Sep 072004

Tomorrow. Did I say tomorrow? I meant the last syllable of recorded time.

Now where were we? Oh yes: nowhere. Philosophy to date has yielded no explanations, no predictions, no tools unless we classify logic generously, and very little practical advice, much of it bad. And then from “cogito ergo sum,” or “existence exists,” philosophers expect to explain the world, or at least a good chunk of it. Tautologies unpack only so far. No matter how much you cram into a suitcase, you cannot expect to fill a universe with its contents.

I was a little unfair to the Greeks in Part 1. They didn’t have 300 years of dazzling scientific advance to build on. What they had was nothing at all, and as Eddie Thomas pointed out in the comments, you have to start somewhere. But 2500 years later, do we have to start from nothing all over again? In what follows I will take for granted that the external world exists, that we are capable of knowing it, and doubtless many other truths of metaphysics and epistemology that everyone knows but philosophers still hotly dispute. If you want to argue that stuff, the comments are still raging on Part 1.

I propose to begin with the First and Second Laws of thermodynamics. You can follow the links for some helpful refreshers, but in brief, the First Law states that energy is always conserved. It is neither created nor destroyed, merely transferred. And since we know, from relativistic physics, that matter is merely energy in another form, we conclude that everything that ever happens is an energy transfer.

This profound fact about the universe has gone almost entirely unnoticed by philosophers, whether from ignorance or indifference I cannot say. But it leads almost immediately to two other profound facts. First, all events are commensurable at some level. They are all instances of the same thing. Second, all events are measurable, at least in theory. We need only to be able to measure each thermodynamic consequence, and add them all up.

Now let’s set up a little thermodynamic system. Call it Eustace. Eustace need not be biological, or at all fancy; it is best to think of him as just a cube of space. Eustace would be pretty dull without a few things going on, so to liven up matters we will assume that at least something in the way of atomic state change is going on. Particles will dart in and out of our little cube of space.

To describe Eustace, we have recourse to the Second Law. As ordinarily formulated, it states that energy, if unimpeded, always tends to disperse. Frying pans cool when you take them off the stove. Water ripples outward and fades to nothing when you throw a pebble in a still lake. Iron rusts. Perpetual motion machines run down. Rocks don’t roll uphill.

Vast quantities of ink have been spilled in attempts to explain entropy, but really it is nothing more than the measure of this tendency of energy to disperse.

The Second Law is, fortunately, only a tendency. Energy disperses if unimpeded. But it is often impeded, which makes possible life, machines, and anything that does work, in the technical as well as the ordinary sense of the word. The lack of activation energy impedes the Second Law: some external force must push a rock poised atop a cliff, or take the frying pan off the fire. Covalent bond energy impedes the Second Law as well, which is why solid objects hang together. The Second Law has been formulated mathematically in several ways. The most useful for describing Eustace is the Gibbs-Boltzmann equation for free energy, which states:


This is one of the most important equations in the history of science; it has been shown to hold in every context that we know of. The triangles, deltas, represent change. Gibbs-Boltzmann compares two states of a thermodynamic system — Eustace in our case, but it could be anything. As for the terms: G, or free energy, is simply the energy available to do work. The earth, for example, receives new free energy constantly in the form of sunlight. Free energy is the sine qua non; it is why I can write this and you can read it. It does not, unfortunately, necessarily become work, as no one knows better than I. Let alone useful work: this depends on how it is directed. I do work when I paint your car and work when I scratch it.

H is enthalpy, the total heat content of a system. We are interested here in changes (Δ), and since we know from the First Law that energy is neither created nor destroyed, that nothing is for free, any increase in enthalpy has to come from outside the system. T is temperature, and S is entropy, which can be either positive or negative. Negative entropy is, again, good; it leads to more free energy by subtracting a negative from a negative. Positive entropy is what you lose, and one of the consequences of the Second Law is that you always lose something.

