibilities that were always physically available but were not previously available as possibilities for thought.

The Earth had always been capable of moving around the Sun.

But heliocentrism required more than that physical possibility.

It required the conceptual possibility of treating the Earth's motion as fundamental to the explanation of what appeared to be celestial motion.

This distinction matters.

There can be possibilities in the world that are not yet possibilities within a conceptual system.

Conceptual evolution partly consists in bringing these two spaces into new relations.

The world does not wait for us to conceptualise it.

But what the world can become for thought depends upon the concepts through which its relations are organised.

When the centre moves

Copernicus therefore gives us a third way in which concepts can become possible.

Darwin showed us convergence: an idea can become increasingly afforded by an intellectual environment until independent thinkers arrive at it.

Watson and Crick showed us constraint: a structure can emerge as multiple pieces of evidence become mutually constraining.

Copernicus shows us recentring: a possibility can emerge when a relation that seemed fixed is treated as variable.

The centre moves.

And once it does, the possibilities move with it.

This does not mean that every conceptual revolution begins by changing the centre. Nor does it mean that Copernicus simply invented heliocentrism out of nothing.

His work depended upon an immense inheritance of astronomical observation, mathematical technique and earlier cosmological thought.

But the crucial act was not the discovery of another observation.

It was the discovery that the organisation of the observations could be otherwise.

That is a profound kind of possibility.

Before Copernicus, the question was largely:

How can the heavens be represented from the centre?

After Copernicus, another question became available:

What happens if the centre itself moves?

Sometimes, to make a new world of thought possible, we do not need more facts.

We need to discover that where we are standing is not where we have to stand.

How Concepts Become Possible: II. When Evidence Takes Shape

An idea can be in the air before anyone has formulated it.

But sometimes the situation is different. The problem is not that a solution is becoming increasingly imaginable. Rather, a scattered collection of observations begins to exert pressure on one another until a particular structure starts to emerge.

The discovery of the structure of DNA is a remarkable example.

It is usually remembered as the discovery of the double helix by James Watson and Francis Crick in 1953. But the story is more complicated, and more interesting, than that.

The double helix was not simply imagined and then confirmed.

Nor was it simply deduced from a single decisive experiment.

It emerged from a field of mutually constraining relations.

A structure waiting to be found?

By the early 1950s, much was already known about DNA.

The molecule was known to be extraordinarily important biologically. Evidence had accumulated that DNA was the carrier of hereditary information. Its chemical constituents were known. Erwin Chargaff had established regularities in the proportions of its bases. X-ray diffraction studies, particularly those associated with Rosalind Franklin and Maurice Wilkins, were revealing something about its physical structure.

But these facts did not announce a double helix.

They were pieces of evidence belonging to different experimental and conceptual contexts.

The problem was to find a structure capable of bringing them into relation.

This is a different kind of intellectual possibility from the one we encountered with Darwin.

With Darwin, an explanatory principle was becoming increasingly available within an intellectual environment.

With DNA, the challenge was more like this:

What structure could make all these different observations true at once?

The distinction matters.

Constraints that constrain one another

Chargaff's observations suggested relationships among the bases.

The chemical properties of the nucleotides constrained the ways in which they could be arranged.

The X-ray diffraction evidence constrained the overall geometry of the molecule.

The known dimensions of the molecule constrained possible arrangements still further.

And the biological requirement for replication imposed another extraordinary condition: whatever structure was proposed had somehow to make heredity physically intelligible.

Each constraint changed the significance of the others.

A proposed structure that satisfied one piece of evidence could fail another.

A chemically plausible arrangement might conflict with the physical dimensions suggested by diffraction.

A geometrically elegant model might fail to explain the observed relationships among bases.

The problem therefore wasn't simply to accumulate facts.

It was to find a configuration in which the facts could constrain one another coherently.

The discovery was a structure that could survive the whole network of constraints.

The model as a possibility

This is where Watson and Crick's model-building becomes particularly revealing.

A model is not merely a picture of something that already exists. It is a way of proposing a set of relations and asking whether the world will permit them.

A successful model therefore occupies an unusual position between imagination and evidence.

It begins as a possibility.

Then the evidence either sustains that possibility or destroys it.

In this respect, scientific discovery is not simply a matter of looking harder at reality. It is often a matter of constructing possibilities that reality can constrain.

The double helix became compelling because it did more than resemble the available evidence. It made disparate constraints mutually intelligible.

The pairing of bases, the complementary strands and the geometry of the molecule were not independent facts. They became aspects of a single relational structure.

