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On 2024-10-01 21:20, MitchAlsup1 wrote:On Tue, 1 Oct 2024 15:51:36 +0000, Thomas Koenig wrote:
David Brown <david.brown@hesbynett.no> schrieb:
Science is not a religion.
And as someone (whose name I have forgotten) once said, "Science is
about unanswered questions. Religion is about unquestioned answers."
That is the ideal of science - scientific hypotheses are proposed.
They have to be falsifiable (i.e. you have to be able to do experiments
which could, in theory, prove the hypothesis wrong). You can never
_prove_ a hypothesis, you can only fail to disprove it, and then it
will gradually tend to become accepted. In other words, you try
to make predictions, and if those predictions fail, then the theory
is in trouble.
For example, Einstein's General Theory of Relativity was never
proven, it was found by a very large number of experiments by a
very large number of people that it could not be disproven, so
people generally accept it. But people still try to think of
experiments which might show a deviation, and keep trying for it.
Same for quantum mechanics. Whatever you think of it
philosophically, it has been shown to be remarkably accurate
at predicting actual behavior.
Mathematics is not a sciene under this definition, by the way.
Indeed, Units of forward progress in Math are done with formal
proofs.
Yes, in the end, but it is interesting that a lot of the progress in
mathematics happens thruogh the invention or intuition of /conjectures/,
which may eventually be proven correct and true, or incorrect and
needing modification.
An open (neither proved nor disproved) conjecture often collects lots of
"observed evidence", either by suggesting some interesting corollaries
or analogies that are then proved independently, or by surviving
energetic efforts to find counterexamples to the conjecture. In this
sense an open conjecture resembles a theory in physics.
A list of conjectures:
https://en.wikipedia.org/wiki/List_of_mathematical_conjectures
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