The Thanksgiving holiday we celebrate here in the USA has some unfortunate overtones regarding its colonial origin. Still, the idea of a festival of thanks is an ancient one — thanks for a good harvest or a good hunt. Or, in our case, thanks for helping us not die last winter.
As with Christmas or the Copenhagen interpretation, we tend to take a “shut up and calculate!” approach to the holidays. “Shut up and shop!” in the case of the Winter Solstice, and “Shut up and give thanks!” today.
One thing we can be very thankful about is patterns…
More specifically, that we live in a reality where simple rules involving only handfuls of objects give rise to patterns of astonishing richness and complexity.
A very small piece of the Mandelbrot set. [click for big]
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We have especially good reason for thanks considering a basic fact about the nature of the universe: The fact of entropy.
Entropy (the second law of thermodynamics) is the universe’s way of saying that, not only can’t you win, you can’t even break even. Everything you do involves an energy tax.
So the basic tendency of the universe is to age, to decay, to break down. Order inevitably and always turns to disorder. Stars burn out, and even black holes eventually evaporate into nothing.
The end of everything, as they say, is dust.
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Yet the universe has a redeeming, almost magical, underlying property that counters — at least for a while — this overall downward trend.
Simple rules involving a small number of objects (plus some energy) result in highly complex systems.
Here are some examples:
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I’ve posted about the Mandelbrot many times. It’s a pattern of infinite complexity, and it’s based on this simple rule:
That is all there is to it.
It results in images like this (or the one above):
Another very small piece of the Mandelbrot.
Note the “while” term in the rule. This, and the n and n+1 business, indicate this rule is algorithmic.
Implementing the rule requires a looping construct. We apply the basic rule (the part before the “while”) over and over so long as both tests after the “while” are true. (Which one eventually fails determines whether C is in or out of the Mandelbrot set.)
In other words, implementing this rule requires a process, and that is frequently the case. (Hence, in part, the need for energy.)
The Mandelbrot is an abstraction, pure information at root, so the process needed is an algorithmic one (i.e. a numeric one).
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Everything that we see, touch, taste, hear, or smell, is made of matter.
Which consists of just two quarks, one called up, one called down, and one lepton, the good old electron.
These three particles (plus energy) plus the rules of the Standard Model, result in all the 118 different types of atoms that exist. These are our basic elements.
The periodic table of elements.
Atoms combine (according to the rules of chemistry) in nearly infinite ways to give us everything from air to stone to water to fire. Not to mention plants, animals, and people.
In fact, nature herself only produces 94 elements, humans synthesized the other 24. What’s more, some of the 94 natural elements exist in only trace amounts, so nature generally works from an even smaller palette.
For humans, it boils down to an even smaller subset of crucial importance: Carbon, Oxygen, Nitrogen, Hydrogen, and a handful of others.
A small set of basic objects (two quarks and the electron), energy, and some rules, and all of physical existence emerges.
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Let’s talk a little more about the electron.
All of chemistry (hence much of the behavior of atoms) is based on the interaction of electrons in atoms. (Specifically in just the “outermost” electrons.)
So electrons, plus the rules of electron interaction, give us chemistry.
Electrons can be really beautiful, too!
We’ve also harnessed the electron in the form of electricity for lights, motors, heating, and cooking, as well as to give us highly powerful computing machines.
So all of our electrical machinery, from toothbrushes to supercomputers, is based on the electron and the rules of electron behavior.
The internet exists, and you can read this, because of electrons.
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That we can see anything we owe to photons, another basic particle.
Photons are light, of course, but also radio waves and microwaves. They’re also x-rays and gamma rays. (We can apparently thank high energy photons for the Hulk.)
Photons, streaming through fiber optics, also enable the internet as we know it. Electrons just can’t keep up.
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DNA is the blueprint for living beings, and it uses an “alphabet” that consists of just four “letters” — C, G, A, T.
Every person ever born, every person who will ever be, is due to a design implemented in just four objects.
(But then, all conventional computing is done with just two objects, a one and a zero, and a few simple logical rules.)
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This tendency towards complexity from rules is so built in to reality there’s no real name for it that I know of. It’s not itself a rule or principle.
If one were so inclined, one might see the hand of some god or teleology at work. It does seem almost miraculous given the ruthless nature of entropy that such complex order can grow from simple beginnings.
Regardless, if there is something to be thankful for, we can certainly be thankful for whatever it is. We couldn’t be here without it.
Here’s hoping you and yours have a wonderful and safe Thanksgiving!
Stay in the pattern, my friends!
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