Back to Fractals

Figure 2: (top) 2-simplex for {1/a} Sierpinski Gasket, and bottom: after collapsing a2-a3 to a single point Figure 1: Solution for space {3/a} Sierpinski Gasket

We start with the solution to the problem posed at the end of the last blog entry. The sketch of the correct {3/a} space is shown in Fig. 1. Note the vertices of the holes are all self-consistent which is an important part of the solution. Thus, the three holes are presented so there is no overlap of their vertices.

As before the fractal mass density is: rho(f) = {N(s) - N(h)/ N(s)}

so: rho (f) = {9 - 3/ 9} = {6/9} = 2/3

The fractal dimension D_f = 1/ rho(f) = 1/ (2/3) = 3/2

Now, let's look at the {1/a} base space but in a new guise, this time as an oriented 2-simplex(see Fig. 2- top). For this oriented 2-simplex we can write: a1a2a3 = a2a3a1 = a3a1a2 = -a1a3a2 = - a3a2a1 = -a2a1a3, so that provided the arrows can also be applied to the Sierpinski Gasket {1/a} base space, the two are homeomorphic. Consider now the boundary of a similar 2-simplex such that:

@2(a1a2a3) = a2a3 - a1a3 + a1a2

By definition, the group C_n(x) of oriented n-chains (e.g. a2 a3 is a 1-chain) of x is the free-abelian group generated by oirentied simplexes of x. Thus, every element of C_n(x) is a finite sum of form SIGMA_i s(i)m(i) where the s(i) are the n-simplexes of x and m(i) ( Z.

Problem:

Take the 2-simplex at the top of Fig. 2 and let a2, a3 collapse to a point as shown. Call the lower branch of the loop 'Y' - a sub-complex of the simplicial complex X.

If the generators for C1(x) are: a1a2, a2a3, a3a1, find:

a) the generators of C1(Y)

b) the value of Z1(X,Y) and H_k(X,Y) = kth relative homology group arising frmo sub-complex (C(Y)) of chain complex C(X)

Hints: The factor quotient group H_n(x) = Z_n(x)/B_n(x); for all chains of Y set = 0

We will look at this solution next time.

Some Basic Aspects of Fractals

Fig. 1 - Base space gasket

Fig. 2: 2-space gasket

We return to fractals again, this time to examine them in more detail at a basic level. Here I want to compare two simple fractal spaces based on an object known as "the Sierpinski gasket". The most elemental form is depicted in Fig. 1 above and can be compared with Fig 2 which is generated from it.

For Fig. 1, we regard the simple (1/a) space as the generator of more complex fractal spaces F that are essentially infinite. To undertake the cyclic generation process we require that the specification of the vertices (a1, a2, a3) be non-degenerate, i.e. no more than one eigenvalue: a1, a2, or a3 can be assigned for any triangular space. The fundamental space depicted in Fig. 1 we shall call a "Planckian gasket" and note that its fractal mass density can be found as well as its fractal dimension.

The fractal mass density can be computed from:

rho(f) = {N(s) - N(h)}/ N(s)

or the number of scale elements minus "hole" elements divided by scale elements. In this case: N(s) = 1, and N(h) = 0, so:

rho(f) = {1 - 0}/ 1 = 1

The fractal dimension D_f is the inverse, or: D_f = 1/ rho(f)

In this case, D_f = 1

Now, examining the larger space in Fig. 2 defined by {2/a}, we again obtain the vertex designation (a1, a2, a3).

However, we further note that to get from the primitive space to the space {2/a} we require the transposition (see the blog entry on transpositions from two years ago):

(a1, a2, a3) -> (a1, a3, a2)

That is, a1 remains fixed, and a2 - a3 are "mirrored" through a bsiector axis identificed above from a1-a1. Note that the "hole" (in black) represents the inversion space (or negative space: -a1a2a3) a result of the inversion of the positive space of the primitive {1/a}.

The fractal mass density can be computed from:

rho(f) ={4 - 1}/ 4 = 3/4 = 0.75

And the fractal dimension is:

D_f = 1/ rho(f) = 1/ 0.75 = 1.333

Exercise for the adventurous reader: Draw the space for {3/a} with three symmetric holes of oriented vertices a1, a2, and a3 inside it. Then work out the fractal mass density and fractal dimension. We will look at the solution in the next instalment, and also see how algebraic homology can be applied to these triangular spaces!

