I propose a challenge to Maximal Flow theories by a new theory:Indifferent Time

I'm giving people an early peek at a new theory that I have developed in response to essentially another kind of theory, (or a system of theories) which involves optimal energy dissipation and or system flow optimization. So called "Flow optimization" as well as optimal heat dissipation are related in principal, a principal that I specifically am addressing with my own work. I hope this derivation will serve as a chapter in a larger work.
The theory that I am specifically disproving here is a flow optimization theory, called "constructal theory." But this formal disproof would also apply to other maximization theories, such as maximal entropy production.


 [This discussion is relating to a very large kind of theory, a very broad theory about systems. It is not of course specific in any way to specific experiments or individuals or in any way related to specific engineering feats, but to a theory relating to how systems work which encompass behaviors/phenomenon at a very high level, say the "40,000 foot view" but possibly higher. It would not have anything to do with the quality of someones experiment they did on a Tuesday, this discussion relates to what that work itself might mean in terms of thermodynamics, the heat dissipation of the building etc., to use perhaps an awkward analogy which is partly true, as dissipation should be independent of "how" people are working as should the "optimized" work flow of their activities. After all, constructal theory HAS been applied itself to such wide ranging examples as to why a World Cup Football team wore white instead of a darker color..(*constructal.org)]


If my derivation is correct, then this notion of constructal law" and OTHER dissipative or optimizing theories, would not be relevant at this level, which is again very theoretical and broadly encompassing. The "constructal law" has been widely promoted by Dr Bejan as a thermodynamic law, with some 10,000 scientific references, and is accepted as a text book on thermodynamics (see link to Constructal.org). So my derivation challenging the constructal law, would certainly be significant.



One of the very difficult things about constructal theory is to understand what it is, in fact claiming. That is to say, to find a definitive scientific argument. This is unfortunate. In general, most scientific papers should not be so difficult to read, and it is not simply because it is technical. I would reference (by way of general comparison), Prigogine’s Nobel lecture, England’s paper (which I blogged on earlier), or any number of chemical papers that I read routinely where one can list the main arguments, the relevant data and the clear discussion about how the hypothesis might account for them. The thesis is easily understood, as are the claims. Sadly, this is not the case for constructal theory. It seems that some other standard of science applies to these papers, but what is striking are the few references to other obvious subjects, like biology and chemistry, and possibly if there were more of these, Dr. Bejan would not make claims like "Science generally believes that evolution cannot be observed in our lifetime..." a claim that seems truly uninformed about papers in biology that study mutation in bacteria. But there is also the general claim of a theory linking the inanimate with the animate that never mentions genetics or biochemistry? One of the terms I have attempted to understand in constructal theory is Dr Bejan’s use of “evolution”. It is not clear at all what this term means physically in the larger “constructal theory”.  I have at least three text books of advanced chemistry on my desk, and none of these ever talks about “evolution” as a chemical descriptor of chemical behavior. So what exactly is this meaning? I highly doubt you will find, this theory in any physics text book. And for good reason. The particle theories have been formulated to descrirbe these very behaviors discussed in "constructal law", in chemical and physical terms. I hope that my disproof of theories like Constructal law will help rather than hurt progress forward. I cannot imagine that a misinformed theory at best, taught in schools, should in any way help progress forward in science. It appears that its proponents are not too keen to share their knowledge or answer questions. What nonsense is this? And what does it say about the status of theoretical science?

At the Constructal.org Blog itself, I posted [1][2] what I thought was a fair question on this point, attempting to get more description or clarification about constructal paper. Unfortunately, the Constructal.org blog editors it seems, are not really interested in replying to scientific inquiries or even clarifying what they mean. You can read the exact post I made here, which is not on the Constructal site because it is still “awaiting moderation”.  The Constuctal.org blog is said to be “an intimate” blog of Dr Adrien Bejan, who postulated constructal theory in 1996.

Let me state very generally, that I simply don’t agree with constructal theory’s misconstruction or reconstruction of physics, whatever the case may be. It is a reversal in my opinion, of progress in science.This kind of physics, in which inanimate nature is deliberately imbued with function and purpose in order to operate, was moved away from thousands of years ago. The paper itself is laden with anthropomorphic presumptions. There is a very big difference between using expressions or metaphors, and invoking these as direct mechanisms ,or even "laws". I note also that Dr Bejan claims in some recent papers that the Constructal Law is (comparable) to the Second Law of Thermodynamics. [I have pointed this out specifically in a previous reply (see this one) as I believe many of these arguments essentially “beg the question,” that is, they must be first accepted in order to make the premise itself, tenable. That is another point I explore previously, and if that is really the case, then that is truly unfortunate. What are the objectives of this essay? They are very clear: to explore the SCIENCE of these notions expressed by constructal theory, they are obviously defining in their numerous scientific papers and teaching books, a "territory" of science. So the exploration of a scientific hypothesis, is in a sense, an exploration of science itself, that is the objective on equal grounds with virtually any other scientific pursuit. The other objective is to delineate and differentiate my own theories from what is extant.]

