Saturday, 30 July 2016 14:28

The way from the natural numbers through the real numbers to the two-element numbers

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The role of the concept of computability in physics

“It would require infinite precision for the coordinates of a phase-space point- i.e. all the decimal places!- in order for it to make sense to say that the point is non-computable. (A number described by a finite decimal is always computable.) A finite portion of .a decimal expansion of a number tells us nothing about the computability of the entire expansion of that number. But all physical measurements have a definite limitation on how accurately they can be performed, and can only give information about a finite number of decimal places. Does this nullify the whole concept of 'computable number' as applied to physical measurements?” (Roger Penrose, The Emperor’s New Mind – Concerning Computers, Minds, and The Laws of Physics, Chapter 5; The classical World, Phase space)

Contents

1. The natural numbers and the qualitative characteristic of infinite
2. The positional numeral systems and the two-element numbers
3. “Actualization” of the potentially infinite – examples in physics
4. Epilogue

Appendix

 

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Read 650 times Last modified on Saturday, 11 May 2019 08:43
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