The world is full of simulators (part 3)

There is nothing quite like a simulator which works. I’ve seen them in action in electrical and mechanical systems – after lumbering through several hours of calculations, a simulator will tell you where exactly a bridge will buckle, or how much current exactly would flow through a transistor, and lo! it would be true. Simulators of bridges and transistors don’t simulate every atom and electron in their subject of simulation, but that’s the wonder of engineering: you don’t need to make a simulator so exact – the results are very nearly the same even if you use a vastly simplified model of the object being simulated.

That is the crux of one of my favorite science fiction stories, Greg Egan’s ‘Dust’. Egan rewrote this short story as a novella called Permutation City (which I haven’t read). In the world of Dust (which is set in Sydney about 50 years in the future), engineers are able to build a model that simulates the brain. The computer simulator in Dust doesn’t simulate every single neuron, but it is able to simulate a brain in enough detail to be able to model thought processes and communication. In tandem with the simulator, scientists also find a way to ‘initialize’ the model with a real brain (from a living, sleeping human) through a series of scans. The output of the simulator is ‘speech’, so the brain being simulated is able to communicate with the user of the simulator, and you could have a ‘conversation’ with the simulated brain. However, the simulator runs 17 times slower than the real brain, so you’d have to speed up or slow down a video recording to communicate with it.

The protagonist of the story is trying to explore his own consciousness by building a model of his own brain, simulating it under various conditions, and seeing if it ‘thinks’ the same thoughts. In a fascinating sequence of experiments, he runs the simulation in a random sequence of time-slices (so that the system simulates t=5s first, then t=1s, then t=3s, and so on), and then on a ‘cloud’ of servers distributed all over the world. And knowing that this ‘brain’ is nothing more random bits flipping in random machines in a random sequence all over the world – and yet able to tease ‘consciousness’, in the form of the ‘brain’ being self-aware – he has the epiphany that human consciousness is nothing more than dust.

My final thought about simulators is something that began with Feynman many decades back. Feynman was interested in the physics of computation, and towards the end of his life, he began working on what he called ‘exact simulators’. A simulator is, by its nature, approximate – either because it has finite precision, or because it reduces the number of parameters in a system to a much lower number than are really there. Feynman was interested, however, in quantum simulators, where one quantum system would exactly replicate the quantum behavior of another quantum system. He spoke about it at a landmark keynote address he gave at a conference on physics and computation just a few months before I was born. Here is the paper, which is generally readable, except for a few bits for which you need some background in quantum physics: http://www.cs.berkeley.edu/~christos/classics/Feynman.pdf

Feynman, in his paper, drew the outlines of how it was indeed possible to simulate one quantum system with another. As he described the technique in detail, someone from the audience asked him a question: “Doesn’t this reduce to the ordinary boundary value, as opposed to initial-value type of calculation?” And Feynman’s profound answer:  “Yes, but remember this is the computer itself that I’m describing.”

In other words, his technique gives us a computer that is capable of simulating itself…! Such are the bizarre properties of a quantum computer.

One of Feynman’s fellow scientists went about calculating a few more bounds on quantum computer simulators, and he discovered a very peculiar thing: that in order to simulate a quantum system of a certain volume, you need a quantum computer of a lower volume. And to simulate the quantum states of the entire universe, — and this is the nice bit –, all you need is a computer the size of a biggish star.

This is one of the great unsolved mysteries of the universe, up there with dark matter: dark complexity. The universe can be exactly simulated with a computer that is 10^69 times smaller than the universe itself.

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4 thoughts on “The world is full of simulators (part 3)

  1. Hi Q – very nice blog. This is Dinesh, a classmate of Neville/Cue from IIT-M. Not sure if you remember me. Anyway, wanted to recommend another of Egan’s short story called Luminous – the action parts are unconvincing but the story has a really cool way of looking at mathematical statements and when/why they are true.

    1. Thanks, Dinesh! glad to get back in touch with you. Thanks for the EgaN recommendation… Will definitely check out the story. As an aside, you can’t have been both Nevilles and Cues classmate 🙂 unless perhaps in some physics or humanities course. So which one?

  2. […] got my first tangible reward for my conscientious blogging yesterday: Dinesh had commented on my Simulators post, recommending a Greg Egan book called Luminous, and I bought it. An introduction to a new book: […]

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