and cosmology
, digital physics is a collection of theoretical perspectives based on the premise that the universe
is, at heart, describable by information
, and is therefore computable
. Therefore, the universe can be conceived as either the output of a computer program or as a vast, digital computation device (or, at least, mathematically isomorphic
to such a device).
Digital physics is grounded in one or more of the following hypotheses; the hypothesis are listed in order of increasing weight. The universe, or reality
, is:
- essentially informationInformationInformation in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
al (although not every informational ontologyOntology (computer science)In computer science and information science, an ontology formally represents knowledge as a set of concepts within a domain, and the relationships between those concepts. It can be used to reason about the entities within that domain and may be used to describe the domain.In theory, an ontology is...
needs to be digital); - essentially computableComputationComputation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc...
; - can be described digitalDigitalA digital system is a data technology that uses discrete values. By contrast, non-digital systems use a continuous range of values to represent information...
ly; - in essence digital
- itself a computer;
- the output of a simulated realitySimulated realitySimulated reality is the proposition that reality could be simulated—perhaps by computer simulation—to a degree indistinguishable from "true" reality. It could contain conscious minds which may or may not be fully aware that they are living inside a simulation....
exercise.
History
Every computermust be compatible with the principles of information theory
, statistical thermodynamics, and quantum mechanics
. A fundamental link among these fields was proposed by Edwin Jaynes in two seminal 1957 papers. Moreover, Jaynes elaborated an interpretation of probability theory
as generalized Aristotelian logic
, a view very convenient for linking fundamental physics with digital computers, because these are designed to implement the operations of classical logic
and, equivalently, of Boolean algebra.
The hypothesis that the universe
is a digital computer was pioneered by Konrad Zuse
in his book Rechnender Raum (translated into English as Calculating Space
). The term digital physics was first employed by Edward Fredkin
, who later came to prefer the term digital philosophy
. Others who have modeled the universe as a giant computer include Stephen Wolfram
, Juergen Schmidhuber, and Nobel laureate Gerard 't Hooft. These authors hold that the apparently probabilistic nature of quantum physics is not necessarily incompatible with the notion of computability. Quantum versions of digital physics have recently been proposed by Seth Lloyd
, David Deutsch
, and Paola Zizzi
.
Related ideas include Carl Friedrich von Weizsäcker
's binary theory of ur-alternatives, pancomputationalism, computational universe theory, John Archibald Wheeler
's "It from bit", and Max Tegmark
's ultimate ensemble
.
Overview
Digital physics suggests that there exists, at least in principle, a programfor a universal computer which computes the evolution of the universe
. The computer could be, for example, a huge cellular automaton
(Zuse 1967), or a universal Turing machine
, as suggested by Schmidhuber (1997), who pointed out that there exists a very short program that can compute all possible computable universes in an asymptotically optimal way.
Some try to identify single physical particles with simple bits. For example, if one particle
, such as an electron
, is switching from one quantum state to another, it may be the same as if a bit is changed from one value (0, say) to the other (1). A single bit suffices to describe a single quantum switch of a given particle. As the universe appears to be composed of elementary particles whose behavior can be completely described by the quantum switches they undergo, that implies that the universe as a whole can be described by bits. Every state is information
, and every change of state is a change in information (requiring the manipulation of one or more bits). Setting aside dark matter
and dark energy
, which are poorly understood at present, the known universe
consists of about 1080 proton
s and the same number of electron
s. Hence, the universe could be simulated
by a computer capable of storing and manipulating about 1090 bits. If such a simulation is indeed the case, then hypercomputation
would be impossible.
Loop quantum gravity
could lend support to digital physics, in that it assumes space-time is quantized. Paola Zizzi
has formulated a realization of this concept in what has come to be called "computational loop quantum gravity", or CLQG. Other theories that combine aspects of digital physics with loop quantum gravity are those of Marzuoli and Rasetti and Girelli and Livine.
Weizsäcker's ur-alternatives
Physicist Carl Friedrich von Weizsäcker's theory of ur-alternatives (archetypal objects), first publicized in his book The Unity of Nature (1980), further developed through the 1990s, is a kind of digital physics as it axiom
atically constructs quantum physics from the distinction between empirically observable, binary alternatives. Weizsäcker used his theory to derive the 3-dimensionality of space and to estimate the entropy
of a proton
falling into a black hole
.
