@ Tin Man

Yeh, covered in fluff and that greasy stuff that collects behind the washing machine.

@ The OP

I will only pick up one one of these moronic assertions viz:
There is nothing to back up evolution and yet it is still being taught in our schools.

There is much more evidence for evolution than there exists contemporary evidence for your jesus figure's existence. Yet you want christianity taught everywhere.....

My irony meter just exploded again.

@ You know

"Where are the transitional fossils?
There should be hundreds and thousands of transitional fossils discovered"

Archaeopteryx ... Google it. As far as the expected number of fossils, they are incredibly rare because it requires very special circumstances to create any fossil.

"Second law of thermodynamics
If we are evolving, why aren’t we super human yet?
Instead we are falling apart with cancer and other diseases"

You do not understand evolution. It does not work towards more complexity or a superior offspring, but only whatever it takes to survive. More than 99% of all the species that have existed are now extinct. Most of those species went down the wrong path, they did not improve (as you assume evolution does).

"Evolution is a religion that requires more faith then Christianity
There is nothing to back up evolution and yet it is still being taught in our schools."

Evolution is not a religion. It is a recognized scientific theory. Before I get too deep, you must understand that a scientific theory is not just a hunch or a meandering mind, but instead, from Wiki https://en.wikipedia.org/wiki/Scientific_theory

"A scientific theory is an explanation of an aspect of the natural world that can be repeatedly tested and verified in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, theories are tested under controlled conditions in an experiment. In circumstances not amenable to experimental testing, theories are evaluated through principles of abductive reasoning. Established scientific theories have withstood rigorous scrutiny and embody scientific knowledge."

Evolution is a result of following the evidence, and deriving a valid and reasonable explanation based on all of the evidence. Please do not confuse evolution with religion, that has absolutely zero anything to back it up.

Carbon dating is not flawed. What is flawed are the levels of understand of this technique by stubborn and ignorant theists.

@You (Don't) Know

"Is there any actual evidence for one KIND changing into another KIND?
There isn’t is there? We have evidence of adaptions of the same KINDS but nothing transitional"

You tell 'em budy.

I've been trying to make the same point. All the "Kinds" were on the Ark. Did some monkey just give birth to a human? I tell ya these atheists just don't understand anything,

And what a brilliant take on Lucy. Don't ever let 'em confuse you with "scientific evidence" whatever the fuck that is supposed to mean.

I don't offer up praise this high very often, but even though the year is early, I'm putting in an early nomination for you for the prestigious Ken Ham Award. Congratulations.

Troll?

Or just ineffably ignorant and not too bright?

Either way ,a complete drongo. .

Wow, so much shit to deal with in one concentrated package.

Let's start with this shall we?

Where are the transitional fossils? There should be hundreds and thousands of transitional fossils discovered

Here's a clue for you. Are you identical to either of your parents? No? Thought not.

Are you identical to any of your offspring? No? Thought not.

Which means that YOU are a "transitional form" between your parents and your offspring. Which is the case for every sexually reproducing eukaryote in the biosphere. The planet is, in effect, littered with "transitional fossils", except that many of them are still alive.

As for fossils embedded in geological strata, well, you obviously never paid attention in class. There are entire series of transitional fossils in existence. I'm aware of the following:

[1] Tetrapod series:

Eusthenopteron, Panderichthys, Tiktaalkik, Ventastega, Acanthostega, Ichtyostega

[2] Horse fossils:

Eohippus, Protorohippus, Orohippus, Eiphippus, Mesohippus, Miohippus, Kalobatippus, parahipps, Merychippus, Hipparion, Pliohippus, Dinohippus, Plesippus, Equus (This latter Genus persisting to the present)

[3] Maniraptorian theropods to birds:

Sinosauropteryx, Sinornithosaurus, Oviraptor, Scansoripoteryx, Xiaotingia, Yixianosaurus, Pedopenna, Aurornis, Serikornis, Eosinopteryx, Archaeopteryx, Rahonavis, Jeholornis, Jixiangornis, Sapeornis, Iberomesornis, Yanornis, Ichthyornis, followed by the basal members of the clade Neoaves.

[4] Whales:

Indohyus, Pakicetus, Ambulocetus, Kutchicetus, Remingtonocetus, Rodhocetus, Protocetus, Dorudon, Squalodon, Kentriodon, Aulophyseter, Brymophyseter, Aetiocetus, Janjucetus, Cetotherium.

While you're at it, you can spend the next ten years learning about comparative anatomy, and its rigorous application to palaeontological finds.

Moving on ... what drivel do we have to examine next? Oh, that's right:

Second law of thermodynamics

If you're stupid enough to think that the second law of thermodynamics prohibits evolution, then you really are a fucking idiot. Even before I launch into a proper, rigorous treatment of the subject, originating with the work of Rudolf Clausius, the first quention to throw at you is "See that big yellow thing in the sky?" If you don't understand how that's providing the energy for life on Earth, then you need to re-take all of your science classes from scratch.

In the meantime, as to that treatment of thermodynamics by Clausius, let's cover this in more detail, shall we? And then, move on to some scientific papers that flush your drivel down the toilet hard. We start with Clausius' treatment of the First Law of Thermodynamics, which in its precise form is written:

dU = δQ - &deltalW

This tells us that the total internal energy change in a system, equals the energy supplied to the system from its surroundings (δQ) minus the amount of work done by the system on the surroundings (δW).

For a reversible process, Clausius defined the entropy of a system via the folowing equation:

dS = δQ/T

where T is the thermodynamic temperature of the system. In short, change in entropy (hence the use of differentials) is defined as change in the energy a system receives from the surroundings. Entropy is a state function, and is therefore expected to hold for non-reversible systems as well, but first, we'll rearrange the above equation to give us:

δQ = T dS

In the case of pressure-volume work, δW can be rewritten as:

δW = P dV

where P is pressure, and dV is the instantaneous change in volume associated with that pressure, and hence, we end up with the fundamental thermodynamic relation:

dU = T dS - P dV

Now, since entropy is defined as total internal energy divided by thermodynamic temperature (and has units of Joules per Kelvin), the entropy as thus defined for a given system will increase by definition as the temperature falls. So, even in the absence of any other interactions, the entropy of any given system in the universe will increase over time, as a result of the ambient temperature of the universe falling, as a consequence of space-time expansion. Of course, matters become more interesting when we factor in those other interactions.

But, when Clausius formulated his relations, he explicitly stated that the Second Law of Thermodynamics applies to different classes of system, but in different ways. He listed the three classes of system as follows:

[1] Isolated systems are systems that engage in no exchange of matter or energy with their surroundings. Such systems are therefore reliant upon the internal energy that they already possess. However, isolated systems constitute an idealisation that is almost never achieved in practice, and are mostly useful as a starting point for developing thermodynamic theory prior to extending it to the other classes of system.

[2] Closed systems are systems that engage in exchange of energy with the surroundings, but no exchange of matter. A good example of a closed system would be a solar panel, which does not exchange matter with its surroundings, but which, when illuminated, is a net recipient of energy in the form of visible light, which it then converts to electricity, which we can use.

[3] Open systems are systems that engage in exchange of both energy and matter with the surroundings. Living organisms plainly fall into this latter category.

When Rudolf Clausius erected his original statement of the Second Law of Thermodynamics, he stated it thus:

In an isolated system, a process can only occur if it increases the total entropy of the system.

The trouble with the 2LT is that it applies to all of these systems, but the exact manner in which it applies differs between the three classes of system. Clausius' original statement about the application of the 2LT to an isolated system does not apply to the other classes of system in anything like the same manner. Trouble is, creationists alight upon the statement about entropy increasing, which was originally erected by Clausius to describe isolated systems, and think that the formulation Clausius erected to apply to isolated systems applies to all systems in the same manner, when Clausius himself plainly stated that it doesn't.

In a non isolated system, if there is an energy input, that energy input can be harnessed to perform useful work, such as locally decreasing the entropy of entities within the system in exchange for a greater increase in entropy beyond those systems. As long as there exists inhomogeneity within the universe, i.e., there exist regions of differing conditions with respect to material content, energy flux, etc., any net recipient of energy from an outside energy source can harness that energy to perform useful work, including work that results in a temporary local decrease of entropy. The Earth constitutes such a system, because it is engaging in both matter and energy transfer with the surroundings, and is in fact a large net recipient of energy from the surroundings. See that yellow thing in the sky? It's called The Sun. It's a vast nuclear fusion reactor 866,000 miles across that is irradiating the Earth with massive amounts of energy as I type this. Energy that can be harnessed to perform useful work such as constructing living organisms.

Incidentally, as a tangential diversion, the classical formulation has again required revision to take account of more recent developments with respect to observed phenomena, which is why we now have a scientific discipline called Quantum Thermodynamics ... a discipline that was contributed to by, among others, Stephen Hawking, when he published his landmark paper on the radiative nature of black holes that brings them into equilibrium with the Second Law of Thermodynamics. I don't recall him ruling out evolution as a result of this.

Another common fallacy is the wholly non-rigorous association of entropy with "disorder", however this is defined. This has been known to be non-rigorous by physicists for decades, because there exist numerous documented instances of systems whose entropy increases when they spontaneously self-assemble into ordered structures as a result of the effect of electrostatic forces. Lipid bilayers are an important example of this, which are found throughout the biosphere.