 I have, in reply to this paper specifically, a hypothesis which is a stand alone theory, but coincidentally, disproves the constructal theory premise, which I call an “indifferent time” theory. "Indifferent time" states that at any given time point the flow through the system, is indifferent, it is neither optimized nor unoptimized in terms of maximal flow or minimal flow. (1)
I have derived this from Newton’s laws of motion, and it can be shown at microstates or macrostates. The burden as I see it, is on the constructal theory to provide evidence that there is some physical data, or data suggesting that there is an imbalance of forces at some time point. If not, then we can only assume that the normal forces (due to flow) are in perfect equilibrium with the system, be it a river delta or any other inanimate physical system at any time t. The basic premise of a system changing to “optimize” flow would essentially be false as it is always in perfect equilibrium with its surrounding forces. Since the presumption of change (evolved or optimized) can’t be substantiated, the data itself would be challengeable. I object to the use of partial differential equations in this paper (and as I've indicated elsewhere, without physically defined units, it's not at all clear what they might actually reference). In my opinion, one would not provide a formal equation or analysis, until the problem area is clearly established.  What you will find however, in this review, is that I am not actually showing the conflict here between constructal theory itself, but this is more broad in scope and likely encompasses other optimization and/or dissipation theories, really more broadly, to the concept of ones physical state “leading” towards another because it is more preferred. In that sense there are many theories which propose optimization in different forms either via entropy gain or heat dissipation.

According to constructal theory, the earth is an “engine”.

As Bejan states : “Because the flowing Earth is a constructal heat engine, its flow configuration has evolved towards paths that generate less irreversibility.”

The problem with this claim-i.e. the assumption that a physical system will “evolve” is that to evolve, it is implied that such a system would need to be in a less preferred state (at some initial time) and then alter itself (at a later time) to become a more preferred state. That is the understanding that the word “evolve” conveys. The statement..”evolved towards” some path” implies that it is heading in a direction and is obviously, not yet there. And actually, Bejan does indicate that this is what these systems do, and in fact some are not “alive” but will be once they take on the property of maximal flow.

As he indicates in Fig. 4, “(Bejan & Paynter 1976; Bejan 1982, 2006). The constructal law governs how the system emerges and persists: by generating a flow architecture that distributes imperfections through the flow space and endows it with configuration. The ‘engine’ part evolves in time towards generating more power (or less dissipation), and as a consequence, the ‘brake’ part evolves towards more dissipation.” There is an implication in that statement, that there is a physical difference that can be made, tested or proven to exist, between for example, a system which dissipates “less”, and a system that dissipates more. The further implication is that at some point in time t, the physical system is not optimized, or not configured” to dissipate. In reality, there is no physical distinction here, which is what we would expect of a natural system. (2)
As I have just stated in Indiffernt Time: any system, is already dissipating its "ideal" amount of energy in accordance with the localized physical laws that apply. The physical laws are not "behaving" differently in one region or another, thus we have no reason to believe that these laws would "care" to increase or decrease optimization. Nor would we be able to state that at one time point the system was NOT optimized and at another point it WAS optimized. (3)
It is not clear how one would go about showing what this difference is. (4)
What is clear, and what I believe constructal theory is not realizing, is that even when a system doesn't APPEAR to be optimized for heat dissipation, it actually is. Again, it is indifferent, and Nature cares not if you view a system perfectly "functioning" hurricane, or a light trade wind, each of these systems is in perfect harmonic balance with the localized forces that apply. And we further can see the universality of this statement and the implications of my hypothesis, Indifferent Time, to other theories which portend to operate upon the assumption of "preferred" or optimized dissipation of energy. (5)
The surprising result is that there is no optimal dissipation of energy in a given system it is always optimized because the forces are in balance at any time t. Further, the notion that a system is not optimally dissipative at one time point, and more optimally dissipative or flowing at another time point is anthropomorphically applying rules that aren't there. You can do that with equations, you can make various relationships and possibly make the claim, but what I'm saying is that you won't be able to prove this with the physical model. (6)

Constructal theory apparently claims that there is some distinction (be it flow optimization or heat dissipation) that can be made between a system at different times, which we might call configuration I, II, III etc. This is the problem specifically with the implication, the strong implication of animation and of anthropomorphing something like a river delta or erosion patterns on a mountain. Unless some argument is provided to the contrary, or some evidence is provided, we must assume the system is the same, (in terms of "optimal" heat or mass flow) before there are any river patterns, in other words it is already “optimized” at every time point. System state “I” is identical to II and identical to III and so on. That is a fact about these physical systems that is incorrectly asserted in this paper. It is purely anthropomorphic to observe that the flow of the river is much higher and thus it is more efficient. Nature makes no such assessment of efficiency. (7)

TEST: One can also easily show that constructal theory cannot be a "physical law" that such a river pattern is an optimized physical dictate, like gravity or the second law of thermodynamics, both laws which are inviolable under ANY condition. We NOTE that the river actually can be made more efficient? How? By the use of machines, ships or other devices that pump water down stream, are far more efficient. Yes they take energy, but that is beside the point. We have deomonstrated that we can violate constructal law. We cannot do such an experiment with the 2nd law of thermodynamics, or with gravity, etc. [3]

Fig. 1 Showing a microstate of the river bank and relevant forces.