And this is why the discovery is more interesting than the phrase "Watson and Crick discovered the double helix" suggests.

What was discovered was not merely a shape.

It was a way in which many things could be related.

The importance of Franklin

The historical story also warns us against treating conceptual discovery as the achievement of an isolated mind.

The evidence from Rosalind Franklin's X-ray diffraction work was crucial to understanding the physical structure of DNA. Her famous diffraction image, together with other experimental results, placed strong constraints on the possible geometry of the molecule.

This doesn't turn the discovery into a simple collective achievement in which everyone contributed an interchangeable piece.

Different people were doing different kinds of intellectual work.

Some produced observations.

Some developed chemical knowledge.

Some identified mathematical or geometrical constraints.

Some constructed models.

Some recognised that a particular arrangement could satisfy several constraints simultaneously.

The discovery therefore illustrates something important about conceptual evolution:

A conceptual possibility can be distributed across a community before it becomes concentrated in a particular formulation.

No single investigator necessarily possesses the whole possibility.

The possibility exists in the relations among their activities.

When evidence takes shape

This may be the key difference from our first case.

With Darwin and Wallace, the intellectual environment was becoming fertile for a particular explanatory principle. Independent discovery revealed the strength of that convergence.

With DNA, the evidence itself was becoming structurally organised.

The distinction is subtle.

Evidence does not simply sit there waiting to be collected. What counts as a constraint depends partly on the questions being asked and the conceptual possibilities being entertained.

The X-ray pattern becomes evidence for molecular geometry because someone has a reason to ask what geometry could produce it.

Chargaff's ratios become structurally significant because someone asks how the bases might be related within a molecule.

The evidence therefore does not determine the conceptual possibility from outside.

It participates in its formation.

This suggests a more reciprocal picture:

Possibilities generate tests; tests reshape possibilities.

A proposed structure makes certain observations relevant.

Those observations constrain the structure.

The revised structure makes new relationships visible.

Those relationships generate further constraints.

Discovery becomes a movement between possibility and constraint.

Not deduction, not guesswork

This is why scientific discovery is difficult to describe as either deduction or inspiration.

Deduction begins with premises and derives what follows.

But the double helix was not simply deduced from the known facts. There were many possible arrangements, and the relevant structure had to be constructed.

Nor was it mere guesswork.

A guess becomes scientifically productive when it enters a field of constraints capable of selecting among possibilities.

The creative act is therefore not necessarily the production of something unconstrained.

It can be the production of a possibility that is sufficiently structured for the world to answer it.

This may be one of the deepest roles of scientific imagination.

Imagination opens a possibility-space.

Evidence closes some of its paths.

The interaction between the two can make a previously invisible structure visible.

The structure changes the questions

There is another important feature of the DNA case.

Once the double helix had been established, it did not merely answer the question of DNA's structure.

It created new questions.

If the strands are complementary, how are they separated?

How does each strand participate in replication?

How is information encoded in the sequence?

How does a sequence of bases relate to the production of proteins?

The new structure therefore became an affordance for further discoveries.

A concept or model does not merely occupy a possibility-space.

It can reshape the possibility-space that follows it.

The discovery of structure creates possibilities for explanation.

And those explanations create possibilities for new questions.

This is conceptual evolution in a particularly concrete form.

A second kind of possibility

We can now add a second form to our emerging picture.

Some conceptual possibilities become increasingly probable because the intellectual environment is converging upon them.

Natural selection is our first example.

Other possibilities emerge because multiple constraints can suddenly be satisfied within one relational structure.

The double helix is an example of this.

In the first case, the question is:

What explanatory principle is the intellectual environment beginning to afford?

In the second:

What structure could make these apparently separate constraints belong together?

These are not the same kind of discovery.

And neither is inevitable in quite the same sense.

The evidence may strongly constrain what can survive, without uniquely determining what will be proposed. The conceptual possibility still has to be constructed.

This leaves us with a small but important modification to our earlier picture.

An affordance does not merely make some ideas easier to think.

A constraint does not merely eliminate possibilities.

Together, affordances and constraints can participate in the emergence of a structure that was previously unavailable as an intelligible possibility.

The double helix was not simply waiting inside the data.

Nor was it invented independently of the data.

It emerged between possibility and constraint.

And that "between" may turn out to be where much of conceptual evolution takes place.

The next case will complicate matters further.

For Copernicus, the crucial move was not to discover a structure that satisfied a growing collection of constraints.

It was to ask whether the centre itself had been placed in the wrong place.