The following scientific paper is apposite here:

Gentle Force Of Entropy Bridges Disciplines by David Kestenbaum, Science, 279: 1849 (20th March 1998)

Normally, entropy is a force of disorder rather than organization. But physicists have recently explored the ways in which an increase in entropy in one part of a system can force another part into greater order. The findings have rekindled speculation that living cells might take advantage of this little-known trick of physics.

Phospholipids being an excellent example thereof. In fact, any chemical system in which there exists the capacity for electrostatic forces to apply to either aggregating or reacting molecules can exhibit this phenomenon. Which is why scientists have long since abandoned the notion that "entropy" equals "disorder", which requires a thorough statistical mechanical treatment in terms of microstates in any case.

This is applied to the physics and physical chemistry of lipid bilayers in the following paper:

Electrostatic Repulsion Of Positively Charged Vesicles And Negatively Charged Objects by
Helim Aranda-Espinoza, Yi Chen, Nily Dan, T. C. Lubensky, Philip Nelson, Laurence Ramos and D. A. Weitz, Science, 285: 394-397 (16th July 1999)

in which the authors calculated that the entropy of the lipid bilayer system increased when it arranged itself spontaneously into an ordered structure in accordance with the laws of electrostatics.

Entropy, as rigorously defined, has units of Joules per Kelvin, and is therefore a function of energy versus thermodynamic temperature. The simple fact of the matter is that if the thermodynamic temperature increases, then the total entropy of a given system decreases if no additional energy was input into the system in order to provide the increase in thermodynamic temperature. Star formation is an excellent example of this, because the thermodynamic temperature at the core of a gas cloud increases as the cloud coalesces under gravity. All that is required to increase the core temperature to the point where nuclear fusion is initiated is sufficient mass. No external energy is added to the system. Consequently, the entropy at the core decreases due to the influence of gravity driving up the thermodynamic temperature. Yet the highly compressed gas in the core is hardly "ordered".

More to the point, there are scientific papers in existence establishing that evolution is perfectly consistent with the 2LT. Two important papers being:

Entropy And Evolution by Daniel F. Styer, American Journal of Physics, 78(11): 1031-1033 (November 2008) DOI: 10.1119/1.2973046

Natural Selection As A Physical Principle by Alfred J. Lotka, Proceedings of the National Academy of Sciences of the USA, 8: 151-154 (1922) [full paper downloadable from here]

Evolution Of Biological Complexity by Christoph Adami, Charles Ofria and Travis C. Collier, Proceedings of the National Academy of Sciences of the USA, 97(9): 4463-4468 (25th April 2000) [Full paper downloadable from here]

Order From Disorder: The Thermodynamics Of Complexity In Biology by Eric D. Schneider and James J. Kay, in Michael P. Murphy, Luke A.J. O'Neill (ed), What is Life: The Next Fifty Years. Reflections on the Future of Biology, Cambridge University Press, pp. 161-172 [Full paper downloadable from here]

Natural Selection For Least Action by Ville R. I. Kaila and Arto Annila, Proceedings of the Royal Society of London Part A, 464: 3055-3070 (22nd july 2008) [Full paper downloadable from here]

Evolution And The Second Law Of Thermodynamics by Emory F. Bunn, arXiv.org, 0903.4603v1 (26th March 2009) [Download full paper from here]

Let's take a look at some of these, shall we?

First of all, we have this from Lotka in 1922:

In a paper presented concurrently with this, the principle of natural selection, or of the survival of the fittest (persistence of stable forms), is employed as an instrument for drawing certain conclusions regarding the energetics of a system in evolution.

Aside from such interest as attaches to the conclusions reached, the method itself of the argument presents a feature that deserves special note. The principle of natural selection reveals itself as capable of yielding information which the first and second laws of thermodynamics are not competent to furnish.

The two fundamental laws of thermodynamics are, of course, insufficient to determine the course of events in a physical system. They tell us that certain things cannot happen, but they do not tell us what does happen.

In the freedom which is thus left, certain writers have seen the opportunity for the interference of life and conciousness in the history of a physical system. So W. Ostwald [2] observes that "the organism utilizes, in manyfold ways, the freedom of choice among reaction velocities, through the influence of catalytic substances, to satisfy advantageously its energy requirements." Sir Oliver Lodge also, has drawn attention to the guidance [3] exercised by life and mind upon physical events, within the limits imposed by the requirements of available [4] energy. H. Guilleminot [5] sees the influence of life upon physical systems in the substitution of guidance by choice in place of fortuitous happenings, where Carnot's principle leaves the course of events indeterminate. As to this, it may be objected that the attribute of fortuitousness is not an objective quality of a given. event. It is the expression of our subjective ignorance, our lack of complete information, or else our deliberate ignoring of some of the factors that actually do determine the course of events. Admitting, however, broadly, the directing influence of life upon the world's events, within the limits imposed by the Mayer-Joule and the Carnot-Clausius principles, it would be an error to suppose that the faculty of guidance which the established laws of thermodynamics thus leave open, is a peculiar prerogative of living organisms. If these laws do not fully define the course of events, this does not necessarily mean that this course, in nature, is actually indeterminate, and requires, or even allows, some extra-physical influence to decide happenings. It merely means that the laws, as formulated, take account of certain factors only, leaving others out of consideration; and that the data thus furnished are insufficient to yield an unambiguous answer to our enquiry regarding the course of events in a physical system. Whether life is present or not, something more than the first and second laws of thermodynamics is required to predict the course of events. And, whether life is present or not, something definite does happen, the course of events is determinate, though not in terms of the first and second laws alone. The "freedom" of which living organisms avail themselves under the laws of thermodynamics is not a freedom in fact, but a spurious freedom [6] arising out of an incomplete statement of the physical laws applicable to the case. The strength of Carnot's principle is also its weakness: it holds true independently of the particular mechanism or configuration of the energy transformer (engine) to which it is applied; but, for that very reason it is also incompetent to yield essential information regarding the influence of mechanism upon the course of events. In the ideal case of a reversible heat engine the efficiency is independent of the mechanism. Real phenomena are irreversible; and, in particular, trigger action, [7] which plays so important a role in life processes, is a typically irreversible process, the release of available energy from a "false" equilibrium. Here mechanism is all-important. To deal with problems presented in these cases requires new methods, [8] requires the introduction, into the argument, of new principles. And a principle competent to extend our systematic knowledge in this field seems to be found in the principle of natural selection, the principle of the survival of the fittest, or, to speak in terms freed from biological implications, the principle of the persistence of stable forms.

For the battle array of organic evolution is presented to our view as an assembly of armies of energy transformers-accumulators (plants), and engines (animals); armies composed of multitudes of similar units, the individual organisms. The similarity of the units invites statistical treatment, the development of a statistical mechanics of which the units shall be, not simple material particles in ordinary reversible collision of the type familiar in the kinetic theory, collisions in which action and reaction were equal; the units in the new statistical mechanics will be energy transformers subject to irreversible collisions of peculiar type-collisions in which trigger action is a dominant feature.

So, even as far back as 1922, scientists were arguing that evolution is not in violation of the Second law of Thermodynamics. Interesting revelation, yes?

Lotka continues with this:

In systems evolving toward a true equilibrium (such as thermally and mechanically isolated systems, or the isothermal systems of physical chemistry), the first and second laws of thermodynamics suffice to determinate at any rate the end state; this is, for example, independent of the amount of any purely catalytic substance that may be present. The first and the second law here themselves function as the laws of selection and evolution, as has been recognized by Perrin [9] and others, and exemplified in some detail by the writer, for the case of a monomolecular reversible reaction. [10] But systems receiving a steady supply of available energy (such as the earth illuminated by the sun), and evolving, not toward a true equilibrium, but (probably) toward a stationary state, the laws of thermodynamics are no longer sufficient to determine the end state; a catalyst, in general, does affect the final steady state. Here selection may operate not only among components taking part in transformations, but also upon catalysts, in particular upon auto-catalytic or auto-catakinetic constituents of the system. Such auto-catakinetic constituents are the living organisms, [11] and to them, therefore the principles here discussed, apply.

Now this, as I've jsut stated, was written as far back as 1922, which means that scientists have been aware that thermodynamic laws and evolution are not in conflict for eighty-seven years.

Moving on, let's look at the more recent papers. Let's look first at the abstract of the Adami et al paper:

To make a case for or against a trend in the evolution of complexity in biological evolution, complexity needs to be both rigorously defined and measurable. A recent information-theoretic (but intuitively evident) definition identifies genomic complexity with the amount of information a sequence stores about its environment. We investigate the evolution of genomic complexity in populations of digital organisms and monitor in detail the evolutionary transitions that increase complexity. We show that, because natural selection forces genomes to behave as a natural ‘‘Maxwell Demon,’’ within a fixed environment, genomic complexity is forced to increase.

Oh look. A point I've been arguing for a long time here, namely that a rigorous definition of complexity is needed in order to be able to make precise categorical statements about complexity. I also note with interest that the authors of this paper perform detailed experiments via simulation in order to establish the fact that complexity can arise from simple systems (the behaviour of the Verhust Equation I've mentioned here frequently establishes this, and indeed, the investigation of such systems as the Verhulst Equation and similar dynamical systems is now the subject of its own branch of applied mathematics).

