Tuesday, May 25, 2010

Bend it, move it....

Young Earth Creationists bend the second law of thermodynamics.

On Uncommon Descent the erroneous idea that the second law of thermodynamics contradicts evolution is still being peddled (See here and here). The reason why the second law is consistent with evolution is not difficult to understand. Trouble is, the passionate anti-evolutionists have a strong contingent of Young Earthers in their midst. The latter, going right back to the days of Morris and Whitcomb’s book “The Genesis Flood”, have committed themselves to this fallacy and now they cannot budge from it without becoming a laughing stock. I have tackled this subject several times on this blog, but there is no harm dealing with the subject again from a slightly different angle.

In physics the entropy of a physical system given its stipulated macroscopic conditions is an increasing function of the number of microscopic states consistent with those conditions - the latter number is referred to as the statistical weight of macrostate. For example, if we stipulate that the system is a gas with stated pressure, temperature and density then the entropy will be determined by the number of ways such a system can be realized. If we stipulate that the system is crystalline then it is fairly obvious that the entropy of such a system is relatively low as there are, relatively speaking, not many microstates that realize such a configuration. More abstract macroscopic conditions can be conceived such as requiring that the system is proactively self perpetuating as in the case of living structures. Interestingly, it is clear that living structures are far more “disordered” than crystals in as much as the number of ways it is possible to exist as a proactively self perpetuating configuration are myriad compared to the number of ways a crystal structure can exist. Entropy as a quantity does not pick up on the fact that between the extreme ends of its rather undiscerning spectrum, there are remarkable structures that from an entropy point of view are not differentiated as particularly special. Another limitation of entropy as a quantity is that it only measures the statistical weight of macrostates given the constraints of the physical regime and these meta-constraints remain untouched by thermodynamic decay. Entropy is therefore not a measure of absolute disorder: It is possible to conceive of physical rĂ©gimes that are so restricted that only highly ordered configurations are consistent with those regimes; in such a context entropy only provides a measure of those macrostates with the greatest statistical weighting. Thus increasing entropy does not necessarily imply a decay to absolute disorder.

That the second law of thermodynamics is not inconsistent with evolution becomes clear even if we start by assuming that the cosmos is the product of an intelligent designer. In fact, what now follows is an intelligent design argument against the YEC abuse of the second law of thermodynamics. If our intelligent designer is endowed with the level of omnipotence and omniscient intelligence usually associated with the Judeo-Christian deity, then given a construction set of parts such an entity would be able to conceptually assemble the entire space of configurational possibilities open to that set of parts. This configuration space forms a kind of manifold of points and a Judeo-Christian deity would be able to think about this manifold like a human being thinks about 3D space. As it stands, however, this huge platonic object is pretty dead and static. So the next step is to introduce some kind of physics in order to give it dynamism. To this end our Judeo-Christian deity could proceed to “wire” up this configuration space into a network of connections. Most naturally the metric of this network would recognize the fact that the manifold of configurations naturally forms a network of relations: These natural relations exist by virtue of the spatial relations resulting of the fact that some configurations are only separated by a small distance in terms of the incremental adjustments needed to turn one into the other.

So, now we have a manifold of points connected into a network by some kind of connection metric. But we still have a pretty static object. The next thing is to give this network a dynamic by assigning transition rates to the connections: This means that if the system is known to be in one configuration we can then work out the probability of it making a transition to one of its “nearby” configurations. The manifold now has a dynamic; that is, it has some physics: Given these transition rates the system will now move from one configuration to the next.

Let us represent this dynamic by the function, T(L), that maps the links represented by L to corresponding transition rates T. In its most straightforward form T will consist simply of a list that maps the links between the nodes of the manifold to their respective transition rates. Given the powers of our assumed deity, then it is clear that such a being has available to it an enormous number of choices on how to wire up this network and how to assign transition rates: In particular it would be quite within the powers of this deity to so wire up this network that it would move toward configurations that contain living structures. To achieve this the transition probabilities need not be directionally biased: The function T may form narrow channels of flow where no direction is favoured, but because these channels form such narrow bottle necks the configurations containing life would have relatively high statistical weight thus considerably enhancing the probability that such configurations arise as the system moves through configuration space. If within the specified channels of development the transition rates are isotropic then this implies that the motion within these channels is one of unbiased random walk. From random walk immediately follows the second law of thermodynamics; namely, that the system would tend to move toward those macrostates with the greatest statistical weight - which is all the second law tells us. Since T(L) puts a tight restriction on what is possible, the macrostates with the greatest statistical weight (that is, with the greatest entropy) are not necessarily disordered in absolute terms. Thus configurations containing living structures can evolve and yet the second law not be violated. The second law works within the constraint supplied by the function T(L) whose form is not subject to thermodynamic decay and is selected by divine intelligence to considerably enhance the probability of life arising. Here then is the rub for those who naively think the second law to contradict evolution: The above system would simply migrate towards its most probable macrostate, that is the macrostate with the greatest “disorder”, and yet if T(L) is carefully chosen by our super–intelligent deity these so called "disordered" states may contain what in absolute terms are the highly complex ordered configurations of living structures.

