| Unmatched sewell_itb_ch3-4-5.txt | Matched sewell_itb_ch3-4-5.txt | Matched sewell_second_look.txt | Unmatched sewell_second_look.txt |
| A Mathematician s View of Evolution The following article appeared in The Mathematical Intelligencer Sewell 2000 Used with kind permission of Springer Science and Business Media 3 1 Darwin s Black Box In 1996 Lehigh University biochemist Michael Behe published a book entitled Darwin s Black Box Behe 1996 whose central theme is that every living cell is loaded with features and biochemical processes which are irreducibly complex that is they require the existence of numerous complex components each essential for function Thus these features and processes cannot be explained by gradual Darwinian improvements because until all the components are in place these assemblages are completely useless and thus provide no selective advantage Behe spends over 100 pages describing some of these irreducibly complex biochemical systems in detail then summarizes the results of an exhaustive search of the biochemical literature for Darwinian explanations He concludes that while biochemistry texts often pay lipservice to the idea that natural selection of random mutations can explain everything in the cell such claims are pure bluster because there is no publication in the scientific literature that describes how molecular evolution of any real complex biochemical system either did occur or even might have occurred When Dr Behe was at the University of Texas EI Paso in May of 1997 to give an invited talk I told him that I thought he would find more support for his ideas in mathematics physics and computer science departments than in his own field I know a good many mathematicians physicists and computer scientists who like me are appalled that Darwin s explanation for the development of life is so widely accepted in the life sciences Few of them ever speak out or write on this issue howeverperhaps because they feel the question is simply out of their domain However I believe there are two central arguments against Darwinism and both seem to be most readily appreciated by those in the more mathematical sciences 3 2 Irreducible Complexity The cornerstone of Darwinism is the idea that major complex improvements can be built up through many minor improvements that the new organs and new systems of organs which gave rise to new orders classes and phyla developed gradually through many very minor im improvements We should first note that the fossil record does not SUpport this idea for example Harvard paleontologist George Gaylord Simpson Simpson 1960 writes It is a feature of the known fossil record that most taxa appear abruptly They are not as a rule led up to by a sequence of almost imperceptibly changing forerunners such as Darwin believed should be usual in evolution This phenomenon becomes more universal and more intense as the hierarchy of categories is ascended Gaps among known species are sporadic and often small Gaps among known orders classes and phyla are systematic and almost always large These peculiarities of the record pose one of the most important theoretical problems in the whole history of life Is the sudden appearance of higher categories a phenomenon of evolution or of the record only due to sampling bias and other inadequacies An April 1982 Life magazine article excerpted from Francis Hitching s book The Neck of the Giraffe Where Darwin Went Wrong contains the following report When you look for links between major groups of animals they simply aren t there Instead of finding the gradual unfolding of life writes David M Raup a curator of Chicago s Field Museum of Natural History what geologists of Darwin s time and geologists of the present day actually find is a highly uneven or jerky record that is species appear in the fossil sequence very suddenly show little or no change during their existence then abruptly disappear These are not negligible gaps They are periods in all the major evolutionary transitions when immense physiological changes had to take place Even among biologists the idea that new organs and thus higher categories could develop gradually through tiny improvements has often been challenged How could the survival of the fittest guide the development of new organs through their initial useless stages during which they obviously present no selective advantage This is often referred to as the problem of novelties Or guide the development of entire new systems such as nervous circulatory digestive respiratory and reproductive systems which would require the simultaneous development of several new interdependent organs none of which is useful or provides any selective advantage by itself French biologist Jean Rostand for example wrote Rostand 1956 It does not seem strictly impossible that mutations should have introduced into the animal kingdom the differences which exist between one species and the next hence it is very tempting to lay also at their door the differences between classes families and orders and in short the whole of evolution But it is obvious that such an extrapolation involves the gratuitous attribution to the mutations of the past of a magnitude and power of innovation much greater than is shown by those of today Behe s book is primarily a challenge to this cornerstone of Darwinism at the microscopic level Although we may not be familiar with the complex biochemical systems discussed in this book I believe mathematicians are well qualified to appreciate the general ideas involved And although an analogy is only an analogy perhaps the best way to understand Behe s argument is by comparing the development of the genetic code of life with the development of a computer program Suppose an engineer attempts to design a structural analysis computer program writing it in a machine language that is totally unknown to him He simply types out random characters at his keyboard and periodically runs tests on the program to recognize and select out chance improvements when they occur The improvements are permanently incorporated into the program while the other changes are discarded If our engineer continues this process of random changes and testing for a long enough time could he eventually develop a sophisticated structural analysis program Of course when intelligent humans decide what constitutes an improvement this is really artificial selection so the analogy is far too generous If a billion engineers were to type at the rate of one random character per second there is virtually no chance that anyone of them would given the 4 5 billion year age of the Earth to work on it accidentally duplicate a given 20 character improvement Thus our engineer cannot count on making any major improvements through chance alone But could he not perhaps make progress through the accumulation of very small improvements The Darwinist would presumably say yes but to anyone who has had minimal programming experience this idea is equally implausible Major improvements to a Computer program often require the addition or modification of hundreds of interdependent lines no one of which makes any sense or results in any improvement when added by itself Even the smallest improvements USually require adding several new lines It is conceivable that a programmer unable to look ahead more than 5 or 6 characters at a time might be able to make some very slight improvements to a computer program but it is inconceivable that he could design anything sophisticated without the ability to plan far ahead and to guide his changes toward that plan If archeologists of some future society were to unearth the many versions of my PDE solver PDE2D which I have produced over the last 20 years they would certainly note a steady increase in complexity over time and they would see many obvious similarities between each new version and the previous one In the beginning it was only able to solve a single linear steady state 2D equation in a polygonal region Since then PDE2D has developed many new abilities it now solves nonlinear problems time dependent and eigenvalue problems systems of simultaneous equations and it now handles general curved 2D regions Over the years many new types of graphical output capabilities have evolved and in 1991 it developed an interactive preprocessor and more recently PDE2D has adapted to 3D and 1D problems An archeologist attempting to explain the evolution of this computer program in terms of many tiny improvements might be puzzled to find that each of these major advances new classes or phyla appeared suddenly in new versions for example the ability to solve 3D problems first appeared in version 4 0 Less major improvements new families or orders appeared suddenly in new subversions for example the ability to solve 3D problems with periodic boundary conditions first appeared in version 5 6 In fact the record of PDE2D s development would be similar to the fossil record with large gaps where major new features appeared and smaller gaps where minor ones appeared That is because the multitude of intermediate programs between versions or subversions which the archeologist might expect to find never existed because for example none of the changes I made for edition 4 0 made any sense or provided PDE2D any advantage whatever in solving 3D problems or anything else until hundreds of lines had been added Whether at the microscopic or macroscopic level major complex evolutionary advances involving new features as opposed to minor quantitative changes such as an increase in the length of the giraffe s neck or the darkening of the wings of a moth which clearly could occur gradually also involve the addition of many interrelated and interdependent pieces These complex advances like those made to computer programs are not always irreducibly complex sometimes there are intermediate useful stages But just as major improvements to a computer program cannot be made 5 or 6 characters at a time certainly no major evolutionary advance is reducible to a chain of tiny improvements each small enough to be bridged by a single random mutation 3 3 The Second Law of Thermodynamics The other point is very simple but also seems to be appreciated only by more mathematically oriented people It is that to attribute the development of life on Earth to natural selection is to assign to it and to it alone of all known natural forces the ability to violate the second law of thermodynamics and to cause order to arise from disorder It is often argued that since the Earth is not a closed system it receives energy from the Sun for example the second law is not applicable in this case 1 Ironically W E Lonnig s article The Evolution of the Long Necked Giraffe www weloennig de Giraffe pdf has since convinced me that even this is far beyond the ability of natural selection to explain It is true that order can increase locally if the local increase is compensated by a decrease elsewhere i e an open system can be taken to a less probable state by importing order from outside For example we could transport a truckload of encyclopedias and computers to the moon thereby increasing the order on the moon without violating the second law But the second law of thermodynamics at least the underlying principle behind this law simply says that natural forces do not cause extremely improbable things to happen and it is absurd to argue that because the Earth receives energy from the Sun this principle was not violated here when the original rearrangement of atoms into encyclopedias and computers occurred The biologist studies the details of natural history and when he looks at the similarities between two species of butterflies he is understandably reluctant to attribute the small differences to the supernatural But the mathematician or physicist is likely to take the broader view | | |
A second look at the second law Granville Sewell Mathematics Department University of Texas El Paso United States It is commonly argued that the spectacular increase in order which has occurred on Earth does not violate the second law of thermodynamics because the Earth is an open system and anything can happen in an open system as long as the entropy increases outside the system compensate the entropy decreases inside the system However if we define X entropy to be the entropy associated with any diffusing component X for example X might be heat and since entropy measures disorder X order to be the negative of X entropy a closer look at the equations for entropy change shows that they not only say that the X order cannot increase in a closed system but that they also say that in an open system the X order cannot increase faster than it is imported through the boundary Thus the equations for entropy change do not support the illogical compensation idea instead they illustrate the tautology that if an increase in order is extremely improbable when a system is closed it is still extremely improbable when the system is open unless something is entering which makes it not extremely improbable Thus unless we are willing to argue that the influx of solar energy into the Earth makes the appearance of spaceships computers and the Internet not extremely improbable we have to conclude that the second law has in fact been violated here 1 Compensation It is probably fair to say that the majority view of science today holds that physics explains all of chemistry chemistry explains all of biology and biology completely explains the human mind thus physics alone explains the human mind and all it does In fact since there are only four known forces of physics the gravitational electromagnetic and strong and weak nuclear forces this means that these four forces must explain everything that has happened on Earth according to this majority view For example Peter Urone in College Physics writes One of the most remarkable simplifications in physics is that only four distinct forces account for all known phenomena In my 2000 Mathematical Intelligencer article A Mathematician s View of Evolution I argued against this view asserting that the increase in order which has occurred on Earth seems to violate the second law of thermodynamics in a spectacular way I wrote |
| I imagine visiting the Earth when it was young and returning now to find highways with automobiles on them airports with jet airplanes and tall buildings full of complicated equipment such as televisions telephones and computers Then I imagine the construction of a gigantic computer model which starts with the initial conditions on Earth 4 billion years ago and tries to simulate the effects that the four known forces of physics |
I imagine visiting the Earth when it was young and returning now to find highways with automobiles on them airports with jet airplanes and tall buildings full of complicated equipment such as televisions telephones and computers Then I imagine the construction of a gigantic computer model which starts with the initial conditions on Earth 4 billion years ago and tries to simulate the effects that the four known forces of physics | |
| four known forces of physics the gravitational electromagnetic and strong and weak nuclear forces |
four known forces of physics the gravitational electromagnetic and strong and weak nuclear forces | |
