Big Picture
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Big Picture

Sorry, You’re Not In The Matrix

I’m a computer engineer. I was top of my class in Physics. I took a course in quantum computation. And I winced when I heard Neil deGrasse Tyson supporting the harebrained idea that we might all be in a simulation.

Why am I convinced this is nonsense? Because no one has proposed a sensible way that this idea could be compatible with our actual observations about the universe.

Imagine you’re the intelligent designer building a ‘universe simulator’, and you have to choose how your simulation will work. Now, we could certainly imagine that an advanced civilization may be able to make computational elements and memory cells extraordinarily cheaply — far, far beyond our present technology. But no matter how cheap those things may be, their cost will never actually be exactly zero. Even with self-replicating robots that grow exponentially into an immense army whose sole purpose is to build the computer, the cost is not zero because time still counts as a cost, and because the computer will always have a finite size. Once turned on, the time it takes to perform the simulation is also a cost.

And that’s a big problem. Because the evidence is that our universe is either infinite in size, or very nearly infinite. So the memory requirement is already impossible. But the memory requirement is completely dwarfed by the computational requirement. Inside a computer simulation, “energy” is essentially free — it’s just a number in a memory cell, after all. So there’s no need for a law of conservation of energy. But memory and computation are not free. Despite this, our universe not only has virtually infinite size, but the computational requirements seem to be much larger still. Even some of the coldest places in the universe might require similar amounts of computation as the hottest places.

A basic fact about a simulator is that it is necessarily larger and slower than that which is simulated. If you doubt that, consider this question: how can we simulate an atom using a computer that is the same size as an atom?

A first-person video game might look realistic, but the computer actually does very little computation. It doesn’t simulate the inner workings of a person: a simulated physical model of a person is no more complex than a single (classical) molecule in term of its physical behavior. Typically, things like air, walls, mountains and often water are merely drawn, not physically simulated. And simulated time may be quantized to steps as large as 17 milliseconds.

We can only deal with the limitations of our computers by making a simulated universe that is extremely simple compared to the real world, and certainly no more complex than necessary. So the first-person game only does just enough computation to almost fool you into thinking it’s real, for a little while, if you don’t think too much or look too closely. Wouldn’t a designer in the outer universe do the same thing?

To give you a sense of the challenge, here is a glass of water:

It contains seven trillion trillions of water molecules (7 septillion), more or less. All of them in constant motion. Some water molecules at the surface are escaping to the air, while other (fewer, depending on air humidity) water molecules are moving from the air to the water. Although we can’t observe the individual molecules, we know how many there are because our scientists have carefully studied the behavior of water and many other substances (and interactions between them) over hundreds of years. Our conclusions — about water, about the sizes of molecules, how they behave, and how quickly — have been used to create all kinds of modern technologies that wouldn’t work if our conclusions had been wrong.

Whether it’s grains of sand lying on the beach, the water in the ocean, individual atoms in the sun, or radio waves interacting weakly with the solar wind near Pluto, everything is in motion, all the time. Solids vibrate, even if they don’t flow, a phenomenon whose average is called temperature. All of our scientific observations are consistent with this basic fact. Computation is required to decide how anything in motion, interacting with other things, will behave.

Some people bizarrely think that quantum effects are evidence of a lossy “compression algorithm” that makes the simulation more tractable. The reality is that quantum effects make everything more complex and harder to simulate, not easier. There is no evidence of lossy compression artifacts.

Even if our universe were classical (non-quantum), it is hard to overstate how simple and inadequate our own computer simulations are compared to what we would need to accurately simulate, say, the inner workings of a tiny speck of dust. Our supercomputers cannot simulate an entire bacterium at the atomic level, not even classically; the most we’ve managed is a chromatophore. Our technology is perhaps far from theoretically optimal, but not that far, and it requires a processor at least trillions of times larger than the space being simulated. That’s without dealing with any quantum or relativistic effects.

“Chromatophore”: a word I’ve never heard

Not only that, but a simulation of a Chromatophore is extraordinarily slow compared to the real thing. What good is it to simulate a universe, if the simulation is dramatically slower than the real thing?

Presumably the outer universe could have more a favorable ratio between the size of the computer and the amount of matter in the simulated space, but there’s an obvious limit to how small a computer can get. Clearly, a simulator cannot do more computation than the universe in which it is embedded, and yet everything I’ve studied tells me that everything in our universe is doing unimaginably and unnecessarily complex computations constantly, everywhere.

So if there’s an “architect” out there who created our universe in a computer, there are two possibilities. Either the physical laws and facts inferred by scientists really do describe how our universe works, or the “architect” is trying hard to deceive scientists into thinking our universe does far more computations than it actually does.

Scientists have inferred a universe whose complexity at the smallest scales is dramatically, even unfathomably, greater than what is actually needed for micro-organisms (let alone humans) to exist, and whose size at the largest scales is not only beyond our ability to imagine, but indistinguishable from infinite.

It seems, therefore, that we can rule out the first possibility. Surely the size of “the matrix” is not infinite or “almost” infinite, especially since that would imply it took an “almost” infinite length of time to build it. And don’t expect the simulation to run in real time: it would have to achieve up to 1.85x10⁴³ frames per second, at least around places like black holes where precision becomes important. Keeping a computer running for over 13.8 billion years multiplied by a slowdown factor — now that’s patience.

The remaining possibility is that the “architect” is intentionally deceiving us.

But if one of the goals is to deceive scientists into thinking we are not in a simulation, why work so hard at it? If “the architect” were doing enough simplifications to make the simulation tractable (such as running a classical simulation with an “ether”, no relativity, compression zones of reduced computation, limiting precision, and limiting calculations beyond Earth’s surface) why bother to fool us into believing we’re in a dramatically more complex universe than we are actually in? Why fill the sky with stars from which we can witness evidence of other planets and redshifting and the cosmic microwave background, allowing us to infer that the universe is 13.8 billion years old and has a variable rate of metric expansion? Why make atoms so small? Why simulate a microscopic world with five million trillion trillion self-replicating machines we can’t even see without a microscope? Why show scientists complex quantum effects (which, we extrapolate, happen everywhere, constantly) even though life on earth does not require them to function?

If you want to convince humans we’re not in a simulation, there’s an easier way than manipulating the results of science experiments. Just detect whenever humans have the idea “what if we’re in a simulation?” and delete it from their minds.

That tactic would be much easier to pull off.

But really, what would be the point of deceiving us in the first place?

To bypass this argument, some people propose that the outer universe has substantially different laws of physics from our own, laws which conveniently make immense simulations easier. I haven’t seen anyone propose actual laws that would make it easier to simulate our universe, but for the sake of argument, let’s suppose that such laws could exist. The implication of this seems to be that the simulators are not simulating their own past, or civilizations from their own universe, and indeed they might not even know what life might look like in a universe as different as ours. So what could the goal of the simulation be, in that case? If the goal is just to find out what happens under different laws of physics, wouldn’t that goal be immensely easier to achieve by simulating a vastly smaller universe than our own? Wouldn’t it be better to choose laws of physics that would require quadrillions of times less computation to produce interesting results?

There is one version of the hypothesis that makes sense to me: the one-brain hypothesis. In this scenario, you, the reader, are the only person that really exists, and everyone else is a fake, a simulation. (I could insist I’m not fake, but a fake person would say that, wouldn’t he?) But again, the easiest way to convince you you’re not in a simulation is for none of the fake people to bring up the idea in the first place. Remember, our ideas are almost invariably inspired by what we’ve seen or heard from others. It almost certainly never would have occurred to you that your world wasn’t real until somebody suggested it. So if no one suggests it? Mission accomplished.



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