Pancomputationalism or the computational universe theory
Pancomputationalism (also known as pan-computationalism, naturalist computationalism) is a view that the universe is a huge computational machine, or rather a network of computational processes which, following fundamental physical laws, computes (dynamically develops) its own next state from the current one.A computational universe is proposed by Jürgen Schmidhuber
in a paper based on Konrad Zuse's assumption (1967) that the history of the universe is computable. He pointed out that the simplest explanation of the universe would be a very simple Turing machine programmed to systematically execute all possible programs computing all possible histories for all types of computable physical laws. He also pointed out that there is an optimally efficient way of computing all computable universes based on Leonid Levin
's universal search algorithm (1973). In 2000 he expanded this work by combining Ray Solomonoff's theory of inductive inference with the assumption that quickly computable universes are more likely than others. This work on digital physics also led to limit-computable generalizations of algorithmic information or Kolmogorov complexity
and the concept of Super Omegas, which are limit-computable numbers that are even more random (in a certain sense) than Gregory Chaitin
's number of wisdom Omega
.
Wheeler's "it from bit"
Following Jaynes and Weizsäcker, the physicist John Archibald Wheelerwrote the following:
[...] it is not unreasonable to imagine that information sits at the core of physics, just as it sits at the core of a computer. (John Archibald WheelerJohn Archibald WheelerJohn Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...
1998: 340)
It from bit. Otherwise put, every 'it'—every particle, every field of force, even the space-time continuum itself—derives its function, its meaning, its very existence entirely—even if in some contexts indirectly—from the apparatus-elicited answers to yes-or-no questions, binary choices, bits. 'It from bit' symbolizes the idea that every item of the physical world has at bottom—a very deep bottom, in most instances—an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes–no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and that this is a participatory universe. (John Archibald WheelerJohn Archibald WheelerJohn Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...
1990: 5)
David Chalmers
of the Australian National University summarised Wheeler's views as follows:
Wheeler (1990) has suggested that information is fundamental to the physics of the universe. According to this 'it from bit' doctrine, the laws of physics can be cast in terms of information, postulating different states that give rise to different effects without actually saying what those states are. It is only their position in an information space that counts. If so, then information is a natural candidate to also play a role in a fundamental theory of consciousness. We are led to a conception of the world on which information is truly fundamental, and on which it has two basic aspects, corresponding to the physical and the phenomenal features of the world.
Chris Langan also builds upon Wheeler's views in his epistemological metatheory
:
The Future of Reality Theory According to John Wheeler:
In 1979, the celebrated physicist John Wheeler, having coined the phrase “black hole”, put it to good philosophical use in the title of an exploratory paper, Beyond the Black Hole, in which he describes the universe as a self-excited circuit. The paper includes an illustration in which one side of an uppercase U, ostensibly standing for Universe, is endowed with a large and rather intelligent-looking eye intently regarding the other side, which it ostensibly acquires through observation as sensory information. By dint of placement, the eye stands for the sensory or cognitive aspect of reality, perhaps even a human spectator within the universe, while the eye’s perceptual target represents the informational aspect of reality. By virtue of these complementary aspects, it seems that the universe can in some sense, but not necessarily that of common usage, be described as “conscious” and “introspective”…perhaps even “infocognitive”.
The first formal presentation of the idea that information might be the fundamental quantity at the core of physics seems to be due to Frederick W. Kantor (a physicist from Columbia University
). Kantor's book Information Mechanics (Wiley-Interscience
, 1977) developed this idea in detail, but without mathematical rigor.