| forces would have on every atom and every subatomic particle on our planet |
forces of physics would have on every atom and every subatomic particle on our planet | |
| perhaps using random number generators to model quantum uncertainties | | |
every atom and every subatomic particle on our planet |
| If we ran such a simulation out to the present day would it predict that the basic forces of Nature would reorganize the basic particles of Nature into libraries full of encyclopedias science texts and novels nuclear power plants aircraft carriers with supersonic jets parked on deck and computers connected to laser printers CRTs and keyboards If we graphically displayed the positions of the atoms at the end of the simulation would we find that cars and trucks had formed or that supercomputers had arisen Certainly we would not and I do not believe that adding sunlight to the model would help much |
If we ran such a simulation out to the present day would it predict that the basic forces of Nature would reorganize the basic particles of Nature into libraries full of encyclopedias science texts and novels nuclear power plants aircraft carriers with supersonic jets parked on deck and computers connected to laser printers CRTs and keyboards If we graphically displayed the positions of the atoms at the end of the simulation would we find that cars and trucks had formed or that supercomputers had arisen Certainly we would not and I do not believe that adding sunlight to the model would help much | |
| Clearly something extremely improbable has happened here on our planet with the origin and development of life and especially with the development of human consciousness and creativity 2 An unfortunate choice of words I should have said the underlying principle behind the second law is that natural forces do | | |
about probability it uses probability at the microscopic level to predict macroscopic change 3 Carbon distributes itself more and more uniformly in an isolated solid because that is what the laws of probability predict when diffusion alone is operative Thus the second law predicts that natural unintelligent causes will |
| not do macroscopically describable things which are extremely improbable from the microscopic point of view |
not do macroscopically describable things which are extremely improbable from the microscopic point of view | |
| 3 | | |
writes |
| One of the most remarkable simplifications in physics is that only four distinct forces account for all known phenomena |
One of the most remarkable simplifications in physics is that only four distinct forces account for all known phenomena | |
| College Physics Urone 2001 Postscript in 1985 Book The following appeared as a Postscript in my 1985 book Analysis a Finite Element Method PDE PROTRAN Sewell 1985j It is very similar to the first part of the Mathematical Intelligencer article reproduced in the previous chapter but is of some historical interest because of the early date As I begin my 12th year of work on TWODEPEP now PDE PROTRAN I am intrigued by the analogy between the ll year evolution of this computer code and the multi billion year history of the genetic code of life which contains a blueprint for a species encoded into billions of bits of information Like the code of life TWODEPEP began with primitive features being capable of solving only a single linear elliptic equation in Polygonal regions with simple boundary conditions It Passed through many useful stages as it adapted to nonlinear and time dependent problems systems of PDEs eigenvalue problems and as it evolved cubic and quartic elements and isoparametric elements for curved boundaries It grew a preprocessor and a graphical output package and out of core frontal and conjugate gradient methods were added to solve the linear systems Each of these changes represented major evolutionary steps new orders classes or phyla if you will The conjugate gradient method in turn also passed through several less major variations as the basic method was modified to precondition the matrix to handle nonsymmetric systems and as stopping criteria were altered etc Some of these variations might be considered new families some new genera and some only special changes I see one flaw in the analogy however While I am told that the DNA code was designed by a natural process capable of recognizing improvements but incapable of planning beyond the next random mutation I find it difficult to believe that TWODEPEP could have been designed by a programmer incapable of thinking ahead more than a few characters at a time But perhaps it might be suggested a programmer capable of making only random changes but quite skilled at recognizing improvements could given 4 5 billion years to work on it evolve such a program A few simple calculations would convince him that this programmer would have to rely on very tiny improvements For example if he could produce a billion random mutations per second or for a better analogy suppose a billion programmers could produce one mutation per second each he could not statistically hope to produce any predetermined 20 character improvement during this time period Could such a programmer with no programming or mathematical skills other than the ability to recognize and select out very small improvements through testing design a sophisticated finite element program The Darwinist would presumably say yes but to anyone who has had minimal programming experience such an idea is preposterous The major changes to TWODEPEP such as the addition of a new linear equation solver or new element required the addition or modification of hundreds of lines of code before the new feature was functional None of the changes made during this period were of any use whatever until all were in place Even the smallest modifications to that new feature once it was functional required adding several lines no one of which made any sense or provided any selective advantage when added by itself Consider by way of analogy the water tight trap of the carnivorous bladderwort plant which has a double sealed valve like door which is opened when a trigger hair is activated causing the victim to be sucked into the vacuum of the trap described by R F Daubenmire in Plants and Environment Daubenmire 1947 It is difficult to see what selective advantage this trap provided until it was almost perfect This then is the fallacy of Darwin s explanation for the causes of evolution the idea that major complex Improvements can be be broken down into many minor improvements French biologist Jean Rostand in A Biologist s View Rostand 1956 recognized this It does not seem strictly impossible that mutations should have introduced into the animal kingdom the differences which exist between one species and the next hence it is very tempting to lay also at their door the differences between classes families and orders and in short the whole of evolution But it is obvious that such an extrapolation involves the gratuitous attribution to the mutations of the past of a magnitude and power of innovation much greater than is shown by those of today The famous problem of novelties is another formulation of the objection raised here How can natural selection cause new organs to arise and guide their development through the initial stages during which they present no selective advantage the argument goes The Darwinist is forced to argue that there are no useless stages He believes that new organs and new systems of organs arose gradually through many small improvements But this is like saying that TWODEPEP could have made the transition from a single PDE to systems of PDEs through many five or six character improvements each of which made it work slightly better on systems It is interesting to note that this belief is not supported even by the fossil evidence Harvard paleontologist George Gaylord Simpson for example in The History of Life Volume II of Evolution after Darwin Simpson 1960 points out It is a feature of the known fossil record that most taxa appear abruptly They are not as a rule led up to by a sequence of almost imperceptibly changing forerunners such as Darwin believed should be usual in evolution This phenomenon becomes more universal and more intense as the hierarchy of categories is ascended Gaps among known species are sporadic and often small Gaps among known orders classes and phyla are systematic and almost always large These peculiarities of the record pose one of the most important theoretical problems in the whole history of life Is the sudden appearance of higher categories a phenomenon of evolution or of the record only due to sampling bias and other inadequacies Another way of describing this same structure is expressed in a recent Life magazine article Francis Hitching Was Darwin Wrong on Evolution April 1982 which concludes that natural selection has been tested and found wanting which focuses on the curious consistency of the fossil gaps These are not negligible gaps They are periods in all the major evolutionary transitions when immense physiological changes had to take place Unless we are willing to believe that useless developing organs and insect traps which could almost catch insects abounded in the past we should have expected the fossil structure outlined above with large gaps between the higher categories where new organs and new systems of organs appeared Nevertheless depite the fact that the structure of the fossil record is the only argument against Darwin which has received much attention lately this is not the real issue The problem of novelties correctly states the real argument but too weakly Consider for example the human eye with an aperture whose size varies automatically according to the light intensity controlled by reflex signals from the brain with a lens whose curvature vanes automatically according to the distance to the object in view and with a retina which receives the picture on color sensitive cells and transmits it complete with coded intensity and frequency information through the optic nerve to the brain The brain superimposes the pictures from the two eyes and stores this 3D picture somehow in memory and it will be able to search for and recall this image later and use it to recognize an older but familiar face in a different picture Like TWODEPEP the eye has passed through various useful stages in its development but it contains a large number of features which could not reach usefulness in a single random mutation and which provided no selective advantage until useful e g the nerves and arteries which service it and many groups of features which are useless individually The Darwinist may bridge the gaps between taxa with a long chain of tiny improvements in his imagination but the analogy with software puts his ideas into perspective The idea that all the magnificent species in the living world or the human brain with its human consciousness could have arisen from simple organic molecules guided by a natural process unable to plan beyond the next tiny mutation is entirely comparable to the idea that a programmer incapable of thinking ahead more than a few characters at a time could given a lot of time design any sophisticated computer program I suggest that with Jean Rostand we must have the courage to recognize that we know nothing of the mechanism of evolution Can Anything Happen in an Open System 5 1 A Second Look at the Second Law The following is a substantially modified version of an article which appeared in the on line American Spectator www spectator org dsp_article asp art_id 9128 December 28 2005 In the current debate over intelligent design the strongest argument offered by opponents of design is this we have scientific explanations for most everything else in Nature what is special about evolution The layman understands quite well that explaining the appearance of human brains is a fundamentally different and much more difficult sort of problem from finding the causes of earthquakes however to express this difference in terms | | |
entropy can decrease in an open system as long as it is compensated somehow by a comparable or greater increase outside the system For example Isaac Asimov in the Smithsonian journal recognizes the apparent problem You can argue of course that the phenomenon of life may be an exception to the second law Life on earth has steadily grown more complex more versatile more elaborate more orderly over the billions of years of the planet s existence From no life at all living molecules were developed then living cells then living conglomerates of cells worms vertebrates mammals finally Man And in Man is a three pound brain which as far as we know is the most complex and orderly arrangement of matter in the universe How could the human brain develop out of the primeval slime How could that vast increase in order and therefore that vast decrease in entropy have taken place but Asimov concludes that the second law is not really violated because remove the sun and the human brain would not have developed And in the billions of years that it took for the human brain to develop the increase in entropy that took place in the sun was far greater far far greater than the decrease that is represented by the evolution required to develop the human brain Similarly Peter Urone in College Physics writes Some people misuse the second law of thermodynamics stated in terms of entropy to say that the existence and evolution of life violate the law and thus require divine intervention It is true that the evolution of life from inert matter to its present forms represents a large decrease in entropy for living systems But it is always possible for the entropy of one part of the universe to decrease provided the total change in entropy of the universe increases Some other authors appear to feel a little silly suggesting that increases in entropy anywhere in the universe could compensate for decreases on Earth so they are careful to explain that this compensation only works locally for example in Order and Chaos the authors write In a certain sense the development of civilization may appear contradictory to the second law Even though society can effect local reductions in entropy the general and universal trend of entropy increase easily swamps the anomalous but important efforts of civilized man Each localized man made or machine made entropy decrease is accompanied by a greater increase in entropy of the surroundings thereby maintaining the required increase in total entropy 2 The equations of entropy change Of course the whole idea of compensation whether by distant or nearby events makes no sense logically an extremely improbable event is not rendered less improbable simply by the occurrence of compensating events elsewhere According to this reasoning the second law does not prevent scrap metal from reorganizing itself into a computer in one room as long as two computers in the next room are rusting into scrap metal and the door is open 1 Or the thermal entropy in the next room is increasing though I am not sure how fast it has to increase to compensate computer construction To understand where this argument comes from we need to look at the equations for entropy change as given in Appendix D of my 2005 John Wiley book and previously in my 2001 Mathematical