The Fabric of Reality David Deutch

particular, any genuine universal computer must itself be physically
realizable. This leads to a stronger version of the Turing principle:
The Turing principle
(for physical computers simulating each other)
It is possible to build a universal computer: a machine that can
be programmed to perform any computation that any other
physical object can perform.
It follows that if a universal image generator were controlled by a universal
computer, the resulting machine would be a universal virtual-reality
generator. In other words, the following principle also holds:
The Turing principle
(for virtual-reality generators rendering each other)
It is possible to build a virtual-reality generator whose repertoire
includes that of every other physically possible virtual-reality
generator.
Now, any environment can be rendered by a virtual-reality generator of 
some
sort (for instance, one could always regard a copy of that very environment
as a virtual-reality generator with perhaps a very small repertoire). So it also
follows from this version of the Turing principle that any physically possible
environment can be rendered by the universal virtual-reality generator.
Hence to express the very strong self-similarity that exists in the structure of
reality embracing not only computations but all physical processes, the
Turing principle can be stated in this all-embracing form:
The Turing principle
It is possible to build a virtual-reality generator whose repertoire includes
every physically possible environment.
This is the strongest form of the Turing principle. It not only tells us that
various parts of reality can resemble one another. It tells us that a single
physical object, buildable once and for all (apart from maintenance and a
supply of additional memory when needed), can perform with unlimited
accuracy the task of describing or mimicking any other part of the multiverse.
The set of all behaviours and responses of that one object exactly mirrors
the set of all behaviours and responses of all other physically possible
objects and processes.
This is just the sort of self-similarity that is necessary if, according to the
hope I expressed in Chapter 1, the fabric of reality is to be truly unified and
comprehensible. If the laws of physics as they apply to any physical object or
process are to be comprehensible, they must be capable of being embodied
in another physical object — the knower. It is also necessary that processes
capable of creating such knowledge be physically possible. Such processes
are called science. Science depends on experimental testing, which means
physically rendering a law’s predictions and comparing it with (a rendering
of) reality. It also depends on explanation, and that requires the abstract

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laws themselves, not merely their predictive content, to be capable of being
rendered in virtual reality. This is a tall order, but reality does meet it. That is
to say, the laws of physics meet it. The laws of physics, by conforming to the
Turing principle, make it physically possible for those same laws to become
known to physical objects. Thus, the laws of physics may be said to mandate
their own comprehensibility.
Since building a universal virtual-reality generator is physically possible, it
must actually 
be built in some universes. A caveat is necessary here. As I
explained in Chapter 3, we can normally define physically possible process
as one that actually occurs somewhere in the multiverse. But strictly
speaking, a universal virtual-reality generator is a limiting case that requires
arbitrarily large resources to operate. So what we really mean by saying that
it is ‘physically possible’ is that virtual-reality generators with repertoires
arbitrarily close to the set of all physically possible environments exist in the
multiverse. Similarly, since the laws of physics are capable of being
rendered, they 
are rendered somewhere. Thus it follows from the Turing
principle (in the strong form for which I have argued) that the laws of physics
do not merely mandate their own comprehensibility in some abstract sense
— comprehensibility by abstract scientists, as it were. They imply the
physical existence, somewhere in the multiverse, of entities that understand
them arbitrarily well. I shall discuss this implication further in later chapters.
Now I return to the question I posed in the previous chapter, namely
whether, if we had only a virtual-reality rendering based on the wrong laws of
physics to learn from, we should expect to learn the wrong laws. The first
thing to stress is that we 
do have only virtual reality based on the wrong laws
to learn from! As I have said, all our external experiences are of virtual
reality, generated by our own brains. And since our concepts and theories
(whether inborn or learned) are never perfect, all our renderings are indeed
inaccurate. That is to say, they give us the experience of an environment
that is significantly different from the environment that we are really in.
Mirages and other optical illusions are examples of this. Another is that we
experience the Earth to be at rest beneath our feet, despite its rapid and
complex motion in reality. Another is that we experience a single universe,
and a single instance of our own conscious selves at a time, while in reality
there are many. But these inaccurate and misleading experiences provide
no argument against scientific reasoning. On the contrary, such deficiencies
are its very starting-point.
We are embarked upon solving problems about physical reality. If it turns out
that all this time we have merely been studying the programming of a cosmic
planetarium, then that would merely mean that we have been studying a
smaller portion of reality than we thought. So what? Such things have
happened many times in the history of science, as our horizons have
expanded beyond the Earth to include the solar system, our Galaxy, other
galaxies, clusters of galaxies and so on, and, of course, parallel universes.
Another such broadening may happen tomorrow; indeed, it may happen
according to any one of an infinity of possible theories — or it may never
happen. Logically, we must concede to solipsism and related doctrines that
the reality we are learning about 
might be an unrepresentative portion of a
larger, inaccessible or incomprehensible structure. But the general refutation
that I have given of such doctrines shows us that it is irrational to build upon