The toughest nut to crack in Wheeler's research program of a digital dissolution of physical being in a unified physics, Wheeler himself says, is time. In a 1986 eulogy to the mathematician, Hermann Weyl
, he proclaimed: "Time, among all concepts in the world of physics, puts up the greatest resistance to being dethroned from ideal continuum to the world of the discrete, of information, of bits. ... Of all obstacles to a thoroughly penetrating account of existence, none looms up more dismayingly than 'time.' Explain time? Not without explaining existence. Explain existence? Not without explaining time. To uncover the deep and hidden connection between time and existence ... is a task for the future." The Australian phenomenologist, Michael Eldred, comments:
The antinomy of the continuum, time, in connection with the question of being ... is said by Wheeler to be a cause for dismay which challenges future quantum physics, fired as it is by a will to power over moving reality, to "achieve four victories" (ibid.)... And so we return to the challenge to "[u]nderstand the quantum as based on an utterly simple and—when we see it—completely obvious idea" (ibid.) from which the continuum of time could be derived. Only thus could the will to mathematically calculable power over the dynamics, i.e. the movement in time, of beings as a whole be satisfied.
Digital vs. informational physics
Not every informational approach to physics (or ontology) is necessarily digital
. According to Luciano Floridi
, "informational structural realism" is a variant of structural
realism
that supports an ontological commitment to a world consisting of the totality of informational objects dynamically interacting with each other. Such informational objects are to be understood as constraining affordances.
Digital ontology and pancomputationalism are also independent positions. In particular, John Wheeler
advocated the former but was silent about the latter; see the quote in the preceding section.
On the other hand, pancomputationalists like Lloyd (2006), who models the universe as a quantum computer
, can still maintain an analogue or hybrid ontology; and informational ontologists like Sayre
and Floridi embrace neither a digital ontology nor a pancomputationalist position.
Turing machines
Theoretical computer scienceis founded on the Turing machine
, an imaginary computing machine first described by Alan Turing
in 1936. While mechanically simple, the Church-Turing thesis implies that a Turing machine can solve any "reasonable" problem. (In theoretical computer science, a problem is considered "solvable" if it can be solved in principle, namely in finite time, which is not necessarily a finite time that is of any value to humans.) A Turing machine therefore sets the practical "upper bound" on computational power, apart from the possibilities afforded by hypothetical hypercomputers.
Wolfram's
principle of computational equivalence powerfully motivates the digital approach. This principle, if correct, means that everything can be computed by one essentially simple machine, the realization of a cellular automaton
. This is one way of fulfilling a traditional goal of physics: finding simple laws and mechanisms for all of nature.
Digital physics is falsifiable in that a less powerful class of computers cannot simulate a more powerful class. Therefore, if our universe is a gigantic simulation
, that simulation is being run on a computer at least as powerful as a Turing machine. If humans succeed in building a hypercomputer
, then a Turing machine cannot have the power required to simulate the universe.
The Church–Turing (Deutsch) thesis
The classic Church–Turing thesisclaims that any computer as powerful as a Turing machine
can, in principle, calculate anything that a human can calculate, given enough time. A stronger version, not attributable to Church or Turing, claims that a universal Turing machine
can compute anything any other Turing machine can compute - that it is a generalizable Turing machine. But the limits of practical computation are set by physics
, not by theoretical computer science:
"Turing did not show that his machines can solve any problem that can be solved 'by instructions, explicitly stated rules, or procedures', nor did he prove that the universal Turing machine 'can compute any function that any computer, with any architecture, can compute'. He proved that his universal machine can compute any function that any Turing machine can compute; and he put forward, and advanced philosophical arguments in support of, the thesis here called Turing's thesis. But a thesis concerning the extent of effective methods—which is to say, concerning the extent of procedures of a certain sort that a human being unaided by machinery is capable of carrying out—carries no implication concerning the extent of the procedures that machines are capable of carrying out, even machines acting in accordance with 'explicitly stated rules.' For among a machine's repertoire of atomic operations there may be those that no human being unaided by machinery can perform."
On the other hand, if two further conjectures are made, along the lines that:
- hypercomputation always involves actual infinitiesInfinityInfinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...
; - there are no actual infinities in physics,
the resulting compound principle does bring practical computation within Turing's limits.
As David Deutsch
puts it:
"I can now state the physical version of the Church-Turing principle: 'Every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means.' This formulation is both better defined and more physical than Turing's own way of expressing it." (Emphasis added)
This compound conjecture is sometimes called the "strong Church-Turing thesis" or the Church–Turing–Deutsch principle
.
Criticism
The critics of digital physics—including physicists who work in quantum mechanics—object to it on several grounds.
