How Concepts Become Possible: VIII. When No Single Conceptual Path Wins

There is a comforting story about scientific progress.

A problem appears.

Evidence accumulates.

An old idea fails.

A new idea emerges.

The new idea explains what the old one could not, and eventually the scientific community accepts it.

The history of quantum mechanics makes this story difficult to sustain.

Here, the problem was real.

The evidence was increasingly compelling.

The old conceptual framework was under pressure.

But instead of one new conceptual possibility emerging and displacing the old one, several possibilities appeared.

They did not initially agree about what the world was like.

And yet they could all contribute to the construction of the new physics.

Quantum mechanics therefore introduces something different into our story.

Sometimes conceptual evolution does not converge.

Sometimes the furrow branches.

The problem was in the air

By the beginning of the twentieth century, classical physics had achieved an extraordinary degree of success.

Newtonian mechanics described motion.

Maxwell's theory described electromagnetism.

Thermodynamics described heat.

The conceptual world seemed remarkably coherent.

And yet anomalies were accumulating.

Blackbody radiation resisted classical explanation.

The photoelectric effect suggested that light behaved in ways that did not fit comfortably with a purely continuous wave picture.

Atomic spectra displayed discrete patterns.

The stability of atoms itself was difficult to reconcile with classical electrodynamics.

There was therefore a growing problem.

But there was not yet a single solution.

This distinction matters.

The problem could be convergent even when the solution was not.

The evidence could make the old conceptual possibilities increasingly untenable without determining what should replace them.

Planck does not yet give us quantum mechanics

Planck's introduction of quantisation is a useful example.

In trying to account for blackbody radiation, Planck introduced a mathematical assumption involving discrete energy elements.

It worked.

But the conceptual significance of the move was not immediately clear.

Was nature itself quantised?

Was quantisation a feature of matter, of radiation, of the interaction between them, or merely of the mathematical description?

A mathematical device can become a conceptual possibility before its ontological significance is understood.

The furrow has deepened, but no one yet knows where it leads.

Einstein takes the possibility seriously

Einstein went further.

In explaining the photoelectric effect, he treated light itself as possessing a discrete character.

Light could behave as though energy were exchanged in individual quanta.

This was conceptually unsettling because wave theory had become one of the great achievements of nineteenth-century physics.

Light appeared to be a wave.

Now it also behaved as though it came in discrete packets.

The contradiction was not simply an inconvenience.

It was productive.

Two apparently incompatible descriptions could no longer be kept safely apart.

The conceptual field had begun to branch.

Bohr builds a strange bridge

The atom created an even more peculiar problem.

Rutherford's nuclear model provided a new picture of atomic structure.

But classical electrodynamics suggested that orbiting electrons should radiate energy and spiral into the nucleus.

Atoms should not be stable.

Yet they are.

Bohr's model introduced quantised atomic states and transitions between them.

It was extraordinarily productive.

But it was not a comfortable synthesis of classical concepts.

Electrons could occupy certain allowed states while transitions between them involved discrete exchanges of energy.

The atom became a domain in which familiar concepts worked only under unfamiliar conditions.

This is another way in which concepts can become possible.

Sometimes the new conceptual possibility is not a clean replacement for the old framework.

It is a hybrid.

It permits us to work productively before we fully understand what kind of world it describes.

Then the paths multiply

By the 1920s, the situation became still stranger.

Heisenberg developed matrix mechanics.

Schrödinger developed wave mechanics.

The two formulations looked radically different.

One worked with arrays of quantities and observable transitions.

The other described wave-like evolution.

Yet they proved mathematically equivalent.

This is a remarkable event in the history of concepts.

Two conceptual paths can look different while arriving at the same physical structure.

Which one is the real description?

The question is not immediately answerable by experiment.

If two formulations generate the same empirical predictions, evidence alone cannot necessarily select between their conceptual vocabularies.

The problem has therefore changed again.

We are no longer simply asking:

Which theory is correct?

