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People, trucks and even military tanks have tried and failed the task of pulling apart two phone books lying face up with their pages interleaved, like a shuffled deck of cards. While physicists have long known that this must be due to enormous frictional forces, exactly how these forces are generated has been an enigma – until now.
A team of physicists from France and Canada has discovered that it is the layout of the books coupled with the act of pulling that is producing the force.
http://phys.org/news/2015-08-mystery-impossible-interleaved.html
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The Mystery of Why It's Impossible to Pull Apart Interleaved Phone Books - Solved
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(Score: 2) by Zinho on Friday August 28 2015, @04:02PM
So they are replacing science (empiricism) with rationalism (math).
Not at all. They are replacing ignorance with enlightenment, and using science to do it. Many similar efforts have in the past created useful models for the world around us; F=ma and E=mc^2 are famous examples, and familiar to even grade school children.
Where you appear to be mistaken (and the probable reason for your troll mod) is that the difference between empiricism and rationalism isn't the use of math, but the use of experiment to test our reasoned speculations. Rationalism is great at coming up with reasonable explanations for phenomena we observe, but can lead us to wrong conclusions when we have incomplete knowledge of the subject. Empiricism takes the reasoned speculation from rationalism a step further and verifies or refutes the reasoning based on a test.
The current topic for discussion, friction between interleaved books, is a great example. There were several theories proposed for how the friction was caused, all of which were inadequate because they did not account for significant factors of which their proponents were unaware. An approach based on rationalism would simply say "my explanation makes sense, so it must be the correct answer", and continue to be incorrect. The latest experiments, reported on in TFA, disproved the theory that friction would increase linearly with the thickness of the books, found out what the true relationship is, then created a model suitable for making accurate predictions. That model was then tested for validity.
Math as a tool in empiricism is fine. In this case, it brought a poorly-understood phenomenon from the realm of "here's a table of past results" to "here's an equation you can use to design new inventions around this phenomenon". As long as there's a test involved to verify the validity of the equation math will hurdle the gap from rationalism to empiricism with style.
"Space Exploration is not endless circles in low earth orbit." -Buzz Aldrin