The Matrix does not have you

Every now and then I run into an article about how some scientist or other intends to prove there’s a possibility our universe is a simulation. This bugs the crap out of me, for two reasons: 1) Science reporting is pretty terrible across the board and journalists are drawn to anything that has to do with a popular movie, and 2) the idea itself is surpassingly stupid.

This isn’t up there with the theory that our universe could be a hologram. That sounds dumb on its face but I think all it’s really saying is there might be a way to represent our universe in 2D so that a hologram of it would be the 3D universe we know. Essentially I think they’re just talking about an interesting change of perspective. So that I get.

But in a simulation? No.

First off, the scientists approaching this theory are just selling the Matrix analogy as a way of seeking grant money. What they’re actually attempting to do is determine if the universe is pixelated at a very, very small level. The idea is that the Planck length and Planck time, both extremely tiny units, are truly the smallest measurements there can ever be and the entire universe conforms to this grid instead of spacetime being smooth and continuous.

I actually think that idea’s stupid too, but for a different reason. I’ll get to that. But for the moment let’s say this research is legit. If they found out they were right, it doesn’t mean we’re in a simulation. That’s still completely impossible.

I’m a programmer, and this reduces the problem to perfect clarity: There is no way the computing power to simulate our entire universe down to the subatomic level could ever exist, anywhere.

Consider that it takes enormous power just to accurately simulate the atomic bonds between the atoms in one single molecule, or the particles in an atomic nucleus. The problem can be simplified, but it can’t be calculated with true accuracy without really going deep. All particles, everywhere, interact with each other through a number of different forces. It is quite difficult, for instance, just to map the gravitational forces of all the celestial objects in our solar system that we know about; there are many of them, and calculating their interaction on each other is an O(n2) problem—meaning with twice as many objects, the calculation takes roughly four times as long.

The problem can be broken down into smaller pieces, to an extent. The forces I mentioned governing particle interaction can all be summed up, so you can treat a distant galaxy as a single object as far as outside parts of the computation are concerned. As long as you account for the few particles traveling to and from that galaxy you can wall it off into its own “little” separate piece of the puzzle. But simulating the dynamics of every molecule even in a single drop of water is beyond not only any computer we have now, but any that will ever exist.

Well, let’s simplify. Say you have more time. Say you can take 500 years to calculate a single nanosecond of our universe. That doesn’t help as much as you’d think. The memory needed to run the calculation is still literally astronomical. That data has to be stored somewhere, and the storage mechanism is by definition going to be bigger than the system it’s calculating, unless you use some kind of compression scheme. Compression, by the way, would not only add more time to the calculation but would require some sort of partial unzipping to be of any use.

But applying the lessons of game programming, let’s say the programmer cheats, and just saves the complex physics stuff for the big picture. Well, we can observe what’s going on at the molecular level, which means the engine has to know when we’re looking at that level of detail and handle that too. But we can set very tiny electrical and molecular forces into motion and they behave just as we expect: Our computers work that way. So for the engine to cheat here, it has to be compiling every program our computers handle into its own machine code so it can run faster, or else it will quickly be overloaded. Even so we’re still giving it more work. And even in spite of this, we would still notice a discrepancy between the macro and micro level.

It just isn’t possible. Xkcd once explored the possibility of a man on an infinite beach with infinite time on his hands, simulating a universe with stones. The infinite part is what it would take: a universe with far, far more matter than our own, dedicated to the task of simulating ours, running without the long-term threat of heat death. Their laws of physics would probably have to differ from our own by quite a lot. But the laws of math are inviolate; math does not budge.

By the way, the reason I don’t think the whole pixel universe thing works either is because of another issue programmers (and any scientists worth the name) are very familiar with: rounding error. A simple number like pi or the square root of 2 goes on forever without a pattern. Even basic fractions have rounding error if you try to represent them with a limited number of digits at your disposal. At that level, infinitesimal forces that would add up over vast distances and time scales would never have any effect at all, because at some point you’re trying to nudge a photon by 0.3 pixels when it can only move in multiples of 1. Two cycles later, the photon’s position is more wrong than right. Trillions of cycles later, your telescope is looking into the wrong alien’s apartment. Rounding error has an insidious way of creeping up on you over long calculations, and these errors influence each other to produce even bigger errors the more they interact. This would be obvious; therefore that’s not happening either, and these scientists are wasting their time.

Bottom line: Reporters didn’t go into journalism because they tended to score straight A’s in science, and some scientists live to prove that you can get anything published as long as there’s a movie about the idea. So if anyone ever tells you they think it’s a real possibility we’re living in a simulation, that person doesn’t know jack about either science or computing—or the danger of trusting so-called journalists and experts not to tell them a tall tale.

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About Lummox JR

Aspiring to be a beloved supervillain
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