 

To evaluate the causality of a simple flowing system we can perform an operation in which we look at the various forces involved and by a simple process of addition, determine if anything is out of balance. The force of the water against the bank (black) is depicted by the vector in blue (proportional to its velocity), the force acting equally and opposite the force of water, i.e. the river bank, is in black. We also have a downward force of the water, its weight which is the pressure of a column of water.  Note that we are not adding up forces to create a vector, which would be a convention. We are actually doing something very different, this is adding up “causality”, again to simply see if there is some inbalance of cause or forces present in the system. (8)

A stagnant body of water has tremendous weight, if there was no normal force opposing this pressure, the water would break out.

(Force of water against bank, F_bank) + (forces of water weight, F_weight) =(Normal force of river bank opposing water N_bank)+ (normal force of river bottom against river weight N_bottom). Rearranging we have (Force of moving water) + Force of water weight+ Normal force of bank opposing moving water force + Normal force of river bottom opposing weight) OR, more simply…. F_bank  + F_weight  + -N_bank + -N_bottom= 0.  (9)
When F_bank =0, in the case of a non-moving body of water, then we see an identical expression where the normal forces of the river bottom are in balance with the weight of the body of water. (10) (*see note 21)It should be noted that we are neglecting the pressure against the bank, for simplicity, but could express this as F_{bank= (Sum) F pressure+ F bank} )
Now we can also examine this system in accordance to time or a possible change over time. According to Indifferent Time, meaning no preference, we can again look at the same equation of these forces we just did, but at different times: call these arbitrarily, time initial, I,… and II (a time later). What Indifferent Time means is that we do not see a difference between these states I and II in terms of their equilibrium as we just calculated for a micro condition somewhere on the river bank. Since there is no difference in force balance over time, meaning no preference, we state that the system is “indifferent” essentially to changing.  (11) How would this be disproven? In other words how do we test this condition? If we can show that in the equation above, there is in fact some slight change in a force, either the river force or the river weight, that is changing with respect to some other impetus, call it a “wild card” force, then this would in fact disprove my condition of indifferent time. (12)
The more simplified concept is to imagine that we see no direction here in how the equilibrium is fluctuating. In other words, since the forces are always in balance, according to Newton’s law of motion, “any force will see an opposing force directly against it” (i.e. with gravity or collisions of balls), and the additional stipulation I have introduced, “at any time” we can see that we could plot the relationship above and show that it has no trend. This has an implication to dissipative preferential equations and so-called selectively enhanced dissipative equations .(13)

 F_bank + F_weight  + -N_bank+ -N_bottom= Diff at I, and F_bank + F_weight + -N_bank + -N_bottom= Diff at II. Diff I- Diff II/ Diff (time I-time II) would be a formula for showing a rate of the change in the system (moving away from equilibrium, or towards it, greater or lesser). (14)
 Of course the “slight difference” we are defining here would be in theory, a difference between the F_weight and N_bottom, in other words one is out of harmony with the other. When would such a condition exist? It cannot. (And this is actually Newton’s third law of action-reaction F_w=-F_n ) (15)
(See note 28. We are showing with the difference formula (14) that the normalizing force, is the "optimization" intrinsically done by the microstate, or microstates and thus we cannot see optimization between arbitrary states I, II, ...III etc. Any "wild card" vector would have associated with it, a normalizing force. This rule applies as the river undergoes any slight deformation, as delta F= delta N] 

So we have also just proven that there is no causality to be found in a strict formal sense in a natural flowing stream or other natural system. Causality is purely artificial, and can only be demonstrated by artificially assuming that a force is entering the microstate (such as wind, water or other forces), but in reality this only appears to be causal, as these forces are not correctly accounted for and find imbalance only because the model of accounting forces them to be imbalanced. (16)

It is the convention in physics texts to assume that a free floating force will be examined and often times, its source is not relevant to the problem. But that assumption is not valid in these types of problems involving causality.

 

*in reality, these forces are not “entering” the system but are in fact, a part of the system. It is convention, to assume that “a wind blew over the tree”. A true statement in the proper context if one is simply force diagraming the problem. However in the causality problem here, and by the new causal analysis I’m proposing, such convention is misleading. We know that the wind is more accurately understood as a vortex that was resultant from a system of nano-states, molecules absorbing heat, pushed to disequilibrium. Thus their macroscopic vibrations, led to higher order vortices, eventually building to form the wind that blew down the tree.  (17)

**It is true that the ordered motion of a vortex or wave, is a response of the system to dissipate energy, like diffusion spreads out a cluster of molecules. (that is far-from equilibrium dissipation [Prigogine, 1977]). What is not correct is to assume that this is more efficient” or “less efficient” as there is no “less efficient” possibility in the physics. We would not say that diffusion occurs because molecules “need” to spread out their energies uniformly. (18)

[(29) I updated 5.5.15 the expression above to be inclusive of the non-equilibrium state and show its broader and surprising implications to the sun's system (see comment 29)] 

 