Physical symmetries are continuous
One objection is that extant models of digital physics are incompatible with the existence of several continuous characters of physical symmetries, e.g., rotational symmetry
, translational symmetry
, Lorentz symmetry, and electroweak symmetry, all central to current physical theory.
Proponents of digital physics claim that such continuous symmetries are only convenient (and very good) approximations of a discrete reality. For example, the reasoning leading to systems of natural units
and the conclusion that the Planck length is a minimum meaningful unit of distance suggests that at some level space itself is quantized.
Locality
Some argue that extant models of digital physics violate various postulates of quantum physics. For example, if these models are not grounded in Hilbert spaces and probabilities, they belong to the class of theories with local hidden variables
that some deem ruled out experimentally using Bell's theorem
. This criticism has two possible answers. First, any notion of locality in the digital model does not necessarily have to correspond to locality formulated in the usual way in the emergent spacetime
. A concrete example of this case was recently given by Lee Smolin
. Another possibility is a well-known loophole in Bell's theorem
known as superdeterminism
(sometimes referred to as predeterminism). In a completely deterministic model, the experimenter's decision to measure certain components of the spins is predetermined. Thus, the assumption that the experimenter could have decided to measure different components of the spins than he actually did is, strictly speaking, not true.
Physical theory requires the continuum
It has been argued that digital physics, grounded in the theory of finite state machines and hence discrete mathematics, cannot do justice to a physical theory whose mathematics requires the real numbers, which is the case for all physical theories having any credibility.
But computers can manipulate and solve formulas describing real numbers using symbolic computation
, thus avoiding the need to approximate real numbers by using an infinite number of digits.
Before symbolic computation, a number—in particular a real number
, one with an infinite number of digits—was said to be computable if a Turing machine
will continue to spit out digits endlessly. In other words, there is no "last digit". But this sits uncomfortably with any proposal that the universe is the output of a virtual-reality exercise carried out in real time (or any plausible kind of time). Known physical laws (including quantum mechanics
and its continuous spectra
) are very much infused with real number
s and the mathematics of the continuum.
"So ordinary computational descriptions do not have a cardinality of states and state space trajectories that is sufficient for them to map onto ordinary mathematical descriptions of natural systems. Thus, from the point of view of strict mathematical description, the thesis that everything is a computing system in this second sense cannot be supported".
Moreover, the universe seems to be able decide on their values in real time, moment by moment. As Richard Feynman
put it:
"It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?"
He then answered his own question as follows:
"So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the checker board with all its apparent complexities. But this speculation is of the same nature as those other people make—'I like it,' 'I don't like it'—and it is not good to be prejudiced about these things".
For his part, David Deutsch generally takes a "multiverse" view to the question of continuous vs. discrete. In short, he thinks that “within each universe all observable quantities are discrete, but the multiverse as a whole is a continuum. When the equations of quantum theory describe a continuous but not-directly-observable transition between two values of a discrete quantity, what they are telling us is that the transition does not take place entirely within one universe. So perhaps the price of continuous motion is not an infinity of consecutive actions, but an infinity of concurrent actions taking place across the multiverse.” January, 2001 The Discrete and the Continuous, an abridged version of which appeared in The Times Higher Education Supplement.
See also
- A New Kind of ScienceA New Kind of ScienceA New Kind of Science is a book by Stephen Wolfram, published in 2002. It contains an empirical and systematic study of computational systems such as cellular automata...
- Bit-string physicsBit-string physicsBit-string physics is an emerging body of theory which considers the universe to be a process of operations on strings of bits. Bit-string physics is often associated with A.F. Parker-Rhodes' combinatorial hierarchy, which is notable for its relationship with the electromagnetic and gravitational...
- Cellular automata
- Church–Turing thesisChurch–Turing thesisIn computability theory, the Church–Turing thesis is a combined hypothesis about the nature of functions whose values are effectively calculable; in more modern terms, algorithmically computable...
- Church–Turing–Deutsch principleChurch–Turing–Deutsch principleIn computer science and quantum physics, the Church–Turing–Deutsch principle is a stronger, physical form of the Church–Turing thesis formulated by David Deutsch in 1985. The principle states that a universal computing device can simulate every physical process. The principle was originally...
