# The Digital and the Real Universe. Foundations of Natural Philosophy and Computational Physics

^{1}

^{2}

## Abstract

**:**

## 1. Introduction

## 2. Complexity of Quantum and Real Computing

^{−5}s. After the separation of matter and radiation in nearly 300,000 years, the universe became transparent. Gravitation began to form material structures of galaxies, Black Holes, and the first generations of stars. Chemical elements and molecular compounds were generated. Under appropriate planetary conditions, the evolution of life had developed. The evolution of quantum, molecular, and DNA-systems is nowadays a model of quantum, molecular, and DNA-computing.

## 3. Is the Universe Digital?

## 4. Is the Universe Computable?

If ${T}_{2}+\tau $ can prove ${T}_{1}$, this proof is called a reversal. If ${T}_{1}$ proves $\tau $ and ${T}_{2}+\tau $ is a reversal, then ${T}_{1}$ and $\tau $ are said to be equivalent over ${T}_{2}$.

## 5. Computational Complexity of the Universe

- -
- Definitely cannot be reduced to constructive procedures; and
- -
- definitely influence physical experiments,

## 6. Conclusions

## Funding

## Conflicts of Interest

## References

- Mainzer, K. Grundlagen und Geschichte der Exakten Wissenschaften; Universitätsverlag: Konstanz, Germany, 1981. [Google Scholar]
- Mainzer, K. Symmetrien der Natur; De Gruyter: Berlin, Germany; New York, NY, USA, 1988. [Google Scholar]
- Mainzer, K. Information. Algorithmus-Wahrscheinlichkeit-Komplexität-Quantenwelt-Leben-Gehirn-Gesellschaft; Berlin University Press: Berlin, Germany, 2016. [Google Scholar]
- Wheeler, J.A. Information, physics, quantum: The search for links. In Complexity, Entropy, and the Physics of Information; Zurek, W.H., Ed.; Addison-Wesley: Redwood City, CA, USA, 1990. [Google Scholar]
- Mainzer, K. Symmetry and Complexity. The Spirit and Beauty of Nonlinear Science; World Scientific Publisher: Singapore, 2005. [Google Scholar]
- Deutsch, D. Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A
**1985**, 400, 97–117. [Google Scholar] [CrossRef] - Mainzer, K. The Digital and the Real World. Computational Foundations of Mathematics, Science, Technology, and Philosophy; World Scientific Publisher: Singapore, 2018. [Google Scholar]
- Mainzer, K.; Schuster, P.; Schwichtenberg, H. (Eds.) Proof and Computation. Digitization in Mathematics, Computer Science, and Philosophy; World Scientific Publisher: Singapore, 2018; Chapter 1. [Google Scholar]
- Blum, L.; Cucker, F.; Shub, M.; Smale, S. Complexity and Real Computation; Springer: New York, NY, USA, 1998. [Google Scholar]
- Siegelmann, H.T.; Sontag, E.D. Analog computation via neural networks. Theor. Comput. Sci.
**1994**, 131, 331–360. [Google Scholar] [CrossRef] - Feynman, R.P. The Character of Physical Law; The M.I.T Press: Cambridge, MA, USA, 1967. [Google Scholar]
- Bernstein, J. Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that. Rev. Rep. Mod. Phys.
**1974**, 46, 7–48. [Google Scholar] [CrossRef] - Audretsch, J.; Mainzer, K. (Eds.) Philosophie und Physik der Raum-Zeit, 2nd ed.; B.I. Wissenschaftsverlag: Mannheim, Germany, 1994; pp. 39–44. [Google Scholar]
- Penrose, R. An Analysis of the Structure of Space-Time; Adams Prize Essay; Cambridge University Press: Cambridge, UK, 1966. [Google Scholar]
- Everett, H. “Relative state” formulation of quantum mechanics. Rev. Mod. Phys.
