July 6, 2021

Against Bostromian Sophistry

Nick Bostrom's arguments for simulation and superintelligence ignore the fundamental limitations of computing.

Against Bostromian Sophistry

The title is deliberately provocative.

Nick Bostrom's arguments for the simulation hypothesis and for artificial superintelligence have become popular in technologist circles. They have become almost-mainstream enough such that New Yorker magazine has covered them as part of the reporting genre of 'look at what those strange nerds are into now' (heavily quoting Ol' Musky of course). Many people I speak to in these circles are in complete and automatic agreement.

Bostrom's arguments for superintelligence and for the notion that we are likely to be living in a simulation of reality follow roughly the same course, so addressing either one addresses both. I saw the New Yorker piece and associated commentary today so that's the one I'm going to address.

The simulation argument proceeds roughly as follows;

  1. Computers can be used to simulate reality.
  2. Increased computing power has led to an increase in the available fidelity of the simulation.
  3. As computing power continues to increase, we will arrive at an indistinguishable simulation of reality; and eventually one that can be executed cheaply.
  4. Future people will want to make many simulations of everyone especially when they're cheap to run - after all we run many simulations of all sorts of things today.
  5. Since there are many more simulations of everyone than there are 'real' versions, it's much more likely 'you' are simulated than 'real'.

The argument is structured inductively, but Bostrom and his supporters elide the validity of the inductive principle. Or, put another way, everything rests on an unstated If.  

That If lurks in step 3; If it is possible to arrive at an indistinguishable simulation of reality with increased computing power, then the rest of the argument follows. That If seems very natural if you just extrapolate trends a little bit.  

That If is is false for our universe.

As I have written elsewhere in simplified terms and as David Deutsch and others have written in scientific publication, classical computers cannot simulate most kinds of physical systems we observe in our physical universe to arbitrary precision*. Three famous examples of such systems are the n-body gravitational dynamics problem, the problem of fluidic turbulence, and the dynamics of the double pendulum.

Taken together, physics and mathematics do not together permit a perfect simulation of our physical reality, regardless of how much computing power one devotes to the problem - not just for exotic phenomena, but for something as everyday as the bubbles which form in boiling water, or the trajectory of a leaf shed by a tree as it floats to the ground, or the shape taken by a passing cloud. To speak nothing of something so complex as cognition or intelligence, whatever those are exactly.

You could turn every particle, every field excitation of the entire universe, into a logic gate operating at the thermodynamic limit of computation and still not get to arbitrary precision. The maw of infinity outruns you and your Turing Machine, and will continue to do so no matter how vast you get.

Taken in this light, Bostrom's arguments are considerably weaker than they look when one considers the fundamental mathematical-physical limits of computation. Indeed, most of Bostrom's work is downstream of this assumption - he explores the consequences of the hypothetical far more thoroughly than whether the hypothetical is a real possibility. His arguments have value as a philosophical exercise (in the same was as other philosophical thought experiments), but not as statements about material reality.

However, this doesn't completely resolve the question. Indeed this isn't a definitive statment against the simulation hypothesis, merely a weakening of a commonly accepted argument. Three common objections come to mind;

  1. A computer could be invented that is capable of hypercomputation, escaping the limits of the classical computer.
  2. Our simulation 'runs' on a form of 'computing' not available to our physical universe.
  3. You don't actually need perfect fidelity in your simulation to fool the mind sufficiently well.

On 1. the jury is still out, but this is the only really interesting possibility among these three objections. In my view, what is uncovered by the limits of classical computing** are in fact limits to our own mathematical logic and not a property of the physical universe itself*** - i.e. whatever the universe is doing when it 'runs' turbulence in fluids, it's not computing.

Our computers are realizations of our (Turing's) model of computation, which in turn is a complete synthesis of our entire foundational logic - if they can't do dynamics, that's an observation that doesn't conform to the theory, and the theory ought to be revised. There's Alien Mathematics out there. However, this does not argue for or against the simulation hypothesis - we know nothing about the real properties of such alternative systems of logic (by definition!) and can make no claims about how they relate to reality.

2. Is an essentially supernatural argument (which, to his credit, Bostrom himself does not resort to), and at that point why stick with computers? Why not speak of Demiurges and the revealed truth of higher reality? In Deutsch's terms, this is an easily varied explanation and therefore not very powerful.

3. is essentially the same argument as the famous Cartesian Demon, and reducible to sophistry. You are of course free to believe that computers are being used to fool your every sense and nothing in the world 'really' exists, but you'd need to present much more compelling evidence to convince me (or would you? you'd only be convincing yourself after all...). Besides, Boltzmann Brains are a much more physically grounded example of the same idea.

I am not against strange people believing strange things (in fact some of my best friends are strange believers), but those strange beliefs are most valuable when they are tested against reality as we know it; to turn them from ought to is.

Many commenters have argued against Bostrom on moral (our enlightented descendants wouldn't simulate us suffering), ideological (we should focus on problems of the real world as we percieve it instead of arguing unsolved questions), or even sociologiocal (it's probably not very interesting to simulate us a lot, people would rather play vidya) grounds. My intention is to argue from the root of Bostrom's arguments; the possibilities of known physical reality.  

There is nothing explicitly wrong with discussing the consequences of a simulated reality, nor about the hypothetical value system of something called 'superintelligence', but we should not be so quick as to take an interesting philosophical 'what if' for consequential statements about the real world.  

Ah, but what if we did?

* Outline of a formal argument;  The Turing machine whose output is the transition table for turing machines to compute the state of a dynamical system with nonzero Lyapunov time to error within ∂ will not halt as ∂ goes to zero. Other arguments can be made from finite representation, from continuity, etc.

** Quantum computing might do something different or it might not, it seems to be unclear, but QC has problems of its own in terms of its foundations.

*** There are however radicals out there who believe that if computers cannot describe parts of reality, we are mistaken about what constitutes reality. Have your friends or loved ones been radicalized by alt-math ultrafinitist videos on YouTube? Send me a DM on twitter for help.