- Continuous spatial automata
- David DeutschDavid DeutschDavid Elieser Deutsch, FRS is an Israeli-British physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation in the Clarendon Laboratory of the University of Oxford...
- Digital philosophyDigital philosophyDigital philosophy is a direction in philosophy and cosmology advocated by certain mathematicians and theoretical physicists, e.g., Gregory Chaitin, Edward Fredkin, Stephen Wolfram, and Konrad Zuse ....
- Digital probabilistic physicsDigital probabilistic physicsDigital probabilistic physics is a branch of digital philosophy which holds that the universe exists as a nondeterministic state machine. The notion of the universe existing as a state machine was first postulated by Konrad Zuse's book Rechnender Raum...
- EPR paradoxEPR paradoxThe EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...
- The Fabric of RealityThe Fabric of RealityThe Fabric of Reality is a book by physicist David Deutsch written in 1997. It expands upon his views of quantum mechanics and its implications for understanding reality....
- Ed Fredkin
- Fredkin finite nature hypothesisFredkin finite nature hypothesisIn digital physics, the Fredkin Finite Nature Hypothesis states that ultimately all quantities of physics, including space and time, are discrete and finite. All measurable physical quantities arise from some Planck scale substrate for multiverse information processing...
- Holographic principleHolographic principleThe holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon...
- HypercomputationHypercomputationHypercomputation or super-Turing computation refers to models of computation that are more powerful than, or are incomparable with, Turing computability. This includes various hypothetical methods for the computation of non-Turing-computable functions, following super-recursive algorithms...
- Konrad ZuseKonrad ZuseKonrad Zuse was a German civil engineer and computer pioneer. His greatest achievement was the world's first functional program-controlled Turing-complete computer, the Z3, which became operational in May 1941....
- Margolus-Levitin theoremMargolus-Levitin theoremThe Margolus–Levitin theorem, named for Norman Margolus and Lev B. Levitin, gives a fundamental limit on quantum computation . The processing rate cannot be higher than 6 × 1033 operations per second per joule of energy. Or stating the bound for one micro system:The theorem is also of...
- Mathematical universe hypothesis
- Tipler's Omega Point
- Programming the UniverseProgramming the UniverseProgramming the Universe is a 2006 popular science book by Seth Lloyd, professor of mechanical engineering at the Massachusetts Institute of Technology. The book proposes that the universe is a quantum computer, and advances in the understanding of physics may come from viewing entropy as a...
- Physical informationPhysical informationIn physics, physical information refers generally to the information that is contained in a physical system. Its usage in quantum mechanics In physics, physical information refers generally to the information that is contained in a physical system. Its usage in quantum mechanics In physics,...
- Quantum computation
- Seth LloydSeth LloydSeth Lloyd is a professor of mechanical engineering at the Massachusetts Institute of Technology. He refers to himself as a "quantum mechanic"....
- Chris Langan
- Simulation hypothesisSimulation hypothesisThe Simulation Hypothesis proposes that reality is a simulation and those affected are generally unaware of this. The concept is reminiscent of René Descartes' Evil Genius but posits a more futuristic simulated reality...
- Simulated realitySimulated realitySimulated reality is the proposition that reality could be simulated—perhaps by computer simulation—to a degree indistinguishable from "true" reality. It could contain conscious minds which may or may not be fully aware that they are living inside a simulation....
- Ultimate ensembleUltimate ensembleIn physics and cosmology, the mathematical universe hypothesis , also known as the Ultimate Ensemble, is a speculative "theory of everything" proposed by the theoretical physicist, Max Tegmark.-Description:...
Further reading
- Paul DaviesPaul DaviesPaul Charles William Davies, AM is an English physicist, writer and broadcaster, currently a professor at Arizona State University as well as the Director of BEYOND: Center for Fundamental Concepts in Science...
, 1992. The Mind of God: The Scientific Basis for a Rational World. New York: Simon & Schuster. - David DeutschDavid DeutschDavid Elieser Deutsch, FRS is an Israeli-British physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation in the Clarendon Laboratory of the University of Oxford...
, 1997. The Fabric of RealityThe Fabric of RealityThe Fabric of Reality is a book by physicist David Deutsch written in 1997. It expands upon his views of quantum mechanics and its implications for understanding reality....