It all comes down to how the function T(L) maps transition rates to the links between configurations. There is actually nothing really profound here: Given the freedom in choosing any arbitrary T(L) Divine Intelligence is quite capable of contriving a network of transition rates in such way as to favour the evolution of life. The function T(L) effectively defines the physics of the system; that is, it tells us the probability of a system moving for one state to the next. However, it is a funny sort of physics as it simply takes on the form of a list of connections and associated transition rates. This list of connections will contain a high level of information on two counts:

a) It will be a very long list and thus in terms of its linear size it will contain a lot of information.
b) It will be simply one list of many, many possible lists and it will therefore be an extremely rare selection. If, assuming equal a-priori probabilities, we equate this rarity to a selection probability then the implied improbability will entail a very high level of information as defined by the expression for information, –log P. (Which is the expression ID theorist William Dembski uses)

But the profound and difficult questions are these: Is it possible to compress and encode the information in this list into a set of elegant laws? In fact, is our system of physical laws one such compression? I’m not sure I know the answer to these questions, but they are questions I have never seen properly framed let alone addressed on Uncommon Descent or in any of the papers I have read written by anti-evolutionists. Instead the anti-evolutionist stance has a tendency to encourage a spurious dichotomy between “naturalism” and intelligent design. Naturalism is the view that somehow elemental nature can go it alone, a view which is at the heart of atheism. However, no doubt unintentionally, the views expressed by the anti-evolutionists appear to promote the concept of naturalism: The anti-evolutionists who follow William Dembski loudly proclaim the virtues of their design detection science oblivious to fact that it is easy to construe this as suggesting that some things in nature are “designed” and therefore “artificial” and some things need no design and therefore are “natural” , uncreated by intelligence.* I’m sure that in their heart of hearts Dembski and his followers don’t intend this insinuation, but it is all too easy to read the anti-evolutionist thesis as setting up a dualist category of nature versus God. They have created a PR problem for themselves and this is indicated by the fact that Dembski feels the need to address it here.

The fallacious use of the second law by the anti-evolutionist lobby only serves to reinforce this false dichotomy between nature’s creative power and Divine creative power: Thus the anti-evolutionists who have an deep instinctual fear of evolution feel the need to have ready a killer proof of the superiority of Divine creative power over the much feared apparent creative power nature. But the truth is that the second law is no killer argument against evolution and in any case the apparent power of nature to create via evolution must ultimately trace back to the Divine ability to specify the function T(L).

* Some problems are harder than others: The presence of a solution to a difficult problem may give an indication of the level of intelligence that solved it.

Saturday, May 22, 2010

Back of the envelop Mathematical Model Number 1: Power Laws

After a comment from Stuart about the scale invariance of power laws (See here) I pondered the subject a bit and decided I would do a post on it.

The ubiquity of the power law probably ranks it with the Gaussian bell curve. The latter arises whenever there is a random walk, a very general and common phenomenon. Another general curve is the Boltzmann distribution, an example of which can be seen in the way atmospheric density changes with altitude. But power law distributions differ markedly from the Gaussian and Boltzmann distributions in one important respect. Unlike the latter two, power law distributions don’t return well behaved means and variances. (See here)

The Boltzmann and Gaussian distributions contain negative exponentials and these create asymptotic cut offs which ensure that the integrals used to calculate averages and variances are finite. This cut off behaviour is essential given that both probability and energy are limited by conservation laws and finite resources. How then can we make sense of a power law distribution, like say the size of meteors, which if taken too literally would suggest that there are bodies out there of infinite mass?

Some back of the envelop theorising may help to explain this.

Some power laws seem to have their logical roots in the conventional concept of space constructed by taking the Cartesian product of the coordinates of this space. If an object in a Cartesian space has a size defined by some linear parameter x then that object will have a surface area or volume that will be some power of x. That is, the surface area is proportional to x to the power of p where p is a real number.

