The Simulation Hypothesis

The Simulation Hypothesis February 24, 2011

by Eric Steinhart

Atheists can use the traditional arguments for God in strange new ways.  There’s no reason to reject those arguments – on the contrary, I think they should be carefully studied, and their flaws should be repaired.  But I don’t think they lead to God.  I love the Cosmological Arguments.  And the ones I love most are Aquinas’s Third Way and Leibniz’s Sufficient Reason argument.   I also love the universe-level versions of the Design Argument.  These include arguments that aim to explain the fine-tuning of fundamental physical constants as well as arguments that aim to explain the regularity or complexity of our universe.  All those are fascinating arguments.   But not for God.

It’s far more natural to think that these arguments justify the Simulation Hypothesis.  The Simulation Hypothesis says that our universe is a software process running on some deeper computational substrate.  The physicist Ed Fredkin refers to this substrate as “the Engine”.  Using his term, our universe is to the Engine as software is to hardware.  Our universe is analogous to a video game running on the Engine.   The old Cosmological and Design arguments are very nice arguments for the Engine.

The great advantage of the Simulation Hypothesis is that it isn’t mysterious.  Computer science involves precise mathematical definitions of computing machines (e.g. finite state machines, Turing machines, transfinite machines).  Software engineering is a rational discipline.  We know how to construct computer simulations of physical universes (including our universe).  We know how to develop video games.   There is a large and fascinating literature on computational world-design.

Many people have written about the Simulation Hypothesis, including David Chalmers and Nick Bostrom.  Bostrom maintains a website on the hypothesis.  Many of these writers suggest that simulation means that we are being simulated by some superior society.  The idea is that there is some Alien Society.  The engineers in that Alien Society built computers.  They programmed them to run an artificial universe.  This version of the Simulation Hypothesis is familiar from old movies like The Matrix and The Thirteenth Floor.  Dawkins mentions it: “Science fiction authors . . . have even suggested (and I cannot think how to disprove it) that we live in a computer simulation, set up by some vastly superior civilization.” (The God Delusion, p. 98)  And Harris mentions it too: “If intelligently designed, our universe could be running as a simulation on an alien supercomputer.” (Letter to a Christian Nation, p. 73)

But the Alien Society interpretation isn’t the only way to understand the Simulation Hypothesis.  The Engine need not be an artifact.  It might be entirely natural – a product of some sort of evolution.  After all, human beings are very powerful computing machines.  And we are natural products of natural evolution.  Alternatively, if you’re a Platonist, or Neoplatonist, you might want to think of the Engine as a purely mathematical machine.  It would be a machine existing eternally in the non-physical system of Platonic Forms.   On this interpretation, some Platonic objects emanate universes.  They are the relatively abstract grounds of physicality.  They exist eternally and necessarily.

On any interpretation, the Simulation Hypothesis involves the idea that the Engine is running some world-actualizing algorithm.  Perhaps it is just doing a brute-force iteration through some set of possible universes.  Perhaps it is using some optimization algorithm to maximize some feature of universes – it is conducting a rational search for maximally regular universes, or universes that contain the most internal computation.  Perhaps it is using some genetic algorithm to evolve universes – it might be evolving universes for maximum logical depth or for some other type of internal complexity.

Obviously, the Engine has some degree of computational power – it has the power to run some universe of some complexity.  Its power can be measured using standard technical scales (e.g. the cardinality of its state set; the cardinality of its halting conditions – does it halt after finitely many states, or can it run out to transfinite limit cardinals).

Any Engine running something as complex and valuable as our universe has to have some degree of benevolence.  This benevolence need not be anything like human morality.   It is far more likely that it is simply an abstract orientation towards the maximization of certain computational values like logical depth or intensity of information processing.  The Engine would have its own axiological imperatives, and these would all be defined in computational terms.  Perhaps these would be game-theoretic – think of the evolution of cooperation in the prisoner’s dilemma.  Life on earth might have very high computational value because living things encode programs for their own construction.  And evolution shows that they are recursively self-improving.  Now, recursion is computationally deep.  Perhaps the Engine aims to maximize recursive depth or recursive intensity of some type.

What about humans?  Are we valuable because we have consciousness?  Maybe.  But there might be even stranger features of human being that make us computationally valuable.  Our immune systems are capable of running genetic algorithms – they run their own simulations of Darwinian evolution to design antibodies.  This means that, in our immune systems, an evolutionary algorithm is stacked on top of an evolutionary algorithm.  Perhaps this sort of stacking is a primary computational value: more valuable systems support higher stacks of virtual machines, simulations running inside simulations.