Why Is It So Hard to Grasp Science?

This is a question I've always asked myself, especially when I see some of the tripe published as letters in many national newspapers. A recent case in point concerned a spate of letters published under the sub-header: 'Science, Great as it is, Can't Answer Every Question', in the Oct. 19th Wall Street Journal.

One could, inf act, complain about the wording of the header itself, since neither pure science nor applied claims to be able to answer every question. All it claims is the curiosity to ASK a question, and then diligently pursue an answer. That is all science is about at the end of the day.

Nevertheless, the letters embody even more misunderstanding.

For example, John F. Haggerty writes:

"Though evolution may explain the process by which life evolves, it doesn't explain why or how the process began"

As to "why" it began, Haggerty is correct, science doesn't go there. The reason is that 'why' questions lead into teleology and self-reference while delivering no concrete sufficient cause or better, sufficient conditions for the necessity of purpose. Additionally, it necessitates an unwarranted extrapolation beyond what science can actually assert with its data.

Thus, we do not ask "Why do stars shine?" - but the more productive question: HOW do stars shine? The latter enabled diligent pursuit into nuclear fusion processes and quantum mechanics, thereby enabling us to ascertain the stars could only shine via nuclear fusion reactions.
'Why?' remains a mystery, and in any case is irrelevant since the answer doesn't assist us in making future predictions.

By the same token, we refrain from asking WHY species evolve, opting instead for the more productive HOW do they evolve? Well, by a combination of mutation and natural selection.

As to HOW life began, Haggerty hasn't been paying attention. While we don't have a firm lights out theory for the origin of life (which is NOT the same as evolution!) we have a good working hypothesis.

The consensus of current research is already fairly clear about the nature or form of the first primitive organisms. They were prokaryotic autotrophs[1]. More specifically, they were suspended colloidal micro-spheres capable of exchanging energy with their surroundings. To get energy, these self-sustaining coacervate droplets could use one or two basic reactions involving adenosine triphosphate (ATP) and adenosine diphosphate:[2]

L*M + R + ADP + P -> R + L + M + ATP

ATP + X + Y + X*Y -> ADP + X*Y + X*Y + P

In the above, L*M is some large, indeterminate, energy-rich compound that could serve as ‘food’. Whatever the specific form, it’s conceived here to have two major parts capable of being broken to liberate energy. Compound R is perhaps a protenoid, but in any case able to act on L*M to decompose it. Concurrent with the first reaction is the possibility of a second, entailing autocatalytic molecules X*Y. These molecules could accelerate their own formation, using ATP.

On the basis of the chemical reactions, the hypothetical coacervate would consist of the combination: X*Y + R. Now, what properties ought we expect for any such primitive life form? These include: simple organization, ability to increase in size, and ability to maintain itself over extended intervals. Does the coacervate meet these conditions?

Well, it has a simple organization, consisting of the molecules X*Y and R. It can increase its size by synthesizing more of X*Y, growing until hydrodynamically unstable. Finally, it can maintain itself over indefinite intervals, so long as it can extract the chemical components it needs. What about replication? We expect that this is feasible when it splits into ‘daughters’ after growing too large. Then, so long as each has some of the protenoid R there is the capacity for replication.

A logical question is whether there is anything that can remotely compare to the theoretical construct above. In fact, there is, and it’s called a pleuro-pneumonia like organism or PPLO for short. The PPLO is as close to the theoretical limit of how small an organism can be[3]. Some figures clarify this. It has about 12 million atoms, and a molecular weight of 2.88 million Daltons[4].

Compared to an amoeba, it weighs about one billions times less.


Haggerty goes on to assert:

"Evolution doesn't account for the very fact of existence itself".

Again, IF Haggerty means accounting for "the fact of existence" in terms of WHY - he is quite correct. If he means in terms of HOW - he is quite incorrect. Because evolution admirably accounts for the fact of existence itself in terms of HOW all the diverse, observed speciation came to be!

Haggerty then poses the most fundamental ontological problem:

"Why there is something and not nothing is one of man's most basic questions and one natural scientists cannot answer".

