Wednesday, March 3, 2010

Mathematics: The Language of Science

I have occasional e-mails, usually from supporters of some pseudoscience I have challenged on these pages, claiming that presenting the mathematical details on my web sites makes them “too complex” and that I should express the science in 'simpler terms' without the mathematics. 

The language of science is mathematics. 
This is a concept that links back to Galileo (QuoteDB) and is the reason why technology works, because the physical world obeys regular mathematical rules independent of any human belief system.  Scientific concepts are interconnected by the rules of mathematics.  Much has been written about why nature seems to work so well with these techniques (one of the most famous papers on this topic being  “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” by Eugene Wigner.  But all mathematics does not make valid science.  One of the goals of research is to determine which subset of mathematical principles apply in various physical and experimental configurations.

Regardless of why it works, the simple fact is that it does work.  The beauty of this is that mathematics provides a rigorous framework which facilitates communication of scientific ideas

This is why the pseudo-scientists rarely challenge my posts with strong mathematical content.  Most physics-related pseudoscience is communicated not by the rigorous language of mathematics, but by nuanced re-interpretation of terminology and rhetorical tricks.  Pseudoscience is communicated among its supporters more like politics than science.

Do I care that some of the analyses I present on this site are complex? 
One should note that this site actually has a surprisingly broad audience, ranging from high-school science teachers to Ph.D. astronomers who occasionally have to deal with these issues in their classrooms.  I attempt to present the information at the lowest mathematical level needed to illustrate the point.  Most of the mathematics I've presented on this site should be comprehensible to anyone familiar with high-school algebra and physics.  There are only a few pages where I have presented anything at a higher level, such as calculus and differential equations (which are the real workhorse mathematical tools of physics).

I present the details of these analyses because this is how REAL science is done.  Some teachers have expressed interest in using my material as a teaching tool in the classroom, providing examples of how science can test various claims and rule out ideas that don't work.  In science, the ability to identify junk science is just as important, perhaps even more important, than pursuing leading-edge research.  Instructors who wish to use this material usually have the scientific knowledge to distill it to a level for their target audience.

Could my material be presented in 'simpler statements'?
It is certainly possible that complex scientific topics such as Eugene Parker's solar wind model or forbidden spectral transitions could be explained in a few simple sentences, but such explanations would be of little scientific value.  Both of these topics leverage underlying concepts such as fluid dynamics and quantum mechanics that are complex in themselves.  Could an electrical engineer explain the operation of the semiconductor material in a transistor or VLSI chip (the heart of the computer you're reading this on) in a few simple sentences in a form that is scientifically useful and accurate?

When real scientists express their results in 'simple statements', there are usually many actual measurements and numerical models to back it up.  In the case of my refutations of  c-decay or the Electric Sun model, I demonstrate that I have done an actual analysis of the idea and compared the predictions to actual data, not made up a story.  After that, I may use 'simple sentences' to describe the results and some aspects of the mechanism, but I'll usually link to where I've done the work.  I show my assumptions and their consequences. 

The application of mathematics forces honest scientists to explicitly or implicitly define their assumptions, and let the laws of physics work out their implications. 

But even my analysis is not absolute.  Anyone who wishes to challenge my results can see exactly which assumptions I used, modify their assumptions, and redo the analysis.  However, the challenger must still play by the same rules.  If their rebuttals consist of whining that I “didn't include the (unnamed) non-linearities“, or “it's really electrodynamic“, then they are just spewing useless technobabble, indistinguishable from mutterings in really bad television science-fiction.

If the challenger insists that the standards of science be lowered to accommodate their less rigorous analysis, then they are basically admitting that they are doing pseudoscience.  The supporters of Intelligent Design discovered this in Dover, PA (Wikipedia).  The Electric Universe supporters seem to attack all mathematical models which generate predictions that they don't like, while producing no testable mathematical models themselves.

So when the supporters of pseudo-science complain about how difficult I'm making it for them to 'participate in the scientific debate', by pushing them to show that their claims meet the standards of real science, I know I'm doing something right.


Khakjaan Wessington said...

A Lie is Just an Alternate Epistemology [Today's News Poem, March 4, 2010]

“The linkage of evolution and global warming is partly a legal strategy: courts have found that singling out evolution for criticism in public schools is a violation of the separation of church and state. By insisting that global warming also be debated, deniers of evolution can argue that they are simply championing academic freedom in general.”
--Leslie Kaufman, New York Times, March 3, 2010

Deception always wins because the truth
Meets the biggest lies at middle ground,
And being truth, it cedes enough terrain.
Method needs Good Faith of trade to sleuth,
Or else the brazen slur their twists to sound
Truthful. Words resemble air for brains—
A poisonous miasma we must breathe:
Venom hides in words deceivers seethe.

W.T."Tom" Bridgman said...

Bob Grumbine has some comments about dealing with mathematics issues at MoreGrumbineScience.

Do I have to be good at Math to be good at Science?

Coping with Math

His audience and goals are a bit different from mine.

Penguindreams said...

No surprise to you that while my nominal audience and goals for it are different than yours, that I am in agreement with you.

One point your critics (complainers) fail to observe is one I mention in 'Do I have to be good ...'. Namely, math can be unavoidable in some areas. The solution is not to whine about math being present and necessary, it is to find someone who is good at the math needed, and enlist their aid. Or grit your teeth and learn the necessary math yourself.

A quite awful paper got published last year (how is still a mystery) in which the prime failing was that nobody involved understood the necessary mathematical concepts. The concepts involved were not very involved, at least at the conceptual level, so I took that up as well. How not to analyze climate data. If they'd learned the math themselves (3 authors), or at least enlisted the aid of a 4th person who understood sophomore time series analysis, they might have been able to make a contribution.

Troythulu said...

Hey, Tom. An informative entry, and I'll make sure to cite it and any other material of yours in any posts I publish dealing with the relevant subject matter. I'm in the process of rewriting the Electric Universe entry on my own site that you commented on a while back, starting from scratch, since it was severely in need of corrections and updating. It's currently offline as a draft. It's like you said to me: Credit is everything.