Easy solution - it is first grouped by type and then groups are sorted by average length

Now I’m sad

That’s kind of the point I took from it? Would it help if you imagine there was a direction arrow labelled “entropy” between them?

I’ve never been able to explain why I feel the way I do when looking at the bifurcation diagram

Literally both form, function would be an image of supplying nutrients to the rest of the plant which, one might note, it can’t do and so its function is disabled in both.

It’s evenly distributed because it’s all mixed together. Order: 15 buckets of paint in a rainbow of colors. Swirl them all together and you get an increase in entropy, it’s hard to pick out spots with pure color, there are a bunch of weird mixtures where the colors touch, it’s really difficult to paint with. Mix them all up completely and you get a uniform brown sludge. That’s chaos, you can’t separate them back out, all the individual pigments are hopelessly commingled.

Think of a box with 4 particles a, b, c and d. If every particle is on the left side of the box, then there is only 1 way to divide them up. [(a, b, c, d), ()]

If there are 2 particles on the left side of the box and 2 particles on the right side of the box, then there are 6 ways to divide them up:

[(a, b), (c, d)]
[(a, c), (b, d)]
[(a, d), (b, c)]
[(b, c), (a, d)]
[(b, d), (a, c)]
[(c, d), (a, b)]

In total you’ve got 16 possible arrangements, the 2-2 state has the “highest” entropy because you’re more likely to end up with the one that takes up 6/16 arrangements.

Here’s a good way to visualize chaos vs order in this context. Imagine you have a thousand marbles neatly stacked in a pile like cannonballs are. That’s order. They operate as one entity. If you want to move the stack, you must move them all at once and very carefully.

Now imagine those thousand marbles all strewn about your house. They are now a thousand different entities. You can’t interact with all of them at once anymore.

You bring order back to the system by stacking the marbles again. It takes a lot of energy to stack them, and, with enough of it, you can return the marbles back to one entity.

The notion is that entropy increases. That is, the amount of energy you can extract to do work decreases. You need differentials to do work, for example a water wheel works because water at elevation has potential energy which you can use to turn the wheel as it flows downhill to a lower potential energy. When everything is evenly distributed, you can’t extract any more energy to do work.

It dowsnt. It gets harder and harder for humans to describe and comprehend.

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