A Good Explanation

Hello everyone,

I hope you are all flourishing. I find it difficult to tell; I've been doing all sorts of things from learning the programming language Rust, to slowly learning Kanji, spending time in nature and thinking long and hard about Epistemology. The philosophical field that delves into the problem of knowledge; how we know what we know.

I have been thinking about this problem a lot, and I am indeed in the process of writing a long-form article on it. This one has been on the backburner for over a year.

This letter will be a bit of a warm-up. Originally, I wanted to stick to a one-point per letter principle. Each letter I was to introduce you to one thing of interest. I have failed here, time and again and ended up writing entire essays covering a myriad of things—this time I won't.

Today I want to cover, what makes a good explanation.

The Role of Explanation in Science

Science and the growth of human knowledge is entirely driven by our quest for better explanations. This is one the first gems of insight highlighted by the wonderful David Deutsch in his 2011 best-seller The Beginning of Infinity. I have been reading it for quite some time; David's books tend to compel me to keep re-reading parts over and over. A re-read of chapter one inspires this letter.

An explanation is an account of how and why reality is a certain way.

The keyword for me here is why.

A description asks the question "what", an explanation asks the question "why".

If you see science as in the business of explaining how the world is, rather than merely summarising data, accumulating facts or only making predictions about it — you have relinquished one of the biggest misconceptions we make.

But the quest for better explanations is at the heart of all of our growth in knowledge, not only scientific ones. This being the case, what is it that separates the scientific endeavour from the philosophical, practical or cultural?

Karl Popper distinguishes science with what he refers to as his criterion of demarcation. He had the ingenious insight that science and knowledge growth in principle had nothing to do with justifying our beliefs as true — known as verificationism. Some have called Popper's alternative falsificationism.

"Statements or systems of statements, in order to be ranked as scientific, must be capable of conflicting with possible, or conceivable observations."

Karl Popper

In more straightforward language, a scientific theory has to be testable. If the explanation can conflict with possible observations, then we can conduct experiments that could disprove the theory. This is what demarcates science from our other fields of knowledge such as philosophy, art and literature.

To summarise the role of explanation in science:

1. We see things in the world
2. We explain them; we account for how and why the world is that way
3. Our explanations helplessly have implications beyond our original observations. That is; they make predictions.
4. We create conditions where we these predictions could be refuted. This is called experiment.
5. If we have a conflict with our theory, we drop it, if not we hold on to it... until and unless a better theory arises.

An example:

1. We see a ship disappearing on the horizon
2. We explain this by guessing that the Earth is indeed round
3. This explanation implies if we go to a very high point with a good view of the horizon it would be curved, or if we drew an enormous triangle on the surface of the Earth the angles would add up to over 180°, or that if we flew high enough, we would see a sphere.
4. We do these things.
5. If the explanation still holds, we take it as being true, unless a better one comes along or until a future observation is in conflict.

It needs to be hard-to-vary

We can see here that a good theory needs to be falsifiable. That is; we need to know what conditions would have to be, for it to come under scrutiny. Creating these conditions is scientific experiment. Testability is key. Yet, when it comes to a good explanation, it is not enough.

David Deutsch calls a better criterion being "hard-to-vary".

It is possible to conceive of a testable theory of how the world is, which is nonetheless a bad explanation.

In chapter 1 of The Beginning of Infinity, gives an example of this in the ancient Greek myth that explained the seasons.

While being clearly false, this attempt to explain the seasons is entirely testable. If the cause of winter is Demeter's annual grief, then one would expect that winter would touch all four corner of the Earth at once. Had an ancient greek known about the Australian summer happening at the same time, they may have guessed that there was something wrong with the explanation.

But this falsifiability is not enough.

Another greek, upon learning that while the chills descended upon them the heat raged on down under (Australia, not Hades' realm), may conclude that as the gods lived atop Mt Olympus, it makes sense that their influence would not extend to distant lands. Or perhaps that Demeter's mechanism for freezing the land was by displacing the heat from the Northern Hemisphere and releasing it into the Southern, thereby explaining Greek winters and Australian summers in a single swoop.

This is what it means to be easy-to-vary. No matter what observations we come across, we can modify the theory to accommodate them. It may be testable, but it is still a bad explanation: If it can be adapted to explain anything, it really explains nothing.

Let's look at the components of what the ancient Greeks believed.

1. Hades raped Persephone
2. Demeter arranged her freedom in exchange for her hand in marriage and promised she would return each year
3. Hades gives Persephone a magic seed binding her to his realm, so she is compelled to visit every year
4. Demeter's sadness at all of this chills the world as we know it

The reason this explanation is easy-to-vary, is because hardly any of it has anything to do with the phenomenon of winter. Imagine it wasn't Hades, or it wasn't Persephone but characters from another mythology: the explanation would remain the same. What if it wasn't a marriage contract but a business arrangement? Or if it wasn't a seed but a potion? Or not Demeter's sadness but her anger?

