Read Now Season 1

Equilibria and Oscillations

You’re on your way sitting on a train. You look outside and you see Dr Hannibal Lecter standing. He’s just standing there. On an wooden platform. Suddenly, he raises his hand. Waves. He takes a step forward. You jump back. He falls off the wood and before you can regain your courage he’s a hundred metres behind you.

You see, you were on a train. For Lecter to appear still outside your vehicle, he too must have been travelling at exactly the same velocity (upon that wooden platform which was probably that makeshift rail-car TinTin had build in Soviet!). This example is absolutely unreal. What’s true here though is that oftentimes things that appear still and devoid of animation are quite action-packed in the background!

You can check out the post titled Oops! Captain is Dead… and see how a spaceship might approach the space station at the speed of only a few centimeters per second even though both ISS and the spaceship is travelling at about 7.66 km/s.

You may have seen a glass full of water. Aah such still water. Almost reminds you of a still lake. Except, neither is still at a microscopic level. Especially not so at the surface. Molecules keep on evaporating off of the surface of a water body into the atmosphere and molecules keep on condensing into the water body from the atmosphere. There’s always this tug of war between the liquid and vapour state. Pretty much why the surface experiences a vapour pressure.

Had water been colourful, you would have seen a gradient of gradually diminishing colour above the surface as the vapour density decreased with height due to diffusion into the surroundings. Feel like testing it? Heat the glass. That hands over excess energy to the water molecules. They start vibrating and movin’ like crazy. As a result, more escape out into the air when compared to molecules condensing in.

By heating the water you altered the conditions of an equilibrium that existed previously. Nature in turn altered the configuration of the equilibrium and boiled the water off so as to counter the change induced by you. All this points towards the fundamental importance of equilibria in nature.

Some of these equilibria are stable. This means if you try to induce some change into the system you’ll experience negative feedback loops bringing you back to square one. Had the equilibrium been unstable, positive feedback loops would have greeted you in turn.

All this makes us believe that stable equilibria are ultimate. Eventually everything should therefore settle into the lowest energy state and be guarded by negative feedback loop which would prevent any changes to itself. Yet left by itself, many natural systems never settle into a single configuration, it keeps on altering.

Biology has several example of oscillators. The population of prey and predators show such seasonal variations. Too many deers in a forest overpopulate the niche and depletes the edible leaves. As a result the wolf population spikes. When wolves explode in number, too many deers get eaten. This gives the forest the opportunity to grow back leaves with fewer herbivores around. As deer number drops, wolves can’t sustain their colonies. Eventually, wolves too start to die or migrate. This gives rise to a higher deer population once again with the forest invitingly filled with lust green foliage.

Such observations play an important role in establishing a biosphere from scratch which sounds fancy but is pretty much what we try to achieve when creating a garden albeit in a much smaller scale. Monocultures such as plantations are bad for nature as it fails to build up an ecosystem around it and therefore lacks the promise of oscillations. As soon as the environmental parameters stray beyond the comfortable zone no more checks and balances exist to bring it back into the ideal state.

To summarize, we can just appreciate how majorly the commutativity of addition distorts our sense of reality as we often use numbers to represent natural parameters and these values can be subject to two opposing forces which equally influence the parameter in opposite directions and all that a shallow observer would notice is how constant the value appears!

Arkadeep Mukhopadhyay