Butterfly effect and Schrödinger’s cat are 2 very common ways of signalling one’s belonging to the class of the scientifically literate. But they are almost always told wrong. They were both constructed as illustrations of paradoxes or counterintuitive findings in science. Their retelling always misses the crucial ‘as if’.

This is an example of metaphor becoming real through its sheer imagistic and rhetorical power. But it also underscores the need to carefully investigate both domains being mapped onto each other, as well as the act of mapping. Metaphors used generatively are only useful if they are abandoned quickly enough. In this case, the popular imagination not only did not abandon the metaphor, it made it into a literal statement with practical consequences.

The way the two narratives are constructed is usually in the form of:

Science shows us that

Cats can be both dead and alive in a box with an aparatus controlled by superimposed quantum states. Butterflies can cause hurricanes on the other side of the world.

But the actual formulation should be:

Science produces a lot of counterintuitive and (seemingly) paradoxical results some of which are at odds with each other and/or our experience of the world. For instance:

If we were to apply Heisenberg’s quantum uncertainty principle to the world we know, we would have to admit that a cat in a box with a quantum killing machine is dead and alive at the same time. And that is obviously nonsense. If we were to apply what we know about chaos theory to the world of causes and effects, we would have to admit that a butterfly flapping its wings on one side of the world, can cause a hurricane on another side of the world. And that is obviously nonsense because butterflies have no real impact on the world on scales larger than a flower.

Both Schrodinger and Lorenz were trying to illustrate the counterintuitive conclusions of their respective scientific fields – quantum mechanics and dynamic (chaotic) systems. And in both cases, it badly backfired.

Although Schödinger’s dilemma was much more foundational to the structure of our universe, it was Lorenz, whose funny paper to an obscure symposium did the more lasting damage.

It is of no practical consequence whether or not in the retelling of Schrödinger’s paradox, we omit the word ‘paradox’ and assert that ‘science tells us that there are machines that can make cats alive and dead at the same time.’ This is merely par for the course in the general magical nature of the public scientific discourse. And it can even spur the development of new models of the physical universe.

But the ‘butterfly effect’ is more dangerous because it seems like it could have practical applications. Lorenz was not stating a paradox per se, only a counterintuitive conclusion that goes against our most common scenarios of causal relations. Our basic experience of the world is that big things move big things and small things don’t. So any suggestions we can make small things move big things seems intriguing. We know levers and pullies can get us some of the way towards that, so the dream of a magical lever is always there. Homeopathy “works” on the same magical principle. But this is not the lesson of complexity.

The most common reformulation of the ‘Butterfly effect’ is: ‘small actions can have a big impact’. However, this confuses sensitivity to initial conditions with a cumulative cascade effect. Every single snowflake contributes equally to an avalanche as do all the other aspects of the environment. Although none of them individually have any effect on the world at human scale, when combined, they can move much larger objects. But it is that combination (into a larger whole) that has the impact.

Whether any particular snowflake is the last to fall or somebody clapped loudly near a snow drift just before the avalanche fell says nothing about the ability of small things to have big effects. Only about our inability to measure small variations in big things accurately enough.

It is not true that a butterfly’s wings cause anything but minute variations of air right next to them. But it may be true that they are one of the infinite variations of the whole weather system that is simply impossible to measure with finite precision. It’s not that it is hard to calculate all the variations, it is that there are more variations than we have atoms to calculate them with.

Sure, we can talk about proximate and ultimate causes, but that again hides the problem of calculation. And if we ignore the practical problems of measuring the infinite with finite tools, we only get mired in philosophical musings on prime movers and free will. And these have yet to lead anywhere in two and a half millennia.

The only thing we can learn from the butterfly effect is that we cannot measure complex systems accurately enough to predict their behavior over the long term with enough precision. The big mismatch is that while the variation in ‘initial conditions’ is too small to measure, the variation in the outcomes is not. And that feels wrong.

Complexity is unsurprisingly too complicated to be captured by a single metaphor. The ‘butterfly effect’ is a good metaphor for the sensitivity to initial conditions aspect of it. But only if we understand that it is a metaphor that illustrates the counterintuitive nature of complexity and not complexity itself.

The larger lesson here is that metaphor is a process. It doesn’t just lie in a bit of text waiting for us to encounter it and understand it. It is picked up as part of stories. It is told, retold, reexamined, abandoned, readopted, and so on. If you unleash a generative metaphor on the world, you should keep an eye on it to make sure it’s still doing the job you meant it to do. That means a lot of talking and then more talking. Just like with butterflies, the ultimate outcome is never certain. That is fine. Metaphors are supposed to open up new spaces. But some of those spaces may have lions in them and we do know that lions have big impacts on human scales. Bon appetit!

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