Skip to main content
×
Home
    • Aa
    • Aa

Introduction: computability of the physical

  • CRISTIAN S. CALUDE (a1) and S. BARRY COOPER (a2)
Abstract

Albert Einstein encapsulated a commonly held view within the scientific community when he wrote in his book Out of My Later Years (Einstein 1950, page 54)

‘When we say that we understand a group of natural phenomena, we mean that we have found a constructive theory which embraces them.’

This represents a dual challenge to the scientist: on the one hand, to explain the real world in a very basic, and if possible, mathematical, way; but on the other, to characterise the extent to which this is even possible. Recent years have seen the mathematics of computability play an increasingly vital role in pushing forward basic science and in illuminating its limitations within a creative coming together of researchers from different disciplines. This special issue of Mathematical Structures in Computer Science is based on the special session ‘Computability of the Physical’ at the International Conference Computability in Europe 2010, held at Ponta Delgada, Portugal, in June 2010, and it, together with the individual papers it contains, forms what we believe to be a special contribution to this exciting and developing process.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Introduction: computability of the physical
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Introduction: computability of the physical
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Introduction: computability of the physical
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

C. H Bennett , P. Gàcs , M. Li , M. B. Vitányi and W. H. Zurek (1998) Information distance. IEEE Transactions on Information Theory 44 14071423.

C. S. Calude and M. A Stay (2008). Most programs stop quickly or never halt. Advances in Applied Mathematics 40 295308.

C. S. Calude and M. A. Stay (2006) Natural halting probabilities, partial randomness, and zeta functions. Information and Computation 204 17181739.

C. S. Calude , L. Staiger and S. A. Terwijn (2006) On partial randomness. Annals of Pure and Applied Logic 138 2030.

G. Chaitin (1975) A theory of program size formally identical to information theory. Journal of the ACM 22, 329340.

H. F. Dowker (2005) Causal sets and the deep structure of space–time. In: A. Ashtekar (ed.) 100 Years of Relativity – space–time Structure: Einstein and Beyond, World Scientific445464.

E. Fredkin and T. Toffoli (1982) Conservative logic. International Journal of Theoretical Physics 21 219253.

Y. Manin (2010) A Course in Mathematical Logic (the second, expanded Edition), Springer-Verlag.

R. J. Solomonoff (1964) A formal theory of inductive inference, part I. Information and Control 7 122.

L. Szilard (1929) On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings. Zeitschrift für Physik 53, 840856. (English translation (2003) In: H. S. Leff and A. F. Rex (eds.) Maxwell's Demon 2: Entropy, Information, Computing, Adam Hilger.)

K. Tadaki (2002) A generalization of Chaitin's halting probability Ω and halting self-similar sets. Hokkaido Mathematical Journal 31 219253.

K. Tadaki (2009) Fixed point theorems on partial randomness. In: Proceedings of the Symposium on Logical Foundations of Computer Science 2009. Springer-Verlag Lecture Notes in Computer Science 5407 422440.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 15 *
Loading metrics...

Abstract views

Total abstract views: 51 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st September 2017. This data will be updated every 24 hours.