All of these details can easily be subbed out for others, equally irrelevant. When we distil the explanation to its core, and trim all of the fat, we are left with the gods did it. This is an answer that could apply to anything, and we can add any surrounding lore we like, and the explanation is the same.

If the world were different, if we had eight seasons, or if they changed every day rather than three months, the explanation "the gods did it" could still apply. The account has nothing to do with what we see in the world, and therefore is easy-to-vary and a terrible explanation.

Now let's have a look at the actual explanation of the seasons.

The Earth spins on its axis, that is; it is tilted. This means one hemisphere is always receiving more sunlight, while the other is away from it. Summer is simply what happens when your half of the Earth is tilted towards the Sun, and winter is when it is titled away.

The part of the Earth that is tilted towards the Sun, isn't static though. As the Earth orbits around the Sun, the hemisphere that is facing towards it predictably changes. Since it takes one year for us to sail around the Sun, so too does the cycle of the seasons repeat itself annually.

So what do we have here?

1. The Earth tilts on its axis, leaving a part of the Earth more exposed to sunlight and another hidden away (causing summer and winter)
2. As the Earth orbits the Sun, the part of the Earth tilting away from the sun changes (causing the change in seasons)
3. It takes one year for the Earth to complete its orbit around the Sun (and thus the cycle of the seasons takes place every year)

Here we don't have a single irrelevant detail. Every single part of the account explains why it is we see what we see. We cannot change the fact that the Earth is tilted as it is essential to explain why summer is summer and winter is winter. We cannot change the orbit of the Earth as it does the job of explaining why seasons change and why their cycle is one year. If we change any part of the account, the observations that we should expect to make would be different. If the Earth were to orbit the Sun in one day, you would expect all the seasons to pass in that time. If it didn't orbit the Sun at all, the seasons would never change. And if the Earth weren't at all titled, there would be no seasons and the Northern and Southern Hemispheres would be just as warm all year round.

This is what David means when he says a good explanation is hard-to-vary; every piece of the theory is tied intimately to how the world appears. If our observations failed to match its predictions, then rather than alter the explanation, we would be forced to scrap it. It sticks its neck out so to speak.

A bad explanation ≠ A false one

So now we have the makings of a good explanation all laid out. A good explanation should be hard-to-vary; all the pieces of the explanation have a role in explaining so that none can be easily changed. Changing any details in the explanation, would mean it ceases to explain why the world is as it is.

To demonstrate this, I followed David's example of comparing the Ancient Greek's lore explaining the seasons with our modern understanding.

But doing so, I may have caused confusion.

The Greek mythos' account for the seasons is false. Our explanation of the Earth tilt being responsible, is indeed the case.

However, when I use the terms "good explanation" and "bad explanation" I do not merely mean true and false ones.

Another example that David has used is that of a magician. Imagine they performed your favourite trick, maybe sawing a woman in half.

A bad explanation that is nonetheless true is "the magician did something".

This statement is true, but fails to explain anything. Furthermore, it's remarkably easy-to-vary.

Had the magician pulled a rabbit from a hat, or predicted an ace of spades from a deck of playing cards, it would still hold.

If it "explains" anything, it explains nothing.

The gods did it is an example of a false statement that is a bad explanation, it could apply to the world no matter what we saw in it.

The magician did it is an example of a true statement, that is nonetheless a bad explanation, it could apply to any conjuring trick and therefore doesn't do the job of accounting for what we see.

The point I want to make here, is that by bad explanation I meant something altogether different to it being false. I mean, that is fails to do the job of explaining. Being testable, isn't enough, it needs to be hard-to-vary.

Resources

• David Deutsch — What is Truth? (~10 minutes, David talks about what makes an explanation)

• David Deutsch — A New Way to Explain Explanation (~20 minutes, A TED Talk on explanation)

• An Explanation of Explanation: A previous letter where I attempt to explain explanation.

• The Seed of Certainty: A previous letter I've written on how we can prefer some theories over others, and how science works.

• The Reach of Explanations (~ 1 hour): YouTuber Brett Hall, reads out parts of the first chapter of Beginning of Infinity and provides commentary

And we've reached the end of another letter, how did I go? Do you feel you know more than when you started to read this letter?

If you now understand the difference between a good explanation and a bad one (that they are hard-to-vary), then I have succeeded.

If you understand that the demarcation between science and other fields such as philosophy is testability, then that's a bonus!

If you now see that explanations are about asking the question "why" and that the quest for better explanation is the basis for science and all of our growth in knowledge — well, consider that to be the cherry on top.

I sincerely hope that you have benefitted from reading this letter. If you have any questions, comments or feedback, please don't hesitate to reply to me — I would love to hear from you.

A tiny bit of an update before I go: The Interview I had with Maria on Radio is now available for anyone to listen to on Apple podcasts, Google Podcasts, Spotify or Tune In.

Or if you would prefer, on the 2RPH website.

Thank you for reading until the end of yet another letter; without you, this writing would not have any meaning. I am grateful for your existence.

Take care everyone,

Sashin