Dear Friends,
Be Well.
David
In the beginning was the code
A transcript of Jürgen Schmidhuber’s TEDx talk in
Belgium
March 15, 2013 by Jürgen Schmidhuber
A supercomputer simulation of the evolution of the
universe (credit: Andrey Kravtsov/University of Chicago)
There is a fastest, optimal, most efficient way of
computing all logically possible universes, including ours — if ours is
computable (no evidence against this). Any God-like “Great Programmer” with any
self-respect should use this optimal method to create and master all logically
possible universes.
At any given time, most of the universes computed so
far that contain yourself will be due to one of the shortest and fastest
programs computing you. This insight allows for making non-trivial predictions
about the future. We also obtain formal, mathematical answers to age-old
questions of philosophy and theology.
I will talk about the simplest explanation of the
universe. The universe is following strange rules. Einstein’s relativity.
Planck’s quantum physics. But the universe may be even stranger than you think.
And even simpler than you think
.
Is the universe being created by a computer program?
Konrad Zuse
Many scientists are now taking seriously the
possibility that the entire universe is being computed by a computer program,
as first suggested in 1967 by the legendary Konrad Zuse, who also built the world’s first working general
computer between 1935 and 1941. [1]
Zuse’s 1969 book Calculating Space discusses how a particular computer, a cellular
automaton, might compute all elementary particle interactions, and thus the
entire universe.
The idea is that every electron behaves the same,
because all electrons re-use the same subprogram over and over again.
First consider the virtual universe of a video game
with a realistic 3D simulation. In your computer, the game is encoded as a program,
a sequence of ones and zeroes. Looking at the program, you don’t see what it
does. You have to run it to experience it.
Reality has still higher resolution than video games.
But soon you won’t see a difference any more, since every decade, simulations
are becoming 100–1000 times better, because computing power per Swiss Franc
is growing by a factor of 100–1000 per decade.
A few decades imply a factor of a billion. Soon, we’ll
be able to simulate very convincing heavens and hells. It will seem quite
plausible that the real world itself also is just a simulation.
To a man with a hammer, everything looks like a nail.
To a man with a computer, everything looks like a computation.
Skeptics might say: What about quantum physics, and
Heisenberg’s uncertainty principle, and Bell’s inequality? Don’t they imply that the universe cannot be
produced by a deterministic program? Not at all. Bell himself knew well that
deterministic universes including deterministically computable observers are
fully compatible with all available physical observations.
The universe as the sum of all mathematics
“Calculating space,” a painting by Konrad Zuse
When my brother Christof was a teenager in the early
1980s in Munich, he told me and others: the universe, or quantum multiverse, is
the sum of all mathematics. I believe he is the reason why such ideas emerged
in Munich.
He was younger than me. He still is. He also was
smarter than me. He went on to become a physicist at Munich, Caltech,
Princeton, and CERN, and he lived in Berne next door to where Einstein lived.
It took me a while to understand what my brother
meant. In 1996, I formalized his idea through a computation. I generalized Everett’s many worlds theory, pointing out that
there is a very short and fast program that not only computes our own universe,
or multiverse, but also all other logically possible universes, even those with
different physical laws. For example, universes with anti-gravity.
In fact, there is a fastest,
optimal, most efficient
way of computing all logically possible universes, including ours — if ours is computable (no evidence against this).
(Credit: TEDx)
The optimal method can be programmed with only ten
lines of code. I wrote it down for you — here it is! [Holds up a piece of
paper.] [2]
Any God-like “Great Programmer” with some self-respect should use this optimal
method to create and master all logically possible universes.
Suppose he runs it for a while. At some point, many of
the executed programs will have computed universes that containyou! You,
as you are sitting here and staring at me with incredulous eyes.
You could even become a “Great Programmer” yourself,
using the optimal method [holds note up again] to simulate all possible universes in
nested fashion.
(But this would not necessarily help to figure out the future faster than by
waiting for it to happen. The computer on which to run this program would have
to be built within our universe, and as a small part of the latter would be
unable to run as fast as the universe itself.)
Anyway, now it’s easy to see that due to the nature of
the optimal method, at any given time, most of the universes
computed so far that do contain yourself will be due to one of
the shortest and fastest programs computing: YOU.
Predictions
This insight allows for making non-trivial predictions
about the future. There are many possible futures of your past so far. Which
one is going to happen? Answer: given the probability distribution induced by the optimal method, most likely one
of the few regular, non-random futures with a fast and short program.[3] (Because the weird futures where suddenly the rules
change and everything dissolves into randomness are fundamentally harder to
compute, even by the optimal method. Random stuff by definition does not have a
short program.)
This implies that the decay of neutrons, widely believed
to be random, most likely is not random, but pseudo-random, like the decimal
expansion of PI, which looks random, but isn’t, because it is computable by a
short and fast program.
Why quantum computing may never scale
The optimal method also implies that quantum
computation will never work well, essentially because it is consuming so many
basic computational resources. I first made this prediction a dozen years ago.
Since then there has not been any progress in practical quantum computation,
despite lots of efforts. (The biggest number factored into its prime factors by
any existing quantum computer is still 15.) Quantum computation is sexy, but
dead.