But why should we? Truth be told, the question is more apropos to religionists and God believers than secular scientists. Consider this: If nothingness be the more perfect state (no gross defects, no sin, no atavistic impulses to cause crimes, etc.) and if God knew about how much havoc and tragedy creating a cosmos would incept (since he presumably had the attribute of omniscience), WHY do it? THIS is an eminently religious question, not a scientific one!

Why then add to what was already perfect? Why indeed add what God had to know before all time would be manifestly IMPERFECT?

Since religion is concerned with the matters of right and wrong, this is their domain, not science's! Science can at least posit the spontaneous inception of the cosmos via quantum bootstrapping and have an answer for how it all began, which isn't perfect - but nonetheless is adequate for most serious scientists. More importantly, it is a physical agency not contingent on supernatural effects.

By the same token, Haggerty's ending endorsement of the "need for Man to find meaning to his existence" may be a supreme task for most humans, but to practicing scientists it isn't necessary to find some transcendent meaning in our lives. We obtain our meaning (purpose) in the work, research that we do to extend the frontiers of knowledge.

Meanwhile, the next writer, David Maj - appeals to fairy stories and legends:

"The real clash, as I see it, is spelled out with great wisdom in the story of creation where Adam and Eve ate from the tree of the knowledge of good and evil because they wanted the power to define what is right and wrong".

But, of course, Maj blithely skips over the fact that what "is right and wrong" is relative, never absolute. He or others may not like this, but there it is. Thus, it is "wrong" to kill - but perfectly okay if it means you are gassing a murderer to death in a state-approved execution, or waging war against some distant, proclaimed enemy.

So okay, yeah, it's "wrong" ---- with exceptions! But, if it has exceptions then it clearly can't be an absolute!

Invoking "Adam and Eve" and a "tree of the knowledge of good and evil" clarifies little. What is far more productive is to examine the brain in detail, and see how it is configured and how it can easily be the cause of our split lives - aspiring to always do "good", but more often than not failing.

What people refer to as “evil” is easily explainable in terms of brain evolution. Thus, Homo Sapiens is fundamentally an animal species with a host of animal/primitive instincts residing in its ancient brain or paleocortex.Meanwhile, the paleocortex sits evolutionarily beneath the more evolved mesocortex and neocortex, the latter of which crafts concepts and language. One clever person has compared this tri-partite brain structure to a car design welding a Lamborghini to a Model T Ford chassis, with a 1957 Chevy engine to power the Lamborghini. If an automotive engineer can conceive of such a hybrid beast, I'd be interested to know exactly how he thinks it would run.

Given the preceding brain structural defect, there is much evidence that the aggregate of human behavior will get progressively worse as the complexity inherent in technological and globalized societies increases, but brain evolution is unable to keep pace with it. Basically, we are a species with the capability of making nuclear weapons and intercontinental missiles – but with Cro-Magnon brains – and a swatch of reptilian tendencies.

Indeed, the mixed brain design, in terms of adaptability to technological society, is already theorized as one major cause of depression and mental illness in such societies (e.g. The Noonday Demon, Chapter 11, ‘Evolution’, p 401). The behavior resulting from this hybrid brain is bound to be morally mixed, reflecting the fact that we literally have three “brains” contending for emergence in one cranium. Imagine a thinking human, ape and crococdile fighting with each other for supremacy. That's what goes in your brain non-stop every waking minute of every day. Some people can't handle it which is why they "lose it" then we hear about the "quiet guy that killed six people at the bank and no one ever saw him get mad before".


Behavior will therefore range from the most selfless acts (not to mention creative masterpieces) to savagery and murder, carnal lust run amuck and addictions that paralyze purpose.The mistake of the religionist is to associate the first mode of behavior with being “human” and not the latter.

The last clueless letter writer, a Jim Reardon, asserts that we "secularists fail to realize that the arguments for the immateriality of the human intellect do not begin and end with religion"

Fair enough. At which point he avers:

"Aristotle reasoned that while the material brain and sensory organs are a necessary basis for human understanding, they are not sufficient causes"

But who is Aristotle? This is the same guy who developed a physics of motion relying on the principle that when bodies fall they are under the impetus of their "desire to fall" and the one that wishes to fall faster, will. Contrast this with Galileo's meticulous data and experiments that showed all objects fall to Earth with the same acceleration at the same place and this is the result of no internal desire but of the Earth's gravitational attraction.

