The Horizon of Construal: 12. The Singularity

There is perhaps no clearer image of a horizon in physics than the singularity.

The mathematics approaches a point at which quantities become infinite, undefined, or otherwise cease to behave in the way the theory requires.

It is tempting to say that we have discovered something extraordinary about the world.

The universe contains an infinity.

A physical quantity really becomes infinite.

Reality itself has reached an extreme.

But there is another possibility.

Perhaps what has become extreme is not the world.

Perhaps it is the description.

A singularity is not simply a very large value. It is a point at which the mathematical structure we are using no longer gives us a meaningful physical description.

That distinction matters.

If a theory tells us that density becomes infinite, we need not immediately conclude that the physical world contains an infinitely dense object. The infinity may instead indicate that the relations which allowed us to construe density in the first place can no longer be extended into that domain.

The equation has reached its horizon.

This does not make the singularity unreal.

Quite the opposite.

It makes the singularity extraordinarily informative.

It tells us that something about our present way of construing the physical world has reached a limit.

And once again, the limit points backwards.

What assumptions allowed the description to work so successfully everywhere else?

What distinctions did it depend upon?

What relations were being treated as stable?

What did we take for granted about space, time, matter, measurement or causation?

The singularity can therefore be read not as a physical object waiting at the end of the universe, but as a diagnostic of the theory that encounters it.

This is why replacing an infinity with another description is not simply a matter of removing an embarrassment from the mathematics.

A new description must change something.

It must find a way of construing the situation in which the old distinction between finite and infinite, perhaps even the old distinction between space and time, is no longer the final word.

The singularity is then a peculiar kind of horizon.

It does not tell us:

Here is where reality ends.

It tells us:

Here is where this way of making reality intelligible can go no further.

And that may be the more interesting discovery.

For at the horizon of a description, the question is no longer merely what the world contains.

The question becomes:

What kind of world would require us to construe it differently?