The authors open their paper thus:

Darwinian evolution is a simple yet powerful process that requires only a population of reproducing organisms in which each offspring has the potential for a heritable variation from its parent. This principle governs evolution in the natural world, and has gracefully produced organisms of vast complexity. Still, whether or not complexity increases through evolution has become a contentious issue. Gould (1), for example, argues that any recognizable trend can be explained by the ‘‘drunkard’s walk’’ model, where ‘‘progress’’ is due simply to a fixed boundary condition. McShea (2) investigates trends in the evolution of certain types of structural and functional complexity, and finds some evidence of a trend but nothing conclusive. In fact, he concludes that ‘‘something may be increasing. But is it complexity?’’ Bennett (3), on the other hand, resolves the issue by fiat, defining complexity as ‘‘that which increases when self-organizing systems organize themselves.’’ Of course, to address this issue, complexity needs to be both defined and measurable.

In this paper, we skirt the issue of structural and functional complexity by examining genomic complexity. It is tempting to believe that genomic complexity is mirrored in functional complexity and vice versa. Such an hypothesis, however, hinges upon both the aforementioned ambiguous definition of complexity and the obvious difficulty of matching genes with function. Several developments allow us to bring a new perspective to this old problem. On the one hand, genomic complexity can be defined in a consistent information-theoretic manner [the ‘‘physical’’ complexity (4)], which appears to encompass intuitive notions of complexity used in the analysis of genomic structure and organization (5). On the other hand, it has been shown that evolution can be observed in an artificial medium (6, 7), providing a unique glimpse at universal aspects of the evolutionary process in a computational world. In this system, the symbolic sequences subject to evolution are computer programs that have the ability to self-replicate via the execution of their own code. In this respect, they are computational analogs of catalytically active RNA sequences that serve as the templates of their own reproduction. In populations of such sequences that adapt to their world (inside of a computer’s memory), noisy self-replication coupled with finite resources and an information-rich environment leads to a growth in sequence length as the digital organisms incorporate more and more information about their environment into their genome. Evolution in an information-poor landscape, on the contrary, leads to selection for replication only, and a shrinking genome size as in the experiments of Spiegelman and colleagues (8). These populations allow us to observe the growth of physical complexity explicitly, and also to distinguish distinct evolutionary pressures acting on the genome and analyze them in a mathematical framework.

Moving on, the authors directly address a favourite canard of creationists (though they do not state explicitly that they are doing this), namely that information somehow constitutes a "non-physical" entity. Here's what the authors have to say on this subject:

Information Theory and Complexity. Using information theory to understand evolution and the information content of the sequences it gives rise to is not a new undertaking. Unfortunately, many of the earlier attempts (e.g., refs. 12–14) confuse the picture more than clarifying it, often clouded by misguided notions of the concept of information (15). An (at times amusing) attempt to make sense of these misunderstandings is ref. 16. Perhaps a key aspect of information theory is that information cannot exist in a vacuum; that is, information is physical (17). This statement implies that information must have an instantiation (be it ink on paper, bits in a computer’s memory, or even the neurons in a brain). Furthermore, it also implies that information must be about something. Lines on a piece of paper, for example, are not inherently information until it is discovered that they correspond to something, such as (in the case of a map) to the relative location of local streets and buildings. Consequently, any arrangement of symbols might be viewed as potential information (also known as entropy in information theory), but acquires the status of information only when its correspondence, or correlation, to other physical objects is revealed.

Nice. In brief, the authors clearly state that information requires a physical substrate to reside upon, and a mechanism for the residence of that information upon the requisite physical substrate, in such a manner that said information constitutes a mapping from the arrangement of the physical substrate upon which it resides, to whatever other physical system is being represented by that mapping. I remember one creationist claiming that because the mass of a floppy disc doesn't change when one writes data to it, this somehow "proves" that information is not a physical entity: apparently said creationist didn't pay attention in the requisite basic physics classes, or else he would have learned that the information stored on a floppy disc is stored by materially altering the physical state of the medium, courtesy of inducing changes in the magnetic orientation of the ferric oxide particles in the disc medium. In other words, a physical process was required to generate that information and store it on the disc. I am indebted to the above authors for casting this basic principle in the appropriate (and succinct) general form.

The authors move on with this:

In biological systems the instantiation of information is DNA, but what is this information about? To some extent, it is the blueprint of an organism and thus information about its own structure. More specifically, it is a blueprint of how to build an organism that can best survive in its native environment, and pass on that information to its progeny. This view corresponds essentially to Dawkins’ view of selfish genes that ‘‘use’’ their environment (including the organism itself), for their own replication (18). Thus, those parts of the genome that do correspond to something (the non-neutral fraction, that is) correspond in fact to the environment the genome lives in. Deutsch (19) referred to this view by saying that ‘‘genes embody knowledge about their niches.’’ This environment is extremely complex itself, and consists of the ribosomes the messages are translated in, other chemicals and the abundance of nutrients inside and outside the cell, and the environment of the organism proper (e.g., the oxygen abundance in the air as well as ambient temperatures), among many others. An organism’s DNA thus is not only a ‘‘book’’ about the organism, but is also a book about the environment it lives in, including the species it co-evolves with. It is well known that not all of the symbols in an organism’s DNA correspond to something. These sections, sometimes referred to as ‘‘junk-DNA,’’ usually consist of portions of the code that are unexpressed or untranslated (i.e., excised from the mRNA). More modern views concede that unexpressed and untranslated regions in the genome can have a multitude of uses, such as for example satellite DNA near the centromere, or the polyC polymerase intron excised from Tetrahymena rRNA. In the absence of a complete map of the function of each and every base pair in the genome, how can we then decide which stretch of code is ‘‘about something’’ (and thus contributes to the complexity of the code) or else is entropy (i.e., random code without function)?

A true test for whether a sequence is information uses the success (fitness) of its bearer in its environment, which implies that a sequence’s information content is conditional on the environment it is to be interpreted within (4). Accordingly, Mycoplasma mycoides, for example (which causes pneumonialike respiratory illnesses), has a complexity of somewhat less than one million base pairs in our nasal passages, but close to zero complexity most everywhere else, because it cannot survive in any other environment—meaning its genome does not correspond to anything there. A genetic locus that codes for information essential to an organism’s survival will be fixed in an adapting population because all mutations of the locus result in the organism’s inability to promulgate the tainted genome, whereas inconsequential (neutral) sites will be randomized by the constant mutational load. Examining an ensemble of sequences large enough to obtain statistically significant substitution probabilities would thus be sufficient to separate information from entropy in genetic codes. The neutral sections that contribute only to the entropy turn out to be exceedingly important for evolution to proceed, as has been pointed out, for example, by Maynard Smith (20).

In Shannon’s information theory (22), the quantity entropy (H) represents the expected number of bits required to specify the state of a physical object given a distribution of probabilities; that is, it measures how much information can potentially be stored in it. In a genome, for a site i that can take on four nucleotides with probabilities

{p(C)(i), p(G)(i), p(A)(i), p(T)(i)}, [1]

the entropy of this site is

H(-) = -Σ p(j)(i) log[p(j)](i) [2]

(Here, the sum is over the index j, covering the four nucleotides and their insertion probabilities - see the full paper for the details)

The maximal entropy per-site (if we agree to take our logarithms to base 4: i.e., the size of the alphabet) is 1, which occurs if all of the probabilities are all equal to 1/4. If the entropy is measured in bits (take logarithms to base 2), the maximal entropy per site is two bits, which naturally is also the maximal amount of information that can be stored in a site, as entropy is just potential information. A site stores maximal information if, in DNA, it is perfectly conserved across an equilibrated ensemble. Then, we assign the probability p = 1 to one of the bases and zero to all others, rendering H(i) = 0 for that site according to Eq. 2. The amount of information per site is thus (see, e.g., ref. 23)

I(i) = H(max) - H(i) [3]

In the following, we measure the complexity of an organism’s sequence by applying Eq. 3 to each site and summing over the sites. Thus, for an organism of l base pairs the complexity is

C = l - Σ(i) H(i) [4]

It should be clear that this value can only be an approximation to the true physical complexity of an organism’s genome. In reality, sites are not independent and the probability to find a certain base at one position may be conditional on the probability to find another base at another position. Such correlations between sites are called epistatic, and they can render the entropy per molecule significantly different from the sum of the per-site entropies (4). This entropy per molecule, which takes into account all epistatic correlations between sites, is defined as

H = Σ(g) p(g|E) log p(g|E) [5]

and involves an average over the logarithm of the conditional probabilities p(g|E) to find genotype g given the current environment E. In every finite population, estimating p(g|E) using the actual frequencies of the genotypes in the population (if those could be obtained) results in corrections to Eq. 5 larger than the quantity itself (24), rendering the estimate useless. Another avenue for estimating the entropy per molecule is the creation of mutational clones at several positions at the same time (7, 25) to measure epistatic effects. The latter approach is feasible within experiments with simple ecosystems of digital organisms that we introduce in the following section, which reveal significant epistatic effects. The technical details of the complexity calculation including these effects are relegated to the Appendix.

Quite a substantial mathematical background, I think everyone will agree. I'll let everyone have fun reading the rest of the details off-post, as they are substantial, and further elaboration here will not be necessary in the light of my providing a link to the full paper.

Moving on to the Kaila and Annila paper, here's the abstract:

The second law of thermodynamics is a powerful imperative that has acquired several expressions during the past centuries. Connections between two of its most prominent forms, i.e. the evolutionary principle by natural selection and the principle of least action, are examined. Although no fundamentally new findings are provided, it is illuminating to see how the two principles rationalizing natural motions reconcile to one law. The second law, when written as a differential equation of motion, describes evolution along the steepest descents in energy and, when it is given in its integral form, the motion is pictured to take place along the shortest paths in energy. In general, evolution is a non-Euclidean energy density landscape in flattening motion.