On the other hand, evolution at least as a theory, is a term that is clearly conveyed and defined in biology . And there is little point in defining it here, except to say that evolution implies that an organism is changing in some way that is a response to its environment or to its competitors. And so although Dr. Bejan clearly is making the argument that a river delta “ages” over time and might even be “born”, this statement lacks physical evidence to suggest that the rocks and dirt and the stream itself, are anything physically different than they were at any other time point (with respect to their capacity to carry flow, which [we recall] is a self defined instrinsic property of the system in question. (19)
The "flow capacity" of a river is obtained by formula, but this capacity alters proportionately to other parameters that define the physics. We can see with the aid of microstate analysis I perform here, that the river only increases flow  capacity as the volume of water increases, not before and not after, its physical shape is dictated by fundamental laws). (15)
 Are we to believe as constructal theory claims, that a river delta “ages” and if so, what physically differentiates it at a “young” age vs a much older age in terms of flow? Of course constructal theory suggests that rivers increase in flow over time, they get larger, so size would be a factor, but the inherent problem with this suggestion is that we know when a river was “born” and even where it was born… And what a river is, meaning what its boundaries are. Unlike particles with finite mass, and radius, rivers are highly ambiguous. Does the mississipi river delta really only encompass certain states or does it include every tributary, minor tributary, and even the tiny etchings on a mountain sides? What is a rivers’ boundaries? Chaos theory comes to mind. Neither of these physical boundaries issues are even discussed in the paper. But that is the trap that anthropomorphic theories fall into. (20)

 

 [note](There are basic problems with so called "optimization theories" which relate to flow. Of course, it many not even be true that a given river we are observing is at optimized flow, if we are to accept that the context is a valid physical model. What if the river that particular week or year, sub-optimal in terms of run-off? There would be no guarantee that the volume of water is moving at its theoretical capacity, whatever that capacity might be. In reality, the same problems can be raised with other optimization theories, such as Dewar's Entropy Maximization Theory (Dewar, 2006) which proposes to measure the optimal heat dissipation of an ATP processing enzyme. The paper speculates on how the function of the ATP enzyme is specifically designed for maximum entropy generation. Maximized" carries with it the implication that there are less than "optimal" entropy productions of the ATPase, and it is not clear how one would make this assertion, except to assume that the maximal level is somehow already known or pre-dictated. (21)

That carries a strong anthropomorphic implication to a natural system, not to mention that it fails to explain why the entropy production is not indifferent to maxima or minima, to a theoretical state that the enzyme is not "aware" of. It is not clear why the values given for the entropy generation are not precisely the values that are generated by the system at any time t, neither optimal nor sub-optimal. Furthermore, I can provide several tests, as entropy is a universal property of all molecular systems, not just ATPases (but also not just molecular systems). (22)

I do not run a cell toxicity experiment and consider if a drug species is "optimized" for cell toxicity or not, such labels would have no physical basis in chemistry. Nor would I expect that the combination of a certain inorganic salt with water, a process that creates entropy in a fixed molar quantity, is at an optimized level. (23)

Is there a sub-optimal generation of entropy in the dissolution of calcium carbonate in water? Again, for the given experimental conditions, it is exactly what the system generates. If we consider the experimental tables of Dewar in his paper, are we to assume that some of the values calculated for replicate entropy generation of ATPase were "less optimized" whereas other values of the entropy were "more optimized"? By the physical analysis I employ with "Indifferent Time" a working hypothetical test, each of these data points would be a precisely what was generated, not a maximum or minimum, which implicitly assumes that they should in fact be some other value than they are. ) [4]

Based on my theory of “indifferent time” , I believe there is no physical difference between a river system a thousand years ago, and today, in terms of its expected flow or any other normal forces it encounters. And this is completely independent of what age one arbitrarily assigns to the river. (24)

Again, I have searched this paper (and others) for evidence to the contrary, but according to my time indifference argument,(time is “indifferent” as are the normal forces, to what state a physical system is in). A natural system at time t is “optimized” for maximum flow of all its components flowing through it, and is not more optimized at a later time t=t2, in other words it is optimized” at any time t for any flow material passing through it. (11)
It appears as though the trenches are deeper, but we cannot claim that this system is more “optimized” than a prior system. Why? Because of the rather obvious fact that the prior system was already optimized for the given flow requirements that it encountered. This derivation I provide, stems directly from the basic laws of motion. (15)
But mathematically, it is a sound argument since the net flow capacity would always be normalized to what the capacity is of the system at any time point. We note that the capacity of a river might increase, but mathematically, so does the potential of the system, in exact proportion. Unexpectedly, we might see that this is a product of the system, it is the system generating the flow potential.

When Bejan claims that a system has in fact reached an “optimized configuration”, as he states here…“Because the engines of engineering and biology are constructal, they morph in time towards easier flowing configurations. They evolve towards producing more mechanical power (under finiteness constraints), which, for them, means a time evolution towards less dissipation, or greater efficiency.”) does he believe that this “snapshot” or drawing of the system, is really somehow different than its state at some other time point? Is it really optimized” now, when in fact it wasn’t optimized before? More importantly, how do we know this? What physical measurements indicate that the system is in fact “better at flowing” because implicit in this assumption is that it needs to be better than it is.