In terms of "sufficient causes", Reardon is quite right that the mere existence of the brain and sense organs isn't enough. Critical cortical thresholds must be crossed for conscious brain function, and these begin with the resting action potential as applied to the axon membrane walls of the neuron. A baseline wave pulse amplitude of ~ (-70) mV is required and this results from an uneven distribution of potassium (K+) ions across the axon cell membrane relative to a collection of negatively charged protein molecules inside the cells.

Too much to get into right now, but we can re-visit it at a later date!




------
[1] A prokaryote has one chromosome only, dispersed in its cytoplasm. An autotroph is an organism that doesn’t depend on others for nutrition.
[2] See, e.g. Zindler, Frank: 1989, How Did Life Begin- Part III, The American Atheist, April, 1989, page 42.
[3] Viruses are smaller, of course, but they’re not regarded as free living organisms. That is, they require a host in order to live, replicate.
[4] One Dalton: roughly the mass-weight of a hydrogen atom or 1.66 x 10^-27 kg.

Is It Time to Put Rover on the Menu?

Dressed doggies: Time to put 'em on the Menu?

Stewed Dog (Wedding Style)- Classic Filipino Recipe:

Obtain 1 medium-sized dog (euthanized)

Burn off fur over hot fire, then carefully remove the skin while still warm and set aside for later (can be used in other recipes).

Marinade meat in mixture of vinegar, peppercorn, salt and garlic for 2 hours.

Fry meat in oil using large wok over an open fire, then add onions and chopped pineapple and saute until tender.

Pour in tomato sauce and boiling water, add green peppers, bay leaf and tobasco.

Cover and simmer over warm coals until meat is tender.

(Optional): Blend in puree of dog's liver and cook additional 5-7 minutes
----


Source: 'Let Them Eat Dog: A Modest Proposal for Tossing Fido in the Oven': by Jonathan Safran Foer, in The Wall Street Journal, Weekend Journal, page A-10.



For any readers whose brain has by now gone into meltdown mode and whose eyes are bulging wildly with terror (as they clutch little Roscoe, Barney, Lassie or Rebel to their bosoms) rest easy. There is little chance of dog getting on any American menus anytime soon. The cultural milieu that regards dogs as companions, friends and more ...wouldn't allow it. At the same time it would be erroneous to conclude that Foer's piece was "tongue in cheek", it wasn't.

In a world starving for protein, Foer makes an excellent case to incorporate canines into the menu and not look back. His reasoning is as cold, calculated and rational as most of the investment articles on ETFs and hedge funds that appear in the Journal.

First and foremost, unless you are a vegetarian who never touches beef, you are already consuming someone's Rover or Fido, at least in a second hand mode. Consider: some two and a half million doggies on the loose eventually end up at the Pound, and 90% of these are euthanized annually. Ever wonder where they end up?

Ever watch the flick 'The Misfits', starring Clark Gable and Marilyn Monroe? The gist of it was a clique of cowpokes head off to Nevada to rustle up wild horses to be dispatched (for $$$) to a rendering plant....as dog food! (Marilyn's role- in her character- is to cry and whimper and otherwise try to set all the wild horsies free).

That was 1962. Now, fast forward some 35 years. The remains of millions of Rovers, as well as abandoned kitties, are being rendered in massive plants each year. The remains then end up in enormous cattle feedlots and mixed in with a mishmash of millions of tons of unnameable stuff and fed to the cattle. (See the film, Fast Food Nation, if you haven't yet)

When you consume the cattle - unless you know they are free range, and forage on plain old grains, you are eating those remains!

Foer's argument is 'why not just remove the middle men'? Why not just eat the overpopulated, abandoned (soon to be rendered) dogs and done? As Foer puts it:

"This need not challenge our civility. We won't make them suffer any more than necessary...we can all agree that if we are going to eat them, we should kill them quickly and painlessly, right? "

Foer then continues, tying the purpose to ecology on a planetary scale:

"Few people sufficiently appreciate the colossal task of feeding a world of billions of omnivores who demand meat with their potatoes. The inefficient use of dogs- conveniently already in areas of high human population should make any good ecologist blush. One could argue that the various 'humane' groups are the worst hypocrites, spending enormous amounts of money and energy in a futile attempt to reduce the number of unwanted dogs while at the same time propagating the no dog-for-dinner taboo'"

As a former Humane Society member, I recall shelling out hundreds of bucks in donations to save stray dogs, only to find out later that the Humane Society did more euthanizations than dog giveaways. That was emphatically not what my money was for. It was to find HOMES for abandoned canines, not eliminate them!

