Reversibility and machine
This essay is about the intersection of computational
reversibility and machine
It argues that reversibility is important for intelligent systems, and
that this association impacts on the probability of the hypothesis that we exist inside a computer simulation.
The benefits of reversibility
has well-known benefits relating to minimizing power consumption and
These are a consequence of the thermodynamic cost of erasing
bits - an idea known as Landauer's
However there are also some times when reversibility helps with actually
running a system in reverse - for example when providing 'undo' functionality or
when backtracking. The need for backtracking is common when performing
a tree search -
and tree searches are used ubiquitously in the forecasting component of machine
When performing a tree search it is common to want to go back and reconsider
a previous node.
For example, in a game of go if you play A, your opponent plays B, you play
C and your opponent plays D - and then your position evaluation tells you
that you are going to lose the game after this, you may want to back track
and reconsider your move at C. If no move at C seems any good you may want
to back track further to reconsider your move at A. This process involves
running your simulation of the game both forwards and backwards.
This example involves an adversary and a series of branching points
corresponding to agent actions, but the same situation applies to
practically any forecasting problem involving uncertainty. What
makes the tree of future possibilities branch is not necessarily a
choice between possible actions, but any form of uncertainty
which could potentially lead to multiple possible outcomes. This
makes the need for reversibility very widespread in forecasting
Another thing to mention is that forecasting systems are a central
and ubiquitous component of machine intelligence systems.
Forecasting the possible consequences of actions to allow an agent
to choose between the resulting outcomes is a the primary function
of animal brains. Machine intelligence works on the same principle.
For more on this topic, see my essay titled:
broad scope of inductive inference.
The simplest way to run a system backwards is to store a complete
history of previously-considered nodes in the tree. However, that is
often very inefficient. More often, you want to do something like store
a diff. That's where reversible logic comes in. Reversible logic lets
you efficiently run any computation in reverse. It uses
the system backwards.
universality allows a reversible computer to
simulate any irreversible computation. A classic text about
egnineering reversibile systems is the book
Automata Machines by Tommaso Toffoli and Norman Margolus.
Reversibility and simulism
It has been widely speculated that we may be
living inside a computer simulation.
The possibility has long been a staple of science fiction with early
Tunnel under the World (1955),
Time Out of Joint (1959) and
Thirteenth Floor (1999)
Lawnmower Man (1992)
Days (1995) and
The topic has become of interest to scientists and philosophers.
Frank Tipler's (1997) book,
Physics of Immortality: Modern Cosmology, God and the Resurrection of
the Dead speculated that modern humans might be resurrected n
future computer simulations. Hans Moravec's (1998) paper
Consciousness, Existence was another early contribution to the
topic. Nick Bostrom's 2003
You Living In a Computer Simulation? also went on to address the
The laws of physics appear to exhibit microscopic
reversibility. They are time symmetric
This observation was contested in the 20th century by quantum physics
pioneers who claimed that a hypothetical irreversible process known as
"wave function collapse" might play a significant role in physics. However,
there is no evidence that wavefunction collapse is a real phenomenon.
As it turns out, quantum physics does not depend on the idea in any
way. The best evidence we have is consistent with exact microscopic
Not all possible laws of physics exhibit reversibility. For example,
irreversible rules massively outnumber reversible ones in cellular
automata. Of the 256 Wolfram rules, only 6 are reversible. The
proportion of reversible rules goes down rapidly as the complexity of
the rule increases. In one of the next simplest one dimensional systems, 62 rules out of 4 billion are reversible.
One possible explanation of reversibility invokes observation selection effects.
Maybe mature living systems can only exist in universes with reversible physical
laws - since in irreversible universe the information in them is
and before intelligent life has time to evolve, it is all gone. However, this
possibility doesn't seem sufficient to explain the observations. Life
exist in irreversible universes - and it may also be able to persist
for billions of
years - provided that the degree of irreversibility is not so great
that the universe
rapidly leaks away all the information inside it. Exact physical
to be not fully explained by this idea.
One possible explanation for physical reversibility is that the
universe is the product of
helps to minimize power requirements and heat generation. The link
intelligence and reversibility described in this essay provides some
Reversibility could be important to function in other ways.
Reversibility allows the
implementation of a "rewind" function - allowing the simulation to be
examined at any point in time.
Also, reversibility is a likely property of world simulations that
exist inside advanced minds.
These are likely to be engineered using reversibility to allow for
Some critics have suggested that advanced machine intelligences would
not squander resources
on detailed ancestor simulations. However, we are quite interested in
our history and origins.
Understanding the past is key to predicting the future. Major
evolutionary transitions are
likely to be of particular interest to our descendants. In particular, in
the alien race,
it could be important to understand how the transition to an
engineered future turns out,
because that might be our best clue about the possible forms of aliens
we might meet. Understanding
the forms aliens could take could be key strategic information -
should we ever meet them.
Physical reversibility thus appears to be a piece of evidence that
favors simulism over other
possibilities. If our universe is the product of intelligent design
that makes sense of our
reversible laws of physics. Otherwise, we seem faced with a massive
coincidence - physical law is
reversible - although the odds of it being reversible would seem to be
Tim Tyler |