Suppose you are God…

…how would you do it?

Karl Svozil /ITP/TUViennasvozil@tuwien.ac.athttp://tph.tuwien.ac.at/~svozilThis source athttp://tph.tuwien.ac.at/~svozil/publ/2003-dw.ppt

Copyright (c) 2003 Karl Svozil @ svozil@pop.tuwien.ac.at Permission is granted to copy, distribute and/or modify these documents under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".

Some broader context…awakening• Are we at the center of the Universe? — No, but

we seem to be quite conveniently located within our galaxy.

• Are our bodies made-up of solid stuff? — No, our bodies are „almost“ empty. Things only appear to be solid.

• Were we created in a different way than other species? — No, we evolved and spread just like locusts & everyone else around.

• Are we up to further disillusionments? Are we „fleshware,“ units inside a (what to us appears gigantic) simulation/computation?

Pythagoras (6th cent. B.C.)

… considered numbers as the essence and principle of all things, and attributed to them a real and distinct existence; so that, in his view, they were the elements out of which the universe was constructed.

http://www.google.at/search?q=pythagoras+world+as+numbers&ie=UTF-8&oe=UTF-8&hl=de&meta=http://www.bartleby.com/181/341.html

Thomas Bulfinch (1796–1867).  Age of Fable: Vols. I & II: Stories of Gods and Heroes.  1913.

Plato (c. 427- c. 347 B.C.)

„God geometrizes“ [Plutarch (Convivialium disputationum,

liber 8,2): „Plato said God geometrizes continually“]

http://sunsite.utk.edu/math_archives/.http/hypermail/historia/may99/0202.html

K. F. Gauss (1777-1855)

…„o theos arithmetizei“ = “God computes“

http://sunsite.utk.edu/math_archives/.http/hypermail/historia/may99/0202.html

D. Hilbert (1862-1943)

Twenty-three problems of 1900:#2: The compatibility of the

arithmetical axioms #6: Mathematical treatment of the

axioms of physics #10: Determination of the

solvability of a diophantine equation

http://babbage.clarku.edu/~djoyce/hilbert/problems.html

Gödel (1906-78) & Turing (1912-54)• Formalization of Mathematics

by coding of axiomatic systems, which are representable as (universal) computer programs

• Precise definition of „Universal Computation“ (Turing machine is modeled after pencil&paper operations) wich is „robust“

• „true > provable“

E. Wigner (1902-1995)

„The unreasonable effectiveness of mathematics in the natural sciences“

Richard Courant Lecture delivered at New York University, May 11, 1959 and published in Communications on Pure

and Applied Mathematics 13, 1 (1960).

Von Neumann (1903-57)

„Theory of Self-Reproducing [[Universal Cellular]] Automata“

(1966)

E. F. Moore

• „Gedanken-Experiments on Sequential Machines“ (1956)

• Automaton Uncertainty Principle• Two modes of measurement

Automata Studies, ed. by C.E.Shannon and J.McCarthy, Princeton Univ. Press, Princeton, pp. 129-153.

K. Zuse (1910-1995)

„Rechnender Raum“

= „Calculating Space“ Konrad Zuse, Rechnender Raum, Friedrich Vieweg & Sohn, Braunschweig, 1969. English

translation: Calculating Space, MIT Technical Translation AZT-70-164-GEMIT, MIT (Proj. MAC), Cambridge, Mass. 02139, Feb. 1970

http://www.idsia.ch/~juergen/digitalphysics.html

T. Toffoli & E. Fredkin

• Reversible Computation• Role of the Observer in Uniform Systems• Digital Mechanics • „The Universe is a cellular automaton “• Digital Philosophy

http://www.digitalphilosophy.org/http://digitalphysics.org/

S. Wolfram (et al ;) … Is there any physics

left to be done after ANKOS (=A New Kind of Science)?

http://www.math.usf.edu/~eclark/ANKOS_reviews.html

The (humble?) rest …

Not too many researchers pursuing Digital Mechanics:

J. Schmidhuber, N. Margolus, K.Svozil (not very lately), Jim Crutchfield…. , among others…

Some of my results…

• Automaton logic

• Intrinsic =/= extrinsic

• Space-time frame generation by intrinsic observersK. Svozil, ``Randomness and Undecidability in Physics'‚ (World Scientific, Singapore, 1993), xvi+292 p.

Space-time of intrinsic CA observers

• CA rules of a light clock (below), and• CA light clock evolution (right)• „universality“ and „robustness“ makes this Model independent

Let‘s face it: Digital Physics is utterly non mainstream & off-topic!

• Today‘s physics is continuum physics; even quantum theory just discretizes the number of quanta within a mode. Modes are still continuous!

• What is it good for? Is it Ideology (according to Popper, but who cares about Popper anyway)?

• What about „non-locality“ and „contextuality“?

• Not good for your career as a physicist!

Some mind-boggling speculations

• Automaton Logic very similar to Quantum Logic

• Relativity-Type transformation laws of frames constructed by radar coordinates (Alexandrov‘s theorem,…)

• Intrinsic-Extrinsic setup (Systems Science)

• Interfaces & Dualism & the Eccles Telegraph

… continued…• „Atomism“ is very suitable for digital simulation

(identical parts, recyclable,…)• Physical undecidability by uncomputability (Casti‘s

Red Herring http://tph.tuwien.ac.at/~svozil/publ/casti.htm)

• “Zoo hypothesis” (cf. F.Sagan’s “Contact” with aliens)• Maybe we are simulations; e.g., for marketing

purposes• Maybe there is just one consistent Universe?• Maybe free will is an illusion?

Not much empirical evidence … (indeed, is there any?)

• How could we ever find out? Some claims, none convincing. Ultimate physical justification is experiment.

• Competing with “traditional” continuum physics is hard; e.g., take this: anomalous magnetic Moment of the Muon

a(theory) = 11 659 177(7) × 10^-10 a(experi) = 11 659 204(7)(5) × 10^-10 http://arxiv.org/abs/hep-ex/0211044

or this: http://link.aps.org/abstract/RMP/v60/p1067

Neutron double slit experiment

… but it is fun & inspiring!

• Daniel F. Galouye, Simulacron 3 (1964);

• stimulated R. W. Fassbender’s “Welt am Draht”

• & “Thirteenth Floor”

• H. Putnam, “Reason, Truth and History” (“Brain in a vat”)

• “Total Recall”

• “Matrix”, of course...

Thank you for listening!