The following is a paper which discusses some of the concerns that many of us in physics have:  that mathematics is the end-all of research.  Math like words are useful in the communication of a theory but neither should replace theory development (a scientific proposition communicated in a logical and clear manner). Editor

Have Equations Taken the Place of Theory? 
           

In physics one gets the feeling that the equations are more respected and are more important than the words used to communicate the theory itself (as one professor of theoretical physics recently assured me in his letter). If this is the case then may the words to follow enlighten…

An equation is something akin to the interaction of qualities (space, mass, etc.) as the essence of more complex qualities (e.g. force). Repetition of the qualities (in quantity) is the real subject matter of the equation, and I fear that physicists, and their brethren, may get carried away with this. Words ("meaningful elements in speech") are better than equations (as argued below), it's just that we probably don't have good enough ones which can be accurately and precisely known because of our lack of understanding. For example while something like “space” is easy to understand, matter and time seems to have “got us.”  The existence of matter and time is unexplained, their definitions being self referential (e.g. "matter is anything with mass," "mass is the attraction of matter for matter" and there's also the inertial definition for mass, still leaving a void in the department of bright ideas on concepts of matter).

Whatever the situation these qualities (time, matter etc) in the equations can only, so far, be defined by words (however bad the definitions are), so the words at least come before the equations. Also, since science is human (an endeavor by man to understand the universe in which he lives) rather than the work product of an omniscient, all knowing intelligence, we require the circumstances which led to an equation’s formulation (e.g. the qualities under consideration, the methods and results) and the circumstances to which it is applied (e.g. we may be looking at a particle circumnavigating a solar system that's a little bit small); contexts which are provided by words. So the qualities in the equations can only be defined by words, as long as the qualities are not secondary (e.g. force, energy; however it would be nice if we could find appropriate words to describe these qualities), plus every equation needs words for its understanding (i.e. definitions) and without which the equations would be meaningless manipulations (there definitely aren't enough words in physics).
            Does modern physics belittle the qualities in its elevation of the measurements (quantities) and their abstract relationships. Certainly the names are getting ridiculous (as if they're less important) e.g. the 'quarks' - up, down, top, bottom, strange and stupid (sorry there's no stupid). Why not nucleon subunit alpha, beta etc or does logic really fly out the window at that level.

Bryan G. Wallace ('the farce of physics') gives some quotes that note the intimidation physicists and mathematicians may like to ascribe to their mathematics. One quote deals with something I empathize with... the lack of explanation for the derivation of an equation in the middle of a research paper, leaving the reader stupefied for not understanding it. He also bandies about the statistic that 90% of what physicists say is understood by less than 10% of other physicists.

It's not that I don't like equations, I think they're hot, it's just that people (scientists, insurers, etc.) shouldn't get too religious with their use. And words, as well as being useful to humans, can be good.

Physics equations may be holy grails for mathematically minded intellects, and when describing boring words like the “angular dynamics of a swirl in a coffee cup” they seem very important, it's just that for other, esoteric things (like time, force, and dimensions with qualities, including qualities like life and consciousness) the words seem more important for true understanding (as a sort of map to a concept), unfortunately we probably don't have the capacity for that understanding, until the appropriate gray matter implants come along. In addition it's not like the words will only become important in the explanation of the fundamentals like movement and time...as illuminatory elements they always are important.

Though mathematics may help optimize scientific practice (for example in genetics where one might want to calculate the melting temperature of a short strand of DNA so he/she can optimize PCR conditions, for example) or in electronics where one might want to know the capacitance) the words are often more important for understanding the science. This is emphasized in a science such as molecular genetics where you won't need many equations to understand the molecules and their functions. And you'll struggle to find equations in a general biochemistry textbook (except for a chapter on enzyme kinetics).

I don't think that understanding the mathematics is the same as understanding the phenomena. Math and equations do have their good points though (the good points might include - their ability to highlight relationships, their presentation, the accuracy and conciseness, their lack of ambiguity, and intellectual joy).

A note of interest - academic physicist Wallace considers the presentation of “scientific” ideas without evidence as "scientific prostitution" for money, status and power. But what's someone like me to do... not search for recognition of an idea that might be true and testable?

Daniel Light

<danielliteau@hotmail.com>