Intelligencer article Can ANYTHING Happen in an Open System Consider the diffusion conduction of heat in a solid R with absolute temperature distribution U x y z t The first law of thermodynamics conservation of energy requires that Qt J 1 where Q is the heat energy density Qt c Ut and J is the heat flux vector The second law requires that the flux be in a direction in which the temperature is decreasing i e J U 0 2 Eq 2 simply says that heat flows from hot to cold regions because the laws of probability favor a more uniform distribution of heat energy 1 It may be noted that something must actually be entering or leaving a system before it can be considered open but if you can see into the next room electromagnetic radiation at least is entering and that is what makes the Earth an open system Thermal entropy is a quantity that is used to measure randomness in the distribution of heat The rate of change of thermal entropy S is given by the usual definition as St R Qt U dV 3 Using 3 and the first law 1 after doing a multidimensional integration by parts we get St R J U U2 dV R J n U dA 4 where n is the outward unit normal on the boundary R From the second law 2 we see that the volume integral is nonnegative and so St R J n U dA 5 From 5 it follows that St 0 in an isolated closed system where there is no heat flux through the boundary J n 0 Hence in a closed system the entropy can never decrease Since thermal entropy measures randomness disorder in the distribution of heat its opposite negative can be referred to as thermal order and we can say that the thermal order can never increase in a closed system Since thermal entropy is quantifiable the application of the second law to thermal entropy is commonly used as the model problem on which our thinking about the other less quantifiable applications is based The fact that thermal entropy cannot decrease in a closed system but can decrease in an open system was used to conclude that in other applications any entropy decrease in an open system is possible as long as it is compensated somehow by entropy increases outside this system so that the total entropy as though there were only one type in the universe or any other closed system containing the open system still increases However there is really nothing special about thermal entropy Heat conduction is just diffusion of heat and we can define an X entropy and an X order X entropy to measure the randomness in the distribution of any other substance X that diffuses for example we can let U x y z t represent the concentration of carbon diffusing in a solid and use Eq 3 again to define this entropy c 1 now so Qt Ut and repeat the analysis leading to Eq 5 which now says that the carbon order cannot increase in a closed system 2 Furthermore Eq 5 does not simply say that the X entropy cannot decrease in a closed system it also says that in an open system the X entropy cannot decrease faster than it is exported through the boundary because the boundary integral there represents the rate at which X entropy is exported across the boundary To see this notice that without the denominator U the integral in 3 represents the rate of change of total X energy if X heat in the system with the denominator it represents the rate of change of X entropy Without the denominator U the boundary integral in 5 represents the rate at which X energy if X heat is exported through the boundary with the denominator therefore it must represent the rate at which X entropy is exported Although I am certainly not the first to recognize that the boundary integral has this interpretation see p 202 this has been noticed by relatively few people no doubt because usually the special case of isotropic heat conduction or diffusion is assumed in which case J K U and then the numerator in the boundary integral is written as K U n and in this form it is not obvious that anything is being imported or exported only that in a closed system the boundary integral is zero Furthermore entropy as defined by 3 seems to be a rather abstract quantity and it is hard to visualize what it means to import or export entropy Stated in terms of order Eq 5 says that the X order in an open system cannot increase faster than it is imported through the boundary According to 4 the X order in a system can decrease in two different ways it can be converted to disorder first integral term or it can be exported through the boundary boundary integral term It can increase in only one way by importation through the boundary 3 A tautology The second law of thermodynamics is all about probability it uses probability at the microscopic level to predict macroscopic change 3 Carbon distributes itself more and more uniformly in an isolated solid because that is what the laws of probability predict when diffusion alone is operative Thus the second law predicts that natural unintelligent causes will not do macroscopically describable things which are extremely improbable from the microscopic point of view 2 Entropy sounds much more scientific than order but note that in this paper order is simply defined as the opposite of entropy Where entropy is quantifiable such as here order is equally quantifiable Physics textbooks also often use the term entropy in a less precise sense to describe the increase in disorder associated with for example a plate breaking or a bomb exploding e g p 651 In such applications order is equally difficult to quantify 3 In Classical and Modern Physics Kenneth Ford writes There |
| a scientist can understand requires a discussion of the second law of thermodynamics |
are a variety of ways in which the second law of thermodynamics | |
| The first formulations of the second law were all about heat a quantity called thermal entropy was defined to measure the randomness or disorder associated with a temperature distribution and it was shown that in an isolated system this entropy always increases or at least never decreases as heat diffuses and the temperature becomes more and more randomly more uniformly distributed If we define thermal order to be the opposite negative of thermal entropy we can say that the thermal order can never increase in a closed isolated system However it was soon realized that other types of order can be defined which also never increase in a closed system for example we can define a carbon order associated with the distribution of carbon diffusing in a solid using the same equations and through an identical analysis show that this order also continually decreases in a closed system With time the second law came to be interpreted more and more generally and today most discussions of the second law in physics textbooks offer examples of entropy increases or order decreases since we are defining order to be the opposite of entropyl which have nothing to do with heat conduction or diffusion such as the shattering of a wine glass or the demolition of a building For example in Basic Physics Ford 1968 Kenneth Ford writes Imagine a motion picture of any scene of ordinary life run backward You might watch a pair of mangled automobiles undergoing instantaneous repair as they back apart Or a dead rabbit rising to scamper backward into the woods as a crushed bullet re forms and flies backward into a rifle Or something as simple as a cup of coffee on a table gradually becoming warmer as it draws heat from its cooler surroundings All of these backward in time views and a myriad more that you can quickly think of are ludicrous and impossible for one reason only they violate the second law of thermodynamics In the actual scene of events entropy is increasing In the time reversed view entropy is decreasing It is a well known prediction of the second law that in a closed system every type of order is unstable and must eventually decrease as everything tends toward more probable states Natural forces such as corrosion erosion fire and explosions do not create order they destroy it S Angrist and 1 Hepler in Order and Chaos Angrist and Hepler 1967 write An arsonist working on a big library is merely speeding up the inevitable result demanded by the second law | | |
open system still increases However there is really nothing special about thermal entropy Heat conduction is just diffusion of heat and we can define an X entropy and an X order X entropy to measure the randomness in the distribution of any other substance X that diffuses for example we can let U x y z t represent the concentration of carbon diffusing in a solid and use Eq 3 again to define this entropy c 1 now so Qt Ut and repeat the analysis leading to Eq 5 which now says that the carbon order cannot increase in a closed system 2 Furthermore Eq 5 does not simply say that the X entropy cannot decrease in a closed system it also says that in an open system the X entropy cannot decrease faster than it is exported through the boundary because the boundary integral there represents the rate at which X entropy is exported across the boundary To see this notice that without the denominator U the integral in 3 represents the rate of change of total X energy if X heat in the system with the denominator it represents the rate of change of X entropy Without the denominator U the boundary integral in 5 represents the rate at which X energy if X heat is exported through the boundary with the denominator therefore it must represent the rate at which X entropy is exported Although I am certainly not the first to recognize that the boundary integral has this interpretation see p 202 this has been noticed by relatively few people no doubt because usually the special case of isotropic heat conduction or diffusion is assumed in which case J K U and then the numerator in the boundary integral is written as K U n and in this form it is not obvious that anything is being imported or exported only that in a closed system the boundary integral is zero Furthermore entropy as defined by 3 seems to be a rather abstract quantity and it is hard to visualize what it means to import or export entropy Stated in terms of order Eq 5 says that the X order in an open system cannot increase faster than it is imported through the boundary According to 4 the X order in a system can decrease in two different ways it can be converted to disorder first integral term or it can be exported through the boundary boundary integral term It can increase in only one way by importation through the boundary 3 A tautology |
| The second law is all about probability it uses probability at the microscopic level to predict macroscopic change |
The second law of thermodynamics is all about probability it uses probability at the microscopic level to predict macroscopic change | |
| the reason | | |
change 3 |
| carbon distributes itself more and more uniformly in an insulated solid is that is what the laws of probability predict when diffusion alone is operative |
Carbon distributes itself more and more uniformly in an isolated solid because that is what the laws of probability predict when diffusion alone is operative | |
| The reason natural forces may turn a spaceship or a TV set or a computer into a pile of rubble but | | |
spontaneous change is from order to disorder The reason natural forces can turn a computer or a spaceship into rubble and |
| not vice versa is also probability of all the possible arrangements atoms could take only a very small percentage could |
not vice versa is probability of all the possible arrangements atoms could take only a very small percentage could | |
| fly to the moon and back or receive pictures and sound from the other side of the Earth or add subtract multiply and divide real numbers with high accuracy The second law is the reason that automobiles will degenerate into scrap metal over time or quickly as in Ford s movie and in the absence of intelligence the reverse process will not occur and it is the reason that Ford s rabbit and other animals when they die decay into simple organic and inorganic compounds and in the absence of intelligence the reverse process will not occur The discovery that life on Earth developed through evolutionary steps coupled with the observation that mutations and natural selection like other natural forces can cause minor change is widely accepted in the scientific world as proof that natural selection alone among all natural forces can create order out of disorder and even design human brains with human consciousness Only the layman seems to see the problem with this logic And where is the overwhelming evidence that justifies not only believing that natural selection can design human brains but justifies branding as antiscience anyone who doubts that it can In his new book The Edge of Evolution Behe 2007 Lehigh University biochemist Michael Behe looks in considerable detail at the struggle for survival between humans and the malaria parasite where in the last 100 years the evolution of far more organisms can be studied than were involved in the entire natural history of mammals He finds that natural selection can be credited with some very minor change but Far and away the most extensive relevant data we have on the subject of evolution s effects on competing organisms is that accumulated on interactions between humans and our parasites As with the example of malaria the data show trench warfare with acts of desperate destruction not arms races with mutual improvements The thrust and parry of human malaria evolution did not build anything it only destroyed things Behe also looks at Richard Lenski s 20 year E coli experiment which a June 9 2008 New Scientist article now claims represents the first time evolution has been caught in the act and concludes that nothing fundamentally new has been produced Behe claims that the minor changes observed in this experiment are all due to breaking some genes and turning others off In any case the New Scientist article contains a remarkable admission that natural selection has never before and not even now according to Behe been actually observed to produce any significant advance To claim that the mechanism which produces such minor changes in bacteria and parasite populations is capable of producing human brains is an incredible extrapolation yet this claim is routinely presented as being as well established as gravity In any other field a scientist making such an extrapolation with such confidence would be the laughingstock of his peers In a 2000 Mathematical Intelligencer article I asserted that the idea that the four fundamental forces of physics alone could rearrange the fundamental particles of Nature into spaceships nuclear power plants and computers connected to laser printers CRTs keyboards and the internet appears | | |
