An explanation of explanation

Hello everyone,

I hope you are all doing well. I feel a little bad about something. I still do not feel close to being able to publish my next article How we know what we know.

Epistemology — the study of knowledge — is deep. I have spent thinking about the problem of knowledge, namely what it is and how we acquire it. Reading through David Deutsch's book The Fabric of Reality and as well as various pieces on LessWrong have been invaluable to me.

In this email I wish to explain explanation, in essence, it might be a shorter more casual version of the article I have in the works. Practice, if you will.

Understanding understanding

What does it mean to know something is the case? To really understand reality for what it is?

Karl Popper describes the quest for knowledge as a continual process of conjecture and refutation.

We posit theories that can account for what we see in the world
We test them against argument and experiment
If a theory we have cannot be refuted by what we can observe and offers a deeper explanation than the alternatives, we consider it to be true.

To really drill in everything here, I will literally repeat what I have said in different wording.

First, we describe how we believe reality is. That is; we form a model of how things are. This is called conjecture. Our explanation should provide us with an answer to why we are observing what we are.

We then examine our model — our conjecture — and see where it leads.

"If reality works like this, if this x is true then a, b and c must also be the case."

Not only is it enough for our explanation to account for observations we have made, but if it were true it would also account for future observations we could make. In other words, based on our model of reality we can make predictions.

Then we test our predictions, this is called experiment.

If an explanation is able to make many predictions to a high level of precision and account for what we observe, we consider it true.

This is reasonable of course, as it is where Occam's razor points.

The alternative is believing that it just so happens that every observation we make, falls into place with the theory. If a theory offers a coherent explanation of how things are and any observations we make fit perfectly into it, to say it is false is to say many coincidences have occurred.

I talk a little about this in my short piece The Value of Evidence.

To spell this out even clearer.

Let's say we have a theory that seems to explain a certain phenomenon really well.
If this explanation were true, many other of its effects should be observable.
We run many experiments to see if the way things are is aligned with the explanation and our observations all match perfectly.
Now it seems like our theory really explains reality (that is; it is true) or we have ourselves some impressive coincidences.

It seems to me that this process is how knowledge advanced. This is how science — which I believe is applied reason — should work in principle.

Let me give you an example.

Imagine you lived at a time when it was believed the Earth was flat. You look out at the horizon to the sea and watch the boats sail away. You notice that as they get further and further away they start to disappear.

Wait a minute? If the world is flat why would this be the case?

You start to conjecture...

"Hmm... what if the world was round?"

You remember basic geometry. The angles of a triangle all add up to 180 degrees... but only on a flat plane!

You draw a really huge triangle on the earth and measure the angles and lo and behold they add up to significantly more than 180.

At this juncture, it is starting to see like round Earth theory is very credible. The single theory of a round Earth now explains both the observations of the triangle as well as that of the boats disappearing on the horizon.

The alternative to believing that the world is round is to believe that two different coincidences have lined up in such a way that makes it seems as if the world is round.

In the real world, we tend to make a lot more than two observations and they can often conform to our theories to a very high level of precision.

A good explanation

David Deutsch is quite remarkable when it comes to explaining explanation. He states that a good explanation is hard-to-vary.

The following example is from this video.

Let's say you watch a magician perform a conjuring trick and wonder how it works.

"It's magic."

A false, bad explanation

This is a bad explanation because it could apply to anything. It doesn't explain anything. If he was performing a very different conjuring trick, the same words here would apply. It is easy to vary the observations and still apply the same answer! Those two words don't get you any closer to understanding how the tricks have worked.

He goes even further. You could say something that is true, and it could still be a bad explanation.

"The magician did something."

A true, bad explanation

This is definitely the case, but it doesn't explain anything as to how the trick was performed.

Being hard-to-vary would also make it falsifiable. If you want to know if an explanation is good, ask yourself; what observation would prove it wrong?

If it isn't possible to imagine a finding that proved an explanation wrong, it is a bad explanation.

I believe that this process of conjecture and refutation is key to how we understand the world. Not we as a society, not just in formal scientific enquiry but in the pursuit of truth as a whole. Even in group decision-making or in the privacy of our own minds, we follow this process. We create models to explain our past experience and test them against the reasoning of others and ourselves as well as observations in the present.

Not that we don't make mistakes of course.

Another update for everyone, I'm hoping to have an archive of all of these emails online to make it easier to share and to refer back to them. Hopefully, this will be of benefit to you.

Also, my new target to finish this article is now the end of this month.

As usual, feel free to reply to this email. I would love to hear what you thought. How do you know what you know?

Until next time,

Sashin