Friday, July 08, 2016

Relax, we're not living in a computer simulation

Since Elon Musk's recent admission that he's a simulationist, several people have asked me what I think of the proposition that we are living inside a simulation.

My view is very firmly that the Universe we are right now experiencing is real. Here are my reasons.

Firstly, Occam's razor; the principle of explanatory parsimony. The problem with the simulation argument is that it is a fantastically complicated explanation for the universe we experience. It's about as implausible as the idea that some omnipotent being created the universe. No. The simplest and most elegant explanation is that the universe we see and touch, both first hand and through our telescopes, LIGOs and Large Hadron Colliders, is the real universe and not an artifact of some massive computer simulation.

Second, is the problem of the Reality Gap. Anyone who uses simulation as a tool to develop robots is well aware that robots which appear to work perfectly well in a simulated virtual world often don't work very well at all when the same design is tested in the real robot. This problem is especially acute when we are artificially evolving those robots. The reason for these problems is that the model of the real world and the robot(s) in it inside our simulation is an approximation. The Reality Gap refers to the less-than-perfect fidelity of the simulation; a better (higher fidelity) simulator would reduce the reality gap.

Anyone who has actually coded a simulator is painfully aware of the cost, not just computational but coding costs, of improving the fidelity of the simulation - even a little bit - is very high indeed. My long experience of both coding and using computer simulations teaches me that there is a law of diminishing returns, i.e. that the cost of each additional 1% of simulator fidelity costs far more than 1%. I rather suspect that the computational and coding cost of a simulator with 100% fidelity is infinite. Rather as in HiFi audio, the amount of money you would need to spend to perfectly reproduce the sound of a Stradivarius ends up higher than the cost of hiring a real Strad and a world-class violinist to play it for you.

At this point the simulationists might argue that the simulation we are living in doesn't need to be perfect, just good enough. Good enough to do what exactly? To fool us that we're living in a simulation, or good enough to run on a finite computer (i.e. one that has finite computational power and runs at a finite speed). The problem with this argument is that every time we look deeper into the universe we see more: more galaxies, more sub-atomic particles, etc. In short we see more detail. The Voyager 1 spacecraft has left the Solar System without crashing, like Truman, into the edge of the simulation. There are no glitches like deja vu in The Matrix.

My third argument is about the computational effort, and therefore energy cost of simulation. I conjecture that to non-trivially simulate a complex system x (i.e. human), requires more energy than the real x consumes. An equation to express this inequality looks like this; how much greater depends on how high the fidelity of the simulation.

Let me explain. The average human burns around 2000 Calories a day, or about 9000 KJoules of energy. How much energy would a computer simulation of a human require, capable of doing all the same stuff (even in a virtual world) that you can in your day? Well that's impossible to estimate because we can't simulate complete human brains (let alone the rest of a human). But here's one illustration. Lee Sedol played AlphaGo a few months ago. In a single 2 hour match he burned about 170 Calories - the amount of energy you'd get from an egg sandwich. In the same 2 hours the AlphaGo machine consumed around 50,000 times more energy.

What can we simulate? The most complex organism that we have been able to simulate so far is the Nematode worm c-elegans. I previously estimated that the energy cost of simulating the nervous system of a c-elegans is (optimistically) about 9 J/hour, which is about 2000 times greater than the real nematode (0.004 J/hr).

I think there are lots of good reasons that simulating complex systems on a computer costs more energy than the same system consumes in the real world, so I'll ask you to take my word for it (I'll write about it another time). And what's more the relationship between energy cost and mass is logarithmic, following Kleiber's Law, and I strongly suspect the same law applies to scaling up computational effort as I wrote here. Thus, if the complexity of an organism o is C, then following Kleiber's Law the energy cost of simulating that organism, e will be

Furthermore, the exponent X (which in Kleiber's law is reckoned to be between 0.66 and 0.75 for animals and 1 for plants), will itself be a function of the fidelity of the simulation, hence X(F), where F is a measure of fidelity.

By using the number of synapses as a proxy for complexity and making some guesses about the values of X and F we could probably estimate the energy cost of simulating all humans on the planet (much harder would be estimating the energy cost of simulating every living thing on the planet). It would be a very big number indeed, but that's not really the point I'm making here.