**1957**, 29, 454–462. [Google Scholar] [CrossRef] - Ludwig, G. Die Grundstrukturen Einer Physikalischen Theorie; Springer: Berlin, Germany, 1978. [Google Scholar]
- Tegmark, M. Our Mathematical Universe; Alfred A. Knopf: New York, NY, USA, 2014. [Google Scholar]
- Doncel, M.G.; Hermann, A.; Michel, L.; Pais, A. (Eds.) Symmetries in Physics 1600–1980; Seminari d‘Història de les Ciències; Universitat Autònoma de Barcelona: Bellaterra (Barcelona), Spain, 1987. [Google Scholar]
- Wolfram, S. The Mathematica Book, 5th ed.; Cambridge University Press: Cambridge, UK, 2005. [Google Scholar]
- Hultsch, F.O. (Ed.) Pappi Alexandrini Collectionis Quae Supersunt 3 Vols; Weidmann: Berlin, Germany, 1876–1878; p. 634ff. [Google Scholar]
- Hintikka, J.; Remes, U. The Method of Analysis—Its Geometrical Origin and Its General Significance; North-Holland: Dordrecht, The Netherlands, 1974. [Google Scholar]
- Mainzer, K. Computer—Neue Flügel des Geistes? De Gruyter: Berlin, Germany; New York, NY, USA, 1994; p. 120ff. [Google Scholar]
- Friedman, H. Some systems of second order arithmetic and their use. In Proceedings of the International Congress of Mathematicians, Vancouver, BC, Canada, 21–29 August 1974; 1. Canadian Mathematical Congress: Montreal, QC, Canada, 1975; pp. 235–242. [Google Scholar]
- Simpson, S.G. Subsystems of Second Order Arithmetic. Perspectives in Mathematical Logic; Springer: Berlin, Germany, 1999. [Google Scholar]
- Simpson, S.G. Reverse Mathematics; Lecture Notes in Logic 21; The Association of Symbolic Logic: Poughkeepsie, NY, USA, 2005. [Google Scholar]
- Friedman, H.; Simpson, S.G. Issues and problems in reverse mathematics. Comput. Theory Appl. Contemp. Math.
**2000**, 257, 127–144. [Google Scholar] - Mainzer, K. Geschichte der Geometrie; B.I. Wissenschaftsverlag: Mannheim, Germany, 1980; p. 30. [Google Scholar]
- Mainzer, K. Die Berechnung der Welt. Von der Weltformel zu Big Data; C.H. Beck: München, Germany, 2014; pp. 130–132, 204. [Google Scholar]
- Weyl, H. Gruppentheorie und Quantenmechanik; Hirzel: Leipzig, Germany, 1931. [Google Scholar]
- Chaitin, G.J. On the length of programs for computing finite binary sequences: Statistical considerations. J. ACM
**1969**, 16, 145–159. [Google Scholar] [CrossRef] - Dodig-Crnkovic, G. Computational dynamics of natural information morphology, discretely continuous. Philosophies
**2017**, 2, 23. [Google Scholar] [CrossRef] - Lesne, A. The discrete versus continuous controversy in physics. Math. Struct. Comput. Sci.
**2007**, 17, 185–223. [Google Scholar] [CrossRef] - Maley, C.J. Analog and digital, continuous and discrete. Philos. Stud.
**2011**, 155, 117–131. [Google Scholar] [CrossRef]

© 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mainzer, K.
The Digital and the Real Universe. Foundations of Natural Philosophy and Computational Physics. *Philosophies* **2019**, *4*, 3.
https://doi.org/10.3390/philosophies4010003

**AMA Style**

Mainzer K.
The Digital and the Real Universe. Foundations of Natural Philosophy and Computational Physics. *Philosophies*. 2019; 4(1):3.
https://doi.org/10.3390/philosophies4010003

**Chicago/Turabian Style**

Mainzer, Klaus.
2019. "The Digital and the Real Universe. Foundations of Natural Philosophy and Computational Physics" *Philosophies* 4, no. 1: 3.
https://doi.org/10.3390/philosophies4010003