How Concepts Become Possible: I. When an Idea Is in the Air

What does it mean for an idea to be possible before anyone has thought it?

We often tell the history of science as a succession of discoveries. Someone sees what others have missed, finds the solution to a problem, and changes our understanding of the world. The discovery is then attributed to the person who made it.

But this picture leaves something important unexplained.

Why do some discoveries appear independently to different people? Why do some ideas emerge almost simultaneously in different places? And why, once a particular idea has appeared, can it sometimes seem almost inevitable — even though nobody had thought of it before?

The history of natural selection offers a particularly revealing case.

Darwin and Wallace

Charles Darwin did not invent the idea of evolution. By the nineteenth century, the possibility that species might change over time was already being actively discussed. Geology had made the immense age of the Earth difficult to ignore. The fossil record revealed forms of life that no longer existed. Comparative anatomy and biogeography showed striking patterns of relationship and distribution.

There was also a growing recognition that organisms vary, and that breeders can deliberately select particular variations and reproduce them.

What was missing was an adequate account of how variation could become cumulative.

Darwin spent years developing such an account. Then, in 1858, he received an essay from Alfred Russel Wallace describing a remarkably similar mechanism of natural selection. The two men's work was presented jointly to the Linnaean Society.

The coincidence is important.

It does not mean that Darwin's achievement was inevitable. Nor does it diminish his originality. Darwin's On the Origin of Species was the product of an extraordinary synthesis of evidence, argument and conceptual development.

But the independent emergence of the same basic mechanism suggests that something had changed in the intellectual environment.

Natural selection had become possible in a new sense.

The possibility did not exist merely in Darwin's imagination. It existed in the relations among a growing number of observations, concepts and problems.

Possibility without inevitability

This is an important distinction.

To say that an idea is in the air is not to say that it must appear.

A possibility can be strongly afforded without being determined.

The evidence for biological variation did not logically entail natural selection. Malthus's argument about population pressure did not entail it. Artificial selection did not entail it. Geological gradualism did not entail it.

But these things could be brought into a relation in which natural selection became increasingly intelligible.

The possibility was therefore not simply a property of one person's mind. It belonged, at least partly, to the relational structure of the intellectual environment.

This gives us a different way of thinking about discovery.

Perhaps an idea does not first exist as a fully formed possibility and then get discovered. Perhaps the possibility itself emerges as relations among things change.

Before Darwin, the facts were already there. What was changing was the way those facts could constrain one another.

Variation could be related to inheritance.

Inheritance could be related to reproduction.

Reproduction could be related to population growth.

Population growth could be related to competition.

Competition could be related to differential survival and reproduction.

And suddenly a new possibility appeared:

selection could occur without a selector.

That last step is crucial. Artificial selection already provided a model in which variation could accumulate because an agent selected among variants. Darwin's conceptual achievement was to see that the same general process could occur without such an agent.

The environment could do the selecting.

The idea was not simply another fact added to the collection. It was a new relation among existing facts.

The difference a possibility makes

This also helps explain why the emergence of a concept can change the possibilities available afterward.

Once natural selection had been formulated, phenomena that previously appeared unrelated could be investigated in relation to it. Adaptation, mimicry, vestigial structures, geographical distribution and comparative anatomy could all become evidence within a new explanatory framework.

The concept therefore did not merely describe an existing field.

It reorganised the field.

This is one of the peculiar characteristics of conceptual evolution. A new concept can become an affordance for further concepts.

The possibility of natural selection made other biological questions possible in new ways. It opened a path through the intellectual landscape that had not previously been visible as such.

And yet that path was not created from nothing.

The landscape mattered.

The furrow and the plough

We might therefore distinguish two ideas that are easily confused.

An intellectual environment can determine a discovery.

Or it can make a discovery more probable.

The first would make conceptual history a kind of logical unfolding: given the preceding conditions, the discovery had to occur.

The second is more interesting.

The preceding conditions create affordances. They make some conceptual moves easier to make, some questions more salient, some solutions more intelligible and some connections more available than others.

But an affordance is not an instruction.

It does not tell the thinker what to think.

This may explain why independent discovery is so revealing. When two people arrive at substantially the same idea without collaborating, we have evidence that the intellectual environment was exerting a strong constraint on the space of possibilities.

But the very fact that they were separate thinkers reminds us that the environment did not itself produce the concept.

Something still had to happen.

Someone had to see the relation.

From possibility to actuality

This gives us a first distinction in the evolution of concepts.

Some conceptual possibilities are convergent.

