Exact terms versus heuristic concepts
– a personal remark

Is there an objective reality that exists without regard to the observer? There are terms of which we can be quite confident that they do refer to an "independend reality", and there are terms that we cannot. What is the difference? Physics can serve as a model to this because its terms are defined mathematically and thus are accessible to this analysis. Moreover, for terms like "temperature" or "atom" the evolution from an heuristic to an exact term can even be traced back in time.


(A somewhat more elaborated article on this subject is available German only by clicking here

I think it is most remarkable and not at all to be expected that some of the concepts we have in everyday life are more than just heuristic. Originally, temperature was not more than this. The term evolved from a sensual perception that things can be warmer or cooler. The quality of the sensation depends on how you feel, it is not &"objective". Take moderately cold water. Put your hand into warm water for a while and then sense that first water sample. It feels colder than when you had put your hand into colder water before feeling the sample's temperature.

Another important example is the term "atom". When Dalton (re-)invented it (1803..1805), it was a mere heuristic concept, useful to explain why the materials in chemical reactions always occurred in the same, constant proportions. But later the concept was found useful to explain a wealth of observations, like diffusion, pressure, crystal structure, x-ray diffraction, convection, and much more. The term evolved to a a extraordinarily powerful and most fundamental concept that can be used to explain every observation or process that can be quantitatively registered. I guess it is this that helps giving us the impression of denoting something "real", that does not depend on an observer.

By far not every scientific concept shares the property of being more than mere heuristics, take hardness or electronegativity for instance. Hardness is not a purely atomic concept, that is, it cannot be traced back to properties of a fundamental concept, nor is its relation to atomic terms evident or simple. Hardness is related to interparticle forces in a solid, but it is not easy to say how, since, for instance, it is also strongly influenced by crystal defects. This is why there are many definitions of hardness that do not give the same result; the hardness of an object depends on how you determine it, and without a mathematical foundation one cannot say which method is "right".

Something similar holds true for electronegativity; this is an intuitive term, used to describe how strongly a bonded atom attracts the electrons of the bond. It is calculated from the "bond energies" of individual bonds in a molecule. The problem here is that the energy of an isolated chemical bond between two atoms of a multi-atom-molecule cannot be measured or even appropriately defined. There is simply no such thing as an isolated bond, this is merely a simplification that helps to clearify things, but you must not take it too serious.

Most interesting, for some concepts like "atom" or "temperature", the evolution from a heuristic to an exact term can be traced back.

As to temperature, the first steps towards an "objective" term were made when it was tried to define a procedure to measure temperature reproducibly. Early thermometers were far from being suited to this. As soon as more precise procedures were available, everybody who adopted one of them could get the same number; in this sense temperature had become an "objective" quantity.

"Temperature" was now "objective" if, and only if, the defining procedure was accepted. It was an operationally defined term. The definition was still arbitrary. No one could tell at this point, if there is something like "temperature" out there in the "universe", or whether it is just a convenient way to speak about things. This is an important limitation of operational definitions. An operational definition constructs what it defines. But "temperature" or "atoms" are believed to mean more than a mere construction.

So how can we be confident that a quantity like "temperature" does "really" exist? After all, it could be just an idea with no correspondence whatsoever to reality, like there are many in history of science, e.g. impetus, phlogiston or caloricum, or the principle of Fermat. It turned out only gradually that there is more to the concept than met the eye. This became obvious only when Kelvin succeded in defining temperature purely mathematically, completely independend of any thermometric substance, basing on the concepts of energy and entropy. Both of these are very fundamental in the sense that any process that can be described quantitatively can make use of them.

Thus temperature is defined based on very general and fundamental concepts. In this sense, because these concepts are that general, temperature can be said to be "universal". Thus "universal" does not mean that the slimy creatures on that very distant planet out there are actually using the same concepts to describe their nature, possibly using the same Kelvin scale <g>.

This means that numbers associated with, say, hardness, are just kind of labels, something like house numbers, whereas temperature is more than a mere label. It is not possible to state with mathematical precision, just as for temperature, what hardness is.

On the other hand, to be able

makes us very confident that an underlying property of physical systems corresponding to temperature must exist independently on the acual definition of the term. In other words, we know that temperature corresponds to something real both because we can reproducibly measure it and because of the existence of an exact, mathematical concept.

Last update Mittwoch, 8. April 2009


© Copyright 1998 .. 2009, Gian Vasta
You may use this text freely for non-commercial and educational purpose, provided you add the copyright notice. Most of the ideas developed here are personal remarks, not widely accepted knowledge. Hence, if you have a good objection, why don't you email me?

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