When I hike a dry gulch in Southern Utah and gaze up at trees and rocks that have been deposited high above, in the now dry banks, I consider F=ma, not constructual theory. I do not imagine for a moment that the river is animate and this is somehow designing itself to carry more jetsome or flotsome. Nor can we imagine that it is “designing” itself to carry more water. According to my theory of indifferent time, it carries precisely the amount of water it carries. If the flood waters are diverted then this canyon will erode (the dry gulch will fill with sand, and it would appear that it is no longer "optimized" for carrying water, though in this case we have now mentioned a wholly different force  that is at work opposing so-called "flow optimization".) (25)
 If constructal theory were to actually hold, I believe that Newton’s F=ma would need to be restated, such that masses would “want” to collide at maximum efficiency. And that really does pose mathematical problems. (26)
We do not justify such a statement because it is clear that the collision is not at disequilibrium. We should not be surprised that the flow in a natural river is optimized for the water that is coursing down it. Any more than we should be not surprised that an incline is not “optimized” for rolling rocks downslope. None of these “optimizations” are really true, and "optimization" is a term that is being introduced artificially, into the equation.

There is another issue too, in the constructal thesis that our engines and other designs are “evolving” towards “less dissipation.” In reality this runs contrary to the accepted notions of thermodynamics, since for engines to exist, greater dissipation of entropy must occur outside these systems to compensate for the increased order. This would occur in the burning of fuels and disorder of other ordered systems to make (highly ordered) engines. That is, the engine is at such a high state of order, that the cost of this lowered entropy is great on the system around it. Dissipation of NET energy must be greater for the system in this case, not less. This is the principal already espoused by Schrodinger, and many others. For example, cells must pump entropy out of their systems in accordance with this theory, so they in fact are dissipating more heat.

So I return to an argument I made earlier (here) that constructal theory is making numerous factual arguments, about how a system at some time point, i.e., is not yet optimized, but perhaps at a later time point is optimized. And yet, if this was the case, we would see disequilibrium. Looking at the system in terms of microstates, we realize from Newton’s laws, that the water against the bank applies a force, but the bank in turn applies an equal and opposite force against the water, thus the “optimization” of forces is in balance at all times. (14,15)
At any time point, the system is already optimized in an absolute sense, to the flowing material passing through it. It will not change or alter itself until it is met by a force which causes a change, at which point it will be instantly “optimized” again. To imply or infer that a river delta system is somehow “doing” anything, other than being molded by forces that are acting in its immediate time frame, strains incredulity.

The constructal theory, (like other optimization theories) has obviously concluded that if a system is evaluated at a later point in time, it will be apparent that it has achieved an “optimized” level of flow that it might not have had at an earlier point in time. Yet there is no physical reason for believing that such evidence does exist to support this alternate, physical view of a system. Moreover, it would not seem possible to envision what kind of data this would be? As I’ve argued previously, there is a distinct lack of any units of measure in which to qualitatively or quantitatively evaluate how a system might be more optimized at one time point and less optimaized at another for the given flow that passes through it. When this theory is evaluated causally, in terms of vectoral diagrams these issues I believe become more obvious.
My theory: "Indifferent time" states that at any given time point the flow through the system, is indifferent (to the normal forces opposing it), it is neither optimized nor unoptimized in terms of maximal flow or minimal flow. (1) Indifferent time would hold that the premise of a system “optimizing itself” or evolving to a more perfected form, is not evidenced and mathematically is not possible. Indifferent time posits that at any time t, the normalized forces are in perfect equilibrium and thus the system is at perfect optimization. Any flow equation that we might establish, just like any other equation resembling F=ma, would be de novo generated from the system itself, and therefore normalized against it. It is neither too optimized nor too underoptimized. This would disprove the contention that a change in optimization is occuring or an evolution, since if both states (I) and (II) for example are already 100% optimized, how can one observe a change towards greater optimization?

Is the Constructal Theory By Adrien Bejan Really Proven or Provable? A challenge to Constructal Theory

I want to preface this article by stating that my attempts to obtain copies of Dr Bejan’s primary reference works, e.g. the peer reviewed articles which highlight his theory, have been unsuccessful, as these are not publicly available. In one site I have to pay $70 to even look at the paper, (which I will not do) and in others it simply states “submit your request for a download, no copies are available”.


Adrien Bejan is a professor of Mechanical Engineering at Duke University. He postulated constructal theory in 1996.
According to Bejan, the constructal theory states… “For a finite-size flow system to persist in time (to live), its configuration must evolve in such a way that provides greater and greater access to the currents that flow through it.”.

Constructal theory is a theory which is and continues to be, vigorously touted by its adherents as being scientifically verified and which has “growing scientific support”(Wikipedia). There are numerous web sites dedicated to the theory itself, one of which is here http://www.scoop.it/t/constructal-design, and which indicates for example the number of peer reviewed citations of Dr Bejan’s theory per year, which it claims are above 10,000. These days, that is considered one of the primary measures of success of any scientific theory, its citation count.
And in January of this year, the American Association of Physics Teachers held a conference in San Diego CA http://www.aapt.org/Conferences/wm2015/session.cfm?type=plenary that had a plenary session on Constructal Theory, so it is apparently accepted in teaching curriculum.