A second look at the second law Granville Sewell Mathematics Department University of Texas El Paso United States It is commonly argued that the spectacular increase in order which has occurred on Earth does not violate the second law of thermodynamics because the Earth is an open system and anything can happen in an open system as long as the entropy increases outside the system compensate the entropy decreases inside the system However if we define X entropy to be the entropy associated with any diffusing component X for example X might be heat and since entropy measures disorder X order to be the negative of X entropy a closer look at the equations for entropy change shows that they not only say that the X order cannot increase in a closed system but that they also say that in an open system the X order cannot increase faster than it is imported through the boundary Thus the equations for entropy change do not support the illogical compensation idea instead they illustrate the tautology that if an increase in order is extremely improbable when a system is closed it is still extremely improbable when the system is open unless something is entering which makes it not extremely improbable Thus unless we are willing to argue that the influx of solar energy into the Earth makes the appearance of spaceships computers and the Internet not extremely improbable we have to conclude that the second law has in fact been violated here 1 Compensation It is probably fair to say that the majority view of science today holds that physics explains all of chemistry chemistry explains all of biology and biology completely explains the human mind thus physics alone explains the human mind and all it does In fact since there are only four known forces of physics the gravitational electromagnetic and strong and weak nuclear forces this means that these four forces must explain everything that has happened on Earth according to this majority view For example Peter Urone in College Physics writes One of the most remarkable simplifications in physics is that only four distinct forces account for all known phenomena In my 2000 Mathematical Intelligencer article A Mathematician s View of Evolution I argued against this view asserting that the increase in order which has occurred on Earth seems |
| to violate the second law of thermodynamics in a spectacular way |
to violate the second law of thermodynamics in a spectacular way | |
| Anyone who has made such an argument is familiar with the standard reply the Earth is an open system it receives energy from the sun and |
Anyone who has made such an argument is familiar with the standard reply the Earth is an open system it receives energy from the sun and | |
| order can increase | | |
any entropy decrease |
| in an open system as long as it is compensated somehow by |
in an open system is possible as long as it is compensated somehow by | |
| in an open system as long as it is compensated somehow by a comparable or greater |
in an open system as long as it is compensated somehow by a comparable or greater | |
| decrease outside the system | | |
the human brain Similarly |
| Peter Urone for example in College Physics Urone 2001 writes Some people misuse the second law of thermodynamics stated in terms of entropy to say that the existence and evolution of life violate the law and thus require divine intervention It is true that the evolution of life from inert matter to its present forms represents a large decrease in entropy for living systems But it is always possible for the entropy of one part of the universe to decrease provided the total change in entropy of the universe increases |
Peter Urone in College Physics writes Some people misuse the second law of thermodynamics stated in terms of entropy to say that the existence and evolution of life violate the law and thus require divine intervention It is true that the evolution of life from inert matter to its present forms represents a large decrease in entropy for living systems But it is always possible for the entropy of one part of the universe to decrease provided the total change in entropy of the universe increases | |
| According to this reasoning then the second law does not prevent scrap metal from reorganizing itself into a computer in one room as long as two computers in the next room are rusting into scrap metal and the door is open Or the thermal |
According to this reasoning the second law does not prevent scrap metal from reorganizing itself into a computer in one room as long as two computers in the next room are rusting into scrap metal and the door is open 1 Or the thermal | |
| order | | |
entropy |
| in the next room is decreasing though I m not sure |
in the next room is increasing though I am not sure | |
| what the conversion rate is between computers and thermal order This strange argument of compensation | | |
entropy change Of course the whole idea of compensation whether by distant or nearby events |
| makes no sense logically an extremely improbable event is not rendered less improbable by the occurrence of |
makes no sense logically an extremely improbable event is not rendered less improbable simply by the occurrence of | |
| other events which are more probable To understand where this argument of compensation comes from one needs to understand that of the example applications mentioned in the Ford text above the coffee cup example is special the application to heat conduction is special not only because it was the first application but because it is quantifiable It | | |
closed system the entropy can never decrease Since thermal entropy measures randomness disorder in the distribution of heat its opposite negative can be referred to as thermal order and we can say that the thermal order can never increase in a closed system Since thermal entropy is quantifiable the application of the second law to thermal entropy |
| is commonly used as the model problem on which our thinking about the other less quantifiable applications is based The fact that thermal |
is commonly used as the model problem on which our thinking about the other less quantifiable applications is based The fact that thermal | |
| order cannot increase in a closed system but can increase | | |
entropy cannot decrease in a closed system but can decrease |
| in an open system was used to conclude that in other applications anything |
in an open system was used to conclude that in other applications any | |
| can happen in an open system as long as it is compensated by order decreases outside this system so that the total order in the universe or any closed system containing the open system still decreases In Appendix D of The Numerical Solution of Ordinary and Partial Differential Equations Sewell 2005 included as section 5 6 I take a closer look at the equations for entropy change which apply not only to thermal entropy but also to the entropy associated with anything else that diffuses and show that they do not simply | | |
occurred on Earth does not violate the second law of thermodynamics because the Earth is an open system and anything can happen in an open system as long as the entropy increases outside the system compensate the entropy decreases inside the system However if we define X entropy to be the entropy associated with any diffusing component X for example X might be heat and since entropy measures disorder X order to be the negative of X entropy a closer look at the equations for entropy change shows that they not only |
| say that order cannot increase in a closed system they also say that in an open system order cannot increase faster than it is imported through the boundary |
say that the X order cannot increase in a closed system but that they also say that in an open system the X order cannot increase faster than it is imported through the boundary | |
| say that in an open system order cannot increase faster than it is imported through the boundary According to |
says that the X order in an open system cannot increase faster than it is imported through the boundary According to | |
| these equations the thermal | | |
to 4 the X |
| order in an open system can decrease in two different ways it can be converted to disorder or it can be exported through the boundary It can increase in only one way by importation through the boundary |
order in a system can decrease in two different ways it can be converted to disorder first integral term or it can be exported through the boundary boundary integral term It can increase in only one way by importation through the boundary | |
| Similarly | | |
is |
| the increase in carbon order in an open system cannot be greater than the |
the following Order can increase in an open system not because the | |
| carbon order imported through the boundary and the increase in chromium order cannot be greater than the chromium order imported through the boundary and so on | | |
is not What happens in a closed system depends on the initial conditions what happens in an open system depends on the boundary conditions as well |
| The compensation argument was produced by people who generalized the model equation for closed systems but forgot to generalize the equation for open systems Both equations are only valid for our simple models where it is assumed that only heat conduction or diffusion is going on naturally in more complex situations the laws of probability do not make such simple predictions Nevertheless in |
The compensation counter argument was produced by people who generalized the model equation for closed systems but forgot to generalize the equation for open systems Both equations are only valid for our simple models where it is assumed that only heat conduction or diffusion is going on naturally in more complex situations the laws of probability do not make such simple predictions Nevertheless in | |
| Sewell 2001 | | |
Open System |
| I generalized the equation for open systems to the following tautology which is valid in all situations If an increase in order is extremely improbable when a system is closed it is still extremely improbable when the system is open unless something is entering which makes it not extremely improbable The fact that order is disappearing in the next room does not make it any easier for computers to appear in our room unless this order is disappearing into our room and then only if it is a type of order that makes the appearance of computers not extremely improbable for example computers Importing thermal order |
I generalized the equations for open systems to the following tautology which is valid in all situations If an increase in order is extremely improbable when a system is closed it is still extremely improbable when the system is open unless something is entering which makes it not extremely improbable The fact that order is disappearing in the next room does not make it any easier for computers to appear in our room unless this order is disappearing into our room and then only if it is a type of order that makes the appearance of computers not extremely improbable for example computers Importing thermal order | |
| makes the appearance of computers not extremely improbable |
makes the appearance of spaceships computers and the Internet not extremely improbable | |
| for example computers Importing thermal order will | | |
thermal order into an open system may |
| make the temperature distribution less random and importing carbon order |
make the temperature distribution less random and importing carbon order | |
| will | | |
may |
| make the carbon distribution less random but neither makes the formation of computers more probable |
make the carbon distribution less random but neither makes the formation of computers more probable | |
| What happens in a closed system depends on the initial conditions what happens in an open system depends on the boundary conditions as well |
What happens in a closed system depends on the initial conditions what happens in an open system depends on the boundary conditions as well | |
| As I wrote in Can ANYTHING Happen in an Open System 7 Sewell 2001 | | |
probable My conclusion from Can ANYTHING Happen in an Open System is the following |
| order can increase in an open system not because the laws of probability are suspended when the door is open but simply because order may walk in through the door If we found evidence that DNA auto parts computer chips and books entered through the Earth s atmosphere at some time in the past then perhaps the appearance of humans cars computers and encyclopedias on a previously barren planet could be explained without postulating a violation of the second law here But if all we see entering is radiation and meteorite fragments it seems clear that what is entering through the boundary cannot explain the increase in order observed here |
Order can increase in an open system not because the laws of probability are suspended when the door is open but simply because order may walk in through the door If we found evidence that DNA auto parts computer chips and books entered through the Earth s atmosphere at some time in the past then perhaps the appearance of humans cars computers and encyclopedias on a previously barren planet could be explained without postulating a violation of the second law here But if all we see entering is radiation and meteorite fragments it seems clear that what is entering through the boundary cannot explain the increase in order observed here | |
| Evolution is a movie running backward that is what makes it so different from every other known process in our universe and that is why it demands a radically different explanation Evolutionists have always countered this argument with the claim that the transformation of a barren rocky planet into what we see today | | |
A second look at the second law Granville Sewell Mathematics Department University of Texas El Paso United States It is commonly argued that the spectacular increase in order which has occurred on Earth |
| does not violate the second law because the Earth |
does not violate the second law of thermodynamics because the Earth | |
| receives energy from the sun Now that the silliness of this argument has become evident we are beginning to hear a new argument which basically says wait a minute the second law of thermodynamics really applies only to thermodynamics after all because otherwise there are so many types of order that order is a meaningless concept In the original Mathematical Intelligencer article Sewell 2000 I made the assertion that the underlying principle behind the second law is that natural forces do not do extremely improbable things The journal and I received several replies arguing that everything Nature does can be considered extremely improbable the exact arrangement of atoms at any time at any place is extremely unlikely to be repeated noted one e mail In another published reply Davis 2001 the author made an analogy with coin flipping and argued that any particular sequence of heads and tails is extremely improbable so something extremely improbable happens every time we flip a long series of coins If a coin were flipped 1000 times he would apparently be no more surprised by a string of all heads than by any other sequence because any string is as improbable as another This critic concedes that it is extremely unlikely that humans and computers would arise again if history were repeated but something would Obviously I should have been more careful with my wording in the first article I should have said that the underlying principle behind the second law is that natural forces do not do macroscopically describable things which are extremely improbable from the microscopic point of view A macroscopically describable event is just any event which | | |