To return to Eustace, we know from the First Law, in the terms of the equation, that ΔG >= 0. We will also assign Eustace a constant temperature, which isn’t strictly necessary but simplifies the math a bit. So we have:

ΔH – TΔS >= 0

We are dealing here with sums of discrete quantities here. Not one big thing, but many tiny things. Various particles are darting around inside Eustace, each with its own thermodynamic consequences. Hess’s Law states that we can add these up in any order and the result will always be the same. So we segregate the entropic processes into the positive and the negative:

ΣH – TΣS negative – TΣS positive >= 0

From here it’s just a little algebra. We take the third term, the sum of the positive entropies, add it to both sides, and then divide both sides by that same term, yielding:

α = (ΣH – TΣS negative) / TΣS positive >= 1

And there we have it. Alpha (α) is just an arbitrary term that we assign to the result, like c for the speed of light. The term TΣS negative (the sum of the negative entropy) is always negative, so the higher the negative entropy, the larger the numerator. And alpha is always greater than or equal to 1, as you would expect. One is the alpha number for a system that dissipates every last bit of its enthalpy, retaining no free energy at all.

Alpha turns out to have several interesting properties. First, it is dimensionless. The numerator and denominator are both expressed in units of energy, which divide out. It is a number, nothing more. Second, it is calculable, at least in principle. Third, it is perfectly general. Alpha applies to any two states of any system. Fourth, it is complete. Alpha accounts for everything that has happened inside Eustace between the two states that we’re interested in.

Which leaves the question of what α is, exactly. It can be thought of as the rate at which the free energy in a system is directed toward coherence, rather than dissipation. It is the measure of the stability of a system. And this number, remarkably, will clear up any number of dilemmas that philosophers have been unable to resolve. Not to get too far ahead of ourselves here, but I intend, eventually, to establish that the larger Eustace’s α number is, the better.

Next (I do not say tomorrow): From physics to ethics in one moderately difficult step.

Update: Edited for clarity. So if you still don’t understand it, imagine what it was like before.

  79 Responses to “The Disconsolation of Philosophy, Part 2: Among the Ruins”

  1. CT:

    I am not sure about what you meant by "pre-BB." Do you mean before anything?

    Time is a human construct. But so are mathematics and science. But they are constructs of something that is naturally there. We have just put labels on it. We’ve had to quantify things so we invented time. Time is the logger of events.

    For human purposes, time is important. We know how important it is if one is late, time wise, and misses an event.

  2. Pre-BB – pre-Big Bang (note that this is not the same as before anything tho it is before time).

    How can time and mathematics be both something that is naturally there *and* human constructs? Perhaps you mean as we use them and understand them they are interpretations of something that exists irrespective of human thought, desires etc..?

    If time is the "logger of events" as you say, than without events there is no time as it has nothing to log. In this sense then events do in fact create time. In the abscence of events, there is no time and if someone disagrees I should very much like to hear 1) what this event-less time is and 2) how is it measured.

    Time is important in all sorts of ways that have nothing whatsoever to do with human purposes or with a human desire to quantify or be punctual. But all of these things are dependent on event transaction. No events, no time. Things exist without time (see pre-BB), but time does not exist without things. So time is not the ether in which events occur as this implies that time could be divorced from events and exist on its own. It cannot as there is no there there.

  3. Ct,

    I suppose I don’t understand time in space. But I do know when I see it, on the wall, in the form of a clock. That’s all that matters to me.

    I suppose history is a form of time. History is a chronology of events. Without time passing there would be no history. So for those who say events make time, time being like history, its true, because events make history, or time.

    I think this time argument is somewhat of a syllogism.

  4. aaron,

    your previous two posts are fabulous. i read some stove after you said 95 % of what you said was him.

    here is something i have compiled for you from a paper he wrote to tell you what is wrong with the thoughts of the greatest philosophers of human thought.

    he says: I have been saying that we need a nosology of thought, and that it would not be – various things. What it would be, I have admitted I do not know. My main object, however, is to convince you that no one knows: that the nosology which we need has not yet even begun to exist: that thoughts – as distinct from sentences, or inferences, or character, or information – can go wrong in a multiplicity of ways, none of which anyone yet understands.

    and i think this is the most brilliant thing he has ever said because you should note the way he bases an entire book on this sentiment, and that his conclusion is derived from an obvious, to him, and he loves to say how obvious it is, but an obvious lack of nosology of thought.

    well, he didnt actually even know what nosology is. see, isn’t that brilliant.

    he means nosology the way one would mean pathology in a sense of catalogued and classified and decompressed (not "decomposed" as you say in your explanation of what happens during an explanation)parts of a whole that, unto themselves, signify a step by step structure of present and actual verity.

    i know you don;t know what nosology is (your starff prolly hasn’t told you) so i will tell you:


    Pathology \Pa*thol"o*gy\ (-j[y^]), n.; pl. Pathologies (-j[i^]z). [Gr. pa`qos a suffering, disease + -logy: cf. F. pathologie.] (Med.) The science which treats of diseases, their nature, causes, progress, symptoms, etc.