Ah, this dovetails nicely with Thomas D. Schneider's presentation of a form of the Second Law of Thermodynamics applicable to biological systems that I've covered in past posts. This can be read in more detail here. Note that Thomas D. Schneider is not connected with Eric D. Schneider whose paper is cited above.

Here's how Kaila and Annila introduce their work:

1. Introduction

The principle of least action (de Maupertuis 1744, 1746; Euler 1744; Lagrange 1788) and the evolutionary principle by natural selection (Darwin 1859) account for many motions in nature. The calculus of variation, i.e. ‘take the shortest path’, explains diverse physical phenomena (Feynman & Hibbs 1965; Landau & Lifshitz 1975; Taylor & Wheeler 2000; Hanc & Taylor 2004). Likewise, the theory of evolution by natural selection, i.e. ‘take the fittest unit’, rationalizes various biological courses. Although the two old principles both describe natural motions, they seem to be far apart from each other, not least because still today the formalism of physics and the language of biology differ from each other. However, it is reasonable to suspect that the two principles are in fact one and the same, since for a long time science has failed to recognize any demarcation line between the animate and the inanimate.

In order to reconcile the two principles to one law, the recent formulation of the second law of thermodynamics as an equation of motion (Sharma & Annila 2007) is used. Evolution, when stated in terms of statistical physics, is a probable motion. The natural process directs along the steepest descents of an energy landscape by equalizing differences in energy via various transport and transformation processes, e.g. diffusion, heat flows, electric currents and chemical reactions (Kondepudi & Prigogine 1998). These flows of energy, as they channel down along various paths, propel evolution. In a large and complicated system, the flows are viewed to explore diverse evolutionary paths, e.g. by random variation, and those that lead to a faster entropy increase, equivalent to a more rapid decrease in the free energy, become, in terms of physics, naturally selected (Sharma & Annila 2007). The abstract formalism has been applied to rationalize diverse evolutionary courses as energy transfer processes (Grönholm & Annila 2007; Jaakkola et al. 2008a,b; Karnani & Annila in press).

The theory of evolution by natural selection, when formulated in terms of chemical thermodynamics, is easy to connect with the principle of least action, which also is well established in terms of energy (Maslov 1991). In accordance with Hamilton’s principle (Hamilton 1834, 1835), the equivalence of the differential equation of evolution and the integral equation of dissipative motion is provided here, starting from the second law of thermodynamics (Boltzmann 1905; Stöltzner 2003). In this way, the similarity of the fitness criterion (‘take the steepest gradient in energy’) and the ubiquitous imperative (‘take the shortest path in energy’) becomes evident. The two formulations are equivalent ways of picturing the energy landscape in flattening motion. Thus, there are no fundamentally new results. However, as once pointed out by Feynman (1948), there is a pleasure in recognizing old things from a new point of view.

I advise readers to exercise some caution before diving into this paper in full, as it involves extensive mathematics from the calculus of variations, and a good level of familiarity with Lagrangian and Hamiltonian mechanics is a pre-requisite for understanding the paper in full.

In the meantime, let's take a look at the Schneider & Kay paper. Here's their introduction:

Introduction

In the middle of the nineteenth century, two major scientific theories emerged about the evolution of natural systems over time. Thermodynamics, as refined by Boltzmann, viewed nature as decaying toward a certain death of random disorder in accordance with the second law of thermodynamics. This equilibrium seeking, pessimistic view of the evolution of natural systems is contrasted with the paradigm associated with Darwin, of increasing complexity, specialization, and organization of biological systems through time. The phenomenology of many natural systems shows that much of the world is inhabited by nonequilibrium coherent structures, such as convection cells, autocatalytic chemical reactions and life itself. Living systems exhibit a march away from disorder and equilibrium, into highly organized structures that exist some distance from equilibrium.

This dilemma motivated Erwin Schrödinger, and in his seminal book What is Life? (Schrödinger, 1944), he attempted to draw together the fundamental processes of biology and the sciences of physics and chemistry. He noted that life was comprised of two fundamental processes; one "order from order" and the other "order from disorder". He observed that the gene generated order from order in a species, that is, the progeny inherited the traits of the parent. Over a decade later Watson and Crick (1953) provided biology with a research agenda that has lead to some of the most important findings of the last fifty years.

However, Schrödinger's equally important but less understood observation was his order from disorder premise. This was an effort to link biology with the fundamental theorems of thermodynamics (Schneider, 1987). He noted that living systems seem to defy the second law of thermodynamics which insists that, within closed systems, the entropy of a system should be maximized. Living systems, however, are the antithesis of such disorder. They display marvelous levels of order created from disorder. For instance, plants are highly ordered structures, which are synthesized from disordered atoms and molecules found in atmospheric gases and soils.

Schrödinger solved this dilemma by turning to nonequilibrium thermodynamics. He recognized that living systems exist in a world of energy and material fluxes. An organism stays alive in its highly organized state by taking high quality energy from outside itself and processing it to produce, within itself, a more organized state. Life is a far from equilibrium system that maintains its local level of organization at the expense of the larger global entropy budget. He proposed that the study of living systems from a nonequilibrium perspective would reconcile biological self-organization and thermodynamics. Furthermore he expected that such a study would yield new principles of physics.

This paper examines the order from disorder research program proposed by Schrödinger and expands on his thermodynamic view of life. We explain that the second law of thermodynamics is not an impediment to the understanding of life but rather is necessary for a complete description of living processes. We expand thermodynamics into the causality of the living process and show that the second law underlies processes of self-organization and determines the direction of many of the processes observed in the development of living systems.

Finally, I'll wind up by introducing Emory F. Bunn's paper, which is a particular killer for creationist canards, because it involves direct mathematical derivation of the thermodynamic relationships involved in evolutionary processes, and a direct quantitative analysis demonstrating that evolution is perfectly consistent with the Second Law of Thermodynamics. Here's the abstract:

Skeptics of biological evolution often claim that evolution requires a decrease in entropy, giving rise to a conflict with the second law of thermodynamics. This argument is fallacious because it neglects the large increase in entropy provided by sunlight striking the Earth. A recent article provided a quantitative assessment of the entropies involved and showed explicitly that there is no conflict. That article rests on an unjustified assumption about the amount of entropy reduction involved in evolution. I present a refinement of the argument that does not rely on this assumption.

Here's the opening gambit:

I. INTRODUCTION

Daniel Styer recently addressed the claim that evolution requires a decrease in entropy and therefore is in conflict with the second law of thermodynamics. [1] He correctly explained that this claim rests on misunderstandings about the nature of entropy and the second law. The second law states that the total entropy of a closed system must never decrease. However, the Earth is not a closed system and is constantly absorbing sunlight, resulting in an enormous increase in entropy, which can counteract the decrease presumed to be required for evolution. This argument is known to those who defend evolution in evolution-creationism debates, [2] but it is usually described in a general, qualitative way. Reference 1 filled this gap with a quantitative argument.

In the following I present a more robust quantitative argument. We begin by identifying the appropriate closed system to which to apply the second law. We find that the second law requires that the rate of entropy increase due to the Earth’s absorption of sunlight, (dS/dt)(sun), must be sufficient to account for the rate of entropy decrease required for the evolution of life, (dS/dt)(life) (a negative quantity). As long as

(dS/dt)(sun) + (dS/dt)(life) ≥ 0,

there is no conflict between evolution and the second law.

Styer estimated both (dS/dt)(sun) and (dS/dt)(life) to show that the inequality (1) is satisfied, but his argument rests on an unjustified and probably incorrect assumption about (dS/dt)(life). [1] I will present a modified version of the argument which does not depend on this assumption and which shows that the entropy decrease required for evolution is orders of magnitude too small to conflict with the second law of thermodynamics.

Once again, I'll let you all have fun reading the paper in full. :)

I think that covers all of those bases. Isn't a proper scientific education wonderful?

Right, having dealt with that lot, time to move on.

If we are evolving, why aren’t we super human yet?

Ahem, biology isn't a fucking Marvel comic plot, idiot. If you had ever bothered to pick up a textbook on the subject, you would have learned that evolutionary processes produce whatever works in a given ecotope. The moment the requisite products stop working in that ecotope, they DIE OUT. As 99.99% of all species to date have done. Unless of course you want to point to any living trilobites that scientists somehow missed when surveying the oceans, for example?

Instead we are falling apart with cancer and other diseases

You really are an idiot, aren't you?

What part of "many of these diseases only put in an appearance when we are past our reproductive prime" did you fail to learn in basic biology classes?

Because at bottom, that's the interaction that's of central importance in biology - production of offspring. Whatever results in maximal production of offspring is whatever is favoured by evolutionary processes. Consequently, diseases that knock you out in infancy, or stop you producing offspring as an adult, render you an evolutionary dead end. And you are duly weeded out as a result. However, once you've produced some offspring, and sent them on their way to lead independent lives, then you are, in effect, superfluous to requirements from that point on. As a corollary, from the standpoint of biology, even if you drop dead at the age of 40 (as indeed a good number of humans in the past did, before we developed advanced civilisations along with medical science), you are still biologically successful if you've left behind you a decent number of descendants before you drop dead. Weirdly enough, even your sad little mythology agrees with scientists on that point, though the ignorant, pre-scientific nomads who scribbled this mythology manifestly knew bugger all about biology, as even an elementary reading of the contents thereof demonstrates amply. That aphorism "go forth and multiply" that appears in your mythology, is nothing more than a statement of the biological imperative that applies to all species, but of course the authors thereof forgot about other, salient biological facts, such as the fact that a a lot of the multiplying ends up providing other species with their lunch.