is not really extremely improbable Not many people are willing to make this argument however in fact the claim that the second law does not apply to open systems was invented in an attempt to avoid having to make this argument And perhaps it only seems extremely improbable but really is not that under the right conditions the influx of stellar energy into a planet could cause atoms to rearrange themselves into nuclear power plants and spaceships and digital computers But one would think that at least this would be considered an open question and those who argue that it really is extremely improbable and thus contrary to the basic principle underlying the second law of thermodynamics would be given a measure of respect and taken seriously by their colleagues but we are not References 4 If we repeat an experiment 2k times and define an event to be simply describable macroscopically describable if it can be described in m or fewer bits so that there are 2m or fewer such events and extremely improbable when it has probability 1 2n or less then the probability that any extremely improbable simply describable event will ever occur is less than 2k m 2n Thus we just have to make sure to choose n to be much larger than k m If we flip a billion fair coins any outcome we get can be said to be extremely improbable but we only have cause for astonishment if something extremely improbable and simply describable happens such as all heads or every third coin is tails or only every third coin is tails For practical purposes almost anything that |
| can be described without resorting to an atom by atom or coin by coin accounting |
can be described without resorting to an atom by atom or coin by coin accounting | |
| Carbon distributes itself more and more uniformly in an insulated solid because there are many more arrangements of carbon atoms which produce nearly uniform distributions than produce highly nonuniform distributions Natural forces may turn a spaceship into a pile of rubble but not vice versa not because the exact arrangement of atoms in a given spaceship is more improbable than the exact arrangement of atoms in a given pile of rubble but because whether the Earth receives energy from the Sun or not there are very few arrangements of atoms which would be able to fly to the moon and return safely and very many which could not The reader familiar with William Dembski s specified complexity concept Dembski 2006 will recognize similarities to the argument here natural forces do not do things which are specified macroscopically describable and complex extremely improbable Both are just attempts to state in more scientific terms what is already obvious to the layman that unintelligent forces cannot do intelligent things Another popular way to state this only intelligence can create information For example Casey Luskin of the Discovery Institute in a December 2 2008 entry at www evolutionnews org reports finding a children s book about life on other planets which provides a recipe for life organic molecules water and energy Luskin points out that One extremely important component that is missing from our recipe is information experience teaches that the sort of information we find in life has only one real common source intelligent agency Molecular biologist Jonathan Wells Wells 2006 says The secret of life is not the physical DNA molecule but the 5 CAN ANYTHING HAPPEN IN AN OPEN SYSTEM 73 information it carries Stephen Meyer in his new book Signature in the Cell Meyer 2009 says information typically degrades over time unless intelligent agents generate or regenerate it The second law of thermodynam_ ics applies to information If we toss a billion fair coins it is true that any sequence is as improbable as any other but most of us would still be surprised and suspect that something other than chance is going on if the result were all heads or alternating heads and tails or even all tails except for coins 3i 5 for integer i When we produce simply describable results like these we have done something macroscopically describable which is extremely improbable There are so many simply describable sequences possible that it is tempting to think that all or most outcomes could be simply described in some way but in fact there are fewer than 230000 different 1000 word paragraphs so the odds are about 2999970000 to 1 that a given sequence will not be that highly orderedso our surprise would be quite justified And if it can t be described in 1000 English words and symbols it isn t very simply describable In the real world it is sometimes much harder to say what the laws of probability predict than in a coin flipping eXperiment thus here it may be even harder to define and measure order but sometimes it is easy In any case with 10 23 molecules in a mole of anything we can be confident that the laws of probability at the microscopic level will be obeyed at least on planets without life as they apply to all macroscopic phenomena this is precisely the assumption the only common threadbehind all applications of the second law Everything the second law predicts it predicts with such high prob 74 IN THE BEGINNING ability that it is as reliable as any other law of sciencetossing a billion heads in a row is child s play compared to appreciably violating the second law in any applica tion One critic Rosenhouse 2001 wrote His claim that natural forces do not cause extremely improbable things to happen is pure gibberish Does Sewell invoke supernatural forces to explain the winning numbers in last night s lottery But getting the right number on 5 or 6 balls is not extremely improbable in thermodynamics extremely improbable events involve getting the right number on 100 000 000 000 000 000 000 000 or so balls If every atom on Earth bought one ticket every second since the big bang about 1070 tickets there is virtually no chance that any would ever win even a 100 ball lottery much less this one And since the second law derives its authority from logic alone and thus cannot be overturned by future discoveries Sir Arthur Eddington Eddington 1929 called it the supreme law of Nature Although it is true that we sometimes are not sure what the second law predicts it is not true that there are so many macroscopically describable phenomena that the second law cannot be expected to hold when applied to all of them there are relatively few simply describable phenomena It is not true as the new argument asserts that there are so many types of order that the appearance of computers and TV sets needs no explanation 5 3 Darwin s Order Source The evolutionist therefore cannot avoid the question of probability by saying that anything can happen in an open system nor can he avoid it by saying that there are so many types of order that order is a meaningless 5 CAN ANYTHING HAPPEN IN AN OPEN SYSTEM 75 concept He is finally forced to argue that | | |
in an open system cannot increase faster than it is imported through the boundary According to 4 the X order in a system can decrease in two different ways it can be converted to disorder first integral term or it can be exported through the boundary boundary integral term It can increase in only one way by importation through the boundary 3 A tautology The second law of thermodynamics is all about probability it uses probability at the microscopic level to predict macroscopic change 3 Carbon distributes itself more and more uniformly in an isolated solid because that is what the laws of probability predict when diffusion alone is operative Thus the second law predicts that natural unintelligent causes will not do macroscopically describable things which are extremely improbable from the microscopic point of view 2 Entropy sounds much more scientific than order but note that in this paper order is simply defined as the opposite of entropy Where entropy is quantifiable such as here order is equally quantifiable Physics textbooks also often use the term entropy in a less precise sense to describe the increase in disorder associated with for example a plate breaking or a bomb exploding e g p 651 In such applications order is equally difficult to quantify 3 In Classical and Modern Physics Kenneth Ford writes There are a variety of ways in which the second law of thermodynamics can be stated and we have encountered two of them so far 1 For an isolated system the direction of spontaneous change is from an arrangement of lesser probability to an arrangement of greater probability 2 For an isolated system the direction of spontaneous change is from order to disorder The reason natural forces can turn a computer or a spaceship into rubble and not vice versa is probability of all the possible arrangements atoms could take only a very small percentage could add subtract multiply and divide real numbers or fly astronauts to the moon and back safely Of course we must be careful to define extremely improbable events to be events of probability less than some very small threshold if we define events of probability less than 1 to be extremely improbable then obviously natural causes can do extremely improbable things But after we define a sufficiently low threshold everyone seems to agree that natural forces will rearrange atoms into digital computers is a macroscopically describable event that is still extremely improbable from the microscopic point of view and thus forbidden by the second law at least if this happens in a closed system But it is not true that the laws of probability only apply to closed systems if a system is open you just have to take into account what is crossing the boundary when deciding what is extremely improbable and what is not What happens in a closed system depends on the initial conditions what happens in an open system depends on the boundary conditions as well The compensation counter argument was produced by people who generalized the model equation for closed systems but forgot to generalize the equation for open systems Both equations are only valid for our simple models where it is assumed that only heat conduction or diffusion is going on naturally in more complex situations the laws of probability do not make such simple predictions Nevertheless in Can ANYTHING Happen in an Open System I generalized the equations for open systems to the following tautology which is valid in all situations If an increase in order is extremely improbable when a system is closed it is still extremely improbable when the system is open unless something is entering which makes it not extremely improbable The fact that order is disappearing in the next room does not make it any easier for computers to appear in our room unless this order is disappearing into our room and then only if it is a type of order that makes the appearance of computers not extremely improbable for example computers Importing thermal order into an open system may make the temperature distribution less random and importing carbon order may make the carbon distribution less random but neither makes the formation of computers more probable My conclusion from Can ANYTHING Happen in an Open System is the following Order can increase in an open system not because the laws of probability are suspended when the door is open but simply because order may walk in through the door If we found evidence that DNA auto parts computer chips and books entered through the Earth s atmosphere at some time in the past then perhaps the appearance of humans cars computers and encyclopedias on a previously barren planet could be explained without postulating a violation of the second law here But if all we see entering is radiation and meteorite fragments it seems clear that what is entering through the boundary cannot explain the increase in order observed here 4 Conclusions Of course one can still argue that the spectacular increase in order seen on Earth does not violate the second law because what has happened here is not really extremely improbable Not many people are willing to make this argument however in fact the claim that the second law does not apply to open systems was invented in an attempt to avoid having to make this argument And perhaps |
| it only seems extremely improbable but really isn t that |
it only seems extremely improbable but really is not that | |
| atoms would rearrange themselves into spaceships and computers and the internet Darwinists believe they have already discovered the source of all this order so let us look more closely at their theory The traditional argument against Darwinism is that natural selection cannot guide the development of new organs and new systems of organs i e the development of new orders classes and phyla through their initial useless stages during which they provide no selective advantage Natural selection may be able to darken the wings of a moth even this is disputed but that does not mean it can design anything complex Consider for example the aquatic bladderwort described in Plants and Environment Daubenmire 1947 The aquatic bladderworts are delicate herbs that bear bladder like traps 5mm or less in diameter These traps have trigger hairs attached to a valve like door which normally keeps the trap tightly closed The sides of the trap are com pressed under tension but when a small form of animal life touches one of the trigger hairs the valve opens the bladder suddenly expands and the animal is sucked into the trap The door closes at once and in about 20 minutes the trap is set ready for another victim In a Nature Encyclopedia of Life Sciences Lonnig and Becker 2004 article on Carnivorous Plants authors WolfEkkehard Lonnig and Heinz Albert Becker acknowledge that it appears to be hard to even imagine a clearcut selective advantage for all the thousands of postulated intermediate steps in a gradual scenario for the ori 76 IN THE BEGINNING gin of the complex carnivorous plant structures examined above The development of any major new feature presents similar problems and according to Lehigh University biochemist Michael Behe who describes several spectacular examples in detail in Darwin s Black Box Behe 1996 the world of microbiology is especially loaded with such examples of irreducible complexity It seems that until the trigger hair the door and the pressurized chamber were all in place and the ability to digest small animals and to reset the trap to be able to catch more than one animal had been developed none of the individual components of this carnivorous trap would have been of any use What is the selective advantage of an incomplete vacuum chamber To the casual observer it might seem that none of the components of this trap would have been of any use whatever until the trap was almost perfect but of course a good Darwinist will imagine two or three far fetched intermediate useful stages and consider the problem solved I believe you would need to find thousands of intermediate stages before this example of irreducible complexity has been reduced to steps small enough to be bridged by single random mutations a lot of things have to happen behind the scenes and at the microscopic level before this trap could catch and digest animals But I don t know how to prove this I am further sure that even if you could imagine a long chain of useful intermediate stages each would present such a negligible selective advantage that nothing as clever as this carnivorous