Friday, August 24, 2007

All odd numbers are prime numbers

There was a joke very popular among graduate students in theoretical physics.
"All odd numbers are prime numbers" someone says.
The mathematician tersely answers: "1 isn't prime. Rule is invalid.". The physicist thinks for a couple of seconds: "Rule is verified for 3, 5 and 7 but breaks for 9. So it is true at the first degree.". The chemist was sitting near the physicist and concludes: "It's true for 3, 5, 7, 11 and 13. So it must be true."
Everyone now turns to the biologist who hesitates: "3 is prime, 5 is prime, err, what was the question again?"

Very unfair joke I agree. Biologists are doing great and hard work. But scientists do study different systems and they have different expectations in term of accuracy.
  • Mathematicians have little tolerance for a proof that has tiny gaps because such demonstrations can yield to a paradox. It is so easy to miss one step and get the end result wrong.
  • Physicists do experiments on very large systems - e.g. they measure the temperature of a gaz that contains huge numbers of atoms of Hydrogen - billions of billions of billions.
  • Biologists observe hundreds of Mitochondria cells under a microscope and adjust the parameters of their model to fit the properties they have measured. Their measurements are statistically less accurate than what physicists typically measure in huge but simple systems - but they are good enough.
  • Pharmaceutical companies and sociologists typically conduct tests on groups of hundreds or thousand of human beings. That's an unacceptably small sample for a physicist. Yet we all come to trust each other. Mathematicians go see their doctor to receive antibiotics or allergy medicine though no one completely and rigorously understands the human immune system.
A good scientist or engineer must know how to do the right approximation. A doctor doesn't care if your temperature is 100.0003 or 99.9997 Fahrenheit. Either way you probably caught your child's flu.

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