Cats and butterflies: 2 misunderstood analogies in scientistic discourse

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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

  1. Cats can be both dead and alive in a box with an aparatus controlled by superimposed quantum states.
  2. 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:

  1. 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.
  2. 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!

3 burning issues in the study of metaphor

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I’m not sure how ‘burning’ these issues are as such but if they’re not, I’d propose that they deserve to have some kindling or other accelerant thrown on them.

1. What is the interaction between automatic metaphor processing and deliberate metaphor application?

Metaphors have always been an attractive subjects of study. But they have seen an explosionof interest since ‘Metaphors we live by’ by Lakoff and Johnson. In an almost Freudian turn, these previously seemingly superfluous baubles of language and mind, became central to how we think and speak. All of a sudden, it appeared that metaphors reveal something deeper about our mind that would otherwise remain hidden from view.

But our ability to construct and deconstruct metaphors was mostly left unexamined. But this happens ‘literally’ all the time. People test the limits of ‘metaphor’ through all kinds of dicoursive patterns. From, saying things like ‘X is more like Y’ to ‘X is actually Y’ or even ‘X is like Y because’.

How does this interact with the automatic, instantaneous and unconscious processing of language. (Let’s not forget that this is more common)

2. What is the relationship between the cognitive (conceptual) and textual metaphor?

Another way to pose this question is: What happens in text and cognition in between all the metaphors? Many approaches to the study of metaphor only focus on the metaphors they see. They seem to ignore all the text and thought in between the metaphorical. But, often, that is most of goes on.

With a bit of effort, metaphors can be seen everywhere but they are not the same kind of thing. ‘Time is money’, ‘stop wasting my time’, and ‘we spent some time together’ are all metaphorical and relying on the same conceptual metaphor of TIME IS A SOMETHING THAT CAN BE EXCHANGED. But they are clearly not doing the same job of work for the speaker and will be interpreted very differently by the listener.

But there’s even more at stake. Imagine a sentence like ‘Stop wasting my time. I could have been weeding my garden spending time with my children instead of listening to you.’ Obviously, the ‘wasting time’ plays a different role than in a sentence ‘Stop wasting my time. My time is money and when you waste my time, you waste my money.’ The coceptual underpinnings are the same, but way they can be marshalled into meaning is different.

Metaphor analysts are only too happy to ignore the context – which could often be most of the text. I propose that we need a better model for accounting for metaphor in use.

3. What are the different processes used to process figurative language

There are 2 broad schools of the psychology of metaphor. They are represented by the work of Sam Glucksberg and Raymond Gibbs. The difference between them can be summarised as ‘metaphor as polysemy’ vs ‘metaphor as cognition’. Metaphor, according to the first, is only a kind of additional meaning, words or phrases have. While the second approach sees it as a deep interconnected underpinning of our language and thought.

Personally, I’m much closer to the cognitive approach but it’s hard to deny that the experimental evidence is all over the place. The more I study metaphor, the more I’m convinced that we need a unified theory of metaphor processing that takes both approaches into account. But I don’t pretend I have a very clear idea of where to even start.

I think such a theory would also have to account for differences in how inviduals process metaphors. There are figurative language pathologies (e.g. gaps in ability to process metaphor is associated with autism). But clearly, there are also gradations in how well individuals can process metaphor.

Any one individual is also going to vary over time and specific instances in how much they are able  and/or willing to consider something to be metaphorical. Let’s take the example of ‘education is business’. Some people may not consider this to be a metaphor and will consider it a straightforward descriptive statement along the lines of ‘dolphins are mammals’. Others will treat it more or less propositionally but will dispute it on the grounds that ‘education is education’, and therefore clearly not business. But those same people may pursue some of the metaphorical mappings to bolster their arguments. E.g. ‘Education is business and therefore, teachers need to be more productive.’ or ‘Education is not business because schools cannot go bankcrupt’.

Bonus issue: What are the cognitive foundations shared by metaphor with the rest of language?

This is not really a burning issue for metaphor studies so much as it is one for linguistics. Specifically semantics and pragmatics but also syntax and lexicography.

If we think of metaphor as conceptual domain (frame) mapping, we find that this is fundamental to all of language. Our understanding of attributes and predicates relies on the same ability to project between 2 domains as does understanding metaphor. (Although, there seems to be some additional processing burden on novel metaphors).

Even seemingly simple predicates such as ‘is white’ or ‘is food’ require a projection between domains.

Compare:

  1. Our car is white.
  2. Milk chocolate is white.
  3. His hair is white.

Our ability to understand 1 – 3 requires that we map the domain of the ‘subject’ on to the domain of the ‘is white’ predicate. Chocolate is white through and through whereas cars are only white in certain parts (usually not tires). Hair, on the other hand, is white in different ways. And in fact, ‘is white’ can never be fully informative when it comes to hair because there are too many models. In fact, it is even possible to have opposite attributes mean the same thing. ‘Nazi holocaust’ and ‘Jewish holocaust’ are both use to label the same event (with similar frequency) and yet it is clear that they refer to one event. But this ‘clarity of meaning’ depends on projections between various domains. Some of these include ‘encyclopedic knowledge’. For instance, ‘Hungarian holocaust’ does not possess such clarity outside of specialist circles.

It appears that understanding simple predicates relies on the same processes as understanding metaphor does. What makes metaphor special then? Do we perhaps need to return to a more traditional view of metaphor as a rhetorical device but change the way we think about language?

That is what I’ve been doing in my thinking about language and metaphor but most linguistic theories treat these as unremarkable phenomena. This leads them to ignore some pretty fundamental things about language.