Taking my cue from things as diverse as interplanetary bodies and internet nodes, I envisage such objects being capable of attracting further material thereby growing in size. If this is the case then I suggest that the object’s surface area (or volume) is the parameter that determines its growth rate because it is via this surface area that the object interfaces with the “outside world”. If the object grows by the assimilation of material through the membrane of this surface then we might expect the growth of this object to be proportional to this surface area. That is, the rate of growth of the object, G, is given by:
... where k is a constant.

So, an object of size x is effectively ‘moving’ along the x axis with a ‘velocity’ equal to G. If the density of the distribution of objects on the x axis at point x is D(x), then the flow F(x) at point x will be given by:
Now, let us assume that the objects are coming into existence with constant rate at the lower end of the x axis. This means that when equilibrium is eventually reached the flow along the x axis will be a constant independent of x Therefore:Hence:

Given the assumptions I have built into this calculation we see a natural power law distribution in x that ultimately traces back to Cartesian dimensionality.

The above simple model really provides a starting point from which more sophisticated models can be contemplated and built. I actually feel rather unsure about the assumption that objects are envisaged to reside in a conventional Cartesian space that allows their surface area/volume to be calculated using a simple power law. In a manifold where nodes are connected randomly, rather than connected in sequence as in Cartesian spaces, the volumes/surfaces areas are an exponential function of the number of steps between the furthest nodes comprising the object. Notice also the assumption that objects can grow indefinitely – that is, it is assumed that there are no limits on the material available driving the growth of the objects. This, of course, may not be valid – or it may be valid only for a limited time. If the latter is the case then only during the period when material is available will the power law hold as a reasonable approximation.

Returning to my original query about how power laws, which don’t return convergent means and variances, can exist in a cosmos of limited resources, then it seems the answer is this: Power laws only work in open systems, that is in systems where there is an input from without. As long as that input lasts the system will move toward an equilibrium that displays a power law distribution. However, this power law distribution will only be approximate; in a cosmos of limited resources the input can never be maintained long enough for an absolute equilibrium to be arrived at. Thus we expect power laws, like geological lakes, to be a temporary phenomenon, eventually causing a maxing out of resources.

Saturday, May 15, 2010

The Gordon Ramsey Foul Mouthed School of Intelligent Design

The following quote comes from Hugh Ross’ web site here. Ross is an “Old Earth” Christian believer. However he doesn’t believe in evolution. Here is his take on the origins of life:

As Fuz and I described in our book, Origins of Life, the existence of liquid water conditions within a few limited refuges at intermittent times throughout 4.38 to 3.85 bya provides a superior explanation for the zircon and rock remains.5 This scenario leaves open the possibility that God intervened every time, or nearly every time, liquid water was present on Earth to create life. When that life was destroyed by a bombardment event, God simply waited for the liquid water to reappear to create life again. (This is why we used the word “origins”–as opposed to “origin”–in our book title.) In More Than a Theory, I suggest that God might have chosen this repeated origins-of-life strategy as a tool to jumpstart the chemical transformation of Earth’s atmosphere.

This strikes me as all rather anthropomorphic. In fact given that some people have likened the big bang to a kind of cosmic cookery and that anthropomorphisms don’t come any stronger than in the banter of TV chef Gordon Ramsey, let’s imagine it was Gordon who cooked up the hot big bang roughly 15 billion years ago. He then travels around his shiny new universe looking for spots suitable for a sophisticated experiment in chemical engineering (which is basically what cookery is all about, I suppose). Trouble is, as far as we know no spot for this work turns up for a long time; about 10 billion years in fact, when at last he discovers the Earth. He intervenes in its chemistry and cooks up some life wherever he finds the suitable ingredients in the primeval soups of its waters. Things are looking up, until suddenly:

“Oh sh*t” said God Gordon “I completely forgot about those f*ck*ng” meteors I created. They’ve completely wrecked my experiment. I’ll have to wait for another few million years before the conditions are right”

A few million years later….

“Right here goes one more time..tum..ti..tum…ti...tum.. ” (sploshing & pouring sounds at this point, along with the occasional clink of Pyrex) ….. There you go, life once again!”

A little later, guess what….

“F*ck! I don’t believe it! Those d*mn meteors have wiped out life again. I’ll have to start all over! If at first you don’t succeed try, try again!

