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What makes a good explanation & how to make better decisions.

How can we responsibly use data to make good predictions? What separates good theories from bad ones? Here I discuss drawing the wrong conclusions and the telltale signs of good explanations.

Extrapolation

It seems like common sense to look at data and use that to create predictions of behaviour. Extending existing data points arbitrarily is called extrapolation. Some real-world examples of extrapolation could be:

  • The sun has risen every morning in recorded history so will rise every morning for as long as I live.
  • The population of the UK has grown every year since the 1960s so will continue to grow
  • Having your money invested in the S&P 500 has averaged you 10% per year for the last 50 years, so having your money invested here is safe as it should continue.

Extrapolation is a dangerous tool because it makes no attempt to predict the reason behind the behaviour. Extrapolation makes no attempt at explanation. This can often lead you astray in ways that seem obvious only when you understand the explanation for behaviour. For example:

  • Previously I have heated up a saucepan full of water to 60°C. As I applied more heat the water has become hotter. This should extend to infinity, the more heat I apply the hotter the water will get until I stop heating it.

We know this isn't the case. We know that when the water hits 100°C it will boil, the water in the saucepan will stay the same temperature because any water that is hotter will have evaporated. The explanation shows us why our extrapolation is wrong. Another example:

  • The year is 1998, I am 6 years old. For the last 900+ years, the calendar year has started with a 1. As something that has happened every day for 900 years is pretty consistent I can predict that in my lifetime at least the calendar year will always start with a 1. ] This example seems absurd because we have an explanation of why the date is the number it is. The number in the date is the number of years that have passed since an arbitrary day and in 2 years' time it would roll over to the year 2000, breaking the pattern. A more sinister example of the same theme is that farm animals see their farmer bring them into this world, feed them, tend their wounds. The farmer must care about them living a long life, right? You get the point.

Using data to create explanations

So what we need are explanations as to why events happen. A step up from extrapolation is induction. Induction is using your data to create explanations.

  • Everyone at the cafe chooses the pizza, therefore must be very tasty.
  • Every swan I have ever seen is white, all swans must be white.
  • This page of my website has the most organic views from Google, its optimisation must be particularly good.

Or perhaps a less obvious example of induction we likely all fall into

  • This burger from McDonalds looks the same as the last one I got. It must contain the same ingredients.

None of these statements are actually true. The pizza might be the cheapest thing in the cafe, the Australian Black Swan exists, your blog post might be in a less competitive SEO space (or just older) and fast-food restaurants often alter recipes for cost-saving and/or supply chain reasons.

Induction seems obviously flawed when listed out like this. I think extrapolation and induction are natural human survival instincts, honed from a much more dangerous world. When we saw certain footprints in the mud and there were then fatal attacks in the woods, it doesn't matter if we induce that its a monster or a real animal, staying out of the woods at that time kept people alive. Induction leads us to have rituals for good luck and pray for better harvests. We train animals by taking advantage of their induction - 'last time I did the action I got a treat and therefore if I do it again I will get another treat'. It's just a very easy trap to fall into 'last time I did this my wife wasn't mad, therefore I can do it again without worry'. Explanations from induction aren't reliable.

So how do we get good explanations? What's the point in data if we cant induce from it or extrapolate it reliably.

Good Explanations

In 'The Beginning of Infinity', Oxford University physicist David Deutsch spends the first chapter talking about what makes a good explanation and how we come up with them. Let's start with where good explanations come from, and then move onto the properties of a good explanation.

Historically (before the Age of Enlightenment) the creation of new knowledge was slow. Entire generations could pass without new things being discovered. We had a culture of accepting what we were told by institutions as proof of knowledge. The greatest and most obvious example of this was the reliance on religion and religious institutions for the explanation of phenomenon. Questioning what you were told was not really done, and in some cases actively punished.

We have created the vast majority of our knowledge since the Age of Enlightenment. The Age of Enlightenment was described by Kant as 'the age of criticism' he said 'and to criticism, everything must submit'. This is a reflection of the rebellion that happened during that time. A rebellion against the acceptance of institutional explanations and the change in culture to one compelling people to question and criticise everything they think they know. This criticism is the core of modern understanding and the true usefulness of our observational data. Our modern scientific theories are (and should be) subject to the most thorough experimental testing. So we know we use our data and observations to test our explanations, but where do these explanations come from?