. New York: Allan Lane. - Michael Eldred, 2009, The Digital Cast of Being: Metaphysics, Mathematics, Cartesianism, Cybernetics, Capitalism, Communication ontos, Frankfurt 2009, 137 pp. ISBN 978-3-86838-045-3
- Edward FredkinEdward FredkinEdward Fredkin is an early pioneer of digital physics. In recent work, he uses the term digital philosophy . His primary contributions include his work on reversible computing and cellular automata...
, 1990. "Digital Mechanics," Physica D: 254-70. - Seth LloydSeth LloydSeth Lloyd is a professor of mechanical engineering at the Massachusetts Institute of Technology. He refers to himself as a "quantum mechanic"....
, Ultimate physical limits to computation, NatureNature (journal)Nature, first published on 4 November 1869, is ranked the world's most cited interdisciplinary scientific journal by the Science Edition of the 2010 Journal Citation Reports...
, volume 406, pages 1047–1054 - Carl Friedrich von WeizsäckerCarl Friedrich von WeizsäckerCarl Friedrich Freiherr von Weizsäcker was a German physicist and philosopher. He was the longest-living member of the research team which performed nuclear research in Germany during the Second World War, under Werner Heisenberg's leadership...
, 1980. The Unity of Nature. New York: Farrar Straus & Giroux. - John Archibald WheelerJohn Archibald WheelerJohn Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...
, 1990. "Information, physics, quantum: The search for links" in W. Zurek (ed.) Complexity, Entropy, and the Physics of Information. Addison-Wesley. - John Archibald Wheeler and Kenneth Ford, 1998. Geons, black holes and quantum foam: A life in physics. W. W. Norton. ISBN 0-393-04642-7.
- Robert WrightRobert Wright (journalist)Robert Wright is an American journalist, scholar, and prize-winning author of best-selling books about science, evolutionary psychology, history, religion, and game theory, including The Evolution of God, Nonzero: The Logic of Human Destiny, The Moral Animal, and Three Scientists and Their Gods:...
, 1989. Three Scientists and Their Gods: Looking for Meaning in an Age of Information. HarperCollins. ISBN 0-06-097257-2. This book discusses Edward FredkinEdward FredkinEdward Fredkin is an early pioneer of digital physics. In recent work, he uses the term digital philosophy . His primary contributions include his work on reversible computing and cellular automata...
's work. - Konrad ZuseKonrad ZuseKonrad Zuse was a German civil engineer and computer pioneer. His greatest achievement was the world's first functional program-controlled Turing-complete computer, the Z3, which became operational in May 1941....
, 1970. Calculating Space. The English translation of his Rechnender Raum.
External links
- Luciano FloridiLuciano FloridiLuciano Floridi currently holds the Research Chair in philosophy of information and the UNESCO Chair in Information and Computer Ethics, both at the University of Hertfordshire, Department of Philosophy...
, "Against Digital Ontology", Synthese, 2009, 168.1, (2009), 151-178. - Edward FredkinEdward FredkinEdward Fredkin is an early pioneer of digital physics. In recent work, he uses the term digital philosophy . His primary contributions include his work on reversible computing and cellular automata...
: - Gontigno, Paulo, "Hypercomputation and the Physical Church-Turing thesis"
- Petrov, Plamen, and Joel Dobrzelewski, 1998. Digital Physics
- Juergen Schmidhuber:
- Konrad ZuseKonrad ZuseKonrad Zuse was a German civil engineer and computer pioneer. His greatest achievement was the world's first functional program-controlled Turing-complete computer, the Z3, which became operational in May 1941....
, [ftp://ftp.idsia.ch/pub/juergen/zuse67scan.pdf PDF scan] of Zuse's paper.
- Digital physics. Mountain Math Software.
- The Oxford Advanced Seminar on Informatic Structures
- Wired: God is the Machine
- Gualtiero PiccininiGualtiero PiccininiGualtiero Piccinini is a philosopher working primarily on the nature of mind and computation as well as on how to integrate psychology and neuroscience. He is an associate professor in the Philosophy and Psychology Departments and the Center for Neurodynamics at the University of Missouri, St...
. Computation in Physical Systems Discusses the metaphysical foundations of digital physics in section 3.4.