In short, from the standpoint of biology, there's no point in preserving an individual beyond a certain age limit, once that individual has produced offspring that are leading independent lives. As a consequence, those individuals that happen to avoid becoming lunch for something else beyond that limit, have a habit of becoming prone to degenerative diseases, because, lo and behold, the protective mechanisms keeping them at bay start malfunctioning themselves beyond that age limit. If evolutionary processes don't have a reason to extend that age limit, they simply won't bother, especially if the species in question is producing enough offspring to replace the losses and keep the population going.

Now of course, from the standpoint of humans considering their own fate, this biological fact takes on a different complexion, and our desire not to die for as long as possible was, of course, a major motivation in the development of medical science. What we are now seeing, as a result of the success of that medical science, is people living long enough for degenereative diseases to become an issue - an issue that wasn't prominent back in the days before modern medicine, when people were routinely dying of cholera and tuberculosis in their 40s. We didn't see many cancers, or much in the way of Alzheimer's, back in the 19th century, because too many people were dying of other diseases first, at an age before those degenerative diseases had time to show up.

But, in the absence of a sound biological reason to extend our life spans, one that becomes necessary in order for us to continue reproducing, evolutionary processes simply won't bother with doing so, just as they won't bother with a whole host of other wish-fulfulment yearnings on our part. Anyone thinking that evolutionary processes exist to do this is, quite simply, an idiot.

Now let's move on to the rest of your drivel:

Evolution is a religion that requires more faith then Christianity

Bollocks. What part of "evolutionary postulates have been tested experimentally, and have passed all the tests thrown at them, do you not understand?

There is nothing to back up evolution

BULLSHIT. Oh, you want some examples of direct experimental tests of evolutionary postulates? Try this little lot, which is only a tiny fraction of the available literature:

Direct Experimental Tests Of Evolutionary Concepts

[1] A Model For Divergent Allopatric Speciation Of Polyploid Pteridophytes Resulting From Silencing Of Duplicate-Gene Expression by Charles R.E. Werth and Michael D. Windham, American Naturalist, 137(4): 515-526 (April 1991) - DEVELOPMENT OF A MODEL TO MATCH OBSERVED SPECIATION IN NATURE

[2] A Molecular Reexamination Of Diploid Hybrid Speciation Of Solanum raphanifolium by David M. Spooner, Kenneth. J. Sytsma and James F. Smith, Evolution, 45(3): 757-764 - DOCUMENTATION OF AN OBSERVED SPECIATION EVENT

[3] Cavefish As A Model System In Evolutionary Developmental Biology by William R. Jeffrey, Developmental Biology, 231:, 1-12 (1 Mar 2001) - contains experimental tests of hypotheses about eye evolution

[4] Chromosome Evolution, Phylogeny, And Speciation Of Rock Wallabies, by G. B. Sharman, R. L. Close and G. M. Maynes, Australian Journal of Zoology, 37(2-4): 351-363 (1991) - DOCUMENTATION OF OBSERVED SPECIATION IN NATURE

[5] Crystal Structure Of An Ancient Protein: Evolution By Conformational Epistasis by Eric A. Ortlund, Jamie T. Bridgham, Matthew R. Redinbo and Joseph W. Thornton, Science, 317: 1544-1548 (14 September 2007) - refers to the reconstruction of ancient proteins from extinct animals by back-tracking along the molecular phylogenetic trees and demonstrating that the proteins in question WORK

[6] Evidence For Rapid Speciation Following A Founder Event In The Laboratory by James R. Weinberg Victoria R. Starczak and Danielle Jörg, Evolution 46: 1214-1220 (15th January 1992) - EXPERIMENTAL GENERATION OF A SPECIATION EVENT IN THE LABORATORY

[7] Evolutionary Theory And Process Of Active Speciation And Adaptive Radiation In Subterranean Mole Rats, Spalax ehrenbergi Superspecies, In Israel by E. Nevo, Evolutionary Biology, 25: 1-125 - DOCUMENTATION OF OBSERVED SPECIATION IN NATURE

[8] Experimentally Created Incipient Species Of Drosophila by Theodosius Dobzhansky & Olga Pavlovsky, Nature 230: 289 - 292 (2nd April 1971) - EXPERIMENTAL GENERATION OF A SPECIATION EVENT IN THE LABORATORY

[9] Founder-Flush Speciation On Drosophila pseudoobscura: A Large Scale Experiment by Agustí Galiana, Andrés Moya and Francisco J. Alaya, Evolution 47: 432-444 (1993) EXPERIMENTAL GENERATION OF A SPECIATION EVENT IN THE LABORATORY

[10] Genetics Of Natural Populations XII. Experimental Reproduction Of Some Of the Changes Caused by Natural Selection by Sewall Wright & Theodosius Dobzkansky, Genetics, 31(2): 125-156 (1946) - direct experimental tests of natural selection mechanisms

[11] Hedgehog Signalling Controls Eye Degeneration In Blind Cavefish by Yoshiyuki Yamamoto, David W. Stock and William R. Jeffery, Nature, 431: 844-847 (14 Oct 2004) - direct experimental test of theories about eye evolution and the elucidation of the controlling genes involved

[12] Initial Sequencing Of The Chimpanzee Genome And Comparison With The Human Genome, The Chimpanzee Genome Sequencing Consortium (see paper for full list of 68 authors), Nature, 437: 69-87 (1 September 2005) - direct sequencing of the chimpanzee genome and direct comparison of this genome with the previously sequenced human genome, whereby the scientists discovered that fully twenty-nine percent of the orthologous proteins of humans and chimpanzees are IDENTICAL

[13] Origin Of The Superflock Of Cichlid Fishes From Lake Victoria, East Africa by Erik Verheyen, Walter Salzburger, Jos Snoeks and Axel Meyer, Science, 300: 325-329 (11 April 2003) - direct experimental determination of the molecular phylogeny of the Lake Victoria Superflock, including IDENTIFYING THE COMMON ANCESTOR OF THE 350+ SPECIES IN QUESTION and NAMING THAT ANCESTOR as Haplochromis gracilior

[14] Phagotrophy By A Flagellate Selects For Colonial Prey: A Possible Origin Of Multicellularity by Martin.E. Boraas, Dianne.B. Seale and Joseph .E. Boxhorn, Evolutionary Ecology 12(2): 153-164 (February 1998 ) - direct experimental test of hypotheses about the origins of multicellularity

[15] Pollen-Mediated Introgression And Hybrid Speciation In Louisiana Irises by Michael L. Arnold, Cindy M. Buckner and Jonathan J. Robinson, Proceedings of the National Academy of Sciences of the USA, 88(4): 1398-1402 (February 1991) - OBSERVATION OF A SPECIATION EVENT IN NATURE

[16] Protein Engineering Of Hydrogenase 3 To Enhance Hydrogen Production by Toshinari. Maeda, Viviana. Sanchez-Torres and Thomas. K. Wood, Applied Microbiology and Biotechnology, 79(1): 77-86 (May 2008) - DIRECT EXPERIMENTAL APPLICATION OF EVOLUTION IN THE LABORATORY TO PRODUCE A NEW BIOTECHNOLOGY PRODUCT

[17] Resurrecting Ancient Genes: Experimental Analysis Of Extinct Molecules by Joseph W. Thornton, Nature Reviews: Genetics, 5: 366-375 (5 May 2004) - direct experimental reconstruction in the laboratory of ancient proteins from extinct animals

[18] Sexual Isolation Caused By Selection For Positive And Negative Phototaxis And Geotaxis In Drosophila pseudoobscura by E. del Solar, Proceedings of the National Academy of Sciences of the USA, 56: 484-487 (1966) - direct experimental test of selection mechanisms and their implications for speciation

[19] Speciation By Hybridisation In Heliconius Butterflies by Jesús Mavárez, Camilo A. Salazar, Eldredge Bermingham, Christian Salcedo, Chris D. Jiggins and Mauricio Linares, Nature, 441: 868-871 (15th June 2006) - DETERMINATION OF A SPECIATION EVENT IN NATURE, FOLLOWED BY LABOARTORY REPRODUCTION OF THAT SPECIATION EVENT, AND CONFIRMATION THAT THE LABORATORY INDIVIDUALS ARE INTERFERTILE WITH THE WILD TYPE INDIVIDUALS

[20] Speciation By Hybridization In Phasmids And Other Insects By Luciano Bullini and Guiseppe Nascetti, Canadian Journal of Zoology 68(8): 1747-1760 (1990) - OBSERVATION OF A SPECIATION EVENT IN NATURE

[21] The Gibbons Speciation Mechanism by S. Ramadevon and M. A. B. Deaken, Journal of Theoretical Biology, 145(4): 447-456 (1991) - DEVELOPMENT OF A MODEL ACCOUNTING FOR OBSERVED INSTANCES OF SPECIATION

[22] The Master Control Gene For Morphogenesis And Evolution Of The Eye by Walter J. Gehrig, Genes to Cells, 1: 11-15, 1996 - direct experimental test of hypotheses concerning eye evolution including the elucidation of the connection between the Pax6 gene and eye morphogenesis, and the experimental manipulation of that gene to control eye development

[23] The Past As The Key To The Present: Resurrection Of Ancient Proteins From Eosinophils by Steven A. Benner, Proceedings of the National Academy of Sciences of the USA., 99(8): 4760-4761 (16 April 2002) - direct experimental reconstruction of ancient proteins from extinct animals

Moving on ...

and yet it is still being taught in our schools.

