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How would the Hodgkin-Huxley equation change when the geometry of dendrites and axons are introduced?
Also can we model a situation of membrane activity during the corse of evolution, hence the equation would be subject to a periodic function ad it varies with time?
Taking the example of membrane transmission of electronic signals(in humans), can we model the change in conduction of the e-signal through the axon as its speed and geometry changes with evolution?
Although you mention evolution, I think what your question is really asking is in your last paragraph: what happens to conduction within dendrites and axons when geometry changes. There might be some evolutionary implications of this question, but you will also find vast variations in geometry among neurons in any one organism, as well.
You might want to look into expansions of Hodgkin-Huxley into compartment models that allow you to test the influences of geometry, see wikipedia for a list of different models at different scales of complexity.
There is a tool available called NEURON that is good for student or curious non-student experimentation, though you will have to read the documentation and hopefully find some examples that are close to what you want and then tweak them.
An open system kinetic transport model for the hodgkin-huxley equations *
A discrete state “ion-hopping” mechanism is developed for the description of potassium ion flows in voltage clamped squid giant axon membranes. Although the mechanism differs from the “gating” mechanism proposed by Hodgkin & Huxley, it yields an identical mathematical description. The discrete state transport mechanism requires interaction between the ions and the channel and is based on the concept of an “open” system. The bathing solutions on each side of the membrane act as ion sources for states within the membrane. The feasibility of a sequential mechanism is explored and the experimental procedures of Hodgkin & Huxley are re-examined to show their consistency with both the gating and sequential, kinetic mechanisms. The basic sequential kinetic scheme
i ⇌ 4 β ( 1 ) α ⇌ 3 β ( 2 ) 2 α ⇌ 2 β ( 3 ) 3 α ⇌ β ( 4 ) 4α →
with the Hodgkin-Huxley rate constants α and β yields the mathematical form of the Hodgkin-Huxley equations. The sequential kinetic model can be differentiated from the gating model by a straightforward experiment which is discussed.
The support of the National Institutes of Health under Grant 1 RO1-NS-11676-01-PHY is gratefully acknowledged.
Math, art, and ideas
I’ve learned something from school: Math isn’t the hard part of math motivation is. Specifically, staying encouraged despite
- Teachers focused more on publishing/perishing than teaching
- Self-fulfilling prophecies that math is difficult, boring, unpopular or “not your subject”
- Textbooks and curriculums more concerned with profits and test results than insight
“…if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done — I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.”
Imagine teaching art like this: Kids, no fingerpainting in kindergarten. Instead, let’s study paint chemistry, the physics of light, and the anatomy of the eye. After 12 years of this, if the kids (now teenagers) don’t hate art already, they may begin to start coloring on their own. After all, they have the “rigorous, testable” fundamentals to start appreciating art. Right?
Poetry is similar. Imagine studying this quote (formula):
“This above all else: to thine own self be true, and it must follow, as night follows day, thou canst not then be false to any man.” —William Shakespeare, Hamlet
It’s an elegant way of saying “be yourself” (and if that means writing irreverently about math, so be it). But if this were math class, we’d be counting the syllables, analyzing the iambic pentameter, and mapping out the subject, verb and object.
Math and poetry are fingers pointing at the moon. Don’t confuse the finger for the moon. Formulas are a means to an end, a way to express a mathematical truth.
We’ve forgotten that math is about ideas, not robotically manipulating the formulas that express them.
Ancient dog breed DNA helps unravel clues about evolution of man's best friend
Credit: Jon Curby
An international study led by UNSW researchers has mapped one of the most intact and complete dog genomes ever generated.
The genome sequence of the Basenji dog could have a big impact on the understanding of dog evolution, domestication and canine genetic diseases.
The Basenji—also known as the barkless dog—is an ancient African dog breed which still lives and hunts with tribesmen in the African Congo.
In the study, published in BMC Genomics, the researchers say the genome of the Basenji, which sits at the base of the dog breed family tree, makes an excellent unbiased reference for future comparisons between dog breeds and evolutionary analysis of dogs.
"The dog was probably the first animal to be domesticated by humans and has subsequently been artificially selected by humans into a great diversity of dog breeds of different sizes and shapes," lead author of the study and senior lecturer in Genomics and Bioinformatics at UNSW Sydney's School of Biotechnology and Biomolecular Sciences, Dr. Richard Edwards says.
"Before this paper, it was difficult to interpret differences between the dog reference genomes and non-domesticated dogs, such as dingoes, jackals, coyotes, wolves and foxes.
"Big changes could be the result of recent artificial selection during creation of the specific reference breed.
"By adding such a high-quality genome at the base of the domestic dog family tree, we have provided an anchor point for studies that can help establish the timing and direction of genetic changes during domestication and subsequent breeding."
Dr. Edwards says the Basenji genome sequence is different to the traditional dog reference genome, CanFam, which is of a highly-derived breed, the Boxer.
He says the choice of dog reference genome can affect the results of future dog genetics studies looking at genetic variants.
"For example, the Boxer is much more closely related to other Mastiffs than other breeds," he says.
"This may introduce biases in genetic analyses across many dog breeds. There is also the risk that breed-specific variation may map poorly—or not at all—to a biased reference. In principle, the Basenji is equally distant from most modern breeds, making it a less biased basis for comparisons."
Dr. Kylie Cairns is an expert in dingo identity and evolution in the Centre for Ecosystem Science in UNSW's School of Biological, Earth and Environmental Sciences.