So my questions of the constructal “law” are the following:

1. The theory is based on a principal or statement, that appears defined, and yet is not definable in terms of actual physical values. What for example, would be the physical values that the theory would input and what would be their outputs, are these in units of force Newtons or dynes or pounds, (energy) joules, seconds, and/or moles of atoms or molecules, or densities Kg per unit volume?
2. I find that the underlying premise is reducible essentially to another, simpler, physical argument (or arguments) already known. It is based on the path of least resistance principal of physics, which is further reducible to Newton’s laws of motion. An object (a body) will continue in its path until it encounters a force resisting its motion. Bodies will naturally take paths of least resistance, as no object or mass will take a path of higher resistance. This very basic law of physics would describe at a microscopic level, virtually all of these phenomenon that are described as being newly encompassed by Bejan’s “constructal law”. Furthermore, we note that Newton’s original postulate is an argument that does contain measurable quantities, Newton’s (N) and mass (kg) but also displacement per unit time (m/s). Based on this evidence, it would appear that Dr Bejan has anthropomorphized an already existing law, that of Newton’s law of motion, since it is more easily, and more accurately, reducible to another already in existence.I don’t doubt that Bejan’s theory does describe phenomenon which themselves are encompassed or encapsulated in terms of known physical units. The point is that the tendencies of matter to take paths of least resistance, Newton’s law of motion, is a more simplified version of what Bejan’s theory is founded upon.  At the center of these laws is of course the conservation of energy and momentum. One would argue that matter behaves the way that it does because of energy conservation, also a principal that has defined physical quantities associated with it. But of course these do not entirely describe behavior, since if we had only the passive transfer of energy and absolute conservation in systems, we would not have the second law. There are other underlying principals of Bejan’s theory which rest in Fourrier’s theory of heat loss and Fick’s law of diffusion of particles. But the fact that particles in an enclosed volume will find by collisions, a stable lower energy state of few collision per time than more, is very intuitive and can be easily seen with billiard balls and mechanical diagrams.These underlying physical principals are key to understanding I believe, what the limiations of Bejan’s theory actually are and how it is defined in terms of actual physical values. Because the theory itself is not stated in these terms, it is instead a very generalized principal.It should not be too surprising that the basic physical laws of motion would always apply universally to every situation possibly imagined, to lungs, rivers, sand dunes, heating and cooling, (as these are particles transferring heat) and to all others. There are no exceptions. Supporters of constructal theory seem to be surprised that their theory applies in so many ways and under so many different conditions, but as we can see, these tests are really only the more simplified laws themselves proved out again and again.