    Note: Pathology is general or special, according as it treats of disease or morbid processes in general, or of particular diseases; it is also subdivided into internal and external, or medical and surgical pathology. Its departments are nosology, [ae]tiology, morbid anatomy, symptomatology, and therapeutics, which treat respectively of the classification, causation, organic changes, symptoms, and cure of diseases.

    he of course was refering to a disease of thought? but a disease is

    A pathological condition of a part, organ, or system of an organism resulting from various causes, such as infection, genetic defect, or environmental stress, and characterized by an identifiable group of signs or symptoms.
    A condition or tendency, as of society, regarded as abnormal and harmful.

    so, of course, his idea for their being a lack of nosology may just come from the fact that people, other than him, do not see in thoughts a condition or tendency that is abnormal or harmful, in and of themselves, only in such a way that they express something, disregarding of course what they express, which, as he says, is immaterial, focusing as he does on what they are expressions of….

    you are stupid

  5. thanks for deleting all my posts im sure it wasn’t because they were accurate and critical of you but rather because they were not accurate and critical of you

  6. Professor Stove (he dead):

    I try to run an open forum here but I cannot do so without the cooperation of my readers. People who cannot take criticism do not run blogs with open comment sections. If you browsed the archives a bit — or even the current threads — you would find plenty of critical commentary. Sometimes it has induced me to change my mind, which I always do in public.

    I deleted your previous posts because they heaped personal abuse on my commentators, my readers, and me, in order of importance. Even so I had misgivings. You were obviously trying to get at something, though I couldn’t figure out what, and neither could anyone else. I will let these stand because they contain comprehensible content. But if you wish to continue to post here you will have to observe the same standards of decorum the other commenters do. You might begin by not concluding posts with "you are stupid."

  7. Of course, I was being childish and asinine and taking great pleasure in it because i was on drugs, and so I apologize.

    however, one more point, this concerning the "good professor" vos post…

    he mentions liking your attempt at building philosophy from some correct thermodynamics (odd that you did not mention to him your ideas about the worth of philosophy from part1), but, he notes, he is assuming you are going to take these philosophies and head "towards nonequilibrium Thermodynamics, and some nonreductionist emergent behavior concepts."

    I would like to briefly pin point weak instances in your argument and then show the good professor what my argument, using the corrected and newly defined points from your own, would look like concerning the areas of extrapolation he sees you going into. Tell me if I was fair to your conceptions please.
    Philosophy to date has yielded no explanations, no predictions, no tools unless we classify logic generously, and very little practical advice, much of it bad.
    I would say philosophy does nothing but yield predictions explanations tools and practical advice. However, who would practically use such things is a matter of dispute, on which (the dispute) of course you see yourself having never used such practically, where such means advice from a philosopher. You have not used their tools, their explanations or noticed their predictions. Ok.

    But let me say that a prediction is nothing other than a set of understood ideas taken for granted that, when considered so, should show what will of course come to be, where the set of understood ideas include the ideas that things happen, and that they happen in a noticeable order. Perhaps you simply meant it has yielded no accurate predictions.
    I say too that an explanation is nothing other than a happening provided for by reason. One explanation may suffice for some, while others need yet another. This is because reasons make sense to people, and people are different. So it will of course take different reasons to make sense to such a disparate lot as humans.
    I would also like to note, much like I imagine your hero David Stove would, that not seeing the reason in an explanation to be of sound principle and actual precedence and empirical basis does not mean you have not used to explanation. You have used it to show yourself what is not so, as well as come a little closer to understanding what is. Thank your judgement for that, or you would believe everything always. There is more to be winnowed here but I leave it for you to do, as there are much more important matters to discuss in your paper.
    …philosophers expect to explain the world, or at least a good chunk of it. Tautologies unpack only so far.
    A tautology is an idea repeated over in a different way, again and again, such that the repetition serves only to further state the repeated idea and not actually enhance it or add to it. A tautology is also a statement that is composed of smaller statements that, when considered, say something logical and verifiable no matter whether each simple statement is true or false, like, say, Tomorrow the sun will not rise, or it will, or I suppose, a third thing involving rising or not but that is not actually either but that contributes and enhances both by demonstrating a new and unique but still relevant idea or happening. I take it, when you say unpack, that you mean to remove the contents of something and not that you mean to, say, take a back pack off. So of course a tautologys contents can only be removed so far, by which Im sure you meant on so many instances, or more colloquially, so much because, to you, it is a statement of limited capacity. This does nothing to refute or discredit philosophy, however, unless we were discussing the infinitely applicable application of tautology to innumerably indicate indefinitely such that it does so so-on and into forever. But let me say, that when you mention that philosophers only go for a good chunk of explanation you are already delimiting their tautologies to a finite application and worth, else you would have said infinitely more than a good chunk. Essentially what you are doing is damning philosophy by arguing its argument for it by describing how much it might accurately expect to explain, and then saying that because of this lack of explanation it might only unpack so much. Well of course that is so. You just made it that way. Moving on.

