Macatea Book Review: Investigations

This is my guess, not Kauffman's; Kauffman's conjecture is presented in a technical form consistent with traditional statements of the first three laws of thermodynamics. (As a tease, I will leave it for you to discover how Kauffman phrases his proposed 4th law.) Nor is it even clear to me whether in any sense the above guess reduces to Kauffman's guess or vice versa. No matter. We're not fixated on being right here, we're trying to expand how we think about things—particularly the things we think we "understand."

Now, if you're thinking that the four statements above are rather pessimistic and disheartening, let's consider what is still allowed to us: if we can't get out of the game nor even change it, what can we do? Well, we can change our approach, we can change strategies, we can change the way we try to make a living—we can even change our attitude. Nothing in the laws prevents alternative ways of making a living, and experience teaches us that some ways are more effective, more congenial, more satisfying than others.

Kauffman gives us much to think about, and it is clear he wants thoughtful questioning, not easy acceptance. So here is a thermodynamic issue that bugs me. To define thermodynamic work, Kauffman adopts a phrase from Atkins [1], "work is the constrained release of energy." I think this is fine as a characterization of work, but I think it fails as a definition. A gas cooking stove serves to constrain the release of energy for cooking, but the energy in this case is heat not work. The heat created by the stove is from combustion, a chemical reaction, and no thermodynamic work is involved in the constrained release of the heat from that reaction. So the Kauffman-Atkins definition fails to distinguish work from heat.

There is a subtler problem with the Kauffman-Atkins definition, which perhaps prompts Kauffman to remark, "… the concept of work is rather puzzling." (p. 96) Note that the Kauffman-Atkins form defines work in terms of energy; this gets the cart before the horse, for at least in all the developments of thermodynamics of which I am aware, energy is defined in terms of work. Work is defined as a force acting through a distance (or a displacement or a deformation). Force is measurable (by some balancing process) and distance is measurable (by comparing to an standard length), so work is measurable. All forms of work—mechanical, magnetic, electrical, what-have-you—reduce to a force acting through a distance, so force, distance, and work all seem, to me, to be unambiguously defined, measurable quantities. If any of this seems puzzling, get some rulers and force meters and take some measurements.

What has always seemed puzzling to me is not work, but energy. (Thankfully, Kauffman avoids the common intellectual quagmire of thinking there is anything puzzling about entropy. So in this sense, Kauffman's thinking seems more in harmony with mine than it might otherwise appear.) Energy is the generalization of work: we say an energy is something that can be replaced or reduced to mechanical work, such as is associated with a piston-cylinder apparatus. If you ask me what kinetic energy is, I would respond: "The kinetic energy of an object having mass m is the minimum amount of work we have to exert on the object to change its velocity from zero to a final value v." Similarly, if you ask for the potential energy of an object in a gravitational field, I respond: "The potential energy of an object is the minimum work we must do to move the object from an arbitrary datum in the field to its current position." I have no idea how Kauffman would define kinetic or potential energy, for he defines work in terms of energy, and he never tries to tell us what energy is. Energy is left undefined. I'm sure Kauffman would say this doesn't matter, all definitions are circular, so he can break into the circle anywhere he likes. But just because every word in a dictionary is defined in terms of other words doesn't convince me that all definitions have to be circular. And even if they are, some entrances into a circle may be more enlightening—less puzzling—than others. And further, definitions only offer a starting point for exploration; we should move beyond definitions to meanings—relationship among things—otherwise, why write books?

Energy is the name for a class of things; members of the class include all the forms of work, heat, enthalpy changes, etc. Work is to energy in the same way that tomato is to fruit. Kauffman has a happy phrase about evolution, "The strange thing about evolution is that everyone thinks he understands it (p. 19)." Maybe what puzzles me about energy is similar: The strange thing about energy is that everybody thinks they understand it.

Investigations

by Stuart Kauffman

§1. A Fourth Law of Thermodynamics?

Literature Cited