She says the Basenji genome now provides a high-quality comparison to all domestic dog breeds for future studies.
"As Basenjis are a very old breed, they provide the perfect comparison to more modern breeds to explore how breeds were developed, the process of domestication and assist in studies looking for disease genes," Dr. Cairns says.
"This genome will also be critical in comparisons to wolves, dingoes and village dogs as an example of an ancient domestic breed."
She says the Basenji genome may allow scientists to more fully unravel the evolutionary history of early dogs and how humans have shaped the first dogs into the companions and breeds we have today.
"Many people wouldn't realize that most dog breeds arose in the last 200-300 years," she says.
"So having access to a high quality refence genome from an ancient breed such as the Basenji gives insight into early breed development and how domestic dogs have been shaped by humans in the last few thousand years.
"We will also be able to tackle lingering questions about the evolutionary history of dingoes and their relatives in New Guinea, with the Basenji acting as a halfway point between non-domesticated dingoes and truly modern dog breeds like pugs, kelpies and poodles. "
Dr. Edwards says the genome of the Basenji is one of only a handful of referenced quality genomes for specific dog breeds.
The first of these was a German Shepherd, Nala, which Dr. Edwards also contributed to last year.
Dr. Edwards says researchers combined three cutting edge genome sequencing technologies to assembly the Basenji dog genome, which is based on a female dog called China.
"Over 99% of the final genome assembly can be found in the 39 pieces that represent the 39 dog chromosomes," he says.
"These chromosomes only have one hundred regions of unresolved sequence, which is the fewest of any published dog genome so far.
"This makes it one of the highest-quality dog genomes produced to date."
The study also features a number of interesting genome assembly case studies that demonstrate the importance of curation and careful analysis, even for high-quality genomes.
"Even the best technologies can still make mistakes," Dr. Edwards says.
For example, the mitochondrial genome—a separate, small genome belonging to the cell's energy generators—had mistakenly been assembled into the middle of one of the chromosomes at one stage.
"Genomics has a come a long way in recent years, but we've not reached perfection yet. At the same time, it is not possible to manually scan over two billion DNA letters for mistakes. Part of what drives the research in my lab is finding improved ways to use computers to help identify and fix these errors."
Observations and Inferences
We typically think of observations as having been seen “with our own eyes,” but in science, observationscan take many forms. Of course we can make observations directly by seeing, feeling, hearing, and smelling, but we can also extend and refine our basic senses with tools: thermometers, microscopes, telescopes, radar, radiation sensors, X-ray crystallography, mass spectroscopy, etc. These tools do a better job of observing than we can! Further, humans cannot directly sense many of the phenomena that science investigates (no amount of staring at this computer screen will ever let you see the atoms that make it up or the UV radiation that it emits) and, in such cases, we must rely on indirect observations facilitated by tools. Through these tools, we can make many more observations much more precisely than those our basic senses are equipped to handle.
Measuring Biodiversity Using Beans
Students analyze a community of beans (pinto, lima, navy) to determine the richness, abundance, and biodiversity index of two communities. The communities are set up in advance, just place bags of beans into a large bowl or bucket, and then have students use a small cup to model sampling. After counting the number of each type of bean, students record data on a table and determine the relative abundance of each “species” of bean.
Student will then use an equation to establish the biodiversity index. Discussion questions ask students to explain why one community has a higher index than the other and to explain why different groups got different results (sampling errors). Discussion follows regarding why the biodiversity index might be important to ecologists who study forests and other ecosystems.
Grade Level: 9-12
Time Required: 20-30 minutes + discussion
HS-LS2-2 Use mathematical representations to support and revise explanations based on evidence about factors affecting biodiversity and populations in ecosystems of different scales.
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Introducing evolution into the Hodgkin-Huxley equation - Biology
Activity One: Teacher Notes
Note: In the following activity we have made several simplifications. We have assumed that rabbits mate once and do not reenter the breeding pool. (Of course, this is not true with real rabbits.) For this reason, the population declines artificially rapidly. The activity helps show the change in frequency of a lethal recessive allele over time, but is not intended to represent exactly what would happen with a population of real rabbits.
To show students the impact that genetics can have on the evolution of a population of organisms
To make students aware of the influence that the environment has on organisms
Procedure Part A: Part Title -->
Divide the class into small groups (preferably four students per group), and distribute the materials. Pass out the Gene Frequency Data form (pdf) and the Discussion Questions (pdf), or ask students to print them from the Student Page.
Have students follow the instructions on the Student Page. You may want to travel around the room at the beginning of the activity to make sure all the groups understand the instructions.
At the conclusion of the lab, ask students to answer the Discussion Questions. The answers can be discussed by groups or by the whole class.
When you discuss question seven, consider the definition of evolution as being the change of gene frequency of a population over time. The natural selection against the furless allele may cause the gene frequencies to change, but random genetic changes due to mutation, migration, and natural disasters may impact the already stressed gene frequencies even more. Also, relate the more general definition of evolution ("descent with modification") with the results observed.
Adapted with permission from a 1994 Woodrow Wilson Biology Institute Laboratory "Evolution and Gene Frequencies: A Game of Survival and Reproductive Success," by Joseph Lapiana.
Introducing evolution into the Hodgkin-Huxley equation - Biology
The Second Law of Thermodynamics,
Evolution, and Probability
Copyright © 1995-1997 by Frank Steiger
This document may be reproduced without royalty for non-profit, non-commercial use.
reationists believe that the second law of thermodynamics does not permit order to arise from disorder, and therefore the macro evolution of complex living things from single-celled ancestors could not have occurred. The creationist argument is based on their interpretation of the relationship between probability and a thermodynamic property called "entropy."