We may have to ask:

How many conceptual descriptions can express the same physical relations?

Probability enters the centre

Then comes Born's interpretation of the wavefunction.

The wavefunction does not straightforwardly tell us where a particle is.

It gives us probabilities for possible outcomes.

Probability is no longer merely a measure of our ignorance about an already determinate state.

It becomes part of the formal structure through which physical possibilities are represented.

This is a profound change.

Earlier in the series, we distinguished the possible from the imagined.

Quantum mechanics makes the distinction even sharper.

A possibility can be physically structured without being a prediction that one definite outcome will occur.

The theory does not merely tell us what happens.

It tells us something about the structured possibilities of what may happen.

And the relation between possibility and actuality becomes part of the physics itself.

No single interpretation wins

The conceptual proliferation continues.

What does the wavefunction represent?

A physical state?

Information?

Knowledge?

A catalogue of possible outcomes?

Does collapse describe a physical process?

Is there a fundamental distinction between measurement and ordinary interaction?

Does every possible outcome occur?

Is the theory complete?

Different interpretations have offered radically different answers.

Some retain collapse.

Some reject it.

Some treat the wavefunction as physically real.

Others give it a more informational role.

The mathematics can remain remarkably stable while the conceptual interpretations diverge.

This is why quantum mechanics is such a useful case for our series.

It reveals that conceptual possibility and conceptual selection are different processes.

A possibility can become viable without becoming uniquely authoritative.

The community becomes part of the ecology

At this point, the social character of conceptual evolution becomes impossible to ignore.

Concepts do not evolve only inside individual minds.

They circulate.

They are compared, criticised, formalised, taught, modified and combined.

A conceptual possibility that seems unpromising in one context can become useful in another.

A mathematical formulation can survive because it is calculationally powerful even while its interpretation remains disputed.

A philosophical objection can stimulate a new formal development.

A formal development can create a philosophical problem that did not previously exist.

The conceptual ecology becomes recursive.

Possibilities alter the environment in which other possibilities are evaluated.

Selection without a single selector

This begins to resemble biological evolution in an unexpected way.

There is variation.

There is constraint.

There is differential persistence.

But there is no single selector deciding in advance which conceptual form should survive.

Some ideas disappear.

Others remain.

Some are transformed.

Some coexist.

Some become incorporated into apparently incompatible frameworks.

The analogy should not be pushed too far. Scientific concepts are not organisms, and intellectual selection is not natural selection.

But the structural resemblance is suggestive.

Conceptual evolution can involve variation without a predetermined destination.

This gives us a new possibility that our earlier cases did not fully reveal.

When equivalence matters more than victory

There is another lesson here.

We often imagine scientific progress as a competition in which one theory defeats another.

But the relationship between wave mechanics and matrix mechanics suggests a different possibility.

Sometimes competing conceptual routes are not competitors at all at the deepest level.

They can be different ways of organising the same underlying relations.

The choice between them may depend on explanatory purpose, mathematical convenience, ontology or interpretation.

A conceptual ecology can therefore preserve diversity without requiring that every difference be resolved.

The world may constrain what can be said without dictating a single vocabulary in which it must be said.

The limits of our taxonomy

Our sequence began to classify different ways in which concepts become possible.

Darwin gave us convergence.

DNA gave us constraint.

Copernicus gave us recentring.

Kepler gave us failure.

Galileo gave us the changing question.

Newton gave us unification.

Einstein gave us reconception.

Quantum mechanics now complicates all of them.

It contains constraint, failure, reconception and unification.

But none of these captures the whole phenomenon.

What emerges is not simply a new conceptual framework replacing an old one.

It is a proliferation of possibilities within a constrained field.

The problem is sufficiently structured that not anything goes.

But it is insufficiently determined to produce one obvious conceptual path.

This may be one of the most important things we have learned so far.

Possibility does not imply convergence.

The furrow branches

Perhaps this is why quantum mechanics feels so different from the stories that came before it.

Darwin gives us a furrow that seems to draw several lines of thought towards the same possibility.

