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Regarding Kurtzweil's "mathematical principle," our mathematics is a reflection of the universe we live in. Mathematics is based on axioms, which make sense to

Regarding Kurtzweil's "mathematical principle," our mathematics is a reflection of the universe we live in. Mathematics is based on axioms, which make sense to us only because we observe them to be always true in our universe. For example, one of Peano's axioms of arithmetic states that "1 is a natural number" (here I am using the base one axiomatic), and another axiom states that "no natural number has 1 as its successor." One could imagine (though not necessarily describe in detail) a strange universe where there is a natural number larger than 1 that has 1 as its successor (i.e. the way modular arithmetic works). To summarize, I do not see why the "mathematical principle" has to be postulated separately from the "anthropic principle," which we all know has an alternative deity-free explanation mentioned by Kurtzweil himself: there could be "a zillion universes, each with a different set of physical laws, and we just happen to live in one that is compatible with life."

stcredzero 16y ago
Regarding Kurtzweil's "mathematical principle," our mathematics is a reflection of the universe we live in. Mathematics is based on axioms, which make sense to us only because we observe them to be always true in our universe. How about: Our mathematics is a reflection of the universe we can perceive.
- bluekeybox 16y ago
  That is correct, except that it puts unnecessary emphasis on perception relativism. We use mathematics especially extensively in areas where our perception is limited (particle physics, climate modeling etc.) In other words, we use mathematics to "augment" and to "test" our perception so as to prevent any kind of perceptual illusions misguiding us in our observation.
  - stcredzero 16y ago
    That is correct, except that it puts unnecessary emphasis on perception relativism. Well, in your mind. :) I didn't mean that in support of a relativistic viewpoint. Perhaps I should have said that we can comprehend. Perception just determines our starting point.

stcredzero 16y ago

bluekeybox 16y ago
That is correct, except that it puts unnecessary emphasis on perception relativism. We use mathematics especially extensively in areas where our perception is limited (particle physics, climate modeling etc.) In other words, we use mathematics to "augment" and to "test" our perception so as to prevent any kind of perceptual illusions misguiding us in our observation.
- stcredzero 16y ago
  That is correct, except that it puts unnecessary emphasis on perception relativism. Well, in your mind. :) I didn't mean that in support of a relativistic viewpoint. Perhaps I should have said that we can comprehend. Perception just determines our starting point.