By way of background, and in order to clarify the creationist position, let me quote from the creationist literature:
The Remarkable Birth of Planet Earth , by Henry Morris:
(p. 14) All processes manifest a tendency toward decay and disintegration, with a net increase in what is called the entropy, or state of randomness or disorder, of the system. This is called the Second Law of Thermodynamics.
(p. 19) There is a universal tendency for all systems to go from order to disorder, as stated in the Second Law, and this tendency can only be arrested and reversed under very special circumstances. We have already seen, in Chapter I, that disorder can never produce order through any kind of random process. There must be present some form of code or program, to direct the ordering process, and this code must contain at least as much "information" as is needed to provide this direction.
Furthermore, there must be present some kind of mechanism for converting the environmental energy into the energy required to produce the higher organization of the system involved. .
Thus, any system that experiences even a temporary growth in order and complexity must not only be "open" to the sun's energy but must also contain a "program" to direct the growth and a "mechanism" to energize the growth.
Scientific Creationism , edited by Henry Morris:
(p.25) The Second Law (Law of Energy Decay) states that every system left to its own devices always tends to move from order to disorder, its energy tending to be transformed into lower levels of availability, finally reaching the state of complete randomness and unavailability for further work.
Of course, the creationist application of the second law of thermodynamics to the development of living things is inconsistent with any model of origins. Creationists get around this problem by invoking the supernatural:
The Genesis Flood , by Whitcomb and Morris:
(p. 223) But during the period of Creation, God was introducing order and organization into the universe in a very high degree, even to life itself! It is thus quite plain that the processes used by God in creation were utterly different from the processes which now operate in the universe!
As will be shown later on, it is only the over-all entropy of a complete, or closed system that must increase when spontaneous change occurs. In the case of spontaneously interacting sub-systems of a closed system, some may gain entropy, while others may lose entropy. For example, it is a fundamental axiom of thermodynamics that when heat flows from subsystem A to subsystem B, the entropy of A decreases and the entropy of B increases. The statement that an increase in order can only occur as the result of a directional mechanism, program, or code is misleading. Any process that can be demonstrated to take place with an increase in order/decrease in entropy is arbitrarily deemed to be the consequence of an undefined "directional mechanism."
Probability, as used in thermodynamics, means the probability that some specific change will occur. Probability is related to the thermodynamic concept of irreversibility. An irreversible physical or chemical change is a change that will not spontaneously reverse itself without some change in the surrounding conditions. Irreversible changes have a high degree of probability. The probability of an irreversible change spontaneously reversing itself without outside interference is zero.
When we say that a change is irreversible (in the thermodynamics sense) it means only that the change will not spontaneously reverse itself without some change in the surrounding conditions. It does not mean that it cannot be reversed by any means at all!
It is important to remember that a change that has a high degree of probability under one set of circumstances may have a very low degree of probability under a different set of circumstances. To illustrate: If the temperature drops below freezing, the probability of water becoming ice is very high. The change from water to ice is thermodynamically irreversible. If the surrounding temperature should happen to rise above the freezing point, the probability of water becoming ice, or remaining as ice, is zero. Under these conditions the reverse change of ice to liquid water is also thermodynamically irreversible.
Failure to understand that in thermodynamics probabilities are not fixed entities has led to a misinterpretation that is responsible for the wide- spread and totally false belief that the second law of thermodynamics does not permit order to spontaneously arise from disorder. In fact, there are many examples in nature where order does arise spontaneously from disorder: Snowflakes with their six-sided crystalline symmetry are formed spontaneously from randomly moving water vapor molecules. Salts with precise planes of crystalline symmetry form spontaneously when water evaporates from a solution. Seeds sprout into flowering plants and eggs develop into chicks.
Thermodynamics is an exact science that is based on a limited number of specific mathematical concepts. It is not explainable in terms of qualitative metaphors. In order to understand the relationship between probability and the second law, the reader must be familiar with the relationship between probability and entropy. Entropy is a mathematically defined entity which is the fundamental basis of the second law of thermodynamics and all of its engineering and physical chemistry ramifications.
In the following sections we will try to explain the true relation between entropy and probability and show why this relationship does not preclude the possibility of order spontaneously arising from disorder.
In describing the laws of thermodynamics we often refer to "systems." A system is a specific entity or object or region in space to be evaluated in terms of its thermodynamic properties and possible changes. It could be an ice cube, a toy balloon, a steam turbine, or even the entire earth itself.
The concept of entropy is fundamental to understanding the second law of thermodynamics. Entropy (or more specifically, increase in entropy) is defined as heat (in calories or Btu's) absorbed by a system, divided by the absolute temperature of the system at the time the heat is absorbed. Absolute temperature is the number of degrees above "absolute zero", the coldest temperature that can exist.
The total entropy in a system is represented by the symbol S. The symbol S is used to represent a given change in the entropy content of a system. If the symbol q is used to represent the amount of heat absorbed by a system, the equation for the resulting entropy increase is:
Where T is the absolute temperature. When heat is absorbed, the entropy of a system increases when heat flows out of a system, its entropy decreases.
