Prove It

By Jessica Lake

There is another problem hidden inside communication.

Suppose my cognition has already reached an answer.

How can I share this answer with others? The “how” is invisible. I cannot just tell you to trust me. Well, I suppose I could. But that is not the point.

Discovery does not necessarily leave behind a neat trail of breadcrumbs. I may have followed an anomaly into another realm, recognized a fundamental principle, followed an association somewhere else, translated a constraint, discarded several possibilities, and eventually arrived at something that simply survives.

I know the answer.

You don’t.

Unfortunately, we have not evolved telepathy yet.

I have to find a means to guide you until you reach the same conclusion.

I need a language device we both trust and understand.

I need to justify or prove it to you.

The proof does not necessarily describe how I arrived at the answer.

A proof serializes sufficient justification. It imposes an order upon the argument so another mind can follow it. The order belongs to the communication. It need not belong to the knowledge.

Instead, after reaching the conclusion, I guide you from where you are now to where you need to be with a persuasion another mind can follow:

premise → premise → relationship → consequence → conclusion

A proof is persuasion that adheres to objective rules of a shared lingo.

Both you and your listener must trust the lingo.

Researchers working within a field possess a shared vocabulary. They know its definitions, notation, assumptions, formalisms, and familiar examples.

Two researchers may recognize the same fundamental principle because each has accumulated enough experience to extract it. But they also possess the lingo necessary to communicate that recognition to one another.

I may arrive at an answer, but without the lingo, I am unlikely to win them to my position.

The answer is trapped.

So I use the lingo I do have.

For me, much of that is computational:

• State.

• Cache.

• Filter.

• Network.

• Node.

• Traversal.

• Declarative.

• Imperative.

• Address.

• Concurrency.

Those words do not necessarily mean that cognition literally implements the computer systems from which I borrowed them.

They are my available encoding.

They allow me to express an answer for which I may not yet possess the terminology of cognitive science, mathematics, neuroscience, or whatever field I have wandered into.

Later I may encounter the established terminology and discover:

Oh.

They have a word for that.

Now translation becomes possible.

This may explain something important about proof itself.

The proof is not necessarily there for the person who discovered the answer.

She already has the answer.

The proof is for everyone else.

A conclusion is a state of one mind.

A proof is a means of reproducing that state in another.