They emerge when an intellectual environment has accumulated enough mutually reinforcing relations that several thinkers can independently arrive at substantially the same reconstruction.

Natural selection is a striking example.

But this is only one way in which concepts become possible.

Sometimes the evidence constrains a structure without uniquely determining it.

Sometimes an apparently impossible unification becomes possible when a new relation is discovered.

Sometimes the conceptual framework itself has to be reconceived.

And sometimes, as we shall see, a problem becomes unavoidable while the conceptual solutions proliferate in several incompatible directions.

The history of science is therefore not simply a history of people finding truths that were already waiting to be found.

It is also a history of possibility itself changing.

Natural selection gives us our first glimpse of this.

Darwin and Wallace did not merely discover the same idea.

They showed us that an idea can become in the air before it becomes anyone's possession.

The furrow can guide the plough.

But it does not determine exactly where the plough will go.

VII. The Country That Was Becoming

The traveller had reached the highest hill in the country.

Below him lay everything he had seen.

The bridge crossed the river.

The old road entered the city.

The garden spread around the house.

The paths divided among the hills.

The library held its old words.

The workshop held its tools.

The town carried decisions made by people whose names no one remembered.

For a long time, the traveller simply looked.

Then the old gardener appeared beside him.

“You have come a long way,” she said.

The traveller smiled.

“I have been trying to understand what the past leaves behind.”

“And what have you learned?”

He looked toward the bridge.

“The past does not leave us its events.”

“No.”

“It leaves what those events have become.”

The gardener nodded.

“The bridge was once a building project. Now it is a relation between two banks.”

“Yes.”

“A decision was once something someone did. Now it is part of the organisation of the town.”

“Yes.”

“A word was once used in a particular way. Now its history belongs to the resources of a living language.”

“Yes.”

The traveller looked across the valley.

“So the past remains.”

“Does it?”

He thought for a moment.

“Not as past.”

The gardener smiled.

“Then how?”

“As actuality incorporated into the present.”

They stood silently.

Below them, the country seemed suddenly different.

The traveller could see traces of countless things that had happened.

But the traces were not monuments to what was gone.

They were structures of what now existed.

Roads.

Bridges.

Languages.

Tools.

Customs.

Institutions.

Distinctions.

Each had once emerged from something that happened.

Each had then become part of the world in which something else could happen.

The gardener pointed toward the horizon.

“And what do you see there?”

“The future.”

“What does it look like?”

The traveller looked carefully.

There were no cities waiting to be built.

No bridges waiting to be crossed.

No events already standing in the distance.

There were only roads that might be taken.

Fields that might be cultivated.

Gates that might be opened.

Paths that might become roads.

Words that might acquire new meanings.

Ideas that might enter new relations.

Possibilities.

“That is strange,” he said.

“What is?”

“The past is everywhere.”

“And the future?”

“Nowhere.”

The gardener laughed softly.

“Not nowhere.”

She touched the traveller's shoulder.

“Here.”

He looked at her.

She pointed toward the country beneath their feet.

“The future is here?”

“As possibility.”

The traveller began to understand.

The future did not wait beyond the horizon.

It was present as what the present could become.

The country already contained roads.

But which roads would be taken?

The city already contained buildings.

But what would happen inside them?

The language already contained words.

But what would people make them mean?

The tools already existed.

But what would people do with them?

The possibilities were present.

The actualities were not yet.

The traveller turned toward the gardener.

“So the present faces in two directions.”

“Yes.”

“Backward, it is what has become.”

“Yes.”

“And forward, it is what can become.”

“Yes.”

He looked down at the valley.

The two directions seemed at first like mirror images.

But then he saw that they were not.

Behind him lay things that had happened.

They could not be unhappened.

The bridge could not be unbuilt simply by wishing it so.

The old word could not become unused merely because its first speakers had vanished.

The decision could not become undecided.

What had become actual had become irreversible as actuality.

But ahead of him lay possibilities.

They were not yet actual.

They could be taken up in different ways.

Some might never be taken up at all.

Some might lead somewhere unexpected.

Some might open possibilities that no one had imagined.

The traveller suddenly saw the difference.

The past was not a menu of possibilities.

It was inheritance.

The future was not an inheritance.

It was an opening.

He looked toward the old road.

“But the two meet.”

“They do.”

“How?”

The gardener pointed to the traveller himself.

“Here.”

The traveller laughed.

“Then I am the present?”

“Not you alone.”

She gestured toward the whole country.

“The present is the field in which what has become can become capable of something else.”