The "surroundings" of a system is everything outside of the system that can interact with it surroundings can usually be defined as the space that surrounds a system. When heat is evolved by a system, that same heat is absorbed by its surroundings. When heat is absorbed by a system, that same heat must necessarily come from its surroundings. Therefore any entropy increase in a system due to heat flow must be accompanied by an entropy decrease in the surroundings, and vice versa. When heat flows spontaneously from a hotter region to a cooler region, the entropy decrease in the hotter region will always be less than the entropy increase in the cooler region, because the greater the absolute temperature, the smaller the entropy change for any particular heat flow. (See equation 1, above)
As an example, consider the entropy change when a large rock at 500 degrees absolute is dropped into water at 650 degrees absolute. (We are using an absolute temperature scale based on Fahrenheit degrees on this scale, water freezes at 492 degrees.) For each Btu of heat that flows into the rock at these temperatures the entropy increase in the rock is 1/500 = 0.0020 and the entropy decrease of the water is 1/650 = 0.0015. The difference between these values is 0.0020 - 0.0015 = 0.0005. This represents the over all entropy increase of the system (rock) and its surroundings (water).
Of course the rock will warm up to, and the water cool to, a temperature intermediate between their original temperatures, thus considerably complicating the calculation of total entropy change after equilibrium is achieved. Nevertheless, for every Btu of heat transferred from water to rock there will always be an increase of over-all net entropy.
As was mentioned before, a spontaneous change is an irreversible change. Therefore an increase in the overall net entropy can be used as a measure of the irreversibility of spontaneous heat flow.
Irreversible changes in a system can, and often do, take place even though there may be no interaction, and negligible heat flow, between system and surroundings. In cases like these the entropy "content" of the system is greater after the change than before. Even when heat flow does not occur between system and surroundings, spontaneous changes inside an isolated system are always accompanied by an increase in the system's entropy, and this calculated entropy increase can be used as a measure of irreversibility. The following paragraphs will explain how this entropy increase can, at least in some cases, be calculated.
It is an axiom of thermodynamics that entropy, like temperature, pressure, density, etc., is a property of a system and depends only on the existing condition of the system. Regardless of the procedures followed in achieving a given condition, the entropy content for that condition is always the same. In other words, for any given set of values for pressure, temperature, density, composition, etc., there can be only one value for the entropy content. It is essential to remember this: When a system that has undergone an irreversible change is restored to its original condition (same temperature, pressure, volume, etc.) its entropy content will likewise be the same as it was before.
In cases where an isolated system undergoes an entropy increase as the result of a spontaneous change inside the system, we can calculate that entropy increase by postulating a procedure whereby the system's entropy increase is transferred to the surroundings in a manner such that there is no further increase in net entropy and the system is restored to its original condition. The entropy increase of the surroundings can then be readily calculated by equation (1): S = q/T, where q = heat absorbed by the surroundings, and T = absolute temperature of the surroundings.
It bears repeating that when the system is restored to its original condition, its entropy content will be the same as it was before its irreversible change. Therefore the amount of entropy absorbed by the surroundings during restoration must necessarily be the same as the entropy increase accompanying the system's original irreversible change, providing that there is no further increase in net entropy during restoration.
This postulated restoration procedure and the postulated properties of the surroundings are for the purpose of calculation only. Since we are not dealing with the surroundings as such, they can be postulated in whatever form necessary to simplify the calculations it is neither necessary nor desirable that the surroundings correspond to any condition that could actually exist. Therefore, we will postulate a theoretical restoration procedure that takes place with no further increase in net entropy, even though such a procedure can not actually be obtained experimentally.
The restoration process, if it were to take place in actuality, would have to be accompanied by at least a small amount of irreversibility, and hence an additional increase in the entropy of the surroundings beyond the entropy increase from the system's original irreversible change. This is because heat will not flow without a temperature differential, friction cannot be entirely eliminated, etc. Therefore the restoring process, if it is to take place with no further increase in over-all net entropy, must be postulated to take place with no irreversibility. If such a process could be actually realized, it would be characterized by a continuous state of equilibrium (i.e. no pressure or temperature differentials) and would occur at a rate so slow as to require infinite time. Processes like these are called "reversible" processes. Remember, reversible processes are postulated to simplify the calculation of the entropy change in a system it is not necessary that they be capable of being achieved experimentally.
It should not be assumed that equation (1) requires that q, the heat absorbed, must necessarily be absorbed reversibly. The concept of reversibility is merely a means to an end: the calculation of entropy change accompanying an irreversible process.
The following example will illustrate the calculation of a reversible restoring process and at the same time develop the equation which is the basis for the thermodynamical relationship between probability and the second law. We will postulate a system consisting of an "ideal" gas contained in a tank connected to a second tank that has been completely evacuated, with the valve between the two tanks closed. The temperature of the system and its surroundings is postulated to be the same. An ideal gas is one whose molecules are infinitely small and have no attractive or repulsive forces on each other. (Under ordinary conditions hydrogen and helium closely approximate the properties of an ideal gas.) An ideal gas is chosen in order to develop the basic relationship without introducing complicating correction factors to account for the size of the molecules and the forces they exert on each other.
When the valve is opened the gas expands irreversibly from V1 (its original volume) to V2 (the volume of both tanks). There is no work of compression by or upon the surroundings. Because the gas is ideal there is no temperature change, and hence no heat flow takes place.
After expanding irreversibly from V1 to V2, the gas is restored to its original condition by reversibly compressing it back to V1. This compression requires work (force applied through a distance) which in turn generates heat in the gas, heat that is absorbed by the surroundings so that there is no increase in the gas temperature. In our mathematical model of this reversible restoring process, the surroundings are postulated to be so large that they also do not undergo any temperature increase. The temperature T remains unchanged during the entire irreversible expansion and subsequent reversible restoration process.
