What Seemed Like Perfect Reasoning Utterly Failed

Does warm water sometimes freeze faster than cold water when placed in the same conditions? “Absolutely no way,” I said, a mere minute after I heard the claim. “People sometimes claim that NASA faked the moon landing too,” I thought to myself.

I pointed out why this claim is impossible. As warm water cools it must eventually reach the same temperature that the cool water started at. From that point on, the warm water will behave just like the cool water, but it will have taken the warm water a while to even get into that state. Freezing occurs at the same temperature for both warm and cold water, but warm water of course will take longer to get to that temperature.

This isn’t quite 1+1=2, it’s more like 23+14=37. I double checked my answer and was 98% confident. It’s amazing what some people will believe, and how powerful reasoning is at solving these sorts of problems.

But I was wrong. And not just a little bit. In fact there are tons of ways that warm water might be able to freeze faster. This is the so-called Mpemba effect, observed by the likes of Aristotle, Descartes, and Francis Bacon.

The fact that the water has previously been warmed contributes to its freezing quickly: for so it cools sooner. Hence many people, when they want to cool hot water quickly, begin by putting it in the sun.

-Aristotle

My wrongness here isn’t so much about being wrong about the effect, per se. The extent to which this effect is real, and under exactly what conditions, can reasonably be debated. My wrongness is in being convinced I was right when I couldn’t have known I was. I couldn’t possibly have ruled out all the possibilities in a single minute. For example, I didn’t even consider these ideas that came up after two minutes of googling:

• Evaporation : the warm water evaporates, meaning there is less water to freeze.
• Frost: the cool water may be more likely to freeze from the top (with the frost trapping in further heat) whereas the warm water may be more likely to freeze from the bottom and sides.
• Convection: warm water and cold water produce different currents, which could alter the heat distribution.
• Supercooling: if free of impurities and in the right conditions, water can actually drop below freezing temperature without freezing, and the propensity for supercooling might be affected by the starting temperature.
• Conductivity: the hotter liquid might melt an existing layer of frost that is preventing the liquid from directly touching a much colder surface.

What could have prevented me from making such a ridiculous error? How could I have noticed that I was being insanely overconfident? There are a few signs that should have tipped me off:

• Lack of expertise: The physics of heat and fluids is outside of my domain of expertise. I should have recognized that this is not a subject I know a lot about and so been more skeptical of my own opinions.
• A simple model: I was employing a very simple model for the situation (involving just the temperature of the water). While beautiful, and easy to work with, really simple models rarely capture all the details of a situation. For instance, I didn’t consider the possibility of evaporation or frost, because those variables weren’t included in my model. If you’re using a simple model, you should consider whether you’re missing important factors.
• Insufficient time: If you haven’t thought about something for very long yet you are already very opinionated, you might want to think about it longer.
• Didn’t consider alternatives:  I didn’t even try to think of ways that this effect could be real. Instead, I came up with an argument why it couldn’t be real, and that argument sounded convincing to me, so I stopped thinking. This problem is the big one. So here’s a 30 minute free mini-course I designed to train you to avoid exactly this problem.

Reasoning is only as good as the reasoner. And we humans don’t have the best track record. The trouble is, it’s easy to find arguments that seem totally convincing. The trick is that we shouldn’t just try to convince ourselves that we are right. We should try to convince ourselves that we are wrong. If we do that in earnest, we’ll be much more likely to end up with the right opinion.

*Ice photograph by Dingske.