trap could ever be produced but I can t prove that either Finally that natural selection seems even remotely plausible depends on the fact that 5 CAN ANYTHING HAPPEN IN AN OPEN SYSTEM 77 while species are awaiting further improvements their current complex structure is locked in and passed on perfectly through many generations in fact errors are constantly corrected and damage is constantly repaired This phenomenon is observed but inexplicable I don t see any reason why all living organisms do not constantly decay into simpler components as in fact they do as soon as they die 3 When you look at the individual steps in the development of life Darwin s explanation is difficult to disprove because some selective advantage can be imagined for almost anything Like most other schemes designed to violate the second law it is only when you look at the net result that it becomes obvious it won t work A November 2004 National Geographic article proclaims that the evidence is overwhelming that Darwin was right about evolution Since there is no proof that natural selection has ever done anything more spectacular than cause bacteria to develop drug resistant strains where is the overwhelming evidence that justifies assigning to it an ability we do not attribute to any other natural force in the universe the ability to create order out of disorder Three types of evidence are cited first the fact that species are so well suited to their environments is offered 3 Some Darwinists use computer programs written by intelligent humans which contain strings that simulate information in the DNA and they run these programs on computers designed and maintained by intelligent humans They introduce random errors into the strings test the new strings for fitness in SOme way and discard the less fit strings and claim the modest progress observed simula tes evolution If they want to see what unintelligent forces alone can accomplish however they should introduce ra ndom errors not only into the strings but throughout the entire program the compiler and operating system it uses and the computer hardware If you are trying to simulate how the accumulation of molecular accidents could produce complex organisms why assume that only the DNA molecules are vulnerable to random damage This analogy was suggested by Gil Dodgen 78 IN THE BEGINNING as evidence that they have adapted to them Of course if they were not well adapted they would be extinct and that would be offered as even stronger evidence against design Second they point to minor changes due to artificial selection where intelligent humans select features already present in the gene pool as evidence of what can be accomplished when natural forces select among genetic accidents But as always the main evidence offered is the evolutionary tree of similarities connecting all species fossil and living These similarities were of course noticed long before Darwin many animals have four legs one head two eyes and a tail all modern science has done is to show that the similarities go much deeper than those noticed by ancient man Although these similarities may to our modern minds suggest natural causes they do not really tell us anything about what those causes might be In fact the fossil record does not even support the idea that new organs and new systems of organs arose gradually new orders classes and phyla consistently appear suddenly Gaps among known orders classes and phyla are systematic and almost always large Simpson 1960 see Section 3 2 An analogy may be useful here If some future paleontologist were to unearth two species of Volkswagens he might find it plausible that one evolved gradually from the other He might find the lack of gradual transitions between automobile families more problematic for example in the transition from mechanical to hydrauliC brake systems or from manual to automatic transmissions or from steam engines to internal combustion engines though if he thought about what gradual transitions would look like he would understand why they 5 CAN ANYTHING HAPPEN IN AN OPEN SYSTEM 79 didn t exist He would be even more puzzled by the huge differences between the bicycle and motor vehicle phyla or between the boat and airplane phyla But heaven help us if he uncovers motorcycles and Hovercraft the discovery of these missing links would be hailed in all our newspapers as final proof that all forms of transporta_ dtieosnig na r ose gradually from a common ancestor without Interestingly although the similarities between species in the same branch of the evolutionary tree may suggest common descent similarities even genetic similarities also frequently arise independently in distant branches where they cannot be explained by common descent This phenomenon known as convergence suggests common design rather than common descent the probability of similar designs arising independently through random processes is very small but a designer could of course take a good design and apply it several times in different places to unrelated species For example in their abovecited Nature Encyclopedia of Life Sciences article L6nnig and Becker 2004 on Carnivorous Plants Wolf Ekkehard L6nnig and Heinz Albert Becker note that carnivory in plants must have arisen several times independently of each other the pitchers might have arisen seven times separately adhesive traps at least four times snap traps two times and suction traps possibly also two times The independent origin of complex synorganized structures which are often anatomically and phYSiologically very similar to each other appears to be intrinsically unlikely to many authors so that they have tried to avoid the hypothesis of convergence as far as possible Since I am well aware that logic and evidence are powerless against the popular perception nurtured by pres 80 IN THE BEGINNING tigious journals such as National Geographic and Nature that no serious scientists harbor any doubts about Darwinism I want to offer here a portion of a November 5 1980 New York Times News Service report Biology s understanding of how evolution works which has long postulated a gradual process of Darwinian natural selection acting on genetic mutations is undergoing its broadest and deepest revolution in nearly 50 years At the heart of the revolution is something that might seem a paradox Recent discoveries have only strengthened Darwin s epochal conclusion that all forms of life evolved from a common ancestor Genetic analysis for example has shown that every organism is governed by the same genetic code controlling the same biochemical processes At the same time however many studies suggest that the origin of species was not the way Darwin suggested Exactly how evolution happened is now a matter of great controversy among biologists Although the debate has been under way for several years it reached a crescendo last month as some 150 scientists specializing in evolutionary studies met for four days in Chicago s Field Museum of Natural History to thrash out a variety of new hypotheses that are challenging older ideas The meeting which was closed to all but a few observers included nearly all the leading evolutionists in paleontology population genetics taxonomy and related fields No clear resolution of the controversies was in sight This fact has often been exploited by religious fundamen 5 CAN ANYTHING HAPPEN IN AN OPEN SYSTEM talists who misunderstood it to suggest weakness in the fact of evolution rather than the perceived mechanism Actually it reflects significant progress toward a much deeper understanding of the history of life on Earth At issue during the Chicago meeting was macroevolution a term that is itself a matter of debate but which generally refers to the evolution of major differences such as those separating species or larger classifications Darwin suggested that such major products of evolution were the results of very long periods of gradual natural selection the mechanism that is widely accepted today as accounting for minor adaptations Darwin knew he was on shaky ground in extending natural selection to account for differences between major groups of organisms The fossil record of his day showed no gradual transitions between such groups but he suggested that further fossil discoveries would fill the missing links The pattern that we were told to find for the last 120 years does not exist declared Niles Eldridge a paleontologist from the American Museum of Natural History in New York Eldridge reminded the meeting of what many fossil hunters have recognized as they trace the history of a species through successive layers of ancient sediments Species simply appear at a given point in geologic time persist largely unchanged for a few million years and then disappear There are very few examples some say none of one species shading gradually into another 81 82 IN THE BEGINNING 5 4 Human Consciousness For the layman it is the last step in evolution that is the most difficult to explain You may be able to convince him that natural selection can explain the appearance of complicated robots who walk the Earth and write books and build computers but you will have a harder time convincing him that a mechanical process such as natural selection could cause those robots to become conscious Human consciousness is in fact the biggest problem of all for Darwinism but it is hard to say anything scientific about consciousness since we don t really know what it is so it is also perhaps the least discussed Nevertheless one way to appreciate the problem it poses for Darwinism or any other mechanical theory of evolution is to ask the question is it possible that computers will someday experience consciousness If you believe that a mechanical process such as natural selection could have produced consciousness once it seems you can t say it could never happen again and it might happen faster now with intelligent designers helping this time In fact most Darwinists probably do believe it could and will happen not because they have a higher opinion of computers than I do everyone knows that in their most impressive displays of intelligence computers are just doing exactly what they are told to do nothing more or less They believe it will happen because they have a lower opinion of humans they simply dumb down the definition of consciousness and say that if a computer can pass a Turing test and fool a human at the keyboard in the next room into thinking he is chatting with another human then the computer has to be considered to be intelligent or conscious With the 5 CAN ANYTHING HAPPEN IN AN OPEN SYSTEM 83 right software my laptop may already be able to pass a lUring test and convince me that I am Instant Messaging another human If I type in My cat died last week and the computer responds I am saddened by the death of your cat I m pretty gullible that might convince me that I m talking to another human But if I look at the software I might find something like this if verb died fprintf l I am saddened by the death of your s noun end I m pretty sure there is more to human consciousness than this and even if my laptop answers all my questions intelligently I will still doubt there is someone inside my Intel processor who experiences the same consciousness that I do and who is really saddened by the death of my cat though I admit I can t prove that there isn t I really don t know how to argue with people who believe computers could be conscious About all I can say is what about typewriters Typewriters also do exactly what they are told to do and have produced some magnificent works of literature Do you believe that typewriters can also be conscious And if you don t believe that intelligent engineers could ever cause computers to attain consciousness how can you believe that random mutations could accomplish this 5 5 Conclusions Science has been so successful in explaining natural phenomena that the modern scientist is convinced that it can explain everything and anything that doesn t fit into this model is simply ignored It doesn t matter that there 84 IN THE BEGINNING were no natural causes before Nature came into existence so he cannot hope to ever explain the sudden creation of time space matter and energy and our universe in the big bang It doesn t matter that quantum mechanics is based on a principle of indeterminacy that tells us that every natural phenomenon has a component that is forever beyond the ability of science to explain or predict he still insists nothing is beyond the reach of his science When he discovers that all of the basic constants of physics such as the speed of light the charge and mass of the electron Planck s constant etc had to have almost exactly the values that they do have in order for any conceivable form of life to survive in our universe he proposes the anthropic principle and says that there must be many other universes with the same laws but random values for the basic constants and one was bound to get the values right When you ask him how a mechanical process such as natural selection could cause human consciousness to arise out of inanimate matter he doesn t understand what the problem is and he talks about human evolution as if he were an outside observer and never seems to wonder how he got inside one of the animals he is studying And when you ask how the four fundamental forces of Nature could rearrange the basic particles of Nature into libraries full of encyclopedias science texts and novels and computers connected to laser printers LCDs and keyboards and the internet he says well order can increase in an open system The development of life may have only violated one law of science but that was the supreme law of Nature and it has violated that in a most spectacular way At least that is my opinion but perhaps I am wrong 5 CAN ANYTHING HAPPEN IN AN OPEN SYSTEM 85 | | |
