Gubachelier: /* Bibtex */

2016-12-27T19:44:23Z

‎Bibtex

Gubachelier: Die Seite wurde neu angelegt: „ == Reference == Donald Spector: Colors and Incomputability. In: Bridges 2016, Pages 337–344. == DOI == == Abstract == This paper explores some su…“

2016-12-26T23:07:55Z

Die Seite wurde neu angelegt: „ == Reference == Donald Spector: Colors and Incomputability. In: Bridges 2016, Pages 337–344. == DOI == == Abstract == This paper explores some su…“

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== Reference ==
Donald Spector: [[Colors and Incomputability]]. In: [[Bridges 2016]], Pages 337–344.

== DOI ==

== Abstract ==
This paper explores some surprising connections between the frequencies of light we observe and foundational
questions in the mathematics of real numbers and the theory of computation. We find that these foundational issues
imply limitations on what can be seen, separate from any limitations from the laws of physics. Furthermore, it
turns out that, given the kinds of observations one can make of light, the most reasonable expectation for the actual
frequency of light underlying any set of observations is that that frequency comes from a particularly unusual class
of uncomputable numbers called generic real numbers.

== Extended Abstract ==

== Bibtex ==
@inproceedings{bridges2016:337,
author = {Donald Spector},
title = {Colors and Incomputability},
pages = {337--344},
booktitle = {Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture},
year = {2016},
editor = {Eve Torrence, Bruce Torrence, Carlo S\'equin, Douglas McKenna, Krist\'of Fenyvesi and Reza Sarhangi},
isbn = {978-1-938664-19-9},
issn = {1099-6702},
publisher = {Tessellations Publishing},
address = {Phoenix, Arizona},
url = {http://de.evo-art.org/index.php?title=Colors_and_Incomputability},
note = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-337.html}}
}

== Used References ==
[1] K. Becker, M. Becker, & J.J. Schwarz. String Theory and M-Theory. Cambridge University Press,
Cambridge, 2007

[2] G. Cantor, U¨ ber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen, Journal fu¨r die
Reine und Angewandte Mathematik 77 (1874) 258.

[3] G. Cantor, Ein Beitrag zur Mannigfaltigkeitslehre, Journal f¨ur die Reine und Angewandte Mathematik
84 (1878) 242.

[4] G. Cantor, U¨ ber eine elementare Frage der Mannigfaltigkeitslehre, Jahresbericht der Deutsche
Mathematiker-Vereinigung 1890-1891, vol 1 (1892) 75.

[5] G. Chaitin. Algorithmic Information Theory. Cambridge Tracts in Theoretical Computer Science.
Cambridge University Press, paperback edition, 2004 (1987).

[6] A. Church, Abstract No. 204, Bull. Amer. Math. Soc. 41 (1935) 332.

[7] A. Church, An Unsolvable Problem of Elementary Number Theory, Amer. J. Math. 58 (1936) 345.

[8] P. Cohen, The independence of the continuum hypothesis I, Proceedings of the National Academy
of Sciences 50 (1963) 1143.

[9] P. Cohen, The independence of the continuum hypothesis II, Proceedings of the National Academy
of Sciences 51 (1964) 105.

[10] K. Go¨del, U¨ ber formal unentscheidbare Sa¨tze der Principia Mathematica und verwandter Systeme,
I, Monatshefte f¨ur Mathematik und Physik 38 (1931) 173.

[11] K. G¨odel, The consistency of the axiom of choice and of the generalized continuum-hypothesis,
Proceedings of the National Academy of Sciences 24 (1938) 556.

[12] J.D. Jackson. Classical Electrodynamics, 3rd ed. John Wiley & Sons, New York, 1999.

[13] E.T. Jaynes, Information theory and statistical mechanics, Phys. Rev. 106 (1957) 620.

[14] E.T. Jaynes, Information theory and statistical mechanics II, Phys. Rev. 108 (1957) 171.

[15] T. Jech. Multiple Forcing. Number 88 in Cambridge Tracts in Mathematics. Cambridge University
Press, Cambridge, 1987.

[16] J. Mai. Territories of Color: Towards a New Model of Simultaneous Color Contrast. Proceedings
of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (2013) 233.

[17] R.J. Nemiroff, R. Connolly, J. Holmes, & A.B. Kostinski, Bounds on Spectral Dispersion from
Fermi-Detected Gamma Ray Bursts, Phys. Rev. Lett. 108 (2012) 231103.

[18] R. Penrose. The Emperor’s New Mind. Oxford University Press, Oxford, 1989.

[19] C. Quigg. Gauge Theories of the Strong, Weak, and Electromagnetic Interactions, 2nd ed. Princeton
University Press, Princeton, 2013.

[20] A.M. Turing, On computable numbers, with an application to the Entscheidungsproblem, Proceedings
of the London Mathematical Society (Second Series) 42 (1936) 230.

[21] A.M. Turing, On computable numbers, with an application to the Entscheidungsproblem: A correction,
Proceedings of the London Mathematical Society (Second Series) 43 (1937) 544.

[22] A. M. Turing. Systems of Logic Based on Ordinals (Ph.D. thesis). Princeton University. 1939.

== Links ==
=== Full Text ===
http://archive.bridgesmathart.org/2016/bridges2016-337.pdf

[[intern file]]

=== Sonstige Links ===
http://archive.bridgesmathart.org/2016/bridges2016-337.html

@@ Zeile 27: / Zeile 27: @@
    publisher   = {Tessellations Publishing},
    address     = {Phoenix, Arizona},
-   url         = {http://de.evo-art.org/index.php?title=Colors_and_Incomputability},
+   url         = {http://de.evo-art.org/index.php?title=Colors_and_Incomputability },
    note        = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-337.html}}
+  }
 == Used References ==

Colors and Incomputability - Versionsgeschichte

Gubachelier: /* Bibtex */

Gubachelier: Die Seite wurde neu angelegt: „ == Reference == Donald Spector: Colors and Incomputability. In: Bridges 2016, Pages 337–344. == DOI == == Abstract == This paper explores some su…“