Kepler reaches a point where an old furrow becomes impassable and another must be found.

Einstein discovers that the terrain itself must be reconceived.

Quantum mechanics gives us a landscape in which several furrows can remain viable.

Some eventually converge.

Some diverge.

Some turn out to be different routes through the same territory.

Some lead into philosophical questions that remain open.

The important point is not that science has failed to choose.

It may be that choice is not always the right model of conceptual development.

Sometimes the conceptual field itself is productive because it supports multiple ways of proceeding.

What, then, evolves?

We began with a deceptively simple question:

How can an idea become possible before anyone has thought it?

We can now see that there is no single answer.

An idea can become possible because the intellectual environment converges upon it.

It can emerge from constraints.

It can appear when a centre is displaced.

It can arise from the failure of an inherited assumption.

It can follow from a new question.

It can unify previously separate phenomena.

It can require the reconception of the framework itself.

Or several conceptual possibilities can emerge together without any single one immediately becoming the winner.

Perhaps, then, what evolves is not simply the stock of ideas.

What evolves is the structure of possibility in which ideas can arise, interact and persist.

And that brings us to the point where individual genius becomes a less satisfactory explanation.

Darwin did not create the world that made natural selection thinkable.

Copernicus did not create the astronomical tensions he reconceived.

Kepler did not create the observations that defeated the circle.

Galileo did not create the phenomena his new questions exposed.

Newton inherited a field already transformed by others.

Einstein inherited tensions within a mature physics.

The quantum pioneers inherited a problem that none of them could completely contain.

Conceptual innovation is therefore not merely something that happens inside a mind.

It happens within an ecology.

And perhaps that ecology is itself capable of evolving.

That is where we must turn next.

How Concepts Become Possible: VII. When the World Must Be Reconceived

Newton showed that many phenomena could become one.

The falling stone and the orbiting Moon, the motion of a projectile and the movement of the planets, could be understood through a common relation: universal gravitation.

For more than two centuries, this was one of the great achievements of scientific thought.

But there was a difficulty.

The Newtonian framework did not merely describe particular phenomena. It carried with it a picture of the world: space as a fixed arena, time as a universal measure, motion as change of position within that arena.

These concepts were so deeply embedded in the framework that they scarcely appeared to be concepts at all.

They appeared to be reality.

Then Einstein changed the question.

Not simply:

What laws govern things moving through space and time?

But:

What if space and time themselves belong to the relational structure that physics must explain?

At that point, the world does not merely require a new law.

It must be reconceived.

When the framework becomes visible

This is one of the most difficult forms of conceptual change.

As long as a conceptual framework works, we tend not to notice it.

We notice the objects within it.

We notice the phenomena it describes.

We notice anomalies when predictions fail.

But the background concepts through which the phenomena become intelligible can remain invisible.

Newtonian physics made space and time extraordinarily successful conceptual resources.

Space provided the arena in which positions could be specified.

Time provided a common measure against which changes could be compared.

The framework was so productive that its assumptions became almost indistinguishable from the world itself.

Einstein's achievement was partly to make those assumptions available for questioning.

The problem was already there

Relativity did not emerge from nowhere.

By the end of the nineteenth century, physics contained tensions that the Newtonian framework could not comfortably absorb.

Electromagnetism described light in ways that did not fit neatly into the classical picture of motion.

The speed of light appeared to have a peculiar status.

The question of how measurements of space and time should relate between observers became increasingly difficult.

Yet none of this logically dictated Einstein's theory.

This matters.

We can look backwards and see that something had to give.

But several possibilities might have been pursued.

Perhaps the equations could be modified.

Perhaps an invisible medium could be retained.

Perhaps transformations of measurement could be treated as mathematical conveniences without altering our conception of space and time.

Perhaps something else entirely.

The conceptual crisis created pressure.

It did not supply the solution.

This is precisely where Einstein differs from the convergence represented by Darwin.

The problem may be strongly constrained while the reconception remains open.

