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The article doesn't actually mention the specific Turing paper. It's "The Chemical Basis of Morphogenesis": http://en.wikipedia.org/wiki/The_Chemical_Basis_of_

The article doesn't actually mention the specific Turing paper. It's "The Chemical Basis of Morphogenesis": http://en.wikipedia.org/wiki/The_Chemical_Basis_of_Morphogenesis http://en.wikipedia.org/wiki/The_Chemical_Basis_of_Morphogen... It should be noted that Turing was a mathematician, not a scientist. He wasn't trying to prove that tiger stripes occur in a specific way but instead he wanted to model mathematically how such large scale structure could arise from uniform homogeneous structure.

unwind 12y ago
The article linked to a PDF of the paper in question, in the first opening paragraph. That's pretty decent. Also, isn't mathematics considered a science? What?
- AimHere 12y ago
  Depends how you look at it. There's lots of crossover between people with scientific and mathematical aptitude, and mathematics is extensively used by science, and mathematics is often lumped in with the science faculties at universities, but at some philosophical level, mathematics and science are totally different disciplines. Mathematics proves theorems rigorously by a priori reasoning, given some set of self-evident axioms and rules of inference. The ultimate test of 'truth' in mathematics is just whether the theorems can be proven from the given axioms. Science attempts to describe how the world works, through experimentation and theorising. The test of 'truth' in science is whether the theory matches with all the known experimental results. Mathematical 'truths', once discovered, are essentially tautologies and are always true, no matter what (unless a mistake has been made in a proof, which does sometimes happen). Scientific 'truths' are theories - as-yet unfalsified guesses about how the world works that might be proven wrong by the next experiment someone does.
- elsjaako 12y ago
  Mathematics doesn't use the scientific method. A lot of people think that makes it not a science. A bachelors degree in mathematics can be a Bachelor of Science or Bachelor of Arts, and some institutions give out a Bachelor of Mathematics.
- gilgoomesh 12y ago
  Oops, I didn't see the link. My mistake, then. Is mathematics a science? I always say "no" but there are different definitions (it's an old word and originally just meant "knowledge"). Abstract fields like mathematics are certainly excluded from the purer definition of "natural sciences" (physics, chemistry, biology, geology) because it doesn't require interaction with the physical world. Relevant xkcd: http://xkcd.com/435/ http://xkcd.com/435/ Mathematics is sometimes called a "formal science" but the term isn't widely accepted. In general: if it doesn't follow the scientific method (which requires experimentation, which mathematics doesn't include) it isn't considered a science. Some mathematical fields do experiment; computational and statistical mathematics can employ stochastic experimental procedure – making them scientific or at least science-like – but they're still abstract and certainly not natural sciences.
  - wolfgke 12y ago
    > Mathematics is sometimes called a "formal science" but the term isn't widely accepted. In German this kind of science is denoted as "Strukturwissenschaft" (structural science) to close mathematics and theoretical computer science off (empirical) sciences.

unwind 12y ago

The article linked to a PDF of the paper in question, in the first opening paragraph. That's pretty decent. Also, isn't mathematics considered a science? What?

AimHere 12y ago
Depends how you look at it. There's lots of crossover between people with scientific and mathematical aptitude, and mathematics is extensively used by science, and mathematics is often lumped in with the science faculties at universities, but at some philosophical level, mathematics and science are totally different disciplines. Mathematics proves theorems rigorously by a priori reasoning, given some set of self-evident axioms and rules of inference. The ultimate test of 'truth' in mathematics is just whether the theorems can be proven from the given axioms. Science attempts to describe how the world works, through experimentation and theorising. The test of 'truth' in science is whether the theory matches with all the known experimental results. Mathematical 'truths', once discovered, are essentially tautologies and are always true, no matter what (unless a mistake has been made in a proof, which does sometimes happen). Scientific 'truths' are theories - as-yet unfalsified guesses about how the world works that might be proven wrong by the next experiment someone does.
elsjaako 12y ago
Mathematics doesn't use the scientific method. A lot of people think that makes it not a science. A bachelors degree in mathematics can be a Bachelor of Science or Bachelor of Arts, and some institutions give out a Bachelor of Mathematics.
gilgoomesh 12y ago
Oops, I didn't see the link. My mistake, then. Is mathematics a science? I always say "no" but there are different definitions (it's an old word and originally just meant "knowledge"). Abstract fields like mathematics are certainly excluded from the purer definition of "natural sciences" (physics, chemistry, biology, geology) because it doesn't require interaction with the physical world. Relevant xkcd: http://xkcd.com/435/ http://xkcd.com/435/ Mathematics is sometimes called a "formal science" but the term isn't widely accepted. In general: if it doesn't follow the scientific method (which requires experimentation, which mathematics doesn't include) it isn't considered a science. Some mathematical fields do experiment; computational and statistical mathematics can employ stochastic experimental procedure – making them scientific or at least science-like – but they're still abstract and certainly not natural sciences.
- wolfgke 12y ago
  > Mathematics is sometimes called a "formal science" but the term isn't widely accepted. In German this kind of science is denoted as "Strukturwissenschaft" (structural science) to close mathematics and theoretical computer science off (empirical) sciences.