That's because, unlike the drivel in your mythology, evolution is AN OBSERVABLE FACT, BACKED BY A SUPERTANKER LOAD OF EVIDENCE. See above.

Carbon dating is flawed and can’t be trusted

BULLSHIT. To deal with this, I'll reprise a previous outing of mine from elsewhere, which covers the relevant material in detail, viz:

Radionuclide Dating Is Rigorous

In order to address this topic at the proper level of detail, something that creationists prefer to avoid at all costs, I shall first begin with a discourse on the underlying physics of radionuclide decay, the precise mathematical law that this process obeys, and how that law is derived, both empirically and theoretically. Note that the decay law was first derived empirically, courtesy of a large body of work by scientists such as Henri Becquerel, Marie Curie, Ernest Rutherford and others. Indeed, the SI unit of activity was named the Becquerel in recognition of that scientist's contribution to the early days of the study of radionuclide decay, and 1 Bq equals one transformation (decay) per second within a sample of radionuclide. However, the underlying physics had to wait until the advent of detailed and rigorous quantum theories before it could be elucidated, and is based upon the fact that the nuclei of radionuclides are in an excited state with respect to the sum total of the quantum energy states of the constituent particles (which, being fermions, obey Fermi-Dirac statistics, and consequently, Pauli's exclusion principle applies). In order for the system to move to a lower energy state, and settle upon a stable set of quantum numbers, various transformations need to take place, and these transformations result in the nucleus undergoing specific and well-defined structural changes, involving the emission of one or more particles. As well as the most familiar modes of decay, namely α and &beta- decay, other decay modes exist, and a full treatment of the various decay modes possible, along with the underlying quantum physics, is beyond the scope of this exposition, as it requires a detailed understanding of the behaviour of the appropriate quantum operators, and as a corollary, a detailed understanding of the behaviour of Hilbert spaces, a level of knowledge that is, sadly, not widespread. With this limitation in mind, however, it is still possible to deduce a number of salient facts about radionuclide decay, which I shall now present.

Empirical Determination Of The Decay Law

Initially, the determination of the decay law was performed empirically, by observing the decay of various radionuclides in the laboratory, taking measurements of the number of decay events, and plotting these graphically, with time along the x-axis, and counts along the y-axis. Upon performing this task, the data for many radionuclides is seen to lie upon a curve, and determination of the nature of that curve requires a little mathematical understanding.

To determine the nature of a curve, various transformations can be performed upon the data. The result of each of these transformations is as follows:

[1] Plot log(y) against x - (NOTE: logarithm to the base e!) if the result is a straight line, then the relationship is of the form:

log(y) = kx + C (where C is some constant, in particular, the y-intercept of the straight line)

which can be rewritten:

log(y) - log[(C(0)) = kx (where C = log(C(0))

which rearranges to:

y = C(0)exp(kx) (NOTE: exp(x) is the exponential function)

where C(0) is derived from the y-intercept of the straight line produced by the transformed plotting, and k is the gradient of the transformed line.

[2] Plot y against log(x) - if the result is a straight line, then the relationship is of the form:

y = k log(x) + C, where k is the gradient of the line, and C is the y-intercept of the straight line.

[3] Plot log(y) against log(x) - if the result is a straight line, then the relationship is of the form:

log(y) = k log(x) + C (where C is the y-intercept of the straight line thus produced)

This rearranges to:

log(y) - log(C(0)) = k log(x) (where C = log(C(0))

Which in turn rearranges to:

log(y/C(0)) = log(x^k)

Which finally gives us the relationship:

y = C(0)x^k, where k is the gradient of the straight line produced by the transformed data, and C(0) is derived from the y-intercept of the straight line produced by the transformed data.

The above procedures allow us to determine the nature of the mathematical relationships governing large bodies of real world data, when those bodies of real world data yield curves as raw plots of y against x. By applying the relevant transformations to radonuclide decay data, it was found that transformation [1] transformed the data into a straight line plot (within the limits of experimental error, of course), and consequently, this informed the scientists examining the data that the decay law was of the form:

N = C(0)exp(kt)

where C(0) and k were constants to be determined from the plot, and which were regarded as being dependent upon the particular radionuclide in question.

Now, if we are start with a known amount of radionuclide, and observe it decaying, then each decay event we detect with a Geiger counter represents one nucleus undergoing the requisite decay transformation. Since the process is random, over a long period of time, decaying nuclei will emit α or β particles in all directions with equal frequency, so we don't need to surround the material with Geiger counters in order to obtain measurements allowing a good first approximation to the decay rate. Obviously if we're engaged in precise work, we do set up our experiments to do this, especially with long-lived nuclei, because the decay events for long-lived nuclei are infrequent, and we need to be able to capture as many of them as possible in order to determine the decay rate with precision. Let's assume that we're dealing with a relatively short-lived radionuclide which produces a steady stream of decay events at a reasonably fast rate, in which case we can simply point a single Geiger counter at it, and work out what proportion of these events we are actually capturing, because that proportion will be the ratio of the solid angle subtended by your Geiger counter, divided by the solid angle of an entire sphere (this latter value being 4π). When we have computed this ratio (let's call it R), which will necessarily be a number less than 1 unless we have surrounded your sample with a spherical shell of Geiger counters, we then start collecting count data, say once per second, and plotting that data. In a modern setup we'd use a computer to collect this mass of data (a facility that wasn't available to the likes of Henri Becquerel, Röntgen and the Curies when they were engaged in their work), in order to have as large a body of data as possible to work with. Before working with the raw data, we transform it by taking each of the data points and dividing it by R to obtain the true count.

Once the data has been collected, transformed and plotted, the end result should be a nice curve. At this point, we're interested in knowing what sort of curve we have, and there are two ways we can determine this. One way is to take the transformed data set, comprising count values c(1), c(2), c(3), ... , c(n), where n is the number of data points collected, compute the following values:

r(1) = c(2) - c(1)
r(2) = c(3) - c(2)
r(3) = c(4) - c(3)
...
r(n-1) = c(n) - c(n-1)

and then plot a graph with r(k) on the vertical axis, and c(k) on the horizontal axis. This should give a reasonable approximation to a straight line, and the slope of that straight line, obtained via regression analysis, will give the first approximation to the decay constant k. At this point, we know we are dealing with a relationship of the form dN/dt = -kN, and you can then apply the integral calculus to that equation (see below). Technically, what we are doing here is approximating the derivative by computing first differences.

However, as a double check, we can also perform a logarithmic regression on the data, plotting log(c(k)) against time, which should also reveal a straight line, and again, the slope of that line will give you the value of k, which should be in good agreement with the value obtained earlier using the more laborious plot of r(k) against c(k). In other words, applying the transformation [1] above to the data set, and extracting an exponential relationship from the data. Since we now know that the data is of the form:

log(N) = -kt

we can then derive the exponential form and check that it tallies with the integral calculus result.

Once we have that function coupling the decay rate to time, we can then work backwards, and feed in the values of the known starting mass and the experimentally obtained decay constant k, and see if the function obtained reproduces the transformed data points. If the result agrees with observation to a very good fit, we're home and dry.

This is, essentially, how the process was done when the decay law was first derived - lots of data points were collected from observation of real radionuclide decay, and the above processes applied to that data, to derive the exponential decay law. When this was done for multiple radionuclides, it was found that they all obeyed the same basic law, namely:

N(t) = N(0)exp(-kt)

where N(0) is your initial amount of radionuclide, N(t) is the amount remaining after time t, and k is the decay constant for the specific radionuclide.

Now, having determined this decay law empirically, it's time to fire up some calculus, and develop a theoretical derivation of the decay law. Which I shall now proceed to do.

Theoretical Derivation Of The Decay Law And Comparison With The Above Empirical Result

Upon noting, using the calculation of first differences in the empirical determination above, that the rate of change of material with time, plotted against the material remaining, is constant, this immediately leads us to conclude that the decay law is governed by a differential equation. An appropriate differential equation is therefore:

dN/dt = -kN

which states that the amount of material undergoing decay is a linear function of the amount of material present (and furthermore, the minus sign indicates that the process results in a reduction of material remaining). Rearranging this differential equation, we have:

dN/N = -k dt

Integrating this, we have:

∫ dN/N = - ∫ k dt

Our limits of integration are, for the left hand integral, the initial amount at t=0, which we call N(0), and the amount remaining after time t, which we call N(t). Our limits of integration for the right hand integral are t=0 and t=t(p), the present time.

Thus, we end up with:

log(N(t)) - log(N(0)) = -kt(p)

By an elementary theorem of logarithms, this becomes:

log(N(t)/N(0)) = -kt(p)

Therefore, exponentiating both sides, we have:

N(t)/N(0) = exp(-kt)

or, the final form:

N(t) = N(0)exp(-kt)

The half-life of a radionuclide is defined as the amount of time required for half the initial amount of material to decay, and is called T{½}. Therefore, feeding this into the equation for the decay law,

½N(0) = N(0)exp(-kt)

Cancelling N(0) on both sides, we have:

½ = exp(-kt)

log(½) = -kt

By an elementary theorem of logarithms, we have:

log(2) = kt

Therefore T{½} = log(2)/k

Alternatively, if the half-life is known, but the decay constant k is unknown, then k can be computed by rearranging the above to give:

k = log(2)/T{½}

Which allows us to move seamlessly from one system of constants (half-lives) to another (decay constants) and back again.