The observer enters the relation

Special relativity makes the issue especially clear.

Suppose two observers move relative to one another.

In Newtonian physics, we can imagine that there is a single time against which both descriptions can ultimately be compared.

Einstein removes that assumption.

Measurements of time and space are not independent of the observer's state of motion.

But this does not mean that reality becomes subjective.

Quite the opposite.

The theory replaces an absolute background with a deeper relational structure.

Different observers may disagree about distances and elapsed times while agreeing about the invariant relations connecting their measurements.

The important thing is no longer an absolute quantity possessed independently of every relation.

It is the structure that remains invariant across transformations of perspective.

This is a profound conceptual shift.

The observer is not simply someone looking at a pre-existing world from a particular location.

The observer's relation to the world becomes part of the physical description.

The world is not a stage

This is why relativity is more than a correction to Newtonian mechanics.

Newton had given physics a magnificent framework for describing bodies moving through space and time.

Einstein asks us to stop treating space and time as the stage on which the drama occurs.

They are part of the drama.

Space and time are not two substances waiting to be distorted. Nor are they simply containers within which relations occur.

They are aspects of the relational structure through which events can be ordered and compared.

Once this possibility becomes available, concepts that had seemed fundamental acquire a different status.

Space can no longer be understood independently of the relations among events.

Time can no longer be understood independently of the physical conditions under which intervals are measured.

The framework itself has entered the field of inquiry.

From special to general

General relativity takes the reconception further.

Gravity had been one of the great successes of Newtonian unification.

But Einstein asks whether gravity should really be understood as a force acting between bodies within an absolute spatial and temporal framework.

The answer is extraordinary.

The geometry through which distances and times are related is itself affected by the distribution of matter and energy.

This is often described as the curvature of spacetime.

The phrase is useful, but it can obscure the conceptual revolution.

The important point is not that some mysterious substance called spacetime gets bent.

It is that the relational structure through which spatial and temporal intervals are defined is not fixed independently of the physical world.

Gravity is therefore no longer simply something that happens within a pre-existing geometry.

The geometry participates in the gravitational relation.

The stage has become part of the action.

A new concept changes old concepts

This illustrates a feature of conceptual evolution that we have not yet encountered quite so sharply.

A new concept does not merely add itself to the existing conceptual inventory.

It can change the meaning and role of concepts that were already there.

After Einstein, space is not quite the Newtonian space.

Time is not quite the Newtonian time.

Simultaneity is not quite the Newtonian simultaneity.

Even motion acquires a different conceptual setting.

This is why conceptual change cannot always be represented as a growing collection of discoveries.

Sometimes the change is structural.

The elements remain recognisable, but their relations change.

And when the relations change, the elements themselves can acquire new significance.

Reconceiving is not abandoning

It would be easy to describe this as the overthrow of Newton.

That is too simple.

Newtonian mechanics remains extraordinarily effective in the domain where relativistic effects are negligible.

The older conceptual structure becomes a limiting case of the newer one.

This is another important feature of conceptual evolution.

A new conceptual framework does not necessarily destroy the possibilities generated by the old one.

It can preserve them within a larger relational structure.

What changes is their status.

The Newtonian world is no longer the final framework of physical possibility.

It becomes an approximation available under particular conditions.

A previous conceptual world can therefore survive as a special case of a new one.

The possibility of reconception

We can now see why Einstein occupies a distinctive position in our sequence.

Darwin:

An idea is in the air.

Watson, Crick, Franklin and others:

Evidence constrains a structure.

Copernicus:

The centre moves.

Kepler:

The circle breaks.

Galileo:

The question changes.

Newton:

The many become one.

Einstein:

The world must be reconceived.

Each step changes the field in which subsequent possibilities can arise.

But Einstein's transformation is distinctive because the framework itself becomes available for revision.

The assumptions that had organised the questions become part of the questions.

That may be one of the deepest forms of conceptual innovation.

The furrow turns back upon itself

We began this series by asking how an idea can become possible before anyone has thought it.