    Wait, I will stop. Now I will ask you would you like me to post or email the continuation of this idea, because I do what I have done to your first paragraph to your entire paper, and then, from the ashes of your really brilliant ideas, together we go exploring what the good professor talked about us doing. Now, I would like to note that I have done nothing intellectual or analytical in the past three years having sold drugs and been a fucking loser, and until I accidentally found your website I hadnt tried using my brain for many moons. So thank you, thanks to your forum, and tell me whether or not you want to see the rest its really long. Before I read your paper I did not know what thermodynamics were, nor what was meant by the failure of homologous chromosomes to break apart into separate sets in the reduction division of meiosis with the result that some gametes have the diploid number of chromosomes nor how such might relate to a philosophical application of thermodynamics and the limitation of axiomatic and empirical truths and the emergence of certain interesting behavior concepts, or perhaps more accurately both an abundance of and a glaring lack thereof. Sorry about being a dick but Im kind of one anyways.

  8. it occurs to me also that disconsolation would be something like grief correct? what are you meaning? disconsolate means gloomy or defected i thought… this was not included in the corrections of my paper so i thought i would add it 🙂

  9. dejected not defected…

  10. ps you are stupid at the conclusion of the paper was kind of me saying that to you but it was more so saying what he was concluding about the thoughts of others in his examinations… sorry about the confusion and the entendre

  11. People,

    How did things happen to get so way off subject?

  12. airth i wrote you my response on dialectics

  13. here is my initial critique of alpha theory 🙂

    following will be an examination of this application into the topics noted by the good professor including nonquilibrium and nonreductionist emergent behavior concepts… here is the continuation of my post above…

    I was a little unfair to the Greeks in Part 1. They didn’t have 300 years of dazzling scientific advance to build on. What they had was nothing at all, and as eddie thomas pointed out in the comments, you have to start somewhere. But 2500 years later, do we have to start from nothing all over again? In what follows…