Like it or not, most of the world is in a protein crisis as much as a water crisis. Protein is still essential to proper brain development but in places like Haiti and Niger is conspicuous by its absence. At the same time, feral dogs are all over the place. Instead of malnourished kids in Haiti having to eat "mud cakes" - prepared by heating local moist mud over an open stove and flavoring it with sugar, why not cook the available dogs up and distribute the cooked meat? American temperaments no doubt rebel at the concept, but as Foer notes, that is totally a cultural emotional reaction, brought on by our peculiar habit to prefer canines as companions rather than edibles.

Why do we cook our pigs up and convert them into bacon, wieners, roasts and chops, and leave our dogs as privileged companions? (Some idiot 'Muricans even going to the extreme of taking dogs to get outfitted in clothing, or having dog birthday parties) In numerous rigorous tests, for example, pigs have been found to be just as intelligent as dogs. Pigs are the closest relatives in terms of their value in human experiments, and pig tissues- even hearts- have sometimes substituted for human. Yet we put them in vast slaughter houses, then butcher then and eat them. As George Orwell once opined (in his great novel, Animal House): "All animals are equal but some are more equal than others".

Now think of how Swine Flu began. It started in a vast factory pig farm in Mexico. Most E Coli cases have originated in huge industrial factories, wherein the cattle are carelessly butchered, as portrayed in 'Fast Food Nation'. Thus, Foer's final point that:

"There is an abundance of reasons to say no to factory-farmed meat: It is the No. 1 cause of global warming, it systematicallu forces tens of billions of animals to suffer in ways that would be illegal if they were dogs."


All of this perhaps is reason enough to agree with Foer when he says: "Dogs are practically begging to be eaten".

Which is to say, I will pass on it, thank you very much. But I won't look down my nose at anyone who is averse to factory farmed meats raised in their filth in slaughterhouses, and who opts to barbecue their Rover- rather than put him down at the local Pound..... for their neighbors to consume with that next cheese burger.

Notes from a first Evolution Lecture

Whilst pouring through old files (and trying to re-organize them) the other day, I came across a manila folder labeled 'Evolution Lecture Notes'. Curious, I opened it up to find sheets that I had used to prepare my first ever lecture on evolution - when I was teaching O-level Biology, in 1974. This was as part of my (then) Peace Corps assignment, at a secondary school in the north of Barbados

The notes were interesting and intriguing, not only for being the first used for a teaching assignment, but because I had used them to answer student questions - then, and in later years in other venues. They were also interesting in that word of my evolution teaching had spread round the school and reached the ears of two Scripture teachers. They then challenged me to a debate, which I happily agreed to. Provided they allow me double the presentation and rebuttal time - to equalize their numbers!

Anyway, the part of the notes that is likely most apropos here, for a short space, has to do with the questions that were asked and the answers I gave. I still find these answers as good then as now, but agree if I were to redo them I'd had many more details to do with the genetics and micro-biology. (The prospective redone parts are given in italics)

So let's start the ball rolling. In each case a student question is numbered and given in black, and then my response to follow.


1. Evolution states that advanced life came from non-life - how can this be?

Actually, the theory of evolution says no such thing, but this is a common error. The concept of life possibly arising from non-life is the theory (actually more hypothesis) of noogensis.

What evolution says is that incremental changes to proteins, and genetic structures are made over time which then become passed on by a process of natural selection to successive generations of an organism. The attributes passed on generally confer a survival advantage.

2. Can you give an example?

Sure! The success of natural selection is measured by the fitness (w) and the selective value (s): E.g. w = 1 – s

As an illustration, consider a German cockroach species with allele D, where D denotes resistance to the pesticide dieldrin, and d denotes non-resistance.

In the population after some defined time, let three genotypes be exhibited in the population: DD, Dd and dd. Now, on average over time let each dd and Dd individual produce one offspring, and each DD produce two. These average numbers can be used to indicate the genotype’s absolute fitness and to project the changes in gene frequency over succeeding generations.