Einstein suggests that the answer cannot be limited to the accumulation of information.

A conceptual possibility may require us to recognise that the very distinctions through which we organise information are no longer adequate.

The furrow does not simply guide the plough forward.

At some point, the plough may reach a place where the furrow itself becomes the object of attention.

The conceptual landscape can become reflexive.

We can ask not merely what lies within the field of possibility, but what structure makes that field possible in the first place.

And once that happens, conceptual evolution can become extraordinarily discontinuous.

The new possibility may not be a better answer within the old world.

It may be a different world in which the old question takes on a different meaning.

But what if there is no new world?

Einstein's achievement might therefore seem like the culmination of the sequence.

The framework fails.

A deeper framework is found.

The world is reconceived.

But the history of quantum mechanics will make this reassuring pattern much harder to sustain.

There, the problem was not simply that an old conceptual framework needed to be replaced by one new and coherent alternative.

Several radically different possibilities emerged.

Wave and particle.

Continuity and discreteness.

Determinacy and probability.

Matrix mechanics and wave mechanics.

Different conceptual paths could describe the same emerging domain, while none initially possessed an obvious claim to conceptual supremacy.

The problem was no longer simply how to reconceive the world.

It was how a conceptual ecology behaves when several reconceptions become possible at once.

That is where the furrow begins to branch.

How Concepts Become Possible: VI. When the Many Become One

There is a moment in the history of ideas when explanation changes its scale.

A falling stone belongs to one world.

The Moon belongs to another.

The planets move through the heavens. Bodies fall towards the Earth. Tides rise and fall. Projectiles follow their trajectories.

For centuries, these phenomena could be studied separately because they appeared to belong to different orders of nature.

Then Newton asked whether they might not be separate at all.

The question was not simply whether one could explain several phenomena with the same theory.

It was more radical:

What if the difference between these phenomena is not fundamental?

What if the same relation operates in all of them?

This is the possibility of unification.

The many are not yet one

By the time Newton began his work, much had already changed.

Copernicus had displaced the Earth from its privileged position.

Kepler had replaced circles with ellipses and discovered mathematical relations governing planetary motion.

Galileo had developed a new way of thinking about motion, using measurement, idealisation and mathematical description.

The pieces were there.

But they did not yet form a single conceptual structure.

The falling body and the orbiting planet remained, in important respects, different problems.

Newton's achievement was not simply to solve each problem.

It was to discover a relation in which both could be understood.

Gravity could be terrestrial and celestial.

The same mathematical relation could describe the fall of an apple and the motion of the Moon.

The many became one.

But this unity was not present merely waiting to be noticed.

It had to become conceptually possible.

The leap is not from ignorance to knowledge

This is where the history of Newton can easily become misleading.

The familiar story makes the apple almost too convenient: Newton sees an apple fall and suddenly asks why the Moon does not fall in the same way.

Whether or not the anecdote captures anything historically useful, it expresses a genuine conceptual possibility.

The Moon is falling.

Its orbit can be understood as continuous falling towards the Earth, combined with its motion across the Earth.

Once this possibility is available, terrestrial and celestial motion can enter the same conceptual field.

But notice what has happened.

Nothing new has been added to the world.

The apple was already falling.

The Moon was already orbiting.

What has changed is the relation in which these events can be understood.

This is a recurring feature of conceptual innovation.

Sometimes the new possibility does not consist in discovering a new thing.

It consists in discovering that two things we had separated belong to the same relation.

Unification is more than similarity

We should be careful here.

It is easy to mistake unification for analogy.

The Moon and an apple are both subject to gravity, but Newton's achievement is not simply to notice that they are somehow similar.

The deeper claim is quantitative.

The same mathematical law governs their interaction.

This matters because a genuine unification does not merely place phenomena beside one another.

It makes their relationship necessary within a common structure.

The orbit of the Moon becomes intelligible as a special case of the same gravitational relation that governs falling bodies.