    Of course you know that nothing exists, right? As an idea and as an actuality of dimensions? Well, I see in that statement a supposition that nothing is not, in fact, just a degree of something, as is a scaling of infinity. So to start at nothing is to start at something, else there was no start at all, and that is not merely lexicographically so, but also to a degree, logically. Moving on.
    I propose to begin with the first and second Laws of thermodynamics. You can follow the links for some helpful refreshers, but in brief, the First Law states that energy is always conserved. It is neither created nor destroyed, merely transferred. And since we know, from relativistic physics, that matter is merely energy in another form, we conclude that everything that ever happens is an energy transfer.
    I would say that though every thing that happens involves an energy transfer, the idea that everything is energy transference is inconclusive in accordance with scientific models. This is because though material is required for an event, an event is not required for immaterial, by the very definition of what an event is. The things we know and can observe do not discredit the unknown and presently unobservable, but rather show mounting evidence of the opposite. Einstein said the more he grew to know, the less he knew he really understood, or maybe the more he knew there was to know. Again I see no conclusive proof that everything that happens is material, or composed of such, but rather that every event occurs because of material. And we must remember that an event is something separate from the final result or outcome which are the indications of privileged measurements or evaluations of material circumstance, or, put another way, the affectation of presence on an understood set of physical circumstances and these circumstances relationship with conceptual models of actuality and verity.
    Rather, in the definition of broadest relevance, *according to our theory*, an event is a phenomenon. This phenomenon is understood to occur, thus is an occurrence, and must be located within a specific and singular point in space-time, which makes it fundamental to the observational being of relativity theory. Understand that relativity takes much for granted, and I have a paper on this that I wrote on special relativity at 15. I will send it to you if you like, but essentially it talks of the scope and the preconceived conceits and caveats that Einstein accepts without axiomatic or even empirical verification to an exacting degree. There are reasons for this however, and they are numerous and tedious. More on that if you wish.
    Now (colloquially speaking), the interesting thing about matters relationship with the first law, namely the observable energy conservation during eventual material interactions and circumstances, aka events, is that to understand or even notice the transference is to perform a conceptual digression in which a standard of actuality is ever-present and necessary within ones mind, a standard that most people do not understand to be at the root of their knowledge, but that certainly is. First, it is a sense of I, with the addendum that this sense entails a separation from other, which would be else, or if you prefer all else, which, put another way, is a scale of degrees using the combinations of conceptual differences and existing separations. Second, to notice an event is to observe the understood standard of then and now. But, sadly, there is a tremendous, almost viral and cancerous, flexibility to our ideas of then and now that occur because of Einsteins relativity, namely, that the laws of space govern the laws of what is understood to be then, as they govern the laws of what is understood to be now.
    So… what am I getting at? Simply this: an event is commensurable because it is measurable by a common standard. There are no level digressions on which to a lot pertinence in accordance with this standard because, just as the act of understanding an event relies on the above mentioned conceits, so too does a component break down of what standards are in evidence. Put another way, you see what you see because you are looking to see it. So looking for levels shows you levels, where in actuality it is merely what it is, or merely the system, or merely all of the components, and only in looking is the idea of where one component is in relation to another at all actual, and then hardly relevant. This is because once you look, you change what was composite by imposing what you will on minutia. In this case will means something akin to a will to power, or a will to knowledge. I assume this to be a will to surety but thats neither here nor there.

    Now, all events are measurable, at least in theory. We need only to be able to measure each thermodynamic consequence, and add them all up.
    Well of course all events are measurable man. Calling something an event is actually assuming the measurement of it as actual or in effect or in evidence or having happened! So the application of the same process can be maintained, namely, that the measurements are placed with the same understanding as was in effect when the event itself was observed. OK OK. Now I must stop right here, to help you out, because I can see where conceptually this might be difficult. What I am saying here, simply, is that you are attempting to prove though a logical petition of actualities, in this case material events, that events as a whole are able to be proven and petitioned. Well, if you cannot see that tautology of this, damn you. It is apparent. But, check this out! What happens when you change the goal of your missive from an exact measurement of something by its nature inexact and only conceptually tractable to simply trying to DESCRIBE the inexactness and tractable components. Check it out. Now you lose all the downsides and strictures of exact and principled rigor in exchange for a flexible and infinitely applicable system of digression whose aim is to be an applicable system of description. There is no more call for permanent exactness because the impermanence is now part of the adaptability of your descriptions and language, and is to be embraced and not spurned because of its manifest difficulty to express! Oddly enough, I know you are trying to describe this sentiment, but you made to many conceptual leaps over the empty parts of your understanding of what an event is to do so. Moving on.
    I have a question: why when the change in available energy is equal to the change in heat content of a system minus the temperature when multiplied by the dispersal of energy which can be either positive or negative does this mean that the tractable result be one, and not, say, 0.8394?
    Also, you must remember that a is simply an expressed relationship to G. Also, what could make the heat content of a system entirely dissipate?
    How does this make a the measure of coherence of a system? A coherence is a consistent relationship between separate components, but what you are speaking of is a convergence of components, or rather, a massive interaction of components. Perhaps a is simply commentary on the interaction, but it can hardly be the standard of consistency can it? Is not consistency something always eventual? Is not a in your equation actually a reflection of outside forces and their THEN eventual interactions, assuming of course that the second law holds true, which seems sage to say, but what of the impediments like covalent bonds? Are they not also then an expression of coherence within a system, similar in most interactive ways, at least conceptually, with a?
    I never even took biology let alone chemistry or physics, so im stupid at this. But these questions seem to be natural. What do you think?

  14. did i respect the proper decorum of open channels there? am i in good graces? hooray for jelly beans!