But the real test of Bejan’s theory, as in any theory, is its applications, its claims. Does it account for some new behavior which is currently unexplainable? And one example of a constructal theory “application” is found broadly in its claim of the equivalence of animate behavior with inanimate behavior. This assumption, is another critical reason why this theory in my opinion is incorrect and undemonstrated. The fact that this point alone has not been tested scientifically is another question but an important one. It is this critical assumption, and that is what it is, an outright de facto assumption, that leads to the very broad conclusions of this theory in the specific area of the animate/inanimate problem.
Many examples are provided which purport to show how the theory links together or shows universality between animate and inanimate behavior. The aerial photos of alluvial fans for example are compared to the branching patterns in the lung of an animal. Key to this comparison is to understand why I made the points above 1 and 2. We can see that simply because one thing is true and physically demonstrable, it does not mean that perhaps circumstantially, another principal must also be true.
Bejan is absolutely correct that the alluvial patterns behave according to the laws of physics which dictate by conservation of momenta and energy, the intricate flow patterns of water against a resistive material, in this case mud and silt. These are entirely natural patterns, the water does not “know” that it must “form” a more efficient flow pattern, the efficient flow pattern is dictated by the conservation of momenta and energy, because it is taking the path of least resistance. The water is composed of particles, we may approximate these in a force diagram, as tiny billiard balls, but the water itself always is governed by the force pulling it downward, F=mg and the resistant normal forces” opposed to it by the silt and mud of the river bottom. The entire problem of liquid flow, though so complex it would likely have to be modeled in a computer, is in fact reducible, in an theoretical form to the force diagram and the simple collisions of billiard ball against a stationary wall or other object. Even with the complex factors of hydrophobicity and molecular stickiness, each body” must take a least resistive net path as it moves. That is the beauty of physics, its reducibility. But in this theoretical analysis, say examining the river/bank interactions one cubic millimeter at a time, we can reproduce a complex river pattern from these microstates of well known particle behavior. My argument is that theoretically, the flow pattern of water is a mass of known density Kg/Liter and velocity not unlike the flow pattern of tiny spheres, particles, down a hill. These conform to Newtonian physics and for this argument their deviation is irrelevant or not in question. An accurate model of flow is not specific as Bejan’s claims are so universal virtually any model.
However, I believe the problems of this theory are more fundamental. And the important point is that none of these claims of engineering physics, have any bearing on Bejan’s claim that these interactions somehow explain or even suggest, the equivalence of animate with inanimate behavior, an equivalence that is somehow assumed by the theory itself. Are we to believe that the flow of water against a bank, a microcosm of this model, is somehow equivalent to a living process?
Likewise, if we were addressing chemical behavior of the water, its wettability, its reason for being a liquid and not a solid, its reactivity perhaps with other solutes, we would have to have consistency between the particle model and the macroscopic behavior observed. The point here is that Bejan’s theory is reducible to another set of theories of particle behavior, the laws of motion of macroscopic bodies and atom sized bodies, and chemical laws.
I am therefore not certain, how a constructal theorist can claim that this is a tested theory. Or even if constructal theory is definable as a theory. That is, if it meets the burden of a scientific theory. It must be capable of describing phenomena, testable phenomena, that cannot be encompassed by an existing simpler theory. What aspect of alluvial fans or lung branching are not encompassed by the physical and chemical theories of particles already established before the 19th century?
Constructal theory claims to describe far ranging phenomenon. For example it is stated in a peer reviewed paper, [again appearing in Nature.com’s publication “Scientific Reports” entitled “Cave spiders choose optimal environmental factors with respect to the generated entropy when laying their cocoon” by Eliodoro Chiavazzo et al.], that spiders make webs in specific locales i.e. in caves, because the web location is at a more preferred energy state than to others, in other words the web patterns are “chosen” by spiders in such a way that it conforms to the flow of energy based on constructal theory. This basic assertion is not supportable if one considers the problem from a different angle, one less biased, in which the spider is not first presumed to be complying with future energy constraints. The paper already assumes that the web structures, in the greater system of the spider, are at lower energy, and does not consider the energy required to build the webs themselves (I address this point in more detail elsewhere). Whereas it may be true that the locations of the web are the most energetically stable, relative to incoming winds etc., this fact does not necessarily connect to the other suppositions of Bejan’s theory or support these contentions. More broadly, we have to consider again, the smaller components which are underlying the physics that explain sufficiently, the inanimate particle behavior. For example would we expect that a beaver is building a dam structure that is unstable? Are the stacking of logs and twigs and mud, going against the “rules of engineering”? Beaver dams are already well documented as engineering feats, which hold up for decades. I think this path of logic is a precarious position. Because in fact, that kind of logic has been applied and shown to be untenable in the biological world. The number of behaviors by organisms, which do not conform to reasonable usages of energy are more. And you could look at the tendency of organisms to become larger for example or even such basic behavior as reproduction. There are in my mind, many easily asked or thought about counter-examples that this theory apparently avoids. How about a spider not making a web at all? Can you actually prove that a bear or other animal, climbs over a mountain, because that is the path of least resistance? Or, do birds take flight because flying is actually simpler or lower resistive than standing still? The constructal theory advocates I’m sure can (and apparently do) imagine all types of scenarios to demonstrate their new theory, and yet it only takes one exception in science to nullify these results. It is usually the simplest question that is the hardest to answer.
And you will not find a single example of a paper by constructal theorists which proves why, for example, a bear might run instead of sleep, a very obvious contradiction to the “organisms build in energy efficient places” but you will find very specific pre-determined conclusions that fit models which really could not be proven some other way. i.e. we already know that spider webs are not built near traffic or in exposed areas, so this data is obvious, or are foregone conclusions, and yet what is assumed by constructal theory is that this cannot be deliberate action on the part of the spider [does a spider not sense winds speeds, noise, predators, and threats?], but must be thermodynamically pre-determined.
And there are other citations claiming to utilize constructal theory in far ranging applications as cancer biology (http://www.nature.com/srep/2014/141024/srep06763/full/srep06763.html)
which purport that constructal theory applies there as well. An article in Nature.com “Scientific Reports” entitled “A thermo-physical analysis of the proton pump vacuolar-ATPase: the constructal approach” 2014 by Umberto Lucia et al., discusses how constructal theory makes such lofty claims to not only account for tumorogenesis or transformation but also cancer cell growth. I excerpted the following to attempt to make sense of it: “..Consequently, the analysis of the flows through the cell membrane appears fundamental in the comprehension of the biophysical and biochemical mechanisms inside the cell¹². But this kind of analysis is powerfully described by the constructal theory. Indeed, by referring to the constructal law, a living system presents two characteristics: it flows and it morphs freely toward configurations that allow all its currents to flow more easily over time¹³. Life and evolution are a physics phenomenon, and they belong in physics¹⁶. Constructal law is a new approach introduced in thermodynamics in order to explain optimal shapes of natural structures^{13, 14, 15, 16, 19, 20, 21}. The fundamental bases of the Constructal law was expressed²¹ as follows: “For a finite-size flow system to persist in time (to live), its configuration must evolve in such a way that provides greater and greater access to the currents that flow through it.”.
If there is a constructal law, what is this law? The variables for evaluating the theory are not definable as written. Moreover, in this paper, there is never any negative hypothesis, in other words what happens if the hypothesis isn’t true? Do the results still agree? These basic elements are completely absent in this paper. And the problem is that you can’t write the thesis of constructal law in the hypothetical:

1. “If a finite system is persisting in time, it’s configuration won’t evolve? Or,
2. For a finite system to persist in time, its configuration will evolve but the flow will not increase.