The work of compressing the gas during restoration is equal to the pressure of the gas times the volume change due to compression. Because the pressure increases during compression, the work of compression must be determined by the calculus integral:
The integral sign indicates the summation of all the individual values of PdV.
The equation relating temperature, pressure, and volume of an ideal gas is:
In the case of a reversible, isothermal compression of an ideal gas we may substitute P from equation (2) into the equation for compression work. When this is done, we have:
Although it is not necessary that our postulated reversible restoration process be capable of being carried out in a practical sense, it is nevertheless sometimes helpful to be able to visualize the process. To this end, the reader may consider the restoring compression process being brought about by a piston fitted into the end of the second tank. On compression from V2 to V1, the piston moves down the length of the second tank, and with no mechanical friction forces all the gas contained therein back into the first tank V1.
Since the work of compression is equal to q, the heat absorbed by the surroundings, q may be substituted in equation (3) to give: From equation (1) the entropy gained by the surroundings during restoration from V2 to V1 is: Substituting from equation (4):
Upon integrating (a calculus procedure for summing up the individual values of dV/V) we have: Where ln(V2/V1) is the natural logarithm of the ratio of expanded volume to the initial volume, and S is equal to the entropy increase in the surroundings upon restoration compression from V2 to V1. As we have seen, S is also equal to the entropy increase of the gas caused by its original expansion from V1 to V2. This is because V1 is the same volume both before expansion and after restoration compression, and therefore has the same entropy content. Therefore the entropy transferred to the surroundings during restoration is equal to that gained by the system in expanding from V1 to V2.
The ratio of the probability that all the gas molecules are evenly distributed between the two tanks to the probability that all the molecules, of their own accord and by random motion, would be in tank V1 is equal to (V2/V1) N , where N is the number of molecules.
If V2/V1 were equal to 2.0, for example, and N were equal to 10, the probability ratio would be 2 to the tenth power, or 1024. For N = 100, the ratio would be approximately 1.27 times ten to the 30th power. It is clear that the random motion of trillions of gas molecules heavily favors a uniform distribution. From the probability equation, we have: Taking the natural logarithm of both sides, and then multiplying both sides by R, the gas constant: Substituting in equation (5):
Equation (6) represents the fundamental relationship between probability and the second law of thermodynamics. It states that the entropy of a gaseous system increases when its molecular distribution changes from a lower probability to a higher probability (X2 greater than X1).
Based on the belief that the laws of thermodynamics are universal, this equation has been assumed to apply to all systems, not just gaseous. In other words, any entropy change is proportional to the logarithm of the ratio of probabilities. Therefore, for the general case equation (6) can be written: Where K is a constant depending on the particular change involved. However, individual values of K, X1, or X2 are seldom, if ever, known for non-gaseous systems.
As we have seen before, S can be either positive or negative. When S is negative equation (7) can be written: Therefore a system can go from a more probable state (X2) to a less probable state (X1), providing S for the system is negative. In cases where the system interacts with its surroundings, S can be negative providing the over-all entropy of the system and its interacting surroundings is positive the over-all change can be positive if the entropy increase of the surroundings is numerically greater than the entropy decrease of the system.
In the case of the formation of the complex molecules characteristic of living organisms, creationists raise the point that when living things decay after death, the process of decay takes place with an increase in entropy. They also point out, correctly, that a spontaneous change in a system takes place with a high degree of probability. They fail to realize, however, that probability is relative, and a spontaneous change in a system can be reversed, providing the system interacts with its surroundings in such a manner that the entropy increase in the surroundings is more than enough to reverse the system's original entropy increase.
The application of energy can reverse a spontaneous, thermodynamically "irreversible" reaction. Leaves will spontaneously burn (combine with oxygen) to form water and carbon dioxide. The sun's energy, through the process of photosynthesis, will produce leaves from water vapor and carbon dioxide, and form oxygen.
If we unplug a refrigerator, heat will flow to the interior from the surroundings the entropy increase inside the refrigerator will be greater than the entropy decrease in the surroundings, and the net entropy change is positive. If we plug it in, this spontaneous "irreversible" change is reversed. Due to the input of electrical energy to the compressor, the heat transferred to the surroundings from the condenser coils is greater than the heat extracted from the refrigerator, and the entropy increase of the surroundings is greater than the entropy decrease of the interior, in spite of the fact that the surroundings are at a higher temperature. Here again, the net entropy change is positive, as would be expected for any spontaneous process.
In a similar manner, the application of electrical energy can reverse the spontaneous reaction of hydrogen and oxygen to form water: when a current is passed through a water solution, hydrogen is liberated at one electrode, oxygen at the other.
As can easily be confirmed experimentally, agitating water raises its temperature. When water falls freely from a higher elevation to a lower elevation, its energy is changed from potential to kinetic, and finally to heat as it splashes at the end of its fall. The second law of thermodynamics states that the water will not spontaneously raise itself to its original elevation using the heat produced on splashing as the sole source of energy. To do so would require a heat engine that would convert all of the heat of splashing to mechanical energy.
The efficiency of a heat engine is thermodynamically limited by the Carnot cycle, which limits the efficiency of any heat engine to T/T, where T is the temperature increase due to splashing, and T is the absolute temperature. Since T is only a small fraction of T, there is no device that could be constructed which would allow all of the water to spontaneously jump back to its former elevation.