What about free will? Free will is overrated. In my
group at the Swiss AI Lab IDSIA, we often program simulated worlds including simulated observers with simulated artificial
brains. Through
pseudo-random trial and error they even learn from experience to become smarter over time, acting as if they
had free will. They have no idea that every thought in their artificial neural networks is computed by a deterministic program. (In a
way, they do have free will — it’s just deterministically computed free will.)
Computational theology
Nevertheless, computer science is now giving us
formal, mathematical answers to old questions of philosophy and theology. One
of the results of my Computational Theology is this: your own
life must be very important in the grand scheme of things.
You may think that your life is insignificant, because
you are so small, and the universe is so big. But given the Great Programmer’s
optimal way of computing all universes, it is probably very hard to edit your life
(or mine) out of our particular universe: Any program that produces a universe
like ours, but without you, is probably much longer and slower (and
thus less likely) than the original program that includes you.
So with high probability, your life essentially has to
be this way, with all of its ups and downs. Your life is notinsignificant.
It seems to be an indispensable part of the grand scheme of
things.[4]
This is compatible with religions claiming that “all
is one,” “everything is connected to everything.” May this thought lift you up
in times of frustration.
Footnotes:
(Credit: iStockphoto)
1. A recent KurzweilAI
news article mentioned
somewhat related ideas by Max Tegmark (1997/1998). How does Schmidhuber’s
approach differ?
“My paper on all computable universes called ‘A computer
scientist’s view of life, the universe, and everything’ got submitted/published
in 1996/1997,” Schmidhuber told KurzweilAI.
“Back then, Max also was based in Munich (at LMU). He
put forth this somewhat vague and not really formally well-defined notion of a
mathematics-based ensemble of universes.
“He assumed a uniform prior distribution on this
ensemble, which unfortunately cannot even exist, as there is no uniform
distribution on countably infinite things. Over the years, Max and I had quite
a few little chats about this :-) . I think a mathematical analysis of this
type really must focus on the formally well-defined, limit-computable
mathematical structures/universes.
“Max also completely ignores computation time, while
the talk above is all about computation time, which makes a big difference
between easy-to-compute and hard-to-compute universes, and greatly affects
their probabilities, and thus the most likely futures of observers inhabiting
them. I also addressed such differences in an additional 2000 paper on all formally describable universes (and also
in the 2012 survey paper for H. Zenil’s book, A
Computable Universe).
“I also wrote that I suspect my brother Christof
Schmidhuber is the real reason why such ideas emerged in Munich. At the
age of 17 he declared that the universe is the sum of all math, inhabited by
observers who are mathematical substructures (private communication, Munich,
1981).
“As he went on to become a theoretical physicist at
LMU Munich, Caltech, Princeton, and CERN, discussions with him about the
relation between superstrings and bitstrings became a source of inspiration for
writing both the first paper and later ones based on computational
complexity theory, which seems to provide the natural setting for his more
math-oriented ideas (private communication, Munich 1981-86; Caltech 1987-93;
Princeton 1994-96; Berne/Geneva 1997–; compare his notion of “mathscape”).”
2. The preprint of a recent overview
paper by
Schmidhuber includes pseudocode (a simplified generic version) for the ten
lines of code mentioned in the talk (see also slides):
FAST Algorithm
for i := 1, 2, . . . do
for i := 1, 2, . . . do
Run each program p with l(p) ≤ i for at most 2i−l(p) steps and reset storage modified by p
end for
[here l(p) denotes the length of program p, a
bitstring]
Schmidhuber explains: “This is essentially a variant
of Leonid Levin’s universal search (1973), but without the search aspect. The
code systematically lists and runs all possible programs in interleaving
fashion. It can be shown that it computes each particular universe as quickly
as this universe’s (typically unknown) fastest program, save for a constant
factor that does not depend on the universe size.
From this asymptotically optimal method, we can derive
an a priori probability distribution on possible universes
called the Speed Prior. It reflects the fastest way of
describing objects, not necessarily the shortest. (BTW, note that
any general search in program space for the solution to a sufficiently complex
problem will create many inhabited universes as byproducts.)”
3. Assume you are running computations for all
universes in parallel, says Schmidhuber. Some contain you at a given time. So
among those universes computed so far that contain you, which are the most
likely ones, that is, what’s your most likely future? In a Bayesian framework,
“Speed Prior” permits non-trivial answers to questions of this
type.
4. “Because most likely the universe to which you owe
your current existence has a high a priori probability,”
explains Schmidhuber. “Other possible variants of your life are less likely because
they are harder to compute, even by the optimal method.”
The insights mentioned in this talk were first
published between 1996 and 2000, and further popularized in the new millennium.
Detailed mathematical papers as well as popular high-level summaries can be
downloaded from Schmidhuber’s overview site on all computable
universes.
For information on a Master’s Degree in Artificial
Intelligence through courses taught by Schmidhuber and colleagues, visit this
site: Master’s Degree in Informatics with
a Major in Intelligent Systems
For new jobs for postdocs and PhD students in
Schmidhuber’s research group, visit this site: http://www.idsia.ch/~juergen/eu2013.html
Dr. Juergen
Schmidhuber is Director of the Swiss Artificial Intelligence Lab, Professor of
Artificial Intelligence at the University of Lugano, Switzerland, and Professor
at The University of Applied Sciences and Arts of Southern Switzerland
No comments:
Post a Comment