The traveller stood very still.

He remembered the seed.

The gate.

The bridge.

The road.

The city.

The tool.

The word.

He saw now that they had all been telling the same story.

Something happened.

Relations changed.

The changed relations became part of the world.

The world opened new possibilities.

Someone took up one of them.

Something became actual.

The relations changed again.

The traveller walked to the edge of the hill.

Below, a group of people were building a new bridge.

He watched them lay the first stones.

The bridge did not yet exist.

But the possibility of crossing was already changing the actions of those who built it.

When the bridge was finished, the country would be different.

Travellers would cross.

Goods would move.

A path would become busier.

Perhaps houses would gather nearby.

Perhaps a village would grow.

Perhaps one day the old bridge would stand at the centre of a city.

The traveller smiled.

He could almost see the future becoming the next past.

But then he realised something even stranger.

The future would not merely add another layer to the country.

It would change the relations among the layers already there.

The new bridge might give an old road a new purpose.

A new city might give an ancient path a new significance.

A new idea might make an old observation suddenly important.

A new word might give an old distinction a new life.

Each actualisation could reorganise the conditions inherited from before.

The traveller turned to the gardener.

“So the future can change the past.”

The gardener shook her head.

“The past remains what happened.”

“Then what changes?”

“What the past can do.”

The traveller looked back at the country.

He finally understood.

The future did not travel backwards.

Nothing reached into yesterday and altered yesterday.

But tomorrow's actualities could become today's relations.

And today's changed relations could alter the possibilities through which yesterday's actualities continued to participate in the world.

The old road could become a city street.

The forgotten observation could become evidence.

The inherited word could become a new resource.

The past remained the same.

But its possibilities did not have to remain the same.

The traveller sat down.

He began to trace a pattern in the earth.

An arrow pointing forward.

Then another.

Then another.

The gardener looked over his shoulder.

“What are you drawing?”

“A circle.”

“Why?”

“Because I thought time was a line.”

“And now?”

“Now I think becoming returns upon itself.”

The traveller wrote:

actualisation

Then:

transformed relations

Then:

possibility

Then:

actualisation

And beneath them, again:

transformed relations.

The gardener nodded.

“Not a circle of repetition.”

“No.”

“A spiral?”

“Perhaps.”

The traveller looked at the country.

“Each time it returns, the country is different.”

“Exactly.”

Something that became actual changed the relations of the world.

Those changed relations opened possibilities.

A participant took one up.

That actualisation changed the relations again.

And so the world did not merely move through time.

It changed its capacity for becoming.

The traveller stood.

He understood now why the present could not be a knife-edge.

A knife-edge divides.

But the present did something else.

It carried.

It opened.

It transformed.

It received the world that had become and gave that world new ways of becoming.

The gardener began walking down the hill.

The traveller followed.

They passed the old road.

They crossed the bridge.

They entered the city.

Everywhere they went, the traveller saw the same mystery.

The past was present.

But it was present as something transformed.

The future was present.

But it was present only as possibility.

And between them was becoming.

They reached the crossroads.

The gardener stopped.

“This is where we began.”

The traveller looked around.

He remembered standing here before.

But the crossroads was no longer the same.

Or perhaps it was the same, and he was no longer the same.

He looked down at the roads.

One had been widened.

Another had become a market street.

A third had almost disappeared.

New paths had appeared.

The country had changed because people had walked through it.

The traveller smiled.

“We never leave the present.”

“No.”

“It is always here.”

“Yes.”

“But it is never simply the same.”

“No.”

“Because what becomes changes what can become.”

The gardener nodded.

“And what can become may become.”

“And then?”

“It changes what can become next.”

The traveller looked toward the horizon.

For the first time, he did not see a boundary separating the present from the future.

He saw an opening.

And behind him, he did not see the past as a dead country.

He saw the foundations of the country beneath his feet.

He understood at last what he had been searching for since the beginning of his journey.

The present was not now.

It was not a point suspended between two absences.

It was not the thin line where one dead world ended and another had not yet begun.

It was a living country.

A country made from everything that had become.

A country opening toward everything that could become.

A country in which every new becoming might alter the relations through which earlier becomings continued to matter.

The traveller took a step.

The road received him.

He took another.

The country changed, if only by the smallest of amounts.

And somewhere behind him, the path he had walked had become part of the world another traveller might inherit.

He looked once more toward the horizon.

Then he understood the deepest secret of the country.

The past had made the present possible.

The present made futures possible.

And those futures, when they became actual, would become part of the present from which still other futures could open.

