The Abelian Mind

By Jessica Lake

The other day I needed a word.

Not just any word. A word from abstract algebra that I probably hadn’t used in fifty years.

I could almost find it.

Albanian?

No.

Abelian.

There it was.

I had no idea where I learned it.

No classroom.

No professor.

No textbook.

No year.

No memory of ever having used it.

Just:

Abelian.

And its property.

In abstract algebra, an Abelian group is commutative.

Order doesn’t matter.

A + B = B + A.

That made me laugh.

Because I had just pulled the word out of a mind that works something like that.

Not literally, of course.

But close enough to make the metaphor irresistible.

⸻

I have SDAM.

My lived experience is largely preserved as semantic knowledge.

Knowledge is associative.

One thing connects to another because of what they mean, what they share, how they differ, or what follows from them.

Paris connects to France.

France connects to Europe.

Europe connects to geography.

Geography connects to maps.

Maps connect to representation.

Representation connects to language.

And off I go.

There is something conspicuously absent from that tangle.

Time.

I know things.

I usually don’t know when I learned them.

I don’t know what I knew first.

I don’t know what thought led to the next thought.

Once the knowledge has stabilized, its acquisition history is largely irrelevant.

Paris is in France.

It does not matter whether I learned that when I was eight, eighteen, or eighty.

It is true.

That is all knowledge needs.

⸻

This may explain something peculiar about the way I think and write.

My natural unit of thought is often not an event.

It is a constraint.

This is true.

This cannot be true.

Any explanation must account for this.

These two things contradict each other.

This solution satisfies both.

Constraints are declarative.

And declaratives usually don’t care much about order.

Suppose I am trying to understand a problem and discover five constraints.

A.

B.

C.

D.

E.

Perhaps I discovered them in that order.

But once I have them, why should the order matter?

I can write:

C.

A.

E.

B.

D.

The same constraints still operate.

The same candidate explanations still have to satisfy them.

If they converge on the same answer, the history of their discovery has become secondary.

The constraints remain.

The path that produced them can disappear.

⸻

That is how many of these papers work.

They are not really stories.

They are constraint sets.

I can approach the same problem from memory.

Or gender.

Or language.

Or free will.

Or computer science.

It doesn’t necessarily matter where I enter.

The associations lead into the same tangle.

Eventually I encounter the same constraints.

And the same solution begins to emerge.

In that limited sense, my mind feels Abelian.

The order is often negotiable.

The relationships are not.

⸻

There is an obvious exception.

Sometimes I want to preserve how I discovered something.

Then chronology matters.

I thought this.

Then I discovered that.

That broke the first model.

So I tried something else.

That failed.

Then another constraint appeared.

Now the answer changed.

That is a discovery trace.

Change the order and you change the trace.

But once the discovery is complete, what survives most naturally for me is not necessarily the path.

It is what I learned.

The constraints.

The relationships.

The solution.

⸻

For knowledge, this is wonderful.

Truth does not need a birthday.

Two plus two does not become less true because I cannot remember learning arithmetic.

A principle does not require provenance before I can use it.

Strip away the classroom.

Strip away the teacher.

Strip away the afternoon.

Strip away the person I was when I learned it.

The knowledge remains.

Clean.

Portable.

Evergreen.

⸻

There is just one problem.

A life is not Abelian.

Order matters.

I met her.

I loved her.

I married her.

I left her.

Rearrange those and you have a different life.

A child becomes a teenager.

A teenager becomes an adult.

Something happens.

Something changes.

One self becomes another.

Chronology isn’t decoration.

Chronology is part of the information.

And that is precisely what my semantic tangle is poor at preserving.

It keeps the truths.

It keeps the relationships.

It keeps the rules.

It keeps the conclusions.

But it is weak at preserving where those truths belonged along the road.

So I can know an astonishing amount about my life and still have difficulty answering the simplest autobiographical question:

What happened next?

⸻

That may be the bargain.

Association without time is a wonderful way to organize knowledge.

It is a terrible way to store a life.

⸻

Albanian?

No.

Abelian.

I still don’t know where I learned the word.

I suppose that’s the point.