Hindsight

By Jessica Lake

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Let us look at a peculiar problem.

Not how we arrive at an insight.

What happens afterward?

Somehow, I know something.

• Perhaps it arrived through observation.

• Perhaps Constraint Convergence eliminated everything else.

• Perhaps association supplied it.

• Perhaps some machinery I have not identified produced it.

It does not particularly matter here.

I have the insight.

You do not.

How do I get it from my mind into yours?

Of necessity this is a Crayons sketch of how that might work.

Dyadic Language

We begin with a model of spoken language.

It consists of two major components: dictionary and syntax.

I split spoken language into a lexicon that holds words and their usage. Usage represents the varieties of meanings a word may express. A usage has a pronunciation, spelling, and syntactic properties afforded.

Syntax governs how those meanings may be combined into larger structures.

I would think the mind uses templates to compose sentences, like Mad Libs. It is faster and efficient. There are templates for interrogatives, declarations, qualifications, and all manner of others. There are usage and contingent blanks that tell you the syntactic properties required.

That gives us a protocol.

But a protocol for what?

Thoughts

A thought may exist in the mind as an abstraction, but to communicate it we must translate it into language.

That distinction is important.

Language does not necessarily produce the thought.

The thought may already be there.

Language gives me a way to express it.

I select meanings and arrange them within a syntactic structure capable of transmitting enough of the idea that another person can reconstruct it.

Spoken language evolved primarily for practical and social communication. It is expressive, adaptive, and tolerant of ambiguity. Its success is measured pragmatically:

Did the listener roughly understand what the speaker meant?

In ordinary conversation, language often points beyond itself toward shared context, imagery, memory, gesture, knowledge, and lived experience.

Much of meaning is supplied implicitly.

That is enormously efficient.

If you and I already agree on what DOG means, I do not have to transmit dog-ness every time I use the word.

I merely say:

Dog.

The word is an address.

You supply the rest.

But an insight presents a harder problem.

Suppose I have reached a conclusion you have not.

I cannot simply hand you my conclusion.

Well, I can.

You might even believe me.

But you would possess my assertion, not necessarily my understanding.

If I want you to understand why the conclusion follows, I need something more.

I need to construct a path.

The Logical Path

This is where language begins to resemble a formula.

A formula does not merely describe.

It constrains.

It expresses relationships, tests assertions, evaluates causality, and determines what follows from what.

Mathematics, formal logic, and computer science have all developed symbolic systems designed to express reasoning under strict syntactic rules.

Here, syntax no longer means grammar merely in the conversational sense.

It means the rules governing admissible combinations of meaning.

Consider an algebraic equation.

It contains constants, variables, and operators arranged according to strict rules. Operators act upon values to produce results. The structure permits unknowns to be resolved through their relationships to known quantities.

A logical explanation can work similarly.

I begin with things I believe you can accept.

Then I establish relationships.

Those relationships constrain what may follow.

Each intermediate conclusion becomes available to the next step.

Eventually, if I have done my job properly, you arrive where I already was.

The insight supplies the destination.

The argument builds the road.

That is different from claiming that the road originally led me to the destination.

Perhaps it did.

Perhaps it did not.

I am no longer certain that matters.

The problem here is reproducibility.

Can I construct a semantic path that another mind can traverse?

Meaning

When I say “dog,” I am usually not recalling a specific animal.

I am invoking a semantic construct assembled from many encounters: properties, behaviors, affordances, limits, and relationships.

Semantic memory does not need to supply a particular dog.

It supplies what DOG means.

Language gives us compact access to that meaning.

The same mechanism applies to abstract ideas, although this becomes harder to perceive because there are no concrete objects to anchor them.

When discussing systems, ideologies, causality, ethics, or processes, we are still manipulating meanings—but meanings defined largely through relationships to other meanings.

In this space, nouns become placeholders for concepts and roles.

Verbs become operators acting upon those concepts.

Clauses establish relationships and constraints.

Syntax keeps the structure admissible.

If an argument can be expressed as a well-formed structure—one that respects the meanings of its terms and the rules governing their interaction—then the structure itself becomes a test.

Something may be possible.

• Impossible.

• Necessary.

• Forbidden.

• Compatible.