Planetary motion becomes connected to terrestrial motion.

The tides can be related to the gravitational effects of the Moon and Sun.

The apparent multiplicity of phenomena is reorganised around a common relation.

A successful unification therefore changes the architecture of possibility.

Once the relation has been established, questions that previously seemed unrelated can be asked together.

The question Galileo changed becomes Newton's bridge

This is where Galileo's contribution becomes especially important.

Galileo helped make motion measurable in terms of relations between quantities.

Newton inherited a world in which motion could increasingly be described mathematically.

That made a new question possible:

Could apparently different motions be manifestations of the same mathematical relation?

The question could not have been asked in quite the same way before the conceptual work that preceded it.

This suggests that conceptual evolution is often cumulative without being linear.

One innovation does not simply lead inevitably to the next.

Rather, it changes the field of possibilities in which subsequent thinkers work.

Copernicus made a different centre possible.

Kepler made a different orbital shape possible.

Galileo made new questions about motion possible.

Newton inherited all three transformations and discovered that they could participate in a still larger relation.

The furrow has deepened.

From description to explanation

There is another important shift.

Kepler had discovered remarkably precise mathematical regularities in planetary motion.

But a regularity is not yet necessarily an explanation.

Why do planets follow elliptical orbits?

Why do their speeds change as they move around those orbits?

Why does the Moon remain in orbit rather than simply falling to Earth?

Newton's gravitational theory connects these questions.

The mathematical description of motion and the physical relation responsible for that motion can be brought together.

This is one reason Newton's synthesis is so powerful.

The laws of motion tell us how bodies respond.

The law of universal gravitation tells us about the relation between masses.

Together they generate consequences across an enormous range of phenomena.

The theory does not merely accommodate what is already known.

It creates new possibilities for prediction.

A relation can unify by generating difference

There is a subtle point here.

To say that many things are instances of one relation does not mean that they become identical.

The apple remains an apple.

The Moon remains the Moon.

The planets remain different from one another.

What becomes one is not the things themselves but the relation governing their behaviour.

Indeed, the common relation makes their differences intelligible.

Different masses, distances and velocities produce different trajectories while remaining governed by the same underlying relation.

Unity therefore does not erase difference.

It explains how difference can arise within a common structure.

This is a much more interesting kind of unity than simple sameness.

The world becomes calculable in a new way

Unification also changes what can be done.

Once terrestrial and celestial phenomena belong to the same mathematical framework, one can move between them.

A phenomenon observed in one domain can constrain expectations in another.

A relation discovered in one context can generate predictions in another.

The conceptual space becomes more densely connected.

This is why powerful theories often feel, in retrospect, as though they have simplified the world.

They have not necessarily reduced the number of phenomena.

They have reduced the number of independent relations required to account for them.

Many observations can be generated from fewer principles.

The economy is conceptual rather than merely numerical.

But unity can be premature

There is also a danger.

Once a unifying concept becomes powerful, it can become tempting to apply it everywhere.

The history of science contains many examples of theories being stretched beyond the conditions under which they were productive.

A conceptual framework is not successful merely because it is broad.

Its unity must survive constraint.

This returns us to the theme of the series.

Possibility is not imagination without resistance.

Newton's unification succeeded because it entered into extraordinarily productive relations with observation, mathematics and prediction.

The theory could be tested.

It could fail.

It could generate consequences that had not been used to construct it.

Its unity was therefore not simply aesthetic.

It was constrained by the world.

The many become one—and the one generates many

Perhaps the most revealing feature of Newton's achievement is what happens after the unification.

A successful unification does not close inquiry.

It multiplies it.

Once gravity becomes a universal relation, new questions proliferate.

How do planets perturb one another?

How stable are their orbits?

How does gravity operate in more complicated systems?

What happens when more than two bodies interact?

Can the same framework explain the tides?

Can it explain comets?

Can it be extended to other astronomical systems?

A new unity creates a new multiplicity.

This is one of the paradoxes of conceptual evolution.

