Ist das Universum ein Computer?
Germany, November 2006, Informatik Jahr
Deutschen Technikmuseum Berlin
From Konrad Zuse’s Invention of the Computer to his “Calculating Space” to Quantum Computing.
Lesson One: For someone with a hammer in his hand the world seems to be a nail. Joseph Weizenbaun.
Lesson Two: Knowing the input and the transition function of a Turing machine we know everything about it. Marvin Minsky.
Dr. Zuse’s futuristic drawing
- The first talk entitled ”What Can We Calculate With?” by Prof. Dr. Bernd Mahr from the Technische Universitat of Berlin was a very good introduction to the standard theory of computation based on Turing’s model and classical mathematical logic. His remarks on the time when computing arose from math because the Greeks discovered they were unable to compute the square root of 2 were interesting. He pointed out some evident but not always explicit facts: Calculation has a subject (the individual who calculates), an object (what is calculated), a medium (how it is calculated), and a symbolic representation (the language -binary, for instance). His use of the Leibniz medallion for explaining starting points, ending points and transitions in a calculation was elementary but interesting (transitions: intermediate calculations). Further explanations of reversibility and non-linearity using transition nets were also illuminating. The context of a calculation (or computation) and the strong relation between the computation itself and its context is such that it is sometimes difficult to distinguish them. Since any process can be seen as an object in itself, the context can become the calculation and the context of the context too. In some way, as we know, the concept of calculation is a constraint of a part of a calculation, and then it is defined in terms of an input, an ouput and a transition. He pointed out too that behind many of these complicated systems there is a Turing machine. It is no longer visible from the top, but it is there.
Dr. Konrad Zuse
- Dr. Horst Zuse’s talk titled “Konrad Zuse’s Calculating Space (Der Rechnende Raum)”:
Dr. Konrad Zuse’s son, Dr. Horst Zuse made some interesting remarks about his father’s book “Calcualting Space”, in which Dr. Zuse proposes studying the universe as a digital system, specifically a cellular automaton. Dr. Horst Zuse is a professor at the Technische Universitat of Berlin and his personal webpage can be found at: www.cs-tu-berlin.de/~zuse and www.zuse.info
Dr. Konrad Zuse’s son, Dr. Horst Zuse
Dr. Zuse’s father’s main question was: “Is Nature Digital, Analog or Hybrid?” It seems that he tended to answer “Digital,” proposing a No-Yes value language (binary). His thoughts were published in the Nova Acta Leopoldina. He evidently did acknowledge that there could be problems attempting to reconcile an explanation of the Universe in terms of Cellular Automata with Quantum Mechanics and General Relativity.
According to Konrad Zuse, laws of physics could be explained in terms of laws of switches (in the computational sense). Physical laws are computing approximations captured by the formulas in our models. He saw that differential equations could be solved by digital (hence discrete) systems.
Dr. Carl Adam Petri at the Berlin conference
- Dr. Carl Adam Petri (yes, the creator of the Petri nets!) on “Rechnender Netzraum” or “Computing Net Universe”:
According to Dr. Petri, at the Planck length quantum computing can be described by digital systems using combinatorial models (net models, kennings, combinat), and therefore the universe can be studied using discrete nets which are even capable of explaining quantum and relativistic fundamentals like Bell’s theorem and Heisenberg’s uncertainty principle. That would mean that discrete systems (for instance those proposed by Stephen Wolfram) would suffice to explain even quantum and relativistic phenomena.
According to Petri, measurement is equivalent to counting. For instance in S.I. one second is 9192631770 Cs periods. In fact Norbert Wiener proposed some axiomatics of measurement.
The correspondence of Petri nets with the Heisenberg uncertainty principle arises from the limitations of our observational capacities when carrying out measurements. When two different types of observations are performed, -for example momentum p and position q- we can only see p or q in a chain of succesive events related by a causality net. His nets as well as his explanations of such phenomena are very neat and elegant. The relevant slides on causality and linear logic may be found at:
He also distributed a CD with his slide presentation at the conference.
For Petri, the Universe is a Petri Net.
Dr. Seth Lloyd’s presentation at the conference in Berlin, Germany
- Dr. Seth Lloyd’s talk entitled “The Universe is a Quantum Computer”:
Some researchers think of information as more fundamental than physics itself. And it is a common practice in science to find all the time more fundamental structures on which previous ones were lying on. Some others such as Seth Lloyd and David Deutsch, however, strongly stand in favor of putting a quantum reality at the lowest level of reality description as they stand for a physical universe where information only makes sense if it is carried and represented by a physical entity. So these authors have developed world theories based in the concept of quantum computation.
A quantum computer differs from a Turing machine in that its bits are quantum bits, and so can exist in a superposition. In addition, it can be instructed to put those bits in superpositions. A universal Turing machine can simulate any other Turing machine in polynomial time but while what a quantum computer does is still Turing computable, a typical quantum computation of T steps on N qubits requires $O(2^N)$ bits on a classical Turing machine, and $O(T 2^2N)$ logical operations. That is, it takes a Turing machine exponential amounts of time and space to simulate a quantum computer or quantum Turing machine.
