There’s a famous story about swans that Nasim Taleb used for the title of his recent book. European zoologists had seen swans, and all the swans they had seen had white feathers, so they said that all the swans in the world were in fact white. Then a European went to Australia and saw swans with black feathers. Taleb’s point is that no matter how much we know, we don’t know what we don’t know, and overconfidence in our knowledge can make us rigid and vulnerable.

Sentences like “There are swans,” or “there are black swans” are what logicians call existential statements. “All swans are white” is a universal statement. In science, the two are very different and require different kinds of evidence.

All it takes to make an existential statement is a single observation. I know that there are swans because I’ve seen at least one. But to say that all swans are white with certainty requires us to have seen every swan. The European zoologists made that universal statement without universal observations, and all it took was one observation of a black swan to prove them wrong.

Now here’s a point that seems to be missed: averages are universal statements. Actually, they’re made with some relatively simple arithmetic applied to data from all members of a category, so they entail universal statements. If the Regal Swan Foundation says “Mute Swans? wingspans average 78 inches,” we take that to mean someone measured all the mute swans (or a representative sample; I’ll get into that in another post). If someone says that and then you find out they only measured swans in their local park, you’d feel deceived, wouldn’t you?

Here’s another one: percentages are universal statements. How can it be a universal statement to say that ten percent of people are left-handed? Well, you have to look at all of them to know for sure that the rest are not. And the same thing goes for “most,” “the majority” and other words that entail statements about fractions. I think this is why Robyn Hitchcock said, “the silent majority is the crime of the century”: if the silent majority really is silent, there’s no way for the person making the claim to know what they think.

On the other hand, statements about units and fractions of units are only existential statements. I have two cats, and I ate half a sausage roll for dinner last night. Words like “many,” “some” and “a few” are also existential statements. I’ve seen many white swans, but I claim no knowledge of the ones I haven’t seen. The only way you could falsify that statement is by process of elimination: showing that there aren’t enough swans in my experience to count as “many.”

So the bottom line is that in order to make a universal statement, including a percentage or an average, you need to have looked at all the members of the group. But in order to make an existential statement, you only need one.

Now here’s why I’m writing this post: this stuff sounds simple, and I feel like I’m writing it for kids, but there are a lot of people who don’t follow it. Either they’ve never been taught about the standards of evidence for universals, or they’ve been taught to ignore them. Most of the times I’ve read “all,” people seem to get that it’s a universal and don’t say it unless they can reasonably claim to have data from all of the things concerned. But a lot of people have trouble with “most” and averages, and especially percentages. You can’t say “most” unless you’ve seen them all.

Well, there actually is a way you can say “most” without seeing them all. It’s called induction, but it’s hard to do, harder than a lot of people seem to think. I’ll talk about that in a future post.

(Update, August 19, 2015: I liked the black swan drawing above so much I decided that it should exist on T-shirts. And you too can call into existence T-shirts, throw pillows, travel mugs – all with the Existential Black Swan on them! I’ll get a cut of the money. Click here for details.)

Over the past few years I’ve realized that there are a lot of scientists who have a different view of science than I do, and most of them don’t even know about my way of thinking. But my way of thinking about science – Instrumentalism – is cool! I’m writing this post to explain what Instrumentalism is, and why I prefer it to other ways of thinking about science. At the very least I can link back to this from future posts so that you’ll understand why I say certain things. Maybe you’ll agree with me that Instrumentalism is cool. Maybe you’re already an Instrumentalist and you didn’t even know it!

Instrumentalism is the idea that scientific theories can never be proven wrong or right. Instead, theories are tools for understanding and prediction. They can be judged as better or worse tools, but that depends entirely on the context: what’s being explained to who and what’s being predicted, under what circumstances. Scientific models have the same status. In one of the most famous cases, the movement of the sun relative to the Earth, neither Ptolemy’s geocentric model nor Copernicus’s heliocentric model would be considered “true” or “false.”

This view of theories does not mean that there is no truth or falsity in science. Observations can still be accurate or inaccurate. And critically, hypotheses can be confirmed or rejected. These hypotheses are usually based on a theory, and a theory that predicts a lot of falsified hypotheses is not a very useful theory. So the heliocentric model is more useful than the simple geocentric model for predicting the movements of planets because those predictions are more often correct.

On the other hand, the geocentric model must still be useful, because most people continue to use it every day. If you’ve ever talked about the sun “rising,” you’ve used a geocentric model. It’s a lot easier than talking about part of the earth’s surface rotating away from the direct rays of the sun. The geocentric model’s predictions about the sun’s behavior are perfectly adequate for day to day human activity.

Since theories are tools for understanding, they are more useful if they are based on a simple analogy to something familiar. The geocentric model compares the sun to flying birds and jumping horses, or to spheres and hoops. In order to explain the apparent “retrograde motion” of the planets, astronomers added the ugly and counterintuitive “epicycles” to the geocentric model. But the sun does not exhibit retrograde motion, so there are no epicycles to spoil its simplicity.

This means that an astronomer (or any of us watching a movie about space) will likely use both the heliocentric model and the geocentric model on the same day, or even in the same hour. In a view of science which says theories are true or false, what does it say about someone that they use two different theories to model the same phenomenon on the same day? Maybe that person is a hypocrite, or even worse, weak-minded for not having the will to consistently apply the true model.

In contrast, instrumentalism is pluralist, tolerant and understanding. Of course sometimes we all act like the sun goes around the earth. It’s the simplest, most straightforward way to think about it!