If the initial amount of substance N(0) is known (e.g., we have a fresh sample of radionuclide prepared from a nuclear reactor), and we observe the decay over a time period t, then measure the amount of substance remaining, we can determine the decay constant empirically as follows:

N(t) = N(0)exp(-kt)

N(t)/N(0) = exp(-kt)

log(N(t)/N(0) = -kt

Therefore:

(1/t) log(N(0)/N(t)) = k

On the left hand side, the initial amount N(0), the remaining amount N(t) and the elapsed time t are all known, therefore k can be computed using the empirically observed data.

Once again, this agrees with the empirical data from which the law was derived in the earlier exposition above, and consequently, we can be confident that we have alighted upon a correct result.

Once we have the decay law in place, it simply remains for appropriate values of k to be determined, which will be unique to each radionuclide. This work has been performed by scientists, and as a result of decades of intense labour in this vein in physics laboratories around the world, vast bodies of radionuclide data are now available.

Kaye & Laby's Tables of Physical & Chemical Constants, devised and maintained by the National Physical Laboratory in the UK, contains among the voluminous sets of data produced by the precise laboratory work of various scientists a complete table of the nuclides, which due to its huge size, is split into sections to make it more manageable, in which data such as half-life, major emissions, emission energies and other useful data are included. The sections are (isotopes given as, for example, U238 in the presentation below):

[1] Hydrogen to Flourine (H1 to F24])

[2] Neon to Potassium (Ne17 to K54)

[3] Calcium to Copper (Ca35 to Cu75)

[4] Zinc to Yttrium (Zn57 to Y101)

[5] Zirconium to Indium (Zr81 to In133)

[6] Tin to Praesodymium (Sn103 to Pr154)

[7] Neodymium to Thulium (Nd129 to Tm177)

[8] Ytterbium to gold (Yb151 to Au204)

[9] Mercury to Actinium (Hg175 to Ac233)

[10] Thorium to Einsteinium (Th212 to Es256)

[11] Fermium to Roentgenium (Fm242 to Rg272)

Now, the above exhaustively compiled data gives rise to yet more data, in the form of the tables covering the major decay series. These arise from the observation of which radionuclides decay into which other radionuclides (or in the case of certain radionuclides, which stable elements are formed after decay), and all of these decay events follow specific rules, according to whether α decay, β- decay, or one of the other possible decay modes for certain interesting radionuclides, takes place. Again, data is supplied in the above tables with respect to all of this.

Now, we come to the question of how this data is pressed into service. Since the above work couples radionuclide decay to time, via a precise mathematical law, we can use this data to provide information on the age of any material that contains radionuclides. This can be performed by performing precise quantitative measurements of parent radionuclides and daughter products, all of which is well within the remit of inorganic chemists (since the chemistry of the relevant elements has been studied in detail, in some cases for over 200 years) and of course, modern gas chromatograph mass spectrometry can be brought to bear upon the process, yielding results with an accuracy that past chemists reliant upon earlier techniques could only dream of. Consequently, it is now time to cover the business of dating itself.

Radionuclide Dating - The Basics

With the data obtained above, it becomes possible to trace the decay of suitably long-lived elements in geological strata, locate specific isotopes, determine by precise quantitative analysis the amounts present in a given sample, and compare these with calculations for known decay observations in the laboratory, whence the time taken for the observed isotope composition of the sample can be determined. Given that several isotopes have extremely long half-lives, for example, U238 has a half-life of 4,500,000,000 years, and Th232 has a half-life of 14,050,000,000 years, and several of the daughter isotopes also have usefully long half-lives, one can determine the age of a rock sample, where multiple isotopes are present, by relating them to the correct decay series and utilising the observed empirically determined half-lives of laboratory samples to determine the age of a particular rock sample, cross correlating using multiple isotopes where these are present and enable such cross correlation to be performed. Thus, errors can be eliminated in age determinations by the use of multiple decay series and the presence of multiple long-lived isotopes - any errors arising in one series will yield a figure different from that in another series, and the calculations can thus be cross-checked to ensure that they are consilient.

Referring to the data tables above, I have selected a number of isotopes of interest. These are isotopes whose half-lives have been determined to lie within a specific range, and which moreover are not known to be produced in the Earth's crust by any major synthesis processes (except for the various Technetium isotopes, which can arise if Molybdenum isotopes are coincident with Uranium isotopes in certain rocks, but this exception is rare and well documented). The isotopes in question, in increasing atomic mass order, are:

Al26 : 740,000 years
Cl36 : 301,000 years
Ca41 : 103,000 years
Mn53 : 3,740,000 years
Fe60 : 1,500,000 years
Kr81 : 213,000 years
Zr93 : 1,530,000 years
Nb92 : 34,700,000 years
Tc97 : 2,600,000 years
Tc98 : 4,200,000 years
Tc99 : 211,000 years
Pd107 : 6,500,000 years
Sn126 : 100,000 years
I129 : 15,700,000 years
Cs135 : 2,300,000 years
Sm146 : 103,000,000 years
Gd150 : 1,790,000 years
Dy154 : 3,000,000 years
Hf182: 9,000,000 years
Re186m : 200,000 years
Pb205 : 15,200,000 years
Bi208 : 368,000 years
Bi210m : 3,040,000 years
Np236 : 154,000 years
Np237 : 2,140,000 years
Pu242 : 373,300 years
Pu244 : 81,700,000 years
Cm247 : 15,600,000 years
Cm248 : 340,000 years

The reason I have chosen these isotopes is very simple. Namely, that they would all be present in measurable quantities in the Earth's crust, and detectable by modern mass spectrometry among other techniques, if the planet was, say, only 6,000 years old, as various enthusiasts for mythology continue to assert. This is because because the half-lives of all these radionuclides are a good deal longer than 6,000 years. So, what do we find when we search for these isotopes in Earth rocks?

NONE of them are present in measurable quantities.

Now, one can safely assume that at the end of 20 half-lives, any measurable amount of a particular radionuclide has effectively vanished - the amount left is ½20, or just 0.000095367% of the original mass that was present originally. So even for isotopes of common elements, this fraction represents a vanishingly small amount of material that would test even the world's best mass spectrometer labs to detect in a sample. So, what does the observation of no measurable quantity of the above isotopes mean? It means that at least 20 half-lives of the requisite isotopes must have elapsed for those isotopes to disappear. Taking each isotope in turn, this means that:

[1] Sn126, being absent, must have disappeared over a period of 20 half lives = 20 × 100,000 years = 2,000,000 years. Therefore the Earth must be at least 2,000,000 years old for all the Sn126 to have disappeared.

[2] Ca41, being absent, must have disappeared over a period of 20 half lives = 20 × 103,000 years = 2,060,000 years. Therefore the Earth must be at least 2,060,000 years old for all the Ca41 to have disappeared.

[3] Np236, being absent, must have disappeared over a period of 20 half lives = 20 × 154,000 years = 3,080,000 years. Therefore the Earth must be at least 3,080,000 years old for all the Np236 to have disappeared.

[4] Re186m, being absent, must have disappeared over a period of 20 half lives = 20 × 200,000 years = 4,000,000 years. Therefore the Earth must be at least 4,000,000 years old for all the Re186m to have disappeared.

[5] Tc99, being absent, must have disappeared over a period of 20 half lives = 20 × 211,000 years = 4,220,000 years. Therefore the Earth must be at least 4,220,000 years old for all the Tc99 to have disappeared.

[6] Kr81, being absent, must have disappeared over a period of 20 half lives = 20 × 213,000 years = 4,260,000 years. Therefore the Earth must be at least 4,260,000 years old for all the Kr81 to have disappeared.

[7] Cl36, being absent, must have disappeared over a period of 20 half lives = 20 × 301,000 years = 6,020,000 years. Therefore the Earth must be at least 6,020,000 years old for all the Cl36 to have disappeared.

[8] Cm248, being absent, must have disappeared over a period of 20 half lives = 20 × 340,000 years = 6,800,000 years. Therefore the Earth must be at least 6,800,000 years old for all the Cm248 to have disappeared.

[9] Bi208, being absent, must have disappeared over a period of 20 half lives = 20 × 368,000 years = 7,360,000 years. Therefore the Earth must be at least 7,360,000 years old for all the Bi208 to have disappeared.

[10] Pu242, being absent, must have disappeared over a period of 20 half lives = 20 × 373,000 years = 7,460,000 years. Therefore the Earth must be at least 7,460,000 years old for all the Pu242 to have disappeared.

[11] Al26, being absent, must have disappeared over a period of 20 half lives = 20 × 740,000 years = 14,800,000 years. Therefore the Earth must be at least 14,800,000 years old for all the Al26 to have disappeared.

[12] Fe60, being absent, must have disappeared over a period of 20 half lives = 20 × 1,500,000 years = 30,000,000 years. Therefore the Earth must be at least 30,000,000 years old for all the Fe60 to have disappeared.

[13] Zr93, being absent, must have disappeared over a period of 20 half lives = 20 × 1,530,000 years = 30,600,000 years. Therefore the Earth must be at least 30,600,000 years old for all the Zr93 to have disappeared.

