Tag: equilibirum

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On packing cubes and better fit

Fold everything up and put it straight in the bag? Or fold everything into packing cubes first, then put these in?

Not an important dilemma — but useful for thinking about utility and fit.

Packing cubes make it easier to find your stuff. That’s a win for utility. But they make it harder to use space efficiently. That’s a loss of fit.

When you pack directly into the case, clothes can mould to the contours of the bag. With cubes, you’re first fitting clothes into rigid boxes, then trying to fit those boxes into the bag. The bigger the chunks, the less well they fit.

Even cubes designed for your bag add extra cell walls. It’s more work to get everything in.

Why does this matter? Because it’s all about equilibrium. The more options a system has, the better it can settle into a state that fits its surroundings.

Of course, both bags — with cubes and without — are at equilibrium once zipped. But cubes trap the system in a constrained equilibrium: ordered, but with wasted potential (unused space). Without cubes, the system has more freedom to find a messier equilibrium that actually fits better.

And there’s entropy at play: to keep clothes in neat cubes takes extra work. Left free, they tumble into arrangements that fit themselves.

From a regenerative point of view, sometimes it’s worth adding structure — boundaries, hierarchies, rules — to make a system function. But structure always reduces adaptability. Keeping a system in a fixed order takes work, and wastes some of its potential to respond.

So the design question is: when is it worth doing the work to hold things in order, and when is it better to let the system find a looser, but better-fitting arrangement?

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The Entropy Bus

When strangers get on a bus, they almost always spread out. Few people sit next to each other unless they really have to.

Partly that’s social norms. And partly it’s probability — and entropy is the name we give to it: the measure of how many possible configurations a system can take.

The social rules push people apart, but entropy makes the scattered state the most likely outcome.

You could put an extra conductor on the bus to tell people where to sit, filling rows neatly from the front. But that takes energy. Take the conductor away, and inevitably everyone spreads out again.

The lesson of the entropy bus is that order is costly, disorder is cheap — and dispersal from order to disorder creates a flow.

The art of regenerative design is to shape systems so that the most likely outcome, and the flow in that direction is also the most life-giving.

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Boltzmann laughter distribution

This week I’ve been playing around with a way to explain the Boltzmann distribution — a mathematical function that predicts how energy is likely to spread out in a volume of gas. 

Imagine you have an audience of 100 people. Imagine there is a fixed amount of laughter to go around. What’s the most likely way the laughter will be distributed in the audience. 

Now, already I can see this analogy breaking down. But let’s just go with it for a little longer. 

We could arrange things so that one person does all the laughing. As there’s 100 people in the room, there’s 100 different ways we could do this: one for each possible solo laugher. 

Now imagine  we have two people laughing each with half the total available laughter. There are now 4,950 ways to pick those two people — in other words 4,950 ways to pick two people from 100.

The more we spread the laughter around, the more ways there are of distributing that laughter. 

The equation is for an audience size of n, and the number of people laughing in the audience, the number of ways of arranging laughter is n!/(k!(n-k)!).

This number of combinations gets very large very quickly. For half the audience laughing, there are approximately 100,000,000,000,000,000,000,000,000,000 ways of doing this.

This idea — the some arrangements have more ways of being achieved than others — is what underlies the Boltzmann distribution. 

Introducing some more formal language:

A macrostate is the overall situation (eg half the room laughing)

A microstate is one specific way of achieving that macrostate (eg exactly which 50 out of the 100 are laughing). 

Now, energy in a system doesn’t decide which microstate to be in. It just jostles around between different microstates. Some energy here, some energy there. But since there are far far more ways of achieving the more distributed macro states than the ones where energy is concentrated, the system almost always ends up in a highly distributed macro state. 

The macrostate with the most microstates is overwhelmingly likely.

This is why energy spreads out in a room. It isn’t a plan, it is just the macrostate that is overwhelmingly more likely. Like billions and billions of times more likely. 

This concept underpins ideas like equilibrium, itself an important underpinning idea in regenerative design. The goal of regenerative design is for humans and the living world to survive, thrive and co-evolve — in other words, thriving in equilibrium.

Of course, any physicists listening to this would laugh me off stage. For one thing, laughter isn’t a fixed quantity. And for another, one person’s laughter can trigger more. And…one person laughing amongst 100 is in itself funny. 

Now if there were 100 physicists in the room…how many would be laughing?