Nothing stood still.

Yet nothing simply disappeared.

What became remained.

What could become opened.

And becoming carried one into the other.

The traveller began walking.

He no longer asked where the present ended.

He knew now that the present had no such boundary.

It was the place where inheritance became possibility.

The place where possibility became actuality.

The place where actuality became a new inheritance.

The place where the world, having become what it was, became capable of becoming something else.

And as he walked, the traveller finally understood what the old gardener had been trying to tell him all along.

The present is not merely now.

It is:

what the world has become, becoming capable of what it has not yet become.

VI. The Road That Became a City

The traveller had been thinking about the old road.

It had been built long before he arrived.

He knew its stones had been laid by people whose names were forgotten.

He knew why it had first been made.

It connected two small villages on opposite sides of the valley.

For generations, people had walked along it carrying grain, tools and letters.

Then, one morning, the traveller noticed something strange.

The road no longer connected two villages.

It ran through the middle of a city.

Houses stood beside it.

Shops opened onto it.

Children played along its edges.

Markets gathered where once there had been fields.

The traveller found the old gardener in the city square.

“The road has changed,” he said.

The gardener looked at him.

“Has it?”

“The road used to connect two villages.”

“It still does.”

“No. Look around.”

The gardener smiled.

“The villages became a city.”

The traveller stared at the road.

The stones were the same.

The road had not been rebuilt.

No one had reached into the past and altered the hands that had laid it.

Yet the road now had a different life.

It had become a street.

“What happened?” asked the traveller.

“The city grew around the road.”

“Then the road changed.”

“No.”

“The city changed.”

“Yes.”

“And because the city changed, the road became something different.”

“Exactly.”

The traveller walked along it.

He had never thought of a road as something that could acquire a new role without changing its stones.

Yet here it was.

The old relation had entered new relations.

And because of those new relations, what the road could do had changed.

He stopped at the city square.

“Then the future has changed the past.”

The gardener shook his head.

“The past is still what it was.”

“But the road is now different.”

“The road is different in the present.”

“So what has changed?”

“The relation between what happened then and what exists now.”

The traveller thought of this.

The builders had built a road.

That remained true.

But later things had happened.

The villages had grown.

The city had formed.

The road had become part of a much larger arrangement.

Nothing about the original event had been rewritten.

Yet its consequences had become something new.

The gardener led him to the library.

There he found a collection of old notebooks.

One contained an observation made by a scientist many years earlier.

The observation had seemed insignificant at the time.

Its discoverer had recorded it and moved on.

“Why is this here?” asked the traveller.

“Because it became important.”

“How?”

“Someone later developed a theory.”

The traveller read the theory.

The old observation was one of its foundations.

“Did the scientist know this would happen?”

“No.”

“Did the observation mean this when it was made?”

“Not in the way it does now.”

The traveller closed the book.

Again, nothing had changed in the past.

The observation remained exactly what it had been.

But the relations surrounding it had changed.

It had acquired a new function.

It could now participate in something that did not yet exist when it was first recorded.

The traveller understood.

The future had not travelled backwards.

It had not whispered into the scientist's ear.

It had not altered the observation.

It had changed the world into which the observation had been carried.

And that changed what the observation could do.

He began to see the same thing everywhere.

An old word entered a new language.

An ancient tool was used for a new purpose.

A forgotten distinction became the foundation of a new way of thinking.

A path once used by shepherds became a road for merchants.

A building constructed for one purpose became a place for something no one had imagined.

The past was not changing.

Yet the things the past had left behind were continually entering new relations.

The traveller returned to the city square.

“So inheritance is not something we receive once.”

“No.”

“Then what is it?”

“The past enters the present.”

“And then?”

“The present changes.”

“And then?”

“The inherited things enter new relations.”

“And then?”

“They acquire new possibilities.”

The traveller looked at the old road.

He saw it differently now.

The road had not carried its future meaning inside itself.

Its first purpose had not secretly contained the city.

The city had emerged later.

And when it did, the road became capable of participating in the city in ways it could never have participated in before.

The gardener picked up a stone from the roadside.

“This stone belonged to the old road.”

“Yes.”

“It now belongs to the city.”

“Yes.”

“Has the stone changed?”

“Not necessarily.”

“Has what it can do changed?”

The traveller smiled.

“Yes.”

The gardener nodded.

“That is the mystery.”

The traveller sat beneath a tree.

He began to think about history differently.

History was not simply a line carrying things forward unchanged.

It was more like a great weaving.