The standard quantum computer as shaped by, among others, Feynman and Deutsch differs from the classical computer in the concept of the qubit. While the concept of qubit takes advantage of a clear asset that the quantum world provides, entanglement, it does not necessarily makes use of the full properties of quantum mechanics as interpreted under the Copenhagen interpretation. The convenient definition of a qubit makes a quantum computer not to compute more but much faster than classical digital computers.
Lloyd’s conclusion is that the universe is not only a computer but a quantum computer. However some questions arise:
1. What exactly is a quantum computer? Does the quantum computer definition actually captures all quantum phenomena? According to the standard model quantum computing is Turing computable (disregarding run time). If Lloyd is assuming the standard model then the universe is indeed a quantum computer, but even more remarkably (since we have scientific and philosophical hypotheses like the Turing thesis) it is Turing computable. However, if he is assuming the more general quantum mechanics model, let’s say the standard model in physics (which basically assumes the possibility of harmless continuity rather than inquiring into it) he is saying that the universe is not a computer (since the term derives from what we mean by Turing computable and hence covers digital computers too). So the assumptions made are significant and cannot be glossed over if one wishes to argue convincingly that the universe is a computer in some standard sense. If what we assume to be computing is something that seems to be deterministic or rule-based, the concept becomes fuzzy and additional remarks need to be made.
2. What if a quantum particle encodes more information than just a 1 or 0 for the spin or any other quantum property? Let’s say a third value, or even worse, a non-computable number of values. In quantum mechanics for example, the superposition of a particle assumes an infinite and non-countable number of places since it is in all the spectra at the same time. If space/time is a continuum then it is evidently in a non -countable number of positions, which leaves us with a non-computable model, or at least with something that’s neither a Turing-computable model nor a standard quantum-computable model. And this is not a simple assumption since it requires another Turing-type thesis which in the final analysis does not answer the most fundamental question, i.e. whether the universe is a computer or not and if it is, what kind of computer (in the computational power sense) it is.
I raised these questions with Seth Lloyd and I will be posting his answers soon.
Seth Lloyd at the conference in Berlin
An interesting concept mentioned by Seth Lloyd is “hacking the universe”. As Charles Bennett used to say, a computer is a handicapped quantum computer. So if Lloyd is right, a computer is not only a handicapped quantum computer but it is not taking advantage of the full computational power of the universe and it is just patching the universe instead of hacking it, as it would be in its power to do. By contrast, a quantum computer uses some particles that are already computing “something” (nothing less and nothing more than the processes in the universe ) to perform the computation that we want it to perform. It can be said to be ”hacking the universe” in Lloyd’s terms.
On the other hand, if the notion of programmer monkeys is valid it should be possible to test it experimentally. Under the supervision of M. Jean-Paul Delahaye, computer science professor at the University of Lille I (http://www2.lifl.fr/~delahaye/) we are undertaking this task. We are exploring Lloyd’s quantum computational universe (or at least a handicapped but representative part, the recursive computational universe), applying some complexity measures (universal distribution, average-case complexity or Levin’s measure) in order to uncover the monkeys behind the Universe, or in other terms, to analyze the average distribution of randomly discrete systems with random inputs.
Is Seth Lloyd falling into the carpenter’s problem of thinking that the universe is a nail and the moon made of wood? Is it because he is a quantum computer scientist that he thinks the universe is a quantum computer? He argues of course that the charge is unfair, but then we have been told by Dr Petri that the Universe is in fact a Petri Net which probably needs neither strong randomness nor quantum mechanics!
Here is a video online in which he explains much of this:
Dr. Zuse’s futuristic drawing 2
- Jurgen Schmidhuber reprised his algorithmic approach to the theory of everything in his talk entitled “The program that computes all computable universes”.
Jurgen Schmidhuber’s major contribution probably is his Speed Prior concept, a complexity measure similar to Algorithmic Information Complexity, except that it is based on computation speed and not program length. i.e. the fastest way of describing objects rather than the shortest.
There is more information on his website: http://www.idsia.ch/~juergen/ (where he includes an unfavorable review of NKS) and in his slide presentation on the Speed Prior at: http://www.idsia.ch/~juergen/speedprior/sld001.htm
Of course Schmidhuber himself has identified a problem with the Prior measure: If every possible future exists, how can we predict anything?
Other interesting talks on philosophical issues: If the Universe is a computer, therefore the human mind should be a computer too.
Is “the Universe is a computer” a metaphor?
My answer: The metaphor is “The Universe is not a Computer”
Lesson Three: Metaphors can be reversed.
Kovas Boguta’s talk was titled ”Is the Computer a Universe?” In it he pointed out the richness of mining the computational universe of simple programs.
Because we were together during the gala dinner I had an interesting exchange with Dr. Konrad Zuse’s son, Dr. Horst Zuse (Also at our table were the Technikmuseum director Dr. Dirk Bondel and my colleague Kovas Boguta from Wolfram Research, among others). He shed some light on his father’s interactions with Alan Turing ( none apparently), with von Neumann (some interaction regarding the controversy over who first built a digital computer and concerning von Neumann’s architecture, which our current digital computers do not conform to, the ALU being separated from the memory as it is in Zuse’s conception but not in von Neumann’s original design).
Zuse’s Z1 first computer “the input device, something equivalent to the keyboard, at the Technikmuseum in Berlin”