We can, at least in theory, calculate the entropy increase of the water resulting from its irreversible change in falling. In a manner analogous to that used in the previous example, the entropy increase would be equal to the heat generated by splashing agitation, divided by the absolute temperature. If some of the energy of the falling water is extracted by a water wheel, there will be less heat of splashing and hence less entropy increase.
A properly designed turbine could extract most of the water's kinetic energy. This is not the same thing as trying to utilize the heat of splashing as an energy source for a heat engine to raise the water. In other words, using the energy before it becomes heat is much more efficient than trying to use it after it becomes heat.
If a water wheel is connected by shafts, belts, pulleys, etc. to a pump, the pump can raise water from the downstream side of the water wheel to an elevation even higher than that of the upstream reservoir. Some of the water would spontaneously raise itself to an elevation even higher than original, but the rest of it would end up below the water wheel on the downstream side.
While it is not possible for all of the water to raise itself to an elevation higher than its initial elevation, it is possible for some of the water to spontaneously raise itself to an elevation higher than initial.
As with any other irreversible change, there will be an increase in over-all entropy. This means that the entropy increase of the water going over the wheel is greater than the entropy decrease of water pumped up to the higher elevation.
This will be confirmed mathematically in the following paragraphs. will stand for the Greek letter gamma, representing unit weight in pounds per cubic foot. An increase in the value of a parameter will be represented by . From the flow equation, energy in = energy out: The total energy available, h, is divided into pump work, f (h + h), and energy lost, T S: Rearranging: When no pump work is done, then: Combining equations (8) and (9), we get: In the case where the water falls freely without turning the water wheel or operating the pump: Equation (10) shows that S' is larger than S, and that the entropy increase due to pump friction and downstream agitation is "backed up" by the even larger entropy increase that takes place when water falls freely. Equation (10) also shows that the lower the value of S, the more efficient the pump, and the greater the value of f, the fraction of water pumped.
Creationists assume that a change characterized by a decrease in entropy can not occur under any circumstances. In fact, spontaneous entropy decreases can, and do, occur all the time, providing sufficient energy is available. The fact that the water wheel and pump are man-built contraptions has no bearing on the case: thermodynamics does not concern itself with the detailed description of a system it deals only with the relationship between initial and final states of a given system (in this case, the water wheel and pump).
A favorite argument of creationists is that the probability of evolution occurring is about the same as the probability that a tornado blowing through a junkyard could form an airplane. They base this argument on their belief that changes in living things have a very low probability and could not occur without "intelligent design" which overcomes the laws of thermodynamics. This represents a fundamental contradiction in which (they say) evolution is inconsistent with thermodynamics because thermodynamics doesn't permit order to spontaneously arise from disorder, but creationism (in the guise of intelligent design) doesn't have to be consistent with the laws of thermodynamics.
A simpler analogy to the airplane/junkyard scenario would be the stacking of three blocks neatly on top of each other. To do this, intelligent design is required, but stacking does not violate the laws of thermodynamics. The same relations hold for this activity as for any other activity involving thermodynamical energy changes. It is true that the blocks will not stack themselves, but as far as thermodynamics is concerned, all that is required is the energy to pick them up and place them one on top of the other. Thermodynamics merely correlates the energy relationships in going from state A to state B. If the energy relationships permit, the change may occur. If they don't permit it, the change can not occur. A ball will not spontaneously leap up from the floor, but if it is dropped, it will spontaneously bounce up from the floor. Whether the ball is lifted by intelligent design or just happens to fall makes no difference.
On the other hand, thermodynamics does not rule out the possibility of intelligent design it is just simply not a factor with respect to the calculation of thermodynamic probability.
Considering the earth as a system, any change that is accompanied by an entropy decrease (and hence going back from higher probability to lower probability) is possible as long as sufficient energy is available. The ultimate source of most of that energy, is of course, the sun.
The numerical calculation of entropy changes accompanying physical and chemical changes are very well understood and are the basis of the mathematical determination of free energy, emf characteristics of voltaic cells, equilibrium constants, refrigeration cycles, steam turbine operating parameters, and a host of other parameters. The creationist position would necessarily discard the entire mathematical framework of thermodynamics and would provide no basis for the engineering design of turbines, refrigeration units, industrial pumps, etc. It would do away with the well-developed mathematical relationships of physical chemistry, including the effect of temperature and pressure on equilibrium constants and phase changes.
[The Greek and mathematical symbols are courtesy of Karen Strom of the University of Massachussetts. They may be downloaded here and used with this attribution and without fee for non-profit purposes only.]
Intelligent Design: An Ambiguous Assault on Evolution
Science can sometimes be a devil's bargain: a discovery is made, some new aspect of nature is revealed, but the knowledge gained can cause mental anguish if it contradicts a deeply cherished belief or value.
Copernicus' declaration in 1543 that the Sun and the heavens were not, in fact, revolving around the Earth and its human inhabitants was one such painful enlightenment. The publication in 1859 of Charles Darwin's book, "The Origin of Species," set the stage for another.
Darwin's truth can be a hard one to accept. His theory of evolution tells us that humans evolved from non-human life as the result of a natural process, one that was both gradual, happening over billions of years, and random. It tells us that new life forms arise from the splitting of a single species into two or more species, and that all life on Earth can trace its origins back to a single common ancestor.
Perhaps most troubling of all, Darwin's theory of evolution tells us that life existed for billions of years before us, that humans are not the products of special creation and that life has no inherent meaning or purpose.
