Search This Blog

Heat: Science vs. Math

This has been an interesting week.  I have been trying to get a handle on the issues and dynamics that have resulted in global warming.  Mainly, I have been trying to understand the actual systems involved and the physical processes upon which they operate.  I am not content to know the statistics or the summaries of multinational government commissioned studies.  I want to understand how these systems work... how heat is generated, where it comes from, how it is effected by all of the other earth systems, the very physics of heat and energy and systems in which it is transfered.

I have a good generalist's grasp of the standard model, of modern science, of modern cosmological theory, of mechanics and relativity.  I have more than an average pedestrian understanding of quantum theory and try to keep up with all of the sundry speculative theories heading towards a grand unified theory (string, multi-verse, etc.).  I am an adherent of a skeptics perspective, I am an atheist in the truest sense... not just as applied to religion or belief, but in all aspects of philosophy.

If something is true, I assume that it will agree with everything that has ever been measured.

Read that sentence again if you have to.  Which makes me a restrained dreamer.  I love to speculate, but I know that speculations need to withstand the test of agreement.  I will write another post about this concept soon... stay tuned.

Anyway, in the process of trying to understand the physics underlying global warming, I have googled and searched and read and asked and I am having trouble getting to the dynamics, the physics of the causal processes.

It's not as if there is a lack of information... there is book after book after web site after web site that contain the mathematics, the formulas that engineers (and scientists) use to calculate the parameters of heat systems.  The math is solid and well tested.  But nowhere have I found causal explanations of heat processes.

In particular, it seems obvious that heat straddles two worlds: the world of classical mechanics and the world of relativistic/quantum radiation.  Chemical heat is the jiggling of atoms and molecules within the confines of the strength of the magnetic fields that hold them together.  When considering chemical heat, transfer demands a physical medium.  There has to be actual atoms and molecules physically bouncing off of one another's magnetic charge in order for this kind of convective heat to travel.  But there is also radiative heat, where the atoms and molecules stay (relatively) put, but a photon is somehow produced and released, and that can then transfer some of the energy of those objects through space (at light's speed).

I have seen and trust the math, the formulas.  But that doesn't tell me how chemical heat and radiative heat actually cause each-other.  When I ask other scientists, I am pointed to the formulas.  

This is disappointing.  I am sure that much of the convenience of modern life is the result of people who work the engineering trenches, who diligently plod forward through the unquestioned use of the treasure of mathematics that has been slowly invented to crunch practical solutions... to get stuff done!  But some of us should at times attempt a deeper causal understanding.

Real life is much the same.  I am not weighed down by the implausible complexity of the rules of english grammar while I write these sentences... I just write.  Still, it behooves me to spend a few moments each year pondering the larger issues... what is language?  What is information?  What is the relationship between rules and data?  How is information produced?  What is the difference between language and meaning?  Between object and abstraction?

Science is powerful precisely because it has made it a point (the point) to demand agreement between ideas and measurements.  You can say anything you want about the unknown.  However, what you say, no matter how wild, no matter how crazily it predicts measurements that have not yet been made, it absolutely has to agree with everything that has already been measured.  This is big... and, it is lost on most non-scientists.  It is even lost on many scientists.  Einstein's relativistic theories pointed to dramatic and un-intuitive ideas about physics at energies and accuracies we had not yet encountered... but they did not argue with any measurements that had already been made (using Newtonian maths).

What Relativity did do, was provide a better model or abstraction, one that explained the mechanics that give rise to the classical properties and behaviors we measure in every day life.  It said, "You already have the math... here is a new math built upon a a more robust model that shows exactly WHY the old math works (and more)."

As our models get better, we gain deeper understandings of the why underneath the phenomena.  Knowing why helps us dig deeper towards even better models, abstractions, and the maths we use to calculate and predict.  But as our models get better, we are increasingly in danger of confusing them with the reality they map.  A model might perfectly map a reality, but it still isn't that reality.  If we obsess on our maps, if we train our telescopes upon the map on our table instead of the stars outside, we forfeit the power of the map.  At the same time, if we don't vigilantly question and remain aware of the differences and similarities between map and mapped, we forfeit the power of reality. 

I remember a story I once read about Richard Feynman.  While an undergraduate he would wonder the halls of the graduate department... looking for frustrated researchers.  He met a person working on a quantum explanation of optics.  Newton and others had gifted us with formulas that worked just fine predicting the behavior of light in interaction with other materials like lenses and mirrors... what light does.  This grad student was trying to dig deeper... to understand WHY light did what it did in the presence of other materials and forces.  Well, supposedly, Feynman went off that night and did it... explained optics at the quantum level (and muddying the career options of a fellow student?).  The old Newtonian math still works just fine... is used in most circumstances... but now we know why it works, what causes it, and this gave us insights into whole new worlds of the possible (predicting materials that would reverse light on incident... mirror mirrors that we have since built, and ways of slowing light down to a stop!).

The danger of shortcuts, (and all math is a shortcut... even Einstein's and Feynman's), is that because it works, the more we begin to believe that the abstraction, the math, the shortcut, IS the phenomenon.  We fall in love with and are blinded by the scaffolding.  The physics we use to explain reality, and the math we use to perform calculations based on that physics are not always very good explanations of the phenomena they represent. Often, they are just practical necessities.  Crutches, saws, recipes... methods blind to meaning.  Methods so beautiful, so useful, that they often obfuscate meaning.

Do you remember that day in middle school math class when the teacher introduced the concept of number bases?  I was blown away when I was forced to realize that most of my hard won understandings of "math" were in fact just arithmetic tricks to do calculations in a counting system that could just as easily have had 1, 13 or 649 digits, could just as easily not had digits at all!  That was the day I first saw the difference between mathematics and arithmetics.  But there is an even more profound difference between science and mathematics.

Once, I had a T-shirt made that said, "The Map Is Not The Territory. But The Map Is Territory".  I was trying to remind the postmodernists who had taken the subject/object split to far... that any abstraction, any scaffolding, any map, any formula was itself a thing, and that that thing was subject to the exact same physical restrictions as any other thing.  The word "house" is subject to different combinations of physical forces than those effecting any real "house" it might represent... but abstractions are things and the minds that processes them are things as well.  No magic needed.  The difference of course is that we construct abstraction systems exactly and precisely to be more flexible than the stuff we model in them.  I can say "I ate my house" without breaking any of the physics (the grammar) of the English language.  Actually having eaten my house would probably not be possible. Language rides the fence between the flexibility needed to play what-if's and the rigidity necessary to honor reality.

So, if anyone can climb outside of the arithmetics of heat formulas long enough to help me understand the actual causal interplay between mechanical heat and radiative heat... please don't be shy.


This content is not yet available over encrypted connections.