The inspiration for this post comes from a Calvin and Hobbes cartoon (if you are from a generation unfamiliar with these Bill Watterson cartoons, then go and discover them after reading this blog). Calvin sees his mum crying in the kitchen, and asks why. She explains that she is cutting up an onion, to which he replies “It must be hard to cook if you anthropomorphize your vegetables.”
Anthropomorphism: ‘the attribution of human characteristics or behaviour to a god, animal or object.’ (Oxford Dictionaries)
It might well be hard to do science if you anthropomorphize basic building blocks of matter, although it was common until the 17th century – Robert Boyle, of Boyle’s Law fame, was one of the first to suggest it might not be entirely applicable.
You have probably encountered such anthropomorphism in situations like pressures trying to equalise in gas flow, like when Goldfinger shoots a bullet through the side of a plane (to continue our James Bond theme from this previous post), or when low pressure anticyclones form in the Atlantic.
But actually pressures don’t try to do anything. And they wouldn’t ‘know’ they had balanced each other out if they managed it. So why do we talk that way? Perhaps there are situations in which this kind of language and analogy can make concepts easier to understand and more relatable to everyday life.
Consider another example. If you were at school in the UK any time in the last 30 years, you almost certainly were taught Chemistry between the ages of 14-16. And you were almost certainly told that elements bond to each other because their electrons are ‘trying to get a full outer shell’ or ‘like to have a full outer shell’. Now, good teachers do this too, because they know they are aiming towards an understanding that processes will tend to happen towards a minimisation of potential energy. Teachers at this stage realise they are dealing at the edges of their students’ comfort zones, and scaffold learning appropriately; working out electronic structures in an atom might be enough of a task for the learner at that stage, without complicating things further with physical reality! But unless this simplification is challenged later, at the next stage of learning, might it not leave misconceptions about the deeper nature of how physical processes actually work?
Going back to gases, framing their flow as trying to equalise the pressures masks the reality of what is really happening (as you can guess, I don’t much care for the saying “Nature abhors a vacuum,” either, unless applied to Gary Larson’s cartoon of that name – just Google it…). A reality that is way more interesting and enlightening if looked at in another way.
When Goldfinger shoots the hole in the plane, the air molecules in the plane (and those outside) have no idea that there even is a hole (indeed, they have no idea about anything – that’s the point we are trying to make). They carry on their business regardless (yeah, ok, they don’t have a business either) and either hit the hole or hit the wall of the plane. They are not trying to go through the hole; they are either travelling in a direction that leads them to the hole, or they aren’t. Those that hit the hole go through it. And that happens in both directions – molecules outside get in, and molecules inside escape. But crucially, there are more molecules per unit volume inside than outside (the cabin has been pressurised), and so more molecules escape than enter. This reduces the pressure of air inside the plane, and eventually it will equalise with the pressure outside, but it wasn’t trying to do that, it just happened through the statistical inevitability of the journeys of trillions of molecules.
Another problem with the ‘trying’ approach is that people might leap to the conclusion that the ‘trying’ will be as quick as possible, and that it will succeed. In fact, the situation of gas flow (and many others, such as radioactive decay) is one in which the rate of change of the quantity is proportional to that quantity (the rate of change of pressure, due to the net exit of molecules, is proportional to the imbalance between the density inside and outside).
Mathematically, for the gas pressures, this can be written
\(\frac{dp}{dt}\propto p\)
And we will be covering this situation in more detail in sections 4 and 5 of the accompanying website sciencebydegrees.com. You don’t need to worry about this in the context of this blog post…
So what does this mean for the equalisation of pressures. Well, as soon as air starts to rush out of the plane (on average, remember, this is a net ‘rush out’ – molecules are rushing out and in, but not in equal numbers. And maybe they’re not rushing – that would imply they had somewhere to be…), the pressure difference decreases, so that the net rate of exit then falls. As the pressure difference falls, the ‘speed’ or rate at which further equalisation happens also falls, leading to a relationship known as an exponential (exponential does not just mean ‘fast’ or ‘a lot’ as might be imagined from its popular misuse), as described here…
So next time you read or give an explanation in terms of objects trying to do things, just maybe wonder whether the explanation is appropriate for your stage of learning, or whether the reality might be more interesting. After all, an onion’s not trying to make you cry (apparently propanethial S-oxide is responsible for that…).