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**Just Chat! / Re: Mathematics is a decent science.**

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**Today**at 09:17:47 »

Mathematical proofs are absolute deductions from clearly stated axioms. So mathematical knowledge, in the form of standard formulae and solutions, grows by expansion with no culling.

Scientific proof is closer to "proof spirit" or the German Prufung - a test. Scientific knowledge is the residue of explanatory hypotheses that have not been disproved by experiment, so it grows almost by contraction towards "unified theories" and the like, and scientific data, the measurements that we use for engineering and for investigating the validity of our hypotheses, grows by expansion and refinement.

The bit in between, where we use known mathematics to model our observations and make predictions, is intellectually treacherous: as can be seen from many threads in this forum, it is tempting to believe that the model is the reality. The simplest case of the behavior of light, demonstrates that you sometimes need two very different models to predict the result of a single reality.

Scientific proof is closer to "proof spirit" or the German Prufung - a test. Scientific knowledge is the residue of explanatory hypotheses that have not been disproved by experiment, so it grows almost by contraction towards "unified theories" and the like, and scientific data, the measurements that we use for engineering and for investigating the validity of our hypotheses, grows by expansion and refinement.

The bit in between, where we use known mathematics to model our observations and make predictions, is intellectually treacherous: as can be seen from many threads in this forum, it is tempting to believe that the model is the reality. The simplest case of the behavior of light, demonstrates that you sometimes need two very different models to predict the result of a single reality.