Something inherited from the past entered the present.

The present changed around it.

New relations formed.

And through those relations, the inherited thing could become capable of something new.

The past therefore constrained the future.

But it did not exhaust it.

If it did, the old road could never become a city street.

The forgotten observation could never become evidence.

The old word could never acquire a new use.

The inherited relation could never participate in a relation that did not yet exist.

The traveller looked toward the horizon.

He suddenly understood why this mattered.

When something new became actual, it did not merely add another event to history.

It changed the arrangement within which earlier actualisations continued to operate.

The past therefore remained powerful.

But its power was not fixed.

It could be recontextualised.

Reused.

Reconnected.

Transformed in function.

The traveller thought of the bridge.

Once, it had simply made crossing possible.

Later, perhaps, houses would gather around it.

Then a market.

Then a city.

Perhaps one day the bridge itself would become a monument.

Nothing about the original crossing had been erased.

But what the bridge could mean, enable, and participate in could continue to change.

The traveller turned to the gardener.

“So the past determines what happened.”

“Yes.”

“But it does not determine everything that can happen with what happened.”

The gardener smiled.

“Now you have said it correctly.”

The traveller stood.

The road before him was old.

The city around it was new.

And he suddenly saw that the two were not separate.

The new had not erased the old.

It had reorganised the relations in which the old could continue to matter.

The traveller looked back toward the valley.

The past remained behind him.

But it was not finished.

Not because it could be changed.

It could not.

What had happened had happened.

Rather, because what had happened could continue to enter new relations.

And each new relation could open possibilities that had not existed before.

He finally understood the strange power of the future.

The future could not reach backwards.

But when something from the future became present, it could change the world in which the past continued to live.

And so the past could acquire a new role without acquiring a new history.

The traveller smiled.

The old road had not become young.

It had become newly situated.

And that was enough.

He looked toward the city.

Then toward the road.

Then toward the distant country still waiting to become.

Perhaps, he thought, this was why inheritance could never be final.

Every generation received the roads of those before it.

But no generation received them in quite the same country.

And what they did with those roads would change the country inherited by those who followed.

The traveller began walking.

Behind him lay the actualities that had become.

Before him lay possibilities that had not yet become.

And beneath his feet lay the strange inheritance between them:

the past, continually entering new relations with whatever the future made actual.

He stopped once more and looked back.

The old road disappeared into the city.

He could no longer tell where the past ended and the new began.

Perhaps that was the wrong question.

Perhaps the better question was:

What can the present make the inherited past capable of becoming?

And beyond that question waited another, stranger still:

Is the present really a point between past and future—or is it the field in which each continually transforms what the other can become?

V. The Gate and the Traveller

The traveller had walked far along the three paths.

Each had seemed possible.

Yet he had noticed something strange.

Some paths he could follow easily.

Others exhausted him.

Some led through country he knew.

Others required skills he did not possess.

There were doors he could open and doors he could not.

He began to wonder whether he had misunderstood possibility.

So he returned to the gardener.

“I have found the paths,” he said.

“And?”

“They are not equally possible.”

The gardener smiled.

“Are they not all open?”

“Yes.”

“Then what is the problem?”

The traveller pointed toward a narrow mountain path.

“I cannot climb that.”

“Can someone?”

“Perhaps.”

“Then the path is possible.”

“But not for me.”

The gardener nodded.

“And now you are asking the right question.”

He led the traveller to a great gate in the wall surrounding the garden.

The gate stood wide open.

Beyond it stretched a beautiful country.

“Can you pass through?” asked the gardener.

“Yes.”

“Then passage is possible.”

The traveller stepped through.

“Could a child pass through?”

“Yes.”

“Could a man carrying a heavy chest?”

“Perhaps.”

“Could someone who could not walk?”

The traveller hesitated.

“Not in the same way.”

The gardener nodded.

“The gate belongs to the field.”

“And the ability to pass through belongs to the traveller.”

“Exactly.”

The traveller looked back at the gate.

He had been thinking of possibility as though it were simply a property of the landscape.

But now he saw that this was incomplete.

The landscape could leave something open.

Whether anyone could take up that opening depended upon who stood before it.

The gardener led him onward.

They came to a workshop.

On the table lay a remarkable tool.

The traveller picked it up.

“What does it do?”

The gardener showed him.

It could shape wood in a way no ordinary tool could.

“With this,” said the gardener, “something new can be made.”

The traveller tried.

He could not make the tool do what the gardener had done.

“Then it is not possible,” he said.

The gardener laughed.