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that possibility. Following Occam, we shall entertain such theories when, and
only when, they provide better explanations than simpler rival theories.
However, there is a question we can still ask. Suppose that someone were
imprisoned in a small, unrepresentative portion of our own reality — for
instance, inside a universal virtual-reality generator that was programmed
with the wrong laws of physics. What could such prisoners learn about our
external reality? At first sight, it seems impossible that they could discover
anything at all about it. It may deem that the most they could discover would
be the laws of operation, i.e. the program, of the computer that operated
their prison.
But that is not so! Again, we must bear in mind that if the prisoners are
scientists, they will be seeking explanations as well as predictions. In other
words, they will not be content with merely knowing the program that
operates their prison: they will want to explain the origin and attributes of the
various entities, including themselves, that they observe in the reality they
inhabit. But in most virtual-reality environments no such explanation exists,
for the rendered objects do not originate there but have been designed in the
external reality. Suppose that you are playing a virtual-reality video game.
For the sake of simplicity, suppose that the game is essentially chess (a first-
person-perspective version perhaps, in which you adopt the persona of the
king). You will use the normal methods of science to discover this
environment’s ‘laws of physics’ and their emergent consequences. You will
learn that checkmate and stalemate are ‘physically’ possible events (i.e.
possible under your best understanding of how the environment works), but
that a position with nine white pawns is not ‘physically’ possible. Once you
had understood the laws sufficiently well, you would notice that the
chessboard is too simple an object to have, for instance, thoughts, and
consequently that your own thought-processes can not be governed by the
laws of chess alone. Similarly, you could tell that during any number of
games of chess the pieces can never evolve into self-reproducing
configurations. And if life cannot evolve on the chessboard, far less can
intelligence evolve. Therefore you would also infer that your own thought-
processes could not have originated in the universe in which you found
yourself. So even if you had lived within the rendered environment all your
life, and did not have your own memories of the outside world to account for
as well, your knowledge would not be confined to that environment. You
would know that, even though the universe seemed to have a certain layout
and obey certain laws, there must be a wider universe outside it, obeying
different laws of physics. And you could even guess some of the ways in
which these wider laws would have to differ from the chessboard laws.
Arthur C. Clarke once remarked that ‘any sufficiently advanced technology is
indistinguishable from magic’. This is true, but slightly misleading. It is stated
from the point of view of a pre-scientific thinker, which is the wrong way
round. The fact is that to anyone who understands what virtual reality is,
even genuine magic would be indistinguishable from technology, for there is
no room for magic in a comprehensible reality. Anything that seems
incomprehensible is regarded by science merely as evidence that there is
something we have not yet understood, be it a conjuring trick, advanced
technology or a new law of physics.

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Reasoning from the premise of one’s own existence is called ‘anthropic’
reasoning. Although it has some applicability in cosmology, it usually has to
be supplemented by substantive assumptions about the nature of ‘oneself’
before it yields definite conclusions. But anthropic reasoning is not the only
way in which the inmates of our hypothetical virtual-reality prison could gain
knowledge of an outside world. 
Any of their evolving explanations of their
narrow world could, at the drop of a hat, reach into an outside reality. For
instance, the very rules of chess contain what a thoughtful player may
realize is ‘fossil evidence’ of those rules having had an evolutionary history:
there are ‘exceptional’ moves such as castling and capturing 
en passant
which increase the complexity of the rules but improve the game. In
explaining that complexity, one justifiably concludes that the rules of chess
were not always as they are now.
In the Popperian scheme of things, explanations always lead to new
problems which in turn require further explanations. If the prisoners fail, after
a while, to improve upon their existing explanations, they may of course give
up, perhaps falsely concluding that there are no explanations available. But
if they do not give up they will be thinking about those aspects of their
environment that seem inadequately explained. Thus if the high-technology
jailers wanted to be confident that their rendered environment would forever
fool their prisoners into thinking that there is no outside world, they would
have their work cut out for them. The longer they wanted the illusion to last,
the more ingenious the program would have to be. It is not enough that the
inmates be prevented from observing the outside. The rendered
environment would also have to be such that no explanations of anything
inside would ever require one to postulate an outside. The environment, in
other words, would have to be self-contained as regards explanations. But I
doubt that any part of reality, short of the whole thing, has that property.
TERMINOLOGY
Universal virtual-reality generator One whose repertoire contains every
physically possible environment.
Cantgotu environments Logically possible environments which cannot be
rendered by any physically possible virtual-reality generator.
diagonal argument A form of proof in which one imagines listing a set of
entities, and then uses the list to construct a related entity that cannot be on
the list.
Turing machine One of the first abstract models of computation.
universal Turing machine A Turing machine with the combined repertoire of
all other Turing machines.
Turing principle (in its strongest form) It is physically possible to build a
universal virtual-reality generator.
On the assumptions I have been making, this implies that there is no upper
bound on the universality of virtual-reality generators that will actually be built
somewhere in the multiverse.

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SUMMARY
The diagonal argument shows that the overwhelming majority of logically
possible environments cannot be rendered in virtual reality. I have called
them Cantgotu environments. There is nevertheless a comprehensive self-
similarity in physical reality that is expressed in the Turing principle: 
it is
possible to build a virtual-reality generator whose repertoire includes every
physically possible environment. So a single, buildable physical object can
mimic all the behaviours and responses of any other physically possible
object or process. This is what makes reality comprehensible.
It also makes possible the evolution of living organisms. However, before I
discuss the theory of evolution, the fourth strand of explanation of the fabric
of reality, I must make a brief excursion into epistemology.

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