• Contradictory.

Each assertion removes possibilities.

The argument converges.

Eventually enough alternatives disappear that the conclusion becomes difficult to avoid.

• That is the goal.

• Not eloquence.

• Not consensus.

• Closure.

Communication

There is another problem.

Your mind is not mine.

We do not possess identical semantic states.

We have different histories, assumptions, knowledge, vocabulary, associations, and experiences.

So before I can lead you down my carefully constructed road, I need some confidence that the road exists in your world.

Communication therefore requires synchronization.

• How much do we already share?

• What assumptions are safe?

• What vocabulary is available?

• Which meanings do we hold in common?

Ordinary conversation performs this negotiation constantly.

The greater our shared state, the less I need to transmit.

• A word may be enough.

• A gesture may be enough.

• A raised eyebrow may be enough.

When our states differ substantially, I must supply more.

• Definitions.

• Context.

• Premises.

• Intermediate steps.

• Examples.

• Corrections.

I am not transmitting my internal state wholesale.

I couldn’t.

I am transmitting enough structure that you can reconstruct what matters using your own.

Language is pathetically slow.

Fortunately, it doesn’t have to carry everything.

Reasonable Conclusions

This changes the way I think about reasoning.

There may be at least two things that we casually call reasoning.

One is whatever process actually produces an insight.

The other is the construction of a reasonable path to that insight.

They need not be the same process.

I may suddenly see the answer and only afterward discover why it must be so.

Then comes the work.

• What do I know?

• What does the listener know?

• Which premises can we share?

• What relationships matter?

• What follows?

• What does not?

• Where is the contradiction?

• What alternatives can be eliminated?

Eventually I can take something that appeared in my mind whole and express it as a sequence another person can follow.

That sequence may look like the reasoning that produced the insight.

Perhaps sometimes it is.

But appearance is not proof of provenance.

1. The explanation may have been constructed afterward.

2. Semantic memory supplies the meanings.

3. Syntax supplies admissible relationships.

4. Shared context supplies compression.

5. The argument supplies a reproducible path.

6. The insight supplies the destination.

In Closing

There is one final turn worth acknowledging.

I originally thought the machinery described in this paper explained how I reasoned my way to an insight.

I am no longer convinced of that.

I may have mistaken the reconstruction for the discovery.

That is an easy mistake to make.

• I have an insight.

• Then I worry it.

• I turn it around.

• I establish premises.

• I find contradictions.

• I search for examples.

• I construct intermediate conclusions.

Eventually I can explain the insight in a form that appears almost inevitable.

Looking backward, the finished argument resembles a path I must have followed.

But perhaps I built the path after I arrived.

That does not make the path unimportant.

Quite the opposite.

An insight trapped inside one mind is private.

A logical structure makes it reproducible.

Language serializes it.

Shared semantic knowledge decompresses it.

And another mind gets the opportunity to arrive at approximately the same place.

I cannot give you my insight.

I can only show you how to get there.

The Explorer and the Navigator

An Explorer and a Navigator sat together at the end of a long day, the harbor quiet behind them. As sailors often do, they shared a little rum.

“Well,” said the Explorer, lifting his glass, “tell me of your greatest adventure.”

The Navigator said nothing.

The Explorer smiled, assuming the silence was merely dramatic pause.

At last the Navigator spoke.

“Ask me anything else.”

The Explorer laughed. “Very well then. Where have you been?”

The Navigator shook his head.

“That is the one question I cannot answer.”

The Explorer frowned, then tried again.

“What was your greatest adventure?”

“Avoiding the wrong one,” the Navigator replied.

The Explorer leaned back, amused.

“Then what do you know?”

The Navigator slowly turned his glass, watching the harbor lights move across the rim.

“I know where the water is shallow. I know where it runs deep. I know the places where the sea appears calm but is not. I know the routes that do not forgive mistakes.”

“And the wonders?” asked the Explorer. “The storms, the strange lands, the stories worth telling?”

The Navigator met his eyes.

“Those were squeezed out,” he said gently. “What remained was enough to get us here.”

For the first time, the Explorer fell silent.

The Navigator raised his glass slightly.

“Ask me something useful,” he said.

“Ask me how to get home.”