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Math versus Science

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Because mathematics appears to be absolutely predictable -- and because nothing else is absolutely predictable -- practically every thinker since the conception of mathematics has attempted to apply mathematics to their thinking.
 
Those most successful in making use of mathematics are called scientists; those least successful, charlatans.
 
What do we mean by successful?  Someone is successful in their thinking if they can predict events based on their thinking.  Success appears to be a qualitative word in which one can talk about success in terms of a scale that ranges from total failure to complete success.  A weatherman, thus, may be 70% successful in predicting the weather and a chemist 99.99% successful in predicting the outcome of a simple chemical reaction (where failure is almost always explained away in terms of slight impurities or imprecise measurements).
 
Any true mathematician is aware that nothing in the real world is perfectly measured by mathematics.
 
Even something as simple as one plus one equals two has no perfect fit on the material world.
 
Solipstically, one can point out that if one adds one pile of sand to another pile of sand, one does not get two piles of sand.  But this can be dismissed as a word game.
 
However, something that seems like a word game actually turns out not to be:  Take a sweet apple and a sour apple.  What do you have when you bring them together?  Two apples?  Yes, in a way.  But you don't have two sweet apples and you don't have two sour apples.  The apples can only be "added" by losing preciseness.  If you are baking an apple pie, a good cook will be daunted by this impreciseness.  The amount of sugar needed will vary depending on the tartness.  Two apples is simply inadequate as a description.  Moreover, one sweet apple and one sour apple will not work either, because the sweet apple might weigh twice as much as the sour apple and this too will affect how much sugar is needed.
 
When a scientist borrows from the world of numbers and attempts to use that world to predict an outcome, the scientist might or might not realize that precision has been lost.  There is no such thing as a perfect centimeter, a perfect hour, a perfect kilogram -- except in the rarified universe of Plato, and then only as an Ideal, a concept clearer to Plato than to many scientists today.
 
No instrument can measure beyond its own imprecision and that imprecision is immeasureable precisely itself.  In fact, in the world of mathematics, imprecision itself is an entire branch, so powerful is its implications.  Any any mathematician studying that branch can inform you that for an unknown function, imprecision is not predictable.  Probability Theory is itself a feeble attempt within the world of mathematics to gain control of the imposition of mathematics upon the real world.  This feebleness is most evident when one considers that most statements within the world of probability read something like this:  "The probability of this event is 99%; and the probability of the prior statement being true is 95%; and the probability of the prior assertion being true is 84.6%; and ...."

It seems ignorant (or perhaps Jesuitical) to make the assertions I have made above.  But appearances aside, the assertions are true; and we have already seen the consequences.
 
Sir Isaac Newton thought (along with fellow physicists for many years) that he had successfully imposed mathematics on the world of motion.  And indeed he had ... for objects not moving "too fast".
 
Then Albert Einstein came along and proved that motion was not so easily pinned down.  His own complex theories (mathematically) modified Newton's laws to make a more precise codification.
 
And we thought that was that.
 
Now, in relatively recent years, it has come about that even more modifications may be necessary.
 
Of all the sciences, physics is the one that seems to have best applied the theories of mathematics.  And yet the math of physics is still open to questions, in large part because physics has had to bend the universe in order to apply mathematics.  The theories of physics relies on materials that are perfectly formed, are unflawed, are describable by equations.  In other words, physics is only perfectly fitted to idealizations that don't occur in nature.  The moment we examine the real world, those idealizations become imperfect and to the extent of those imperfections so too does the predictions of physics become imperfect.