The relative fitness (w) is meanwhile given by:

w = 1 for DD

w = 0.5 for Dd

w = 0.5 for dd

The selection values, relative measures of the reduction of fitness for each genotype, are given respectively by:

s = 1 – 1 = 0 for DD

s = 1 – 0.5 = 0.5 for Dd

s = 1 – 0.5 = 0.5 for dd

As we expect, the dieldrin-resistant genotype displays zero reduction in fitness, and hence maximum survival rate. By contrast the x allele can be regarded as ‘deleterious’. Evolution in this case favors the replication of all those German roaches with genotype DD. Those others (dD, dd) will die out at disproportionate rates. As they die out, therefore, only the hardiest DD genotypes will remain.

Indeed, it can be shown that over successive generations of these roaches the gene frequency (of d) will decrease by:

delta q = -s p q^2 / (1 - sq^2)

where p denotes the frequency of the favored allele, and q the frequency of the "disadvantaged" or "deleterious" allele. Fixing ideas, let's say at a particular time that a gene frequency "snap shot" of the (German) cockroach population under study yields: p(D) = 0.60, q(D) = 0.40. i.e. the favored allele is reproducing at the ratio 3:2 relative to the deleterious one, d.

Assume as before that s = 0.50. A simple table can be constructed (via successive iterations of the previous formula) showing the declining gene frequency of d relative to D:

The Table has headers:

p ---- q -----q^2 -------delta q

Where the 2nd quantity is the one to keep an eye on. The first couple entries - row by row are:

0.60 ----- 0.40-----0.16----- (-0.13)

0.73-------0.27 -----(0.073)----(-0.10)

Each new (delta q) of course feeds back to reduce q in the next iteration. Thereby the loss of 'd' genes through selection is balanced by the gain of the 'D' genes that confer reproductive advantage. This example is based on a starting mutation, but others can be invoked to show how a sipmle minor adaptive change in structure and function - can directly lead to a permanent structure, e.g. the bacterial flagellum - as Watson noted.

Similar evolutionary advantage can be see with the mutations of the influenza virus, which is also why flu vaccines have to be changed each year. The influenza virus change is a perfect example of evolution in action.

3. Don't you assert a tiny probability for any given step happening?

Not at all. another misgiving and misunderstanding. As you can see using the preceding example of the German cockroach, all that is needed is for the gene frequency associated with the favored allele (in this case, DD) to constantly increase relative to the disfavored ones. This happens automatically as the less-favored die out over time, and following the table above shows this. Hence, probabilities are not fixed, say like that to achieve a royal flush in poker, but can be enhanced by the dynamics of the fitness-change.

The error of many creationists is to assume all evolutionary probabilities are fixed, and all are remote. An example often given (misplaced) is the likelihood of taking a Jet apart and having it come back together by itself. This is erroneous since the Jet is already a manufactured item. Hence if one disassembles it there is zero probability of its reconstruction unless extraneous factors are inserted. Like a team of Jet builders!

Natural selection works differently, in that certain features of living things are already selected for then their repetition is enhanced via reproduction. It is not the same at all. In fact, the increased probability is usually already set once a single simple change occurs. This usually starts with micro-evolution. Micro-evolution implies an incremental change in a small proportion of DNA.

Examples of micro-evolution include the re-arrangement of amino acids in proteins such as haemoglobin, or the altered genes for a specific genetic character in successive generations of the fruit fly. For example:

Generation I (AMINO ACID SEQUENCE): AA BBB CC DDD FF GG
Generation XXIII (AMINO ACID SEQUENCE): AC BBB CC DDE FF GG

The preceding illustration discloses re-arrangement of the amino acid sequence, by base substitution, in a succeeding generation of for fruit flies. Such re-arrangement is prima facie evidence for species micro-evolution, i.e. at the microscopic level of observation characterizing genes and amino acids.

4. Why are there no missing links?

"Missing link" is a common erroneous term. It implies there is one and only one transitional species leading from a common ape-human ancestor to humans. This is the wrong end of the stick. In fact, what we are dealing with is a series or sequence of transitional links that have occurred over the past 6-8 million years. The most recent of these finds (and most distant ancestor) was "ardis" described in an earlier blog entry. There are doubtless dozens of others in the fossil record before him -her.