So Gordon keeps at it until at last the late heavenly bombardments ceases and life gets a hold. But Gordon learns a lesson:

“This universe I’ve created is cr*p; it keeps doing things that I don’t want or expect. That’s the last time I create through secondary causes because I can never tell when it’s going to f*ck up. No more Mr. Deist; from now on its going to be Mr. F*ck*ng Interventionist! Then I’ll know where I am”.

So with a bit of chemical tinkering here and there life gets going. The end of Permian extinction and the Cretaceous meteor strike are setbacks, but finally life on planet Earth flourishes. However, after nearly 5 billion years of intelligent design Gordon is in for the shock of his life:

“F*ck! F*ck! It, looks as though I’m back to square one again!

The news? Human beings have appeared on planet Earth along with their free will and weapons of mass destruction.

I think there is something seriously wrong with the above concept of deity. However, the comments that somebody left on my blog here come to mind...

Thursday, May 06, 2010

The Blind Asset Stripper

I’m continuing to work through a set of Adam Curtis documentaries that I received for Christmas on DVD. For the first time in my life I’m finding politics interesting, so Curtis must be doing something right.

The latest series I recently completed watching was entitled the “Mayfair Set”. It tells the story of the rise of free market economics in the UK and America. It introduces us to some of its major personalities on both sides of the Atlantic: Jim Slater, Tiny Roland, James Goldsmith, and Michael Milkin. These men made their fortune by taking advantage of the fact that companies are legally owned by their share holders. In most cases the share holders were passive owners uninvolved with the day to day running of the company, seldom looking beyond their share price. Their blinkered ‘bottom line’ view meant that they were unable to resist a good offer when they saw one, and were very ready to sell their shares at the right price, whatever the ramifications in the wider economic sphere. Enter Slater and co: It wasn’t long before these financially ambitious men owned a string of companies, replacing the previously passive ownership with a much more proactive monopoly shareholder who was prepared to “reorganize” the company in order to increase profits. The reorganization process, which they liked to think created leaner meaner companies, had a more pejorative description: “Asset Stripping”. By laying off workers and selling off assets immediate (and ephemeral?) end of year profits were retuned. However, as far as real long term productivity was concerned the effects of breaking up and selling off company assets was unclear. But in the meantime short term profits stimulated a stock market boom as share holders bought and sold.

That is the background. Whether or not the “asset strippers” helped to create a more productive economy rather than just exploiting a legal way of siphoning off stock market money into their bank accounts is not what I am going to comment on here. What I would like to draw attention to in the context of the evolution/ID debate are the following remarks by “asset stripper” James Goldsmith. They can be found in the third program of the “Mayfair Set” series:

Goldsmith on the “Harshness of Change”:

In nature there can be no continuity because there are predators. And in fact there was some game reserve set up by some well meaning people who said it is horrible that these animals should live under the constant threat of predators. Those animals subsequently became degenerate and died because predators are a necessary stimulant. If you eliminate predators in business and just create comfortable bureaucracies and monopolies with no predators you will have a dead industry and the prosperity of the country will shrivel away and your people will suffer infinitely more than by being subject to constant stimulation, threat and competition.

Goldsmith on corporate responsibility:

The sort of stuff senator Worth is talking about (that is, about corporate responsibility – ed), which is the pastoral America with a little company, a church and university which is going to be there forever and they don’t have to compete with anybody and that competition is awful , is a total mixing up of the difference between doing business and doing good. Doing business is what gives you the fuel to do good. Don’t mix them up. The bee doesn’t make honey because he is doing good. He doesn’t have the soul searching of “Am I doing good?”

What irony; the free market process, so beloved of the American religious right, being described in such folk Darwinian terms! Goldsmith is telling us that individuals need look no further than their own immediate productive interests and hey presto out of the hat pops an organized democratic society. (Although conspicuously, he says nothing about a just society). As in evolution only local and immediate gain need be selected for by otherwise relatively blind local market forces, forces that have no cognizance of the greater whole. Thus, no overall social perspective need be conceived and processed intelligently; the average investor need only act selfishly, looking after his own interests without a mind for the bigger picture. A bonus, according to Goldsmith, is that the investor can even think of himself as doing good; thus he can be both selfish and morally upright at the same time!

In some ways the picture sketched by Goldsmith is how societies inevitably proceed – local decisions are made that, due to limited prescience on the part of finite human intelligence, do not take into account the widest of contexts and long term ramifications. Thus, in a very general abstract sense technological societies evolve, quasi-blindly.

Starting here I did a series of blogs as a follow up to watching Adam Curtis’ documentary series “The Trap”