Perhaps the Engine is intelligent.  Here again, its intelligence has a precise computational analysis.  And the intelligence of the Engine need not be anything like human intelligence.  It might not have a mind.  It wouldn’t have to be conscious or have emotions or desires or beliefs or understanding.  It need not be psychological in any recognizable sense.  It might be a vast statistical machine (like Google Translate).

So the Engine has some degrees of power, benevolence, and intelligence.  Heaven forbid, it looks like God!  Well, no, it doesn’t.  Its power and benevolence and intelligence are all defined in purely naturalistic ways.  And those qualities are not maximal in the way they are for God.  On the contrary, those qualities are defined in precisely technical ways exactly up to specific cardinal numbers.  There is nothing at all mysterious about the Engine.  It is an entirely lawful entity defined using mathematics and computer science.

But where did the Engine come from?  You know the drill: if the Engine created our universe, then what created the Engine?  Here’s a nice quote from Dawkins:

Science fiction authors . . . have even suggested (and I cannot think how to disprove it) that we live in a computer simulation, set up by some vastly superior civilization.  But the simulators themselves would have to come from somewhere.  The laws of probability forbid all notions of their spontaneously appearing without simpler antecedents.  They probably owe their existence to a (perhaps unfamiliar) version of Darwinian evolution: some sort of cumulatively ratcheting ‘crane’.  (The God Delusion, pp. 98-99)

Dawkins is using the Alien Society interpretation of the Simulation Hypothesis.  And that’s fine.  But on the naturalistic interpretation, the Engine is itself a product of a deeper type of evolution.   The Engine is the product of an evolutionary algorithm.  It is the product of some kind of recursively self-improving algorithm.  Perhaps that algorithm is just the deepest algorithm there is.  It is necessary and eternal.  Just as the fact that 1+1=2 does not require an explanation, so the deepest evolutionary algorithm does not require any explanation.  It’s part of the harmony of things.  Here’s a lovely quote from Leibniz:

For it is necessary to refer everything to some reason, and we cannot stop until we have arrived at a first cause – or it must be admitted that something can exist without a sufficient reason for its existence, and this admission destroys the demonstration of the existence of God.  Yet what is the ultimate reason for the divine will?  The divine intellect.  For God wills the things which he understands to be best and most harmonious and selects them, as it were, from an infinite number of possibilities.  Yet what provides the reason for the divine intellect?  The harmony of things.  What the reason for the harmony of things?  Nothing.  For example, no reason can be given for the ratio of 2 to 4 being the same as that of 4 to 8, not even in the divine will.  (Leibniz, in Rescher’s edition of The Monadology, p. 148)

Did Leibniz just admit to being atheist?  Well, that’s a topic for another day.  The point here is that mathematical necessity itself might be the ultimate sufficient reason for the existence of each and every actual physical universe.  Some purely mathematical things, namely, abstract computers, actualize selected possible universes.  The naturalistic interpretation of the Simulation Hypothesis is ultimately mathematical.   It therefore shades off into the Platonic interpretation – they aren’t really different.

On the Platonic interpretation of the Simulation Hypothesis, the Engine is like a number.  It exists in a sequence of engines just like the sequence of numbers.  There is an initial engine.  This is the zero-engine.  For every engine, there is a greater engine.  The sequence of engines is a recursively self-improving sequence just as the sequence of numbers is a recursively self-increasing sequence.  The rules for the existence of engines are just like the rules for the existence of numbers or like the axioms of pure set theory.  Engines, like numbers or sets, are eternal and necessary mathematical objects.

However you decide to work it out, the Simulation Hypothesis is an interesting non-theistic alternative to theism.  It has positive metaphysical and ethical content.  It may even provide an entirely naturalistic theory of life after death.

Guest Contributor Eric Steinhart is an associate professor of philosophy at William Paterson University and the author ofMore Precisely: The Math You Need To Do Philosophy, On Nietzsche (Wadsworth Philosophers Series), and The Logic of Metaphor – Analogous Parts of Possible Worlds (Synthese Library, Volume 299). Professor Steinhart has explained many of his views on metaphysics, philosophy of religion, and Richard Dawkins in an audio interview with The Pale Blue Dot. Abstracts to his papers on the philosophy of mathematics, philosophy of religion, metaphysics, the metaphysics of persons, Nietzsche, and analogy and metaphor can all be found here (in some cases with links to the papers themselves).
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