Why so hard to find? Not because evolution is "wrong" but because the Earth's crust is dynamic. It is not one solid mass but composed of over 15 tectonic plates which continually shift, move and crush up against each other. It is a wonder, given that, we have managed to find any fossils. Bear in mind here: evidence of absence is not absence of evidence!

For this reason, the prima facie evidence of evolution doesn't rest on fossils alone but on genetics.

For example: ·

We know humans and chimpanzees have the exact same cytochrome- c protein sequence. In the absence of common (evolutionary) descent, the chance of this occurrence is conservatively less than 10^-93 (1 out of 10^93). Thus, the high degree of similarity in these proteins is a spectacular corroboration of the theory of common descent.

Furthermore, human and chimpanzee cytochrome- c proteins differ by ~10 amino acids from all other mammals. The chance of this occurring in the absence of a hereditary mechanism is less than 10^29. The yeast Candida krusei is one of the most distantly related eukaryotic organisms from humans. Candida has 51 amino acid differences from the human sequence. A conservative estimate of this probability is less than 10^-25.

In terms of the genetic aspect, we know from the chimp-human chromosome studies (first published in Science; Vol. 215, p. 1525, 1982 by O. Prakash and J; Yunis. ) that a remarkable homology exists between chimp and human chromosomes when heterochromatin is excluded. They found no less than thirteen IDENTICAL chromosome pairs, that included chromosomes: 3, 6-8, 10, 11, 13, 14, 19-22, and XY.


The next question was not in the original set but is added here, since it appears to have become a huge issue with the creationist crowd:

5. Doesn't the 2nd law of thermodynamics prohibit evolution? If the second law asserts everything is winding down and getting more disorderly, how can you have more orderly and advanced biological organisms?


This is directly a result of misinterpretation of the 2nd law. Strictly speaking the law states:

Entropy (the state of disorder) will tend to increase over time in any closed system.

The last part is very crucial but it is exactly the part that the creationist crowd omits, which renders their question a non-starter.

The reason is that neither the Earth nor its biological systems are "closed" systems, hence do not exhibit constantly increasing disorder.

The Earth, for example, is open to the radiant energy of the Sun and receives some 1360 watts per square meter. Plants on the Earth are likewise OPEN to solar energy, and receive it and then use it in the process of photo-synthesis. Other oganisms eat the plants and thereby incorporate that energy into themselves.

Thus, the path is cleared for higher organizational development and speciation.

We do not see a constant wind-down because all these systems are OPEN, not closed.

Hopefully, readers will find the above answers intriguing and thought -provoking.

Let the Kids Have Fun!

It's Halloween, and time for all the play spooks and goblins to come out. I have just one question about this (most popular) annual festivity : Where have all the Devils gone?

Seriously! The Wall Street Journal noted about a week ago the most popular costumes recorded by retail sales, and they ranged from "The Little Princess" (commanding nearly 49% of all those sold) to Spiderman, to Harry Potter, and Angels - but NO Devils! Where the Hell are the Devils?

In my first ever 'trick or treat' excursion alone, ca. 1953, I recall the one costume I prized most was that of a Devil, aka Lucifer. I managed to get my (reluctant Catholic) mom to craft most of it, including the pointed tail, and I found the perfect rubber mask at a Milwaukee variety store on Vliet St. The mask was a grotesque rendering of the Devil and included suitable slanted eyes, dark furrowed brows, a wicked mustache, goatee and small horns. By the time I was all set, I felt like I'd scare the bejeebers out of most of the kids ambling around the streets near Hadley St.

Didn't turn out that way! Nearly one -fourth of the trick or treaters had also adopted Devil attire! No fun!

But where are all the Devils now? Not to be seen. All we behold are the politically correct, pathetic outfits made popular by assorted commercial fare and that is mostly pop junk. But no Devil! The WSJ wouldn't even put an estimate on demonic entity costume sales, which means it was probably below 0.01%. Pathetic! Satan looks like he no longer gets any respect. Maybe he ought to sound off like the late Rodney Dangerfield!

As we know it today, Halloween (or "all Hallows eve") was derived from the ancient Celtic festival of Samhain (pronounced sow-in), “when it was believed that the ghosts of the dead returned to earth."