A concept becomes powerful not when it eliminates possibilities, but when it generates them.

Newton's universal gravitation did not make the world conceptually simpler in the sense of making it less interesting.

It made more phenomena available to a common form of inquiry.

From unification to the next rupture

Our sequence has now taken another step.

Darwin showed us how a possibility can become convergent: an idea can be in the air because many relations are beginning to afford it.

The discovery of DNA showed how a structure can emerge through constraint: heterogeneous evidence can progressively narrow the space of viable possibilities.

Copernicus showed us recentring: changing the organisation of relations can make a different world of thought possible.

Kepler showed us failure as constraint: the collapse of an inherited possibility can open another.

Galileo showed us the changing question: a new way of asking can create a new field of evidence.

Newton shows us unification.

The many phenomena that had occupied different conceptual worlds can become instances of one relation.

Newton's achievement therefore leaves us with a new possibility: perhaps the many can be understood through the one relation.

But what happens when the relation that seemed universal turns out to depend upon concepts we had taken for granted?

What happens when the framework within which phenomena are unified can no longer accommodate what we discover?

Then unification is no longer enough.

The world itself may have to be reconceived.

That is where Einstein enters.

How Concepts Become Possible: V. When the Question Changes

Galileo is often remembered for the experiments.

Objects falling from inclined planes. Balls rolling down ramps. The motion of projectiles. The telescope turned towards the heavens.

But the experiments themselves are not quite the point.

What matters for our purposes is that Galileo helped make a new kind of question possible.

For much of the older natural philosophy, the question posed by motion was something like: What is the nature of this motion, and what causes it?

Galileo increasingly asked a different question:

How does motion change?

The difference may seem small. It is not.

To ask how motion changes is to shift attention from the nature of a thing to the relations governing its behaviour. Acceleration becomes measurable. Time becomes part of the description. Distance travelled can be related mathematically to elapsed time. A falling body need not be understood primarily in terms of its intrinsic tendency toward a natural place.

The question has changed, and with it an entire field of possibilities.

The world does not arrive with its questions attached

This is one of the difficulties in thinking about scientific discovery.

We tend to imagine that nature presents us with problems and scientists solve them. But a problem is never simply sitting there waiting to be picked up. What counts as a problem depends partly on the conceptual resources available for formulating it.

A stone falls.

That is an event.

But it can become many different questions.

Why does the stone fall?

What is its natural place?

What force acts upon it?

How long does it take to fall?

How does the distance travelled depend upon time?

What happens if air resistance is removed?

What would happen if the motion continued without interruption?

These are not merely different ways of wording the same question. They open different spaces of possibility.

Galileo's importance lies partly in making some of the latter questions scientifically productive.

Idealisation changes what can be seen

This required another conceptual move.

Real objects are messy.

A stone falls through air. A ball rolling down a surface encounters friction. A projectile is affected by air resistance. No physical situation is perfectly isolated.

Yet Galileo increasingly used idealised situations to discover relations that could be obscured by those complications.

The famous inclined plane is important for precisely this reason. It slows falling motion enough to make it measurable. A phenomenon that is too rapid to inspect directly is transformed into one whose relations can be investigated.

And once the relation is visible, the mind can ask what would happen if the interfering conditions were progressively removed.

What happens without friction?

What happens without air resistance?

What happens if a body is already in motion and nothing acts to change that motion?

The ideal case need not exist physically in its pure form to become conceptually useful.

This is a profound change in scientific possibility.

An impossibly clean situation can become a resource for understanding messy reality.

Motion becomes a relation

Here the connection with our earlier posts becomes clearer.

Copernicus changed the centre.

Kepler changed the shape.

Galileo changed the question.

The object of inquiry is no longer simply the moving thing. It is the relation between motion, time, distance and change.

This is why mathematical description becomes increasingly powerful.

Mathematics does not merely decorate an already understood physical process. It makes certain relations explicit that ordinary perception does not readily disclose.

A body falling does not announce its acceleration.