“It is possible.”

“For you.”

“For anyone who learns how.”

The traveller tried again.

This time he watched more carefully.

He learned how the tool was held.

He learned how much pressure to use.

He learned when to stop.

Slowly, his hands acquired a new ability.

The tool had not changed.

But what was possible for him had changed.

The traveller looked at his hands.

“I have become capable of something that I was not capable of before.”

“Yes.”

“So possibility can change without the world changing?”

“The world has changed.”

“How?”

“You have changed within it.”

The traveller thought about this.

A road could exist without everyone being able to travel it.

A language could contain a distinction without every speaker being able to use it.

A scientific technique could exist without every researcher knowing how to employ it.

A musical instrument could make sounds possible without every musician being able to produce them.

The field opened possibilities.

Participants possessed capacities for taking them up.

The two were related, but they were not the same.

The gardener led the traveller back toward the crossroads.

“This,” he said, “is where becoming begins.”

“How?”

“Something is possible.”

“And someone can take it up.”

“Yes.”

“And then?”

The gardener pointed toward the road.

“Then something happens.”

The traveller understood.

A possibility was not yet an actuality.

It became actual when someone took it up.

The bridge made crossing possible.

But someone had to cross.

The tool made a new action possible.

But someone had to use it.

The word made a new meaning available.

But someone had to speak it.

The path made a new journey possible.

But someone had to walk it.

The traveller looked back at the paths he had taken.

Everywhere he had gone, the landscape had offered possibilities.

But every step he had made had also changed something.

A path became more worn.

A crossing became familiar.

A practice became established.

A new use of a tool became known.

A word acquired another meaning.

Something that had been possible became actual.

And then the actual became part of the world inherited by whoever came next.

The traveller suddenly saw a great wheel turning beneath the country.

At one point upon the wheel was the past.

At another was the present.

Beyond it was the future.

But the wheel did not turn by itself.

Each becoming changed the shape through which the next becoming could occur.

The traveller spoke aloud:

“So it is not simply:

past, then present, then future.”

“No.”

“Nor is it:

past determines present, which determines future.”

“No.”

“What is it, then?”

The gardener drew three lines in the earth.

The first pointed backward.

The second opened across the ground.

The third pointed forward.

“Something happened,” he said.

“The present was changed.”

“Yes.”

“Then possibilities appeared.”

“And participants had capacities for taking some of them up.”

“Yes.”

“And when they did, the present changed again.”

The traveller looked at the three lines.

The gardener wrote beneath them:

actualisation → transformation → possibility → potential → actualisation

The traveller stared at the pattern.

“The future is not waiting for us.”

“No.”

“Nor is it already determined.”

“No.”

“It emerges when possibilities are taken up.”

“Yes.”

“And when they are taken up, they become part of the world from which further possibilities arise.”

The gardener smiled.

“Now you see why the present is alive.”

The traveller looked across the country.

It was no longer simply a landscape he had inherited.

It was a field in which things could happen.

But neither was it an unlimited field.

The mountains remained.

The rivers remained.

The roads remained.

The gates remained.

His own capacities remained—though they too could change.

Every possibility belonged to a situation.

Every potential belonged to a participant.

And every actualisation could alter the situation for what came next.

The traveller suddenly understood something else.

He had thought of himself as walking through the country.

Now he saw that the country was also being changed by his walking.

His footsteps were becoming part of the road.

His choices were becoming part of the history of the place.

What he took up from the present would become part of the present inherited by others.

He stood at the crossroads.

Behind him was the country that had become.

Around him was the field of what could be taken up.

Before him were futures that did not yet exist.

And within him were capacities—some inherited, some learned, some still waiting to develop.

The gardener looked at him.

“What will you do?”

The traveller looked down each road.

For once, he did not ask which road was the future.

He understood that there was no such road.

There were only possibilities.

And there were those who might take them up.

He placed one foot upon the path.

The road had made the step possible.

His capacity made the step possible for him.

And then he took it.

Something changed.

The traveller smiled.

He had thought that he was merely entering the future.

But perhaps the future was beginning wherever a possibility became an actuality.

And perhaps every such beginning changed the country through which the next traveller would walk.

He turned toward the gardener.

“But if what we do changes the present…”

The gardener waited.

“Can what comes next change what the past has left us?”

The gardener's smile disappeared.

For the first time, he looked serious.

“That,” he said, “is the question you must ask now.”

And beyond the crossroads, the road seemed to lead somewhere the traveller had never imagined.

Can the future change what the present has inherited from the past?