According to history.com:

"In the seventh century, Pope Boniface IV designated November 1 All Saints’ Day ... It is widely believed today that the pope was attempting to replace the Celtic festival of the dead with a related, but church-sanctioned holiday. ... The night before it, the night of Samhain, began to be called All-hallows Eve and, eventually, Halloween.”

Trick-or-treating evolved from English traditions of All Souls’ Day, when the poor would go house-to-house begging for food in exchange for prayers for the families’ deceased relatives. Costumes naturally became a part of this.

Needless to say, Halloween today remains the most egalitarian of holidays, because it is the one time - the one national celebration- when poor or homeless children can also take to the streets in droves, hold their little bags and hands out, and receive the bounty of the wealthier citizens without shame or opprobrium. Even costumes can still be fashioned cheaply, without having to go out and spend a bundle -especially with unemployment still at almost 10%.

What's not to like? Halloween, at least for those of us who've not yet become moral scolds, is the best time of the year - because we let kids pretend to be what they want, without rancor or belittling. The kids enjoy it, being able to make the rounds of many city streets, and return home with loot that can last for days: Snickers bars, Reece's pieces, Hershy's kisses, and even - if lucky- those fancy Cadbury almond and milk chocolate bars.

In my day, it was mostly candy corn!

At the top, a crude rendition or approximation of my devil mask.

No More Fake Meteorite Strikes!

THE BARRINGER METEOR CRATER in ARIZONA

We have already seen how many folks, albeit gullible, were inconvenienced by the "balloon boy" farce, but where it really gets nasty and reckless is when companies have to trick whole nations to promote their products. Such was the case with the recent "meteor strike" publicity stunt, in Latvia, compliments of Tele2 - a Swedish mobile phone company. (This was as reported in The Financial Times, Oct. 28, 'Companies & Markets', p. 13)

Did these jokers really think it would be cute to emulate the arrival of a 0.1 m meteorite (the term "meteor" is reserved for when it is seen in the atmosphere, though the FT story refers to "meteor strike"), to the extent of even digging out a hole over 30 feet wide and 10 feet deep? And then completing the fakery by burning chemicals at the base to create the impression of a smoldering object still around?

As the FT noted (ibid.)

"The Stockholm -based company admitted it had dug the hole and burned chemicals"

Like the balloon story, this one garnered worldwide attention. All the moreso because seldom have cameras or human eyes actually been on hand to witness and record such a momentous strike.

The last one I beheld, in Barbados some 23 years ago, occurred when a meteorite (estimated at 0.4m across) plowed into Mt. Tenantry and raised quite a ruckus. The explosive intensity alone shattered eardrums for over a mile from the site. The impact was written up in an issue of The Journal of the Barbados Astronomical Society.

However, there was no major crater left behind, so - when we investigated (a team of us from the Barbados Astronomical Society) we concluded that nearly all its kinetic energy was converted into sound, and heat. Indeed, you couldn't go near the site and a lot of trees were still burning by the time we arrived.

Needless to say, these strikes are rare- which is just as well. To see one of the biggest impacts ever, check out the Barringer Meteor Crater - shown in the photo at top, and created some 25,000 yrs. ago. The object that made this crater had a diameter of nearly 35m (prompting some to suggest an asteroid did it, not a meteorite - but the distinction is academic since it is still at the limits of the largest meteorites).

The energy was estimated to be 1000 times that of the Hiroshima A-bomb, and the crater left was 1.2 km (0.75 mile) wide and nearly 167 m or 551' deep. If such a monster meteorite had impacted a small suburb, say near Miami Gardens, FL (near Dolphin stadium) the whole region would be almost totally decimated, from the Palmetto Expressway, to way past the Broward County line.

This is another reason it isn't too classy or smart to try to invent fake meteorite hits. Fortunately, in this case, on site inspectors saw a too symmetrical crater - and figured it had to be man-made, not natural. The smoking detritus also aroused suspicion, not to mention why there was already a camera crew on hand filming it. How convenient is that? To be there within seconds of an impact?

As it has turned out, according to the FT report Tele2 has paid the price. The Latvian Interior Ministry has vowed not to do business with them, and Latvian police are evidently to launch a "formal investigation".

Faking meteorite strikes to promote a new product is not to be commended any more than faking balloon flights with a small boy inside, to try and grab a new reality TV-show.