The fundamental issue is this: if my conjecture that to simulate complex system x requires more energy than the real x consumes is correct, then to simulate the base level universe would require more energy than that universe contains - which is clearly impossible. Thus we - even in principle - could not simulate the whole of our own observable universe to a level of fidelity sufficient for our conscious experience. And, for the same reason, neither could our super advanced descendents create a simulation of a duplicate ancestor universe for us to (virtually) live in. Hence we are not living in such a simulation.


  1. The idea of living in a simulated world is just a silly thought that has earned way to much validity because of "pop stars" like Musk. One interesting aspect though is the idea of Fidelity being an illusion. Everything we can reach out and touch, even something as solid as a rock, is a collection of non-touchable sort-of-there elements of electrical charges. SO, in a way, the fidelity that you say is to costly to simulated might well exist on a distributed level. That is, my cat might as well be a lump of matter simulating fur and breathing and begging for food, while my hand is the blank end of a stick simulating what a hand is like.

  2. While I have my own reason for opposing Musk's simulation argument I'm not at all convinced by your reasoning Alan! Breifly:

    1. Using Occam's razor is unconvincing. It is a tool to help one find the most elegant possibilities, not a reason to believe (or disbelieve) any particular possibility.
    2. The reality gap would (or at least could) be invisible to those within the simulation. I don't see how it is an argument against being part of a simulation.
    3 & 4. Here you (and you hypothetical opponents) seem to assume that the universe within which the simulation exists has essentially the same limitations and properties, and indeed physical laws, as the simulation which is preposterous. I'm very familiar with technical development (including coding simulations) and am a physicist so I understand your lines of reasoning here - I just think it is very hard to reason about something we know nothing about (what contains our -possibly- simulated universe and how such a simulation might come about) from inside a simulation which is likely to differ immensely from it ways that we can't even conceive.

    My own counter-reasoning is no more conclusive than Musk's but did fit into a tweet ;-) and is as follows (as far as I can recall it): a simulation is a human concept, and it seems implausible that something so limited and temporary could capture the essence of a universe we are far from comprehending.

    Not conclusive, but I think trying to reason about something beyond our own universe is akin to ants trying to reason about the nature of planet earth. They lack the cognitive functions, and I think we find it hard to accept that we are also limited in that respect, which limits what we can imagine and the ways in which we can relate to our circumstances. I think Douglas Adams' Deep Thought hinted strongly at the problems in this area (with the answer is 42, but now you need to go and discover "the question"). As humans, we are predisposed to see the universe as a problem to understand and explain. Perhaps that is one of the biggest limitations in how we relate to it. So by wondering if this is a simulation or not, we're already limiting ourselves. Perhaps it is legitimate to realise that there is no context to be understood.

    The human mind is a meaning making machine - because that property has enabled us to evolve. That doesn't mean that we have to look for meaning everywhere, or that looking for meaning and explanation is worthwhile in any other context than survival and evolution.

    So when we try to open up to the universe as a whole, asking what it is just might not be "the question". Perhaps there is no question.

    1. Agree. From inside the simulation you can't actually know anything about the hardware or physical laws under which it operates. This becomes an essentially unanswerable question, at which point, I apply Occam.

  3. It's a matter of perspective. If you are inside, clothed in the Holy Spirit of Jesus Christ, you can ask for and receive anything, a state from which all things can be experienced as simulation as one grows spiritually able to change reality, yet following Jesus' example most things are left alone since complete chaos is irrational. Unclothed, naked from the Spirit, one experiences hard cold reality that is unbending relative to the individual's level in the simulation. So secular theories tend to be descriptions of the darkness atheists personally experience.

    1. Did you have anything useful to add?

  4. The simulation hypothesis is very much reminiscent of the discourse around extraterrestrial life, discussions on what is intelligence within cognitive science, as well as social sciences and history (although the historians and anthropologists are better than the rest of us at avoiding this pitfall).

    Intellectuals see our current paradigms as constant when we have trouble even understanding how educated thinkers thought 500 years ago. In fact academia has trouble fathoming just how alien the thought processes of people who have not have had access to modern education are. This is one of the times when a bit of Karl Popper would have helped.

  5. For every question there is an answer, doh.