  15. it occurs to me that time is actually a bit more like gravity and a bit less like history. do explain how you can prove that time isn’t without events. and then go ahead and explain how time isn’t without events. and then go ahead and explain how time has nothing to do with events and everything to do with our understanding of them. then go ahead and explain how an event has nothing to do with the movement of time but rather our understanding that there is movement through time. then go ahead and explain to me why you think captain crunch is better than lucky charms, CT, and i will call you Gosu! as of now you are hasu

  16. when i said time isn’t without events what i meant was, explain to me how time "is no longer there" without events.

  17. Aaron one response its been 3 months :0

  18. ""To return to Eustace, we know from the First Law, in the terms of the equation, that ΔG >= 0.""

    This is not at all evident. Since the Second Law states that free energy tends to decrease, and the First Law says that energy is conserved (both Laws pertaining to closed systems, of which the universe at large is, of course, a prime example), a prerequisite for ΔG >= 0 for Eustace is through influx of energy, something which I do not connect readilty with the postulate of the First Law.

  19. G is one manifestation of E. If any energy is to flow into Eustace, it must be from outside. G can not be spontaneously created in Eustace any more than E can be created.

  20. Of course. As I see it the derivation is flawed. There is nothing which compels ΔG >= 0. You have to presuppose a constant energy influx, or alpha will be ill-defined. Besides, by mistake, alpha has already been set to equal one.

    (ΣH – TΣS negative) / TΣS positive >= 1 = α <------ alpha = 1

  21. Also, I can’t see the point in separating S into S(positive) and S(negative). Since they are coupled, no new information is added.

  22. Alpha is not "set to 1 by mistake." You start with 0 on the right-hand side, add a term to it, divide by that term, and end up with 1. That’s algebra.

    This is also an inequality. Alpha’s smallest possible value is 1; as I said in the essay, this is the case where all free energy is completely dissipated. Obviously any Eustaces of interest have a considerably higher alpha number. Same with the non-controversy about delta G. Eustaces with zero or negative delta G are simply of no interest.

    I simply do not understand the objection to separating S positive and S negative. One may as well object to separating profit and loss on an income statement; after all, "since they are coupled, no new information is added."

  23. Actually, Aaron. The notation implies that alpha is set to 1, since the leftmost equality sign is the prioritized one. That is not algebra, that is the consensus in mathematical notation. If you want it otherwise, change the order or use brackets.

    Regarding S.

    To use your analogy. You’re not interested in profit and loss, you’re interested in the quote profit-divided-by-loss – this single dimensionless quantity which is the only concern for the rest of the theory.

    Regarding G.

    It seems peculiarly ad hoc to impose the condition, nothing else.

  24. I apologize for the use of your first name, which I now realize might have the wrong effect on an anglophone. Please disregard its lone occurence in my previous post, and substitute it for your full name.

  25. Of course, I made a fool out of myself. I intendend of course to say "rightmost equality sign" and not "leftmost equality sign". I hope you will understand the substance of my pointer, and ignore the lapsus linguae.

  26. I felt compelled to expand on the "regarding S"-bit of the other post.

    The purpose of alpha is essentially one of ranking. Defining alpha = dH / TdS (where d is to be understood as delta) would rank any group of different arbitrary thermodynamic systems in the same order, while keeping the expression vastly simpler.

  27. "Aaron" is fine.

    Thanks for pointing out that the equation needed another pair of parentheses, which I added. I had hoped that the context made the meaning clear, but now there should be no doubt.

    Manipulating terms in equations is a time-honored and useful procedure. It never "adds new information"; it teases out the information that is already implicit. Standard thermodynamics already implicitly contains alpha theory; but the gap between implicit and explicit knowledge is vast.

    Alpha is basically a theory of optimal behavior for living systems. Living systems necessarily have positive delta G. That’s all I’m saying here. Nothing ad hoc about it. You could as readily calculate alpha for systems with negative delta G, but who would give a damn?

  28. No. Let’s shoehorn the financial analogy a little more. Consider Company A and B. A invests in some process that takes two years to implement but will potentially be very profitable. Company B spends all of its money on fancy furniture and parties.

    After one year, their net cashflows may look similar but they have considerably different prospects for the future.

    Eustace is ranked on its efficacy in converting dG into self sustaining ends. Negative entropy is one of those ends.

    But you are right about the conventions used in the equation. It should read

    α = (ΣH – TΣS negative) / TΣS positive >= 1

  29. Whoops. Overlap–my comments were intended for Mr. Armasus.

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