A second look at the second law Granville Sewell Mathematics Department University of Texas El Paso United States It is commonly argued that the spectacular increase in order which has occurred on Earth does not violate the second law of thermodynamics because the Earth is an open system and anything can happen in an open system as long as the entropy increases outside the system compensate the entropy decreases inside the system However if we define X entropy to be the entropy associated with any diffusing component X for example X might be heat and since entropy measures disorder X order to be the negative of X entropy a closer look at the equations for entropy change shows that they not only say that the X order cannot increase in a closed system but that they also say that in an open system the X order cannot increase faster than it is imported through the boundary Thus the equations for entropy change do not support the illogical compensation idea instead they illustrate the tautology that if an increase in order is extremely improbable when a system is closed it is still extremely improbable when the system is open unless something is entering which makes it not extremely improbable Thus unless we are willing to argue that the influx of solar energy into the Earth makes the appearance of spaceships computers and the Internet not extremely improbable we have to conclude that the second law has in fact been violated here 1 Compensation It is probably fair to say that the majority view of science today holds that physics explains all of chemistry chemistry explains all of biology and biology completely explains the human mind thus physics alone explains the human mind and all it does In fact since there are only four known forces of physics the gravitational electromagnetic and strong and weak nuclear forces this means that these four forces must explain everything that has happened on Earth according to this majority view For example Peter Urone in College Physics writes One of the most remarkable simplifications in physics is that only four distinct forces account for all known phenomena In my 2000 Mathematical Intelligencer article A Mathematician s View of Evolution I argued against this view asserting that the increase in order which has occurred on Earth seems to violate the second law of thermodynamics in a spectacular way I wrote I imagine visiting the Earth when it was young and returning now to find highways with automobiles on them airports with jet airplanes and tall buildings full of complicated equipment such as televisions telephones and computers Then I imagine the construction of a gigantic computer model which starts with the initial conditions on Earth 4 billion years ago and tries to simulate the effects that the four known forces of physics would have on every atom and every subatomic particle on our planet If we ran such a simulation out to the present day would it predict that the basic forces of Nature would reorganize the basic particles of Nature into libraries full of encyclopedias science texts and novels nuclear power plants aircraft carriers with supersonic jets parked on deck and computers connected to laser printers CRTs and keyboards If we graphically displayed the positions of the atoms at the end of the simulation would we find that cars and trucks had formed or that supercomputers had arisen Certainly we would not and I do not believe that adding sunlight to the model would help much Anyone who has made such an argument is familiar with the standard reply the Earth is an open system it receives energy from the sun and entropy can decrease in an open system as long as it is compensated somehow by a comparable or greater increase outside the system For example Isaac Asimov in the Smithsonian journal recognizes the apparent problem You can argue of course that the phenomenon of life may be an exception to the second law Life on earth has steadily grown more complex more versatile more elaborate more orderly over the billions of years of the planet s existence From no life at all living molecules were developed then living cells then living conglomerates of cells worms vertebrates mammals finally Man And in Man is a three pound brain which as far as we know is the most complex and orderly arrangement of matter in the universe How could the human brain develop out of the primeval slime How could that vast increase in order and therefore that vast decrease in entropy have taken place but Asimov concludes that the second law is not really violated because remove the sun and the human brain would not have developed And in the billions of years that it took for the human brain to develop the increase in entropy that took place in the sun was far greater far far greater than the decrease that is represented by the evolution required to develop the human brain Similarly Peter Urone in College Physics writes Some people misuse the second law of thermodynamics stated in terms of entropy to say that the existence and evolution of life violate the law and thus require divine intervention It is true that the evolution of life from inert matter to its present forms represents a large decrease in entropy for living systems But it is always possible for the entropy of one part of the universe to decrease provided the total change in entropy of the universe increases Some other authors appear to feel a little silly suggesting that increases in entropy anywhere in the universe could compensate for decreases on Earth so they are careful to explain that this compensation only works locally for example in Order and Chaos the authors write In a certain sense the development of civilization may appear contradictory to the second law Even though society can effect local reductions in entropy the general and universal trend of entropy increase easily swamps the anomalous but important efforts of civilized man Each localized man made or machine made entropy decrease is accompanied by a greater increase in entropy of the surroundings thereby maintaining the required increase in total entropy 2 The equations of entropy change Of course the whole idea of compensation whether by distant or nearby events makes no sense logically an extremely improbable event is not rendered less improbable simply by the occurrence of compensating events elsewhere According to this reasoning the second law does not prevent scrap metal from reorganizing itself into a computer in one room as long as two computers in the next room are rusting into scrap metal and the door is open 1 Or the thermal entropy in the next room is increasing though I am not sure how fast it has to increase to compensate computer construction To understand where this argument comes from we need to look at the equations for entropy change as given in Appendix D of my 2005 John Wiley book and previously in my 2001 Mathematical Intelligencer article Can ANYTHING Happen in an Open System Consider the diffusion conduction of heat in a solid R with absolute temperature distribution U x y z t The first law of thermodynamics conservation of energy requires that Qt J 1 where Q is the heat energy density Qt c Ut and J is the heat flux vector The second law requires that the flux be in a direction in which the temperature is decreasing i e J U 0 2 Eq 2 simply says that heat flows from hot to cold regions because the laws of probability favor a more uniform distribution of heat energy 1 It may be noted that something must actually be entering or leaving a system before it can be considered open but if you can see into the next room electromagnetic radiation at least is entering and that is what makes the Earth an open system Thermal entropy is a quantity that is used to measure randomness in the distribution of heat The rate of change of thermal entropy S is given by the usual definition as St R Qt U dV 3 Using 3 and the first law 1 after doing a multidimensional integration by parts we get St R J U U2 dV R J n U dA 4 where n is the outward unit normal on the boundary R From the second law 2 we see that the volume integral is nonnegative and so St R J n U dA 5 From 5 it follows that St 0 in an isolated closed system where there is no heat flux through the boundary J n 0 Hence in a closed system the entropy can never decrease Since thermal entropy measures randomness disorder in the distribution of heat its opposite negative can be referred to as thermal order and we can say that the thermal order can never increase in a closed system Since thermal entropy is quantifiable the application of the second law to thermal entropy is commonly used as the model problem on which our thinking about the other less quantifiable applications is based The fact that thermal entropy cannot decrease in a closed system but can decrease in an open system was used to conclude that in other applications any entropy decrease in an open system is possible as long as it is compensated somehow by entropy increases outside this system so that the total entropy as though there were only one type in the universe or any other closed system containing the open system still increases However there is really nothing special about thermal entropy Heat conduction is just diffusion of heat and we can define an X entropy and an X order X entropy to measure the randomness in the distribution of any other substance X that diffuses for example we can let U x y z t represent the concentration of carbon diffusing in a solid and use Eq 3 again to define this entropy c 1 now so Qt Ut and repeat the analysis leading to Eq 5 which now says that the carbon order cannot increase in a closed system 2 Furthermore Eq 5 does not simply say that the X entropy cannot decrease in a closed system it also says that in an open system the X entropy cannot decrease faster than it is exported through the boundary because the boundary integral there represents the rate at which X entropy is exported across the boundary To see this notice that without the denominator U the integral in 3 represents the rate of change of total X energy if X heat in the system with the denominator it represents the rate of change of X entropy Without the denominator U the boundary integral in 5 represents the rate at which X energy if X heat is exported through the boundary with the denominator therefore it must represent the rate at which X entropy is exported Although I am certainly not the first to recognize that the boundary integral has this interpretation see p 202 this has been noticed by relatively few people no doubt because usually the special case of isotropic heat conduction or diffusion is assumed in which case J K U and then the numerator in the boundary integral is written as K U n and in this form it is not obvious that anything is being imported or exported only that in a closed system the boundary integral is zero Furthermore entropy as defined by 3 seems to be a rather abstract quantity and it is hard to visualize what it means to import or export entropy Stated in terms of order Eq 5 says that the X order in an open system cannot increase faster than it is imported through the boundary According to 4 the X order in a system can decrease in two different ways it can be converted to disorder first integral term or it can be exported through the boundary boundary integral term It can increase in only one way by importation through the boundary 3 A tautology The second law of thermodynamics is all about probability it uses probability at the microscopic level to predict macroscopic change 3 Carbon distributes itself more and more uniformly in an isolated solid because that is what the laws of probability predict when diffusion alone is operative Thus the second law predicts that natural unintelligent causes will not do macroscopically describable things which are extremely improbable from the microscopic point of view 2 Entropy sounds much more scientific than order but note that in this paper order is simply defined as the opposite of entropy Where entropy is quantifiable such as here order is equally quantifiable Physics textbooks also often use the term entropy in a less precise sense to describe the increase in disorder associated with for example a plate breaking or a bomb exploding e g p 651 In such applications order is equally difficult to quantify 3 In Classical and Modern Physics Kenneth Ford writes There are a variety of ways in which the second law of thermodynamics can be stated and we have encountered two of them so far 1 For an isolated system the direction of spontaneous change is from an arrangement of lesser probability to an arrangement of greater probability 2 For an isolated system the direction of spontaneous change is from order to disorder The reason natural forces can turn a computer or a spaceship into rubble and not vice versa is probability of all the possible arrangements atoms could take only a very small percentage could add subtract multiply and divide real numbers or fly astronauts to the moon and back safely Of course we must be careful to define extremely improbable events to be events of probability less than some very small threshold if we define events of probability less than 1 to be extremely improbable then obviously natural causes can do extremely improbable things But after we define a sufficiently low threshold everyone seems to agree that natural forces will rearrange atoms into digital computers is a macroscopically describable event that is still extremely improbable from the microscopic point of view and thus forbidden by the second law at least if this happens in a closed system But it is not true that the laws of probability only apply to closed systems if a system is open you just have to take into account what is crossing the boundary when deciding what is extremely improbable and what is not What happens in a closed system depends on the initial conditions what happens in an open system depends on the boundary conditions as well The compensation counter argument was produced by people who generalized the model equation for closed systems but forgot to generalize the equation for open systems Both equations are only valid for our simple models where it is assumed that only heat conduction or diffusion is going on naturally in more complex situations the laws of probability do not make such simple predictions Nevertheless in Can ANYTHING Happen in an Open System I generalized the equations for open systems to the following tautology which is valid in all situations If an increase in order is extremely improbable when a system is closed it is still extremely improbable when the system is open unless something is entering which makes it not extremely improbable The fact that order is disappearing in the next room does not make it any easier for computers to appear in our room unless this order is disappearing into our room and then only if it is a type of order that makes the appearance of computers not extremely improbable for example computers Importing thermal order into an open system may make the temperature distribution less random and importing carbon order may make the carbon distribution less random but neither makes the formation of computers more probable My conclusion from Can ANYTHING Happen in an Open System is the following Order can increase in an open system not because the laws of probability are suspended when the door is open but simply because order may walk in through the door If we found evidence that DNA auto parts computer chips and books entered through the Earth s atmosphere at some time in the past then perhaps the appearance of humans cars computers and encyclopedias on a previously barren planet could be explained without postulating a violation of the second law here But if all we see entering is radiation and meteorite fragments it seems clear that what is entering through the boundary cannot explain the increase in order observed here 4 Conclusions Of course one can still argue that the spectacular increase in order seen on Earth does not violate the second law because what has happened here is not really extremely improbable Not many people are willing to make this argument however in fact the claim that the second law does not apply to open systems was invented in an attempt to avoid having to make this argument And |
| Perhaps it only seems extremely improbable but really isn t that under the right conditions the influx of stellar energy into a planet could cause atoms to rearrange themselves into nuclear power plants and spaceships and computers But one would think that at least this would be considered an open question and those who argue that it really is extremely improbable and thus contrary to the basic principle underlying the second law would be given a measure of respect and taken seriously by their colleagues but we aren t |
