Re: The Limitations of Mathematics in Physics
- From: Baugh <baconbaugh@xxxxxxxxxxx>
- Date: Sat, 14 May 2005 11:08:23 -0400
Oidua wrote:
The Limitations of Mathematics in Physics
"Great spirits have always encountered violent oppositions from mediocre minds." - A. Einstein
The present philosophy in theoretical physics is to search for mathematical relationships that predict experimental results that are then used to verify the validity of the mathematics in defining our physical Universe, from the microcosmic to the macrocosmic. The philosophy was expressed succinctly by Dr. Hawking in Scientific American when he stated that he didn't care about "reality" because he didn't know what "reality" was, all that he cared about was whether the mathematics correctly predicted the results of experiment. Unfortunately, requiring that the results of observation and of mathematics be in agreement is NECESSARY BUT NOT SUFFICIENT in our study of the Universe around us.
You must state the goals of your study before denying sufficiency. It is *sufficient* for prediction i.e. extrapolation of past behavior into the future. It may not be sufficient to satisfy a person's asthetic sense, or emotional need to believe he "really knows what is underneath it all". But this knowledge must come down to faith as it by definition extends beyond what can be empirically confirmed. It is metaphysics as in "beyond physics". Play that game if you enjoy it but don't try to call it *physics*.
As a research tool, mathematics suffers from two basic limitations:
A:- It is a linear logic process rather than an area logic process. Any error along the line of logic being used can easily propagate throughout the remaining logic chain without giving warning of its presence.
But an error along the line of logic means you've stepped outside the mathematics into random noise. It is not a flaw or limit to mathematic
rather a flaw in someone attempting mathematical deduction.
I would rather say that the limitation of mathematics is that it can only rewrite your axioms and definitions in different form. It cannot say anything about anything by itself.
(A solution using an area logic process, on the other hand, is similar to the solution of a crossword or jigsaw puzzle.
You seem to confuse mathematics with the congnative process of mathematicians. Just because one proof is sufficient doesn't many
many alternative proofs are not likewise possible in the same
standard mathematical system. Mathematicians have long found
that alternative chains of deduction for a given theorem is
a very good means to assure no mistake in reasoning has occured.
But mathematics is just rules to an abstract game.
B:- The logic associated with the mathematical treatment of a process can lead to results in regions of the problem domain where another constraint is imposed by Nature.
Yes but the whole point of translating scientific phenomena into mathematical language is that one can re-use well tested chains
of reasoning. The mathematics is a logic template. Nature doesn't
impose constraints on mathematics.
To a mathematically trained physicist such a constraint may well go unrecognized because it is not inherent in the mathematics. The existence of such a constraint may render the mathematical conclusions involved useless.
If the physicist is properly trained in mathematics he will distinguish mathematical inferences from physical ones. It is the poorly trained speculator in physics who thinks his 'reality model' is anything but a mathematical construct.
One would think that rational men would accept that an error had been made in the derivation of the force transformations and search for that error. Instead, it was assumed that the derivation of the Lorentz Transformations for the Forces had to be correct, after all they were derived mathematically.
And heaven forbid anyone should pay attention to the predictions instead of their own opinion about the asthetics of their method of construction. Let's worry about whether the scaffolding used to
construct a building is as durable as the building needs to be.
Regards, James Baugh .
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