A projectile does not display its trajectory as an equation.

The relation has to be constructed.

And once constructed, it can become a new object of thought.

This is another way in which concepts become possible.

Sometimes we do not discover a new entity.

We discover a new relation in which familiar entities can participate.

The experiment follows the question

There is a temptation to tell the history backwards.

Galileo had an idea. He performed experiments. The experiments confirmed the idea.

But this makes scientific discovery look much more linear than it is.

The experiment itself depends upon what one thinks is worth measuring.

To measure the time taken by a falling body, one must already have begun to conceive of time as a relevant variable.

To compare distances travelled, one must already suspect that the relation between distance and time might matter.

To construct an inclined plane as an experimental device is already to intervene in the phenomenon so that a particular relation becomes more accessible.

The experiment therefore does not simply interrogate nature.

It helps construct a situation in which a particular question can be asked.

This does not mean that the answer is invented.

The world can still refuse the question.

But the question determines which aspect of the world's response becomes intelligible.

A new question creates new evidence

This is why conceptual change and empirical discovery cannot easily be separated.

Once Galileo asks new questions, new kinds of evidence become significant.

Measurements that previously seemed incidental can become decisive.

Small differences in timing become meaningful.

The trajectory of a projectile becomes something that can be analysed.

The behaviour of bodies under altered conditions becomes evidence about general relations rather than merely observations about particular things.

The conceptual field has changed, and therefore the evidential field changes with it.

This is an important principle.

Evidence is not independent of possibility.

What counts as evidence depends partly upon the possibilities we are capable of formulating.

But the relation works both ways. Evidence can destroy a possibility, as it did for Kepler's circles. It can constrain a model, as with the structure of DNA. And it can reveal that a question itself has been too narrowly posed.

The history of science is therefore not simply a history of answers.

It is also a history of questions becoming possible.

The thought experiment

Galileo's thought experiments push this even further.

Consider a body sliding down a slope, or two bodies connected in ways that expose contradictions in an accepted account of falling. Consider what happens when friction is progressively reduced.

The thought experiment does not require the laboratory to reproduce the imagined situation perfectly.

Instead, it explores the relations that would follow if certain conditions were changed.

This is remarkably close to the logic of possibility that has been emerging throughout this series.

A possibility is not merely something we can imagine.

It is something that can occupy a structured relation to other possibilities and constraints.

Galileo's idealisations work because changing one relation allows others to become visible.

The impossible experiment can therefore become a possible thought.

And the possible thought can reveal something about the actual world.

From things to laws

Something even larger is happening.

If the behaviour of a body can be described by a mathematical relation that holds across different circumstances, then explanation begins to shift.

Instead of asking what makes this particular thing behave as it does, we can ask what relation governs the behaviour of things of this kind.

The particular becomes an instance of a more general relation.

This prepares the ground for Newton.

Newton will bring together terrestrial motion and celestial motion in a single mathematical framework. The falling body and the orbiting planet will no longer belong to fundamentally different conceptual worlds.

But Newton's unification depends upon possibilities that Galileo helped make available.

Before one can unify phenomena, one must first have learned to describe them in terms that allow comparison.

The question has to change before the answers can be brought together.

What Galileo changed

Our sequence can now be extended.

Darwin shows us a possibility that is in the air.

Watson, Crick, Franklin and others show us how a structure can emerge under constraint.

Copernicus shows us recentring: a change in the organisation of relations.

Kepler shows us how failure can generate possibility by removing an inherited constraint.

Galileo gives us something different again.

He changes the question.

And when the question changes, the world can begin to appear differently—not because the world has changed, but because a different set of relations has become available for investigation.

This may be one of the deepest ways in which concepts become possible.

A new concept does not always answer an old question better.

Sometimes it makes a different question possible.

And that question opens a different world of inquiry.

The furrow is beginning to look less like a path along which thought travels than a changing field in which some questions can take root.

The plough does not merely follow the furrow.

By changing what it asks of the ground, it may deepen the furrow itself.

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.