perhaps it only seems extremely improbable but really is not that under the right conditions the influx of stellar energy into a planet could cause atoms to rearrange themselves into nuclear power plants and spaceships and digital computers But one would think that at least this would be considered an open question and those who argue that it really is extremely improbable and thus contrary to the basic principle underlying the second law of thermodynamics would be given a measure of respect and taken seriously by their colleagues but we are not | |
| 5 6 Supplement The Equations of Entropy Change The following appears as Appendix D of my book The Numerical Solution of Ordinary and Partial Differential Equations second edition JJ John Wiley Sons Sewell 2005 Reprinted with permission of John Wiley Sons The partial differential equations that govern hea t conduction and diffusion derived in Section 2 0 and studied extensively in this book have some relevance to an interesting philosophical question | | |
is open 1 Or the thermal entropy in the next room is increasing though I am not sure how fast it has to increase to compensate computer construction To understand where this argument comes from we need to look at the equations for entropy change as given in Appendix D of my 2005 John Wiley book and previously in my 2001 Mathematical Intelligencer article Can ANYTHING Happen in an Open System |
| Consider the diffusion conduction of heat in a solid R with absolute temperature distribution U x y z t |
Consider the diffusion conduction of heat in a solid R with absolute temperature distribution U x y z t | |
| rTehqeu ifrierss t tlhaawt | | |
t The first law |
| of thermodynamics conservation of energy Qt 7 J 5 1 Where Q Q cpU is the heat energy density and J is the heat flux vector The second law requires that the flux be in a direction in which the temperature is decreasing i e |
of thermodynamics conservation of energy requires that Qt J 1 where Q is the heat energy density Qt c Ut and J is the heat flux vector The second law requires that the flux be in a direction in which the temperature is decreasing i e | |
| IN THE BEGINNING 86 J e 7U 0 5 2 In fact in an isotropic solid J is in the direction of greatest decrease of temperature that is J J 7U Note that 5 | | |
Qt c Ut and J is the heat flux vector The second law requires that the flux be in a direction in which the temperature is decreasing i e J U 0 2 Eq |
| 2 simply says that heat flows from hot to cold regions because the laws of probability favor a more uniform distribution of heat energy |
2 simply says that heat flows from hot to cold regions because the laws of probability favor a more uniform distribution of heat energy | |
| Thermal entropy is a quantity that is used to measure randomness in the distribution of heat The rate of change of thermal entropy S is given by the usual definition as St |
Thermal entropy is a quantity that is used to measure randomness in the distribution of heat The rate of change of thermal entropy S is given by the usual definition as St | |
| fff dV 5 3 R Using 5 3 and the first law 5 1 we get St 1ff J Ue 2 7U dV 1f | | |
3 Using 3 and the first law 1 after doing a multidimensional integration by parts we get St R J U U2 dV R |
| J Uen dA 5 4 R oR where n is the outward unit normal on the boundary 8R From the second law 5 2 we see that the volume integral is nonnegative and so St |
J n U dA 4 where n is the outward unit normal on the boundary R From the second law 2 we see that the volume integral is nonnegative and so St | |
| 2 1f | | |
n U |
| UdA 5 5 Jen oR From 5 5 it follows that St 2 0 in an isolated closed system where there is no heat flux through the boundary J en 0 Hence in a closed system entropy can never decrease Since thermal entropy measures randomnesS disorder in the distribution of heat its opposite negative can be referred to as thermal order and we can say that the thermal order can never increase in a closed system |
dA 5 From 5 it follows that St 0 in an isolated closed system where there is no heat flux through the boundary J n 0 Hence in a closed system the entropy can never decrease Since thermal entropy measures randomness disorder in the distribution of heat its opposite negative can be referred to as thermal order and we can say that the thermal order can never increase in a closed system | |
| 5 CAN ANYTHING HAPPEN IN AN OPEN SYSTEM 87 Furthermore there is really nothing special about thermal entropy We can define another entropy and another order in exactly the same way | | |
still increases However there is really nothing special about thermal entropy Heat conduction is just diffusion of heat and we can define an X entropy and an X order X entropy |
| to measure randomness in the distribution of any other substance that diffuses for example we can let U x y z t represent the concentration of carbon diffusing in a solid |
to measure the randomness in the distribution of any other substance X that diffuses for example we can let U x y z t represent the concentration of carbon diffusing in a solid | |
| Q is just U now and through an identical analysis show | | |
and repeat the analysis leading to Eq 5 which now says |
| that the carbon order thus defined cannot increase in a closed system |
that the carbon order cannot increase in a closed system | |
| It is a well known prediction of the second law that in a closed system every type of order is unstable and must eventually decrease as everything tends toward more probable states not only will carbon and temperature distributions become more random more uniform but the performance of all electronic devices will deteriorate not improve Natural forces such as corrosion erosion fire and explosions do not create order they destroy it The second law is all about probability it uses probability at the microscopic level to predict macroscopic change the reason carbon distributes itself more and more uniformly in an insulated solid is that is what the laws of probability predict when diffusion alone is operative The reason natural forces may turn a spaceship or a TV set or a computer into a pile of rubble but not vice versa is also probability of all the possible arrangements atoms could take only a very small percentage could fly to the moon and back or receive pictures and sound from the other side of the Earth or add subtract mUltiply and divide real numbers with high accuracy The discovery that life on Earth developed through evolutionary steps coupled with the observation that mutations and natural selection like other natural forces can cause minor change is widely accepted in the scientific world as proof that natural selection alone 88 IN THE BEGINNING among all natural forces can create order out of disorder and even design human brains with human consciousness Only the layman seems to see the problem with this logic In a recent Mathematical Intelligencer article Sewell 2000 after outlining the specific reasons why it is not reasonable to attribute the major steps in the development of life to natural selection I asserted that the idea that the four fundamental forces of physics alone could rearrange the fundamental particles of N ature into spaceships nuclear power plants and computers connected to laser printers CRTs keyboards and the internet appears to violate the second law of thermodynamics in a spectacular way Anyone who has made such an argument is familiar with the standard reply | | |
A second look at the second law Granville Sewell Mathematics Department University of Texas El Paso United States It is commonly argued that the spectacular increase in order which has occurred on Earth does not violate the second law of thermodynamics because |
| the Earth is an open system and order can increase in an open system as long as |
the Earth is an open system and anything can happen in an open system as long as | |
| it is compensated somehow by a comparable or greater decrease outside the system S Angrist and L Hepler in Order and Chaos Angrist and Hepler 1967 | | |
could compensate for decreases on Earth so they are careful to explain that this compensation only works locally for example in Order and Chaos the authors |
| write In a certain sense the development of civilization may appear contradictory to the second law Even though society can effect local reductions in entropy the general and universal trend of entropy increase easily swamps the anomalous but important efforts of civilized man Each localized man made or machine made entropy decrease is accompanied by a greater increase in entropy of the surroundings thereby maintaining the required increase in total entropy |
write In a certain sense the development of civilization may appear contradictory to the second law Even though society can effect local reductions in entropy the general and universal trend of entropy increase easily swamps the anomalous but important efforts of civilized man Each localized man made or machine made entropy decrease is accompanied by a greater increase in entropy of the surroundings thereby maintaining the required increase in total entropy | |
| According to this reasoning then the second law does not prevent scrap metal from reorganizing itself into a computer in one room as long as two computers in the next room are rusting into scrap metal and the door is open A closer look at equation 5 5 which holds not 5 CAN ANYTHING HAPPEN IN AN OPEN SYSTEM 89 only for thermal entropy but for the entropy associated with any other substance that diffuses shows that this argument which goes unchallenged in the scientific literature is based on a misunderstanding of | | |
thermal entropy Heat conduction is just diffusion of heat and we can define an X entropy and an X order X entropy to measure the randomness in the distribution of any other substance X that diffuses for example we can let U x y z t represent the concentration of carbon diffusing in a solid and use Eq 3 again to define this entropy c 1 now so Qt Ut and repeat the analysis leading to Eq 5 which now says that the carbon order cannot increase in a closed system 2 |
| the second law Equation 5 5 does not simply say that entropy cannot decrease in a closed system it also says that in an open system entropy cannot decrease faster than it is exported through the boundary because the boundary integral there represents the rate that entropy is exported across the boundary notice that the |
Furthermore Eq 5 does not simply say that the X entropy cannot decrease in a closed system it also says that in an open system the X entropy cannot decrease faster than it is exported through the boundary because the boundary integral there represents the rate at which X entropy is exported across the boundary To see this notice that without the | |
| integrand is the outward heat flux divided by absolute temperature That this boundary integral represents the rate that entropy is exported seems to have been noticed by relatively few people for example Dixon 1975 p 202 probably because the isotropic case is usually assumed and so the numerator is written as f and in this form the conclusion is not as obvious Stated another way the order in an open system cannot increase faster than it is imported through the boundary According to 5 4 the thermal order in a system can decrease in two different ways it can be converted to disorder first integral term or it can be exported through the boundary boundary integral term It can increase in only one way by importation through the boundary Similarly the increase in carbon order in an open system cannot be greater than the carbon order imported through the boundary and the increase in chromium order cannot be greater than the chromium order imported through the boundary and so on The above analysis was published in my reply Can ANYTHING Happen in an Open System Sewell 2001 to critics of my original Mathematical Intelligencer article In these simple examples I assumed nothing but 90 IN THE BEGINNING heat conduction or diffusion was going on but for more general situations I offered | | |
A second look at the second law Granville Sewell Mathematics Department University of Texas El Paso United States It is commonly argued that the spectacular increase in order which has occurred on Earth does not violate the second law of thermodynamics because the Earth is an open system and anything can happen in an open system as long as the entropy increases outside the system compensate the entropy decreases inside the system However if we define X entropy to be the entropy associated with any diffusing component X for example X might be heat and since entropy measures disorder X order to be the negative of X entropy a closer look at the equations for entropy change shows that they not only say that the X order cannot increase in a closed system but that they also say that in an open system the X order cannot increase faster than it is imported through the boundary Thus the equations for entropy change do not support the illogical compensation idea instead they illustrate |
| the tautology that if an increase in order is extremely improbable when a system is closed it is still extremely improbable when the system is open unless something is entering which makes it not extremely improbable |
the tautology that if an increase in order is extremely improbable when a system is closed it is still extremely improbable when the system is open unless something is entering which makes it not extremely improbable | |
| The fact that order is disappearing in the next room does not make it any easier for computers to appear in our room unless this order is disappearing into our room and then only if it is a type of order that makes the appearance of computers not extremely improbable for example computers Importing thermal order will make the temperature distribution less random and importing carbon order will make the carbon distribution less random but neither makes the formation of computers more probable What happens in a closed system depends on the initial conditions what happens in an open system depends on the boundary conditions as well As I wrote in Sewell 2001 order can increase in an open system not because the laws of probability are suspended when the door is open but simply because order may walk in through the door If we found evidence that DNA auto parts computer chips and books entered through the Earth s atmosphere at some time in the past then perhaps the appearance of humans cars computers and encyclopedias on a previously barren planet could be explained without postulating a violation of the second law here it would have been violated somewhere else But if all we see entering is radiation and meteorite fragments it seems clear that what is entering through the boundary cannot explain the increase in order observed here 1 Entropy sounds so much more scientific than order but if a measure is scientific so is its negative | | |
Thus unless we are willing to argue that the influx of solar energy into the Earth makes the appearance of spaceships computers and the Internet not extremely improbable we have to conclude that the second law has in fact been violated |