Quote:
Originally Posted by Fadingstar
Mathematics: Truth or Tool?
This is a kind of appendum to the thread I made on the unified theory.
It was always my understanding that mathematics was a tool to be used to confirm what we believe to be the truth where it is applicable, and to make sure that conformity is met.
Planetary orbits are plotted, distances measured, designs passed from architect to builder etc etc...
Yet now it seems that if mathematics says it is - then it must be so. It has become the truth of the thing.
And the scientific community seems to be embracing this. Does being the fact it looks good on paper make it so?
I note that in most ATM discussions the first cry is - "Show us your equations!"
But if the equation for the multi-verse was shown would everyone go "Ok, fair enough, it must be mainstream"
Maybe I'm just seeing the thorny bit of general scientific views here, or being a stick-in-the-mud and having my own views on the thing, but I would be interested in BAUT member's feedback on how they feel mathematics should be used, and how far you can take it.
Is it just a tool, or has it become something almost akin to a deity that we most follow without question?
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Mathematics comes from the Greek "learning" which comes from the Egyptian "Maat, Truth Order and Justice". There are three claims for mathematics and God. God has power over mathematics, God is mathematics and God is obedient to mathematics. Kurt Godel shows limits on mathematics but mathematics is none the less a powerful tool.
All the comments about mis-using or mis-applying the tool are correct. Science has two aspects observation and reasoning. Mathematics is useful in reasoning. Especially in long trains of reasoning far from observations.
Observations are not omnipotent and are often erroneous.
Physicists desire that a displacement in the direction of force should be called "energy" en-ergy (energy in). When Quaternion mathematics and observation shows this is ex-ergy (energy out). There are times when mathematics is smarter than physicists and their observations.
A very important example of this is the story of quaternions. Here the laws of mathematics were set aside to follow the laws of "observation". Quaternion Mathematics says dropping a ball releases energy as the displacement and the force are in the same direction. Lifting a ball absorbs energy because the displacement and the force are in the opposite direction. Quaternion rules are observed in nature but physicists "vector mathematics" use a different rule: I^2=J^2=K^2=+1. This Vector Rule causes non-associativity:
(II)J=J but I(IJ)= -J.
Today, quaternion mathematics ,a very powerful mathematics, has been set aside by poor observations. 4D spacetime is quaternion but physicists insist on Minkowski "mathematics" for 4D spacetime. The Universe is Quaternionic, says mathematics, the operation of the Universe is non-commutative and supports a division algebra, i.e. Ax=b is true for physics.