For Americans who view evolution as inconsistent with their intuitions or beliefs about life and how it began, Creationism has always been a seductive alternative.
Creationism's latest embodiment is intelligent design (ID), a conjecture that certain features of the natural world are so intricate and so perfectly tuned for life that they could only have been designed by a Supreme Being.
Real or apparent design?
"The question that we're facing in biology is that when we look at nature, we see design," said Scott Minnich, a microbiologist at the University of Idaho and an ID proponent. "But is it real design or apparent design? There are two answers to the question and both are profound in terms of their metaphysical implications."
In an August interview with National Public Radio, Republican Senator and ID supporter Rick Santorum stated exactly what he believed those implications were for evolution. Asked why he, a politician, felt compelled to weigh in on what was essentially a scientific debate, Santorum replied:
"It has huge consequences for society. It's where we come from. Does man have a purpose? Is there a purpose for our lives? Or are we just simply the result of chance? If we are the result of chance, if we're simply a mistake of nature, then that puts a different moral demand on us. In fact, it doesn't put a moral demand on us."
By adding morality to the equation, Santorum is giving the scientific theory of evolution a religious message, one that does not come on its own, said Kenneth Miller, a biologist at the University of Colorado.
Like Santorum, Miller is a devout Roman Catholic, but he believes evolution can only explain how life arose and how it diversified. Why there is life at all is another question entirely, one that Miller believes is outside the realm of science.
Lawrence Krauss, a physicist at Case Western Reserve University in Ohio, expressed a similar sentiment. "The questions of purpose are not part of science," Krauss said. "How you interpret the results of science is up to you, and it's based on your theological and philosophical inclinations."
The ID nerve center
The ID movement is orchestrated by the Center for Science and Culture (CSC), a subdivision of the Discovery Institute, a conservative Christian think tank based in Seattle.
The CSC strategy for countering evolution is twofold: challenge its soundness as a scientific theory, then replace it with ID.
The CSC is using a campaign called "Teach the Controversy" to carry out the first part of the strategy. The campaign is aimed at public schools and teachers are urged to expose students to the "scientific arguments for and against Darwinian theory." It exploits disagreements among biologists, pointing out gaps in their understanding of evolution in order to portray evolution as a "theory in crisis."
Selling ID as a viable alternative to evolution, however, is proving more difficult. In modern science, a theory must first undergo the gauntlet of peer-review in a reputable scientific journal before it is widely accepted.
Measured by this standard, ID fails miserably. According to the National Center for Science Education, only one ID article by Stephen Meyers (Proceedings of the Biological Society of Washington, 2004) has passed this test and even then, the journal that published the article promptly retracted it. The journal also put out a statement that said "there is no credible scientific evidence supporting ID as a testable hypothesis to explain the origin of organic diversity."
Straddling the fence
The ID movement's greatest strength lies in its ambiguity. It makes no claims about who the designer is or the steps taken to create life. ID does not say whether the designer intervened in the history of life only once or multiple times or even whether the designer is still actively guiding the destiny of life on Earth.
The ambiguity is intentional and part of what Phillip Johnson, a retired law professor from the University of California, Berkeley and one of the ID movement's lead strategists, calls his "big tent" strategy.
By paring the origins debate down to its most essential question&mdash"Do you need a Creator to do the creating, or can nature do it on its own?"&mdashJohnson has managed to create a tenuous alliance between various groups of skeptics and conservative Christians, including Young Earth Creationists&mdashthose who believe that the Earth is only a few thousand years old&mdashand Old Earth Creationists.
In front of mainstream audiences, ID proponents refuse to speculate about the precise nature of the designer. Regarding this crucial point, ID proponents are agnostic. It could be God, they say, but it could also be a superior alien race.
Even if an ID version of science were to prevail, the designer's true identity may still never be revealed, Minnich said.
"I think it's outside of the realm of science," Minnich said in a telephone interview. "You can infer design but the science isn't going to tell you who the designer is. It has theistic implications, and then its up to the individual to pursue that out of interest if they want."
When speaking or writing for Christian audiences, however, ID proponents are more candid. Some have openly speculated about who they think the wizard behind the curtain really is.
"The objective is to convince people that Darwinism is inherently atheistic, thus shifting the debate from creationism vs. evolution to the existence of God vs. the nonexistence of God," Johnson wrote in a 1999 article for Church and State magazine. "From there, people are introduced to 'the truth' of the Bible and then 'the question of sin' and finally 'introduced to Jesus.'"
Also in 1999, a fund raising document used by the Discovery Institute to promote the CSC was leaked to the public. Informally known as the "Wedge Document," it stated that the center's long-term goals were nothing less than the "overthrow of materialism and its cultural legacies," and the replacement of "materialistic explanations with the theistic understanding that nature and human beings are created by God."
The means for achieving these goals was explained using a simple metaphor: "If we view the predominant materialistic science as a giant tree, our strategy is intended to function as a 'wedge' that, while relatively small, can split the trunk when applied at its weakest points."
In a 1999 interview with Insight Magazine, Johnson explained why he singled out evolution when his real target was all of modern science: "Evolution is a creation story and as a creation story, it's the main prop of the materialist explanation for our existence."
After watching and analyzing the CSC's strategy for years, Barbara Forrest, a philosopher at Southeastern Louisiana University, was reminded of another metaphor, one she used for the title of her book, "Creationism's Trojan Horse."
Like the hollow wooden horse the Greeks used to enter the city of Troy, ID is being used as a vehicle to sneak Creationism into public schools.
