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  • - What will happen tomorrow is not random. In other words, it's at least somewhat predictable.

  • I mean, not entirely to be sure, but some things will happen for certain, and other

  • things definitely won't. For example, the sun will rise, water will still freeze at

  • zero degrees celsius,

  • - and you won't become Michael Stevens.

  • - We know this because everything in the universe is made of 12 fundamental particles, and they

  • interact in four predictable ways.

  • - What if I were able to determine the positions and velocities of every single one of these

  • particles in the universe?

  • - Well, you would be the intelligence envisioned by Laplace, who thought if you could really

  • figure out where everything is and how fast it's moving, you would know the entire future

  • of the universe, because you know how every particle interacts with every other particle.

  • - Wow, so nothing would be unpredictable, which means, nothing would be random.

  • - Not even human behavior. Since we are made of the same fundamental particles as everything

  • in the rest of the universe, everything we will ever do, or have ever done, would be

  • determined by the information in the state of the universe at any one time.

  • - But what is information? Well, it seems to be fundamentally about order. The order

  • of molecules in your DNA contain the information needed to make you. It is the order of zeros

  • and ones streaming through the internet that contain all the information required to play

  • this video. It is the order of letters that makes a word, and the order of words that

  • makes a sentence that carries information. So fundamentally, information seems to be

  • about order. Regularity. That is, until you really think about it. I mean, does every

  • letter of a word carry the same amount of information? No. I mean, after a "Q", you

  • know almost for certain that the next letter will be a "U". After a "Th", there will probably

  • be an "E". So these letters carry very little information, because you could predict them

  • beforehand. They are redundant. In fact, the founder of information theory, Claude Shannon,

  • estimated the redundancy of English at about 75%, which is why we can make sense of things

  • like this. So English can be compressed, because it is not random. It has patterns. Similarly,

  • this video is compressible because of its regularities. In each frame, the pixels of

  • similar color cluster together. Plus, from frame to frame, most of the pixels don't change.

  • So you only need to record the ones that do change.

  • - You can take advantage of this technique to create some trippy effects known as datamoshing.

  • It's the application of the movement data from one video, to the pixels of another.

  • - It also means that an average video can be compressed to just one thousandth of its

  • original size.

  • - But what is the most you can compress something?

  • - Well, anything that is not random, any patters or regularities, can be reduced, because they

  • are predictable. So you can continue shrinking a file down until what you're left with is

  • totally random.

  • - And that will contain all of the information of the original item but distilled. Pure information.

  • - So pure information is randomness. If you want to know how much information something

  • contains, you need to know how random it is. And randomness is disorder... What we also

  • call ...

  • - [Both] Entropy.

  • - So information, fundamentally, is entropy. This makes sense if you consider a string

  • of binary digits. For example, this string is perfectly ordered. It has very low entropy,

  • and it contains no information. That's the state of an erased hard drive. Now, this string

  • contains slightly more information, but again, the regularities allow it to be easily compressed.

  • So the string that contains the maximum amount of information is just-- a random set of zeros

  • and ones. It has maximum entropy because it's totally disordered. You could not predict

  • any of those digits by looking at any of the other digits. And if you wanted to send this

  • information to someone, you would have no other option but to send the whole string

  • of digits. There's no way to compress it. But here's the thing about any object that

  • contains maximum information. For us as human beings, they carry no meaning. For example,

  • a video containing maximum information would look like this. It is just white noise. The

  • color of each pixel is independent of all the other pixels, and they all change randomly.

  • This video could not be compressed, because it's already totally random. Now a random

  • sequence of DNA would not make an organism. And a random string of letters does not generally

  • make a word. We are drawn to things that are neither perfectly ordered, containing no information,

  • nor are they perfectly disordered, containing maximum information. Somewhere in the middle,

  • we can recognize complex patterns, and that is where we derive meaning. In music, poetry,

  • and ideas. It is this search for meaning that leads us to propose scientific theories, which

  • if you think about it, are really our way of compressing the universe. For example,

  • general relativity, our current theory of gravity, compresses into one short equation.

  • Everything from how an apple falls to the earth, to how the moon orbits the earth, how

  • all the planets orbit the sun, how the sun orbits a supermassive blackhole at the center

  • of our galaxy, how blackholes form and behave, and how the whole universe expands out from

  • the Big Bang. Now that we have this theory, the future is more predictable. I mean, we

  • can predict eclipses thousands of years into the future. So, with all of our scientific

  • theories, does that mean that the universe is completely not random? That it is perfectly

  • predictable? Well, let's assume for a second that Laplace was right, and that knowing the

  • state of the universe at any one time, means you also know its state at every other time

  • as well. Well, that would mean that the information in our universe would be constant. But if

  • information is entropy, that would mean the entropy of the universe is also constant.

  • And that does not appear to be the universe that we live in. The second law of thermodynamics

  • states that entropy in the universe increases with time. Or in other words, things don't

  • stir themselves apart. But if entropy is going up, that means the information in our universe

  • is constantly increasing. That makes sense, because it would take more information to

  • specify the state of the universe now, than right after the Big Bang. So, where is this

  • new information coming from? My best bet is quantum mechanics. Quantum mechanics describes

  • how the 12 fundamental particles behave. And as spectacularly successful as it is, it is

  • only a probabilistic theory. Meaning that you cannot predict with absolute certainty

  • where an electron, say, will be at some later time. You can only calculate probabilities

  • of where you are likely to find it. So when you do interact with it, and locate the electron

  • at a particular point, you have gained information. You now know something that you couldn't have

  • predicted with certainty beforehand. This drove Einstein crazy. He said, "God does not

  • play dice," referring to this. I mean, he wished that we could compress our theory of

  • quantum mechanics further, so that we could really figure out where these particles were

  • going to be. But maybe the reason why we haven't been able to compress quantum mechanics further,

  • is because fundamentally, it's random. Fundamentally, new information is being generated every time

  • a quantum event like that occurs. In that case, it could be these quantum measurements

  • which are driving up the entropy of the universe. They are creating new information all of the

  • time, and that means the disorder in our universe must go up. This is what we observe as the

  • second law of thermodynamics. You know, we often think about the second law as a curse.

  • As though everything which is ordered is going towards disorder. But maybe, I mean, it's

  • only in a universe where this law is obeyed, that the truly unexpected can occur. That

  • the future can be actually undetermined. For us really to have free will, we need the second

  • law of thermodynamics. Now, you might think that these quantum events are too small to

  • have any meaningful impact on the evolution of the universe, but that is not true. And

  • that's because, there are physical systems which are so dependent, so sensitive to the

  • initial conditions that any tiny change will end up making a big difference later down

  • the track. That's called "chaos." But it's also known as "the butterfly effect." So you

  • and I could be such physical systems. Chaotic systems. And our free will could come from

  • quantum events in our brains. So it looks as though we live in a universe where the

  • future is yet to be determined. That is to say, it is at least somewhat random.

  • - But Derek, what is the most random thing possible in the universe?

  • - That's a good question, Michael.

  • - You know, it's such a good question, I'm talking about it over on Vsauce. Do you wanna

  • go find out about randomness with me?

  • - Let's go check it out.

  • - Alright.

  • - And you can decide whether to click over or not.

  • - Oh, that's nice.

  • - Yeah!

  • - Yeah.

- What will happen tomorrow is not random. In other words, it's at least somewhat predictable.

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ランダムではないものは何ですか? (What is NOT Random?)

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    BH に公開 2021 年 01 月 14 日
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