None of these are possible phrasings that would lead to a possible negative outcome of the claims, and thus be testable. Cancer cells either are or are not responsive to the presence of a specific gene. Cancer morphogenesis is correlative to certain genes, as are all drug-cell interactions. And further, physical arguments the law of gravity, laws of motion, Maxwell’s equations, laws of diffusion, are all in theory, testable and must defeat the negative hypothesis.
My thesis in a grant project was essentially to show that a specific drug molecule, a chemotherapeutic, would be better encapsulated by a host molecule for the purposes of improving its pharmacokinetics. It had myriad implications to improving the therapy or not. So the criteria were carefully established, and because it was real science, the thesis could be shown false or it could be affirmed. That is how all scientific theories are structured.
What I find, and what we must conclude, is that this constructive ‘law’ has a series of presumptions built into it which must be first presumed to be true in order for the predictions to hold, that is, it must be presumed that a volume of an organism is increasing or increased because a larger volume is more beneficial for moving a mass through water (as submarines do). In other words it possibly predicts that a slight advancement will occur, or a change in position, because the final state “will” be more conducive to flow? The future conditions some how pre-determine the present? It is easy to dismantle this kind of theory logic by simply asking What will the physical system do at time t when it is not a (larger volume?). If the answer is that it was already a larger volume, then you have the problem of how it became larger in volume to begin with.
These claims specifically, that constructal flow theory or law is providing incite into the growth of cancer, are too difficult to parse or simply do not provide evidence of how these observations are not explained by known cellular processes or genes. It is not too surprising that these examples in cancer cells do not account for the basic logical problem of how some claims or predictions in the constructal law must be pre-supposed in order for the theory to hold. If anything, they simply obfuscate further by focusing on details of already known cancer morphology. As we have discovered, “pre-advantaged states” of greater flow, would have to dictate a change in the present state of flow. The stated law as written, is impossible to test.
And if, for example, it is clearly shown that the wavelets and other physical phenomena are more easily explainable by particle theories already in existence, why should we assume that constructal theory should somehow provide exceptions to biological phenomena?
Many of these constructal theory papers delve very quickly into formula. Which I will not bother to reproduce here. It should not be surprising that differential equations might be found that apply to cell growth or to chemical behavior. However, if the constructal theory, the thesis of their paper, cannot be proven as written because of logical and definitional issues in the central hypothesis, the differential equations (roughly 3 pages worth) are meaningless, and further highlight the lack of evidence, of the how future states can pre-determine present conditions. If a theory states that a system will do something, cancer cells will grow, in order to become more conducive to flow, you have stated that future states (e.g. the more optimized cancer cell shapes) are determinant and dictating present ones. This logical deduction flows directly from the argument. It is easily tested as I have shown by allowing the present state to exist for some test interval, dt and seeing what then must happen).
These are new findings that are the “take home” message from this analysis. And these are relevant in spite of the claim that there are numerous citations in peer reviewed journals apparently supportive of constructal theory, as these are new issues that have not been discussed previously. Although the requirements for publication as specified, may include previous citations in peer review, in the case of constructal theory, it is apparently not critical that the peer reviewed articles themselves actually support or prove the central thesis that the investigators purport to investigate.
My objective therefore is to bring into question the standards not only for which peer reviewed science is being evaluated but from my perspective, the standards which are highly inconsistent and apparently can be relaxed or tightened, provided that one has sufficient peer review clout. It is I believe, already known or should be obvious to other scientists in the field, that constructal theory is in fact, vague and undefined theory, and not new by definition of what “new” means in research, nor a theory that makes predictions that can be tested or which cannot be easily accounted for by other existing theories in a very obvious way. It is time for “peer review” as a primary standard, to be scrutinized as a primary dictate of scientific merit.
I’ve presented numerous arguments for why this theory should be scrutinized more carefully. But I believe the strongest is the way it is logically constructed. It bears repeating: “For a finite-size flow system to persist in time (to live), its configuration must evolve in such a way that provides greater and greater access to the currents that flow through it.”.
By claiming that forms in nature are somehow dictated or driven by achievement of more efficient flow patterns or rates, constructal theory proponents have predicated that the conclusions or claims are already presumed in the argument. Key to this are loaded phrasings such as “(to live)”. The term in constructual theory “(to live)” of course is not defined but is carefully assumed within the statement that purports, we recall, to account for why things are living or behaving as though they are. You can’t test such a theorem.
So I would invite Constructal Theory advocates and scientists to respond particularly to the last argument I make here, at least first, as the other arguments would take considerably more time to resolve. Does the theory itself presuppose its own claims? And how does a system “know” ahead of time, what its best and most optimal flow pattern should be? As we have discovered here, “pre-advantaged states” of greater flow, at some future times, would have to dictate a change in the present state of flow (at a present time point). That is contrary to the basic arrow of time and thermodynamics.The stated law as written, is impossible to test.










Author notes: This article also appears on "The Crisis Equation"