"They know that if you can get [ID] into a school, you're going to have some teacher who's going to present it as religious creationism," Forrest told LiveScience. "They know that, but they can't admit that until they get their foot in the door of the classroom."
The writers of the Wedge Document laid out a comprehensive roadmap for the CSC that included 5- and 20-year goals and strategies to achieve them. To date, nearly all of those goals&mdashincluding the publication of books, engaging evolutionary scientists in public debates and getting media coverage&mdashhave been achieved. All except for one.
"It was supposed to be their first goal and the foundation of the whole strategy and that's doing science," Forrest said. "They haven't done any because you can't do science in such a way as to test for the supernatural."
Although their arguments have been flatly rejected by the majority of mainstream scientists, ID proponents have managed to successfully pitch their idea to the public.
"They're really exploiting their own audience," Forrest said. "They're taking advantage of the fact that Americans like to be fair, but its really grossly unfair. They haven't done any science, and you don't have the right to argue that anything you've done should find its way into a classroom unless you've done the hard work that other scientists are required to do."
The Darwinist religion
While denying that ID is religiously motivated, ID proponents often portray evolution as its own kind of religion, one that is atheistic and materialistic, whose converts no longer cast their eyes towards heaven but who rather seek to build heaven here on Earth using their scientific knowledge.
The implication is that by destroying the idea that Man is the paragon of God's creation, evolution robs life of meaning and worth. And by limiting God's role in creation, evolution opens up the terrifying possibility for some that there is no God and no universal moral standard that humans must follow.
Forrest thinks this is just silly. "Where did immorality come from before Darwin figured out natural selection?" she asked.
Far from robbing life of meaning, Forrest believes that it is because of evolution that we are capable of living meaningful lives.
"It's evolution that gives us the advanced nervous system we have so that we can interact with our environments at a highly conscious level," Forrest said.
Miller thinks such claims are also self-fulfilling. "You have essentially told people that if that Darwin guy is right, there is no God, there is no morality, there is no law you are obliged to obey," Miller told LiveScience. "I don't know of any evolutionary biologists who would say that, but I do hear a lot of people on the other side saying it."
What's at stake
On its website, the American Association for the Advancement of Science (AAAS) stated that allowing ID into public schools will "undermine scientific credibility and the ability of young people to distinguish science from non-science."
Miller thinks the stakes are much higher than that.
In addition to sowing confusion about what constitutes proper science, ID has the potential to drive people away from science. If classrooms are allowed to become theological battlegrounds, then schoolchildren will basically be told that science is hostile to new ideas and that scientists believe in a ludicrous theory that negates the very existence of God.
"Evolution is not opposed to religion unless people make it so," Miller said. "The message of evolution is that we are just as Genesis told us, we are made out of the dust of the Earth and that we are united in this web of life with every other living creature on the planet, and I think that's a fairly grand notion."
Evolution & Intelligent Design
An Ambiguous Assault on Evolution
This Trojan Horse for Creationism has become very popular. But who is being duped? And what does it all mean for morality?
Intelligent design is presented as a legitimate scientific theory and an alternative to Darwinism, but a close look at the arguments shows they don't pass scientific muster. So why are scientists worried?
As evolution takes a beating, scientists remind us of the difference between fact, theory and belief.
Each time the effort to introduce creationism into classrooms starts up again, so does legislation aimed against evolution. Learn about the rash of recent cases, plus a look at historically pertinent court cases.
Some of the key players in the science of evolution and the increasingly popular notion of intelligent design, and things they've said.
"It is those who know little, not those who know much, who so positively assert that this or that problem will never be solved by science."
The British naturalist who started it all. Darwin's theory of evolution forever changed how humans viewed themselves and their relationships to all other life on Earth.
"You're just asking, can unintelligent undirected, unpurposed laws of chemistry and physics, chance and time produce things that are more sophisticated than the combined intellectual capacity of our engineering community at present. I think that's a valid question."
Minnich is an Associate Professor of Microbiology at the University of Idaho and believes that certain structures in nature are so complex that they could only have been designed by a Supreme Being.
"These people aren't scientists, they're public relations people, and [ID] is a media campaign designed to convince the public that evolution is wrong."
Krauss is a physicist at Case Western Reserve University. Along with two other scientists, Krauss sent a letter to Pope Benedict XVI in July asking for a clarification of the church's position on evolution after a Catholic Cardinal wrote an op-ed piece stating that Catholicism and evolution were incompatible.
"This isn't really, and never has been a debate about science. It's about religion and philosophy."
A retired UC Berkeley law professor, Johnson is considered by many to be the father of the Intelligent Design movement. Johnson is the author of "Darwin on Trial," in which he argues that modern science should allow for supernatural explanations.
"Johnson presents this issue as though teaching evolution is tantamount to teaching atheism, and he's doing that because he wants to scare people to death."
An Associate Professor of Philosophy at Southeastern Louisiana University, Forrest has drawn the ire of ID proponents for her pointed criticisms of ID.
"We live at a time when this country's scientific preeminence is being challenged all over the world. The last thing that we want to contemplate is anything that would further drive our young people away from science."
Miller is a biologist at Brown University in Rhode Island and also a devout Roman Catholic. He is the author of Finding Darwin's God and believes that evolution and a strong belief in God are not mutually exclusive.
Image Credits: University of Idaho (Minnich) Case Western Reserve University (Krauss) InterVarsity Press (Johnson) Southeastern Louisiana University (Forrest) Brown University (Miller)
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