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Topic: Matheology § 257
Replies: 11   Last Post: Apr 23, 2013 5:05 PM

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Registered: 12/4/12
Re: Matheology § 257
Posted: Apr 22, 2013 7:53 AM
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On 4/22/2013 2:03 AM, WM wrote:
> [Gregory Chaitin: "How real are real numbers?" (2004)]

Page 12

"Why should we believe in real numbers, if most of
them are uncomputable? Why should we believe in real
numbers, if most of them, it turns out, are maximally
unknowable like Omega?"

footnote with answer

"In spite of the fact that most individual real
numbers will forever escape us, the notion
of an arbitrary real has beautiful mathematical
properties and is a concept that helps us
to organize and understand the real world.
Individual concepts in a theory do not need
to have concrete meaning on their own; it is
enough if the theory as a whole can be
compared with the results of experiments."

[Gregory Chaitin: "How real are real numbers?" (2004)]

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