The answer to this is charmingly simple - conjecture. In other words guessing. We must guess a mechanism and then use observational tests to try to prove or disprove it. We make good theories by rearranging, combining altering and adding to existing theories - and then use observation to test theories. It's important to remember that every explanation at the moment are just our current best guess and we can't know it as truth, as at any point we could make an observation that doesn't fit with our current explanation, and we would need a new explanation. To assume we won't make an observation that will disprove our current theories is extrapolation, and you have fallen into the trap of the first paragraph. In this sense, science is never finished and we must keep testing and reevaluating what we think we know.

We can't however keep testing every single guess, because we can imagine false reasons all day which would be a waste of our time. Instead, we should test our good explanations. Deutsch proposes we can develop a sense of whether our theory is a 'good explanation' or 'bad explanation' based on the following properties:

  • Good explanations establish a mechanism enabling the behaviour
  • Good explanations are testable
  • Good explanations are hard to vary
  • Good explanations have a far reach

To show these in context we can take the example Deutsch does in 'The Beginning of Infinity' and compare Ancient Greek explanations for the seasons with our current explanation.

Good explanations establish a mechanism enabling the behaviour

The ancient Greeks believed that the Goddess Persephone had to travel to Hades once per year and when she did her mother Demeter would get sad and command the world to get cold and bleak while Persephone was gone. We have no mechanism by which someone commanding something can cause the weather to change so this might be indicative of a bad explanation.

If we contrast this against our modern theories of seasons. The Earth is tilted on an axis and travels around the sun, parts of the world will get different weather/temperature behaviours based on the amount of exposure to the sun they get. This directly explains why some times of the year the weather is hotter than others, with exposure to a hot object (the sun) causing hot weather.

Good explanations are testable

Continuing the above example, we cannot test the moods of the Gods. We don't even have a mechanism for detecting the existence of Gods or measuring their moods to compare the weather. We can't detect other Gods and see the effect they're having or whether when Demeter is less sad it is less cold.

With the Axis tilt theory, we can measure the temperature at different parts of the world but at the same time of the year. We can use the height the sun travels through the sky to see the extent of the tilt. We can create a model of the solar system showing us what parts of the planet should be exposed to the sun and when. Crucial to the axis tilt theory is that the northern and southern hemispheres will have opposite seasons at opposite sides of the world. This extreme testability is indicative of a good explanation.

Good explanations are hard to vary

If we were to go to different hemispheres and opposite sides of the Earth and measure temperatures and December in England showed the same weather patterns as December in Australia then we would have to throw out the whole theory. This would have to happen for the theory to be correct. The tilted axis theory is so specific that if our data falsifies it we cant slightly change the explanation, we must start again.

With our Greek God explanation, we can very easily vary the story. Perhaps Demeter commands different parts of the world to be cold at different times in memory of Persephone's absence. Perhaps on the other side of the world its Achilles. Perhaps it's not her sadness at all, but her tears are the rain.

It's almost as if the complex fragility of an explanation works in its favour. If an explanation is theoretically easy to disprove, but you can't find observations against it - it's likely a good explanation.

Good explanations have a far reach

Demeter's sadness doesn't reach beyond explaining the cold weather of the seasons. All new phenomena require a new theory or a variance of the current theory. If we take our axis tilt theory we can explain many behaviours. Why the more northern you travel, the more the day and nights change the length, as well as how those lengths differ throughout the year. You could even make wild predictions like 'At the extremes of the earth the world the sun won't rise and won't set for many months at a time' - which is independently testable. It isn't even really a theory just based on seasons, it's a theory relating to all celestial bodies with many of the same foundations for what would happen on other planets based on their axial tilts. There is no room for these explanations in Demeter's sadness.

Analytics

As I've written previously I'm involved in a low-key tech startup at the moment and we are making lots of choices for what platforms we want to use. The reporting and analytics of software/platforms are a key decider in what platforms we choose. I'm glad I started reading this book at this time - analytics platforms almost encourage extrapolation and induction. If you visit your 'reporting' page of your software your monkey brain is going to be immediately drawn to making predictions, drawing conclusions and inducing reasons for behaviour from the data. I think it's a general feeling that more data is better and that more data is more power - but we need to use that data correctly or it can lead us down the wrong paths.

Pushing forward I'm going to make an effort to fight my instinct to go straight to the analytics and instead theory-craft first, before seeking to validate theories using analytics. I don't have a solution for this just yet. I wonder if there is a mental model or even a simple worksheet you can fill in to make sure you're thinking in the 'correct order'. I'm hoping to use Deutsch's rules as guideposts for making good predictions.

Thanks for reading. Get in touch if you want to chat.