[14] Gd150, being absent, must have disappeared over a period of 20 half lives = 20 × 1,790,000 years = 35,800,000 years. Therefore the Earth must be at least 35,800,000 years old for all the Gd150 to have disappeared.

[15] Np237, being absent, must have disappeared over a period of 20 half lives = 20 × 2,140,000 years = 42,400,000 years. Therefore the Earth must be at least 42,400,000 years old for all the Np237 to have disappeared.

[16] Cs135, being absent, must have disappeared over a period of 20 half lives = 20 × 2,300,000 years = 46,000,000 years. Therefore the Earth must be at least 46,000,000 years old for all the Cs135 to have disappeared.

[17] Tc97, being absent, must have disappeared over a period of 20 half lives = 20 × 2,600,000 years = 52,000,000 years. Therefore the Earth must be at least 52,000,000 years old for all the Tc97 to have disappeared.

[18] Dy154, being absent, must have disappeared over a period of 20 half lives = 20 × 3,000,000 years = 60,000,000 years. Therefore the Earth must be at least 60,000,000 years old for all the Dy154 to have disappeared.

[19] Bi210m, being absent, must have disappeared over a period of 20 half lives = 20 × 3,040,000 years = 60,800,000 years. Therefore the Earth must be at least 60,800,000 years old for all the Bi210m to have disappeared.

[20] Mn53, being absent, must have disappeared over a period of 20 half lives = 20 × 3,740,000 years = 74,800,000 years. Therefore the Earth must be at least 74,800,000 years old for all the Mn53 to have disappeared.

[21] Tc98, being absent, must have disappeared over a period of 20 half lives = 20 × 4,200,000 years = 84,000,000 years. Therefore the Earth must be at least 84,000,000 years old for all the Tc98 to have disappeared.

[22] Pd107, being absent, must have disappeared over a period of 20 half lives = 20 × 6,500,000 years = 130,000,000 years. Therefore the Earth must be at least 130,000,000 years old for all the Pd107 to have disappeared.

[23] Hf182, being absent, must have disappeared over a period of 20 half lives = 20 × 9,000,000 years = 180,000,000 years. Therefore the Earth must be at least 180,000,000 years old for all the Hf182 to have disappeared.

[24] Pb205, being absent, must have disappeared over a period of 20 half lives = 20 × 15,200,000 years = 304,000,000 years. Therefore the Earth must be at least 304,000,000 years old for all the Pb205 to have disappeared.

[25] Cm247, being absent, must have disappeared over a period of 20 half lives = 20 × 15,600,000 years = 312,000,000 years. Therefore the Earth must be at least 312,000,000 years old for all the Cm247 to have disappeared.

[26] I129, being absent, must have disappeared over a period of 20 half lives = 20 × 15,700,000 years = 314,000,000 years. Therefore the Earth must be at least 314,000,000 years old for all the I129 to have disappeared.

[27] Nb92, being absent, must have disappeared over a period of 20 half lives = 20 × 34,700,000 years = 694,000,000 years. Therefore the Earth must be at least 694,000,000 years old for all the Nb92 to have disappeared.

[28] Pu244, being absent, must have disappeared over a period of 20 half lives = 20 × 81,700,000 years = 1,634,000,000 years. Therefore the Earth must be at least 1,634,000,000 years old for all the Pu244 to have disappeared.

[29] Sm146, being absent, must have disappeared over a period of 20 half lives = 20 × 103,000,000 years = 2,060,000,000 years. Therefore the Earth must be at least 2,060,000,000 years old for all the Sm146 to have disappeared.

This is an inescapable conclusion from observational reality, given that these isotopes are not found in measurable quantities in the Earth and would be found in measurable quantities if the Earth was only 6,000 years old, indeed, hardly any of the Sm146 would have disappeared in just 6,000 years, and it would form a significant measurable percentage of the naturally occurring Samarium that is present in crustal rocks. The fact that NO Sm146 is found places a minimum limit on the age of the earth of 2,060,000,000 years - over two billion years - and of course, dating using other isotopes with longer half lives that can be measured precisely has established that the age of the Earth is approximately 4.5 billion years. Now since the decay of these isotopes obeys a precise mathematical law as derived above, and this law has been established through decades of observation of material of known starting composition originating from nuclear reactors specifically for the purpose of determining precise half-lives, which is one of the tasks that the UK National Physical Laboratory (whose data I cited above) performs on a continuous basis in order to maintain scientific databases, the provenance of all of this is beyond question. The tables I have linked to above are the result of something like half a century of continuous work establishing half-lives for hundreds upon hundreds of radionuclides, and not ONE of them has EVER been observed to violate that precise mathematical law which I opened this post with under the kind of conditions in which those materials would exist on Earth if they were present. The majority of those isotopes are nowadays ONLY obtained by synthesis within nuclear reactors, and observation of known samples of these materials confirms again and again that not only does the precise mathematical law governing radionuclide decay apply universally to all of these isotopes, but that the half-lives obtained are valid as a consequence. The laws of nuclear physics would have to be rewritten wholesale for any other scenario to be even remotely valid, and that rewriting of the laws of nuclear physics would impact upon the very existence of stable isotopes including stable isotopes of the elements that make up each and every one of us, none of which would exist if the various wacky scenarios vomited forth on creationist websites to try and escape this were ever a reality.

Now, having covered this, it's time to deal with a topic of importance, and one that constitutes another of those epistemological bones creationists love to chew upon, without realising that the questions surrounding this topic have already been answered. That question is ...

Transport - And How Scientists Deal With It

Even in the very early days of the development of radionuclide dating techniques, scientists were aware that chemical elements in rock samples might be subject to various chemical processes resulting in the transport of material in or out of a given rock sample. After all, inorganic chemists had been performing detailed investigations of the aqueous chemistry of geologically significant elements for the best part of a century before the development of radionuclide dating. Scientists interested in utilising radionuclides for dating purposes, therefore had a vast body of knowledge from inorganic chemistry to draw upon, in order to determine whether or not transport was likely to take place in a given rock stratum, and given the known behaviour of the relevant elements and their various salts in aqueous conditions, they were able to devise means of testing whether transport was likely to be a significant factor in a given rock stratum of interest. Which they promptly set about doing. For example, a geologist can reasonably conclude that virtually zero transport has taken place in a sample where the radionuclides are found as sulphide salts, because the only sulphides that are soluble in water are those of the alkali metals - ALL other sulphides are insoluble, with solubility constants that are extremely low. Lead (II) sulphide, for example (known geologically as the mineral galena), has a K(sp) of 3.4 × 10^-28, mercury (II) sulphide (cinnabar) has a K(sp) of around 4 × 10^-53, and silver sulphide (acanthite or argentite) has a K(sp) of 1.6 × 10^-49.

Indeed, thanks to the large body of knowledge bestowed upon geologist by inorganic chemists, all manner of tests can be performed in order to determine if transport is likely to be a problem before a sample is submitted for dating analysis, so that this can be taken into account and proper corrections applied to the material in question. Indeed, scientists have spent time devising a technique, known as isochron dating, whose purpose is specifically that of checking whether the isotopes used for dating have been subject to transport, and developing appropriate corrections to the dates that would have been obtained without such checking. This technique takes advantage of the fact that many radionuclides produce a stable decay product that is isotopically different from a typical sample of the daughter element arising non-radiogenically, and appropriate comparisons of the amounts of non-radiogenic daughter element with that of the radiogenic daughter element can be used to determine if transport took place.

Let's see how isochron dating works, shall we?

When an igneous stratum is formed (and dating techniques tend to focus upon igneous strata, because the deep mantle of the Earth is the primary source of the radionuclides required), molten material solidifies, and as it does so, the chemical compounds of various elements crystallise out of the melt differentially, resulting in the formation of well-defined mineral species. Moreover, some melts possess a greater chemical affinity for some elements than others, and consequently, there will be further differentiation, based upon those chemical affinities. Zircons, for example, have a chemical affinity for uranium, and incorporate uranium salts into their crystals far more readily than, say, lead salts. Likewise, some other crystalline formations will incorporate other elements preferentially, including elements that are of utility value in dating. A typical element that is of use is rubidium, with the Rb87 isotope having a half-life of 4.75 × 10^10 years. This decays via β- decay into Sr87, an isotope of strontium, and this decay product is stable. However, a non-radiogenic isotope of strontium, namely Sr86, also exists in geological strata. The utility of this will become apparent shortly.

Now, any melt starting off with a quantity of Rb87 will, after sufficient time has elapsed, start to acquire quantities of Sr87. This will take time, given the long half-life of Rb87, and indeed, detectable quantities of Sr87 amenable to mass spectrometry will only start to appear after 0.001 half-lives have elapsed. In the case of Rb87, this is 45 million years, so a sample that has an Rb87 age that is indistinguishable from zero could be as much as 40 million years old, which means that this is no indication of an allegedly "young" Earth. The moment any detectable traces of Sr87 appear in a sample, however, then we're dealing with a rock that is at least 45 million years old, which flushes blind assertions about the Earth being only 6,000 years old down the toilet to begin with. But, this isn't the point: the point is, that any mineral that acquires quantities of strontium upon formation will acquire a specific ratio of the two isotopes Sr86 and Sr87, and that ratio can be used to determine the initial amount of Rb87 that was acquired during formation as well. Which means that no "assumptions" about initial material present are needed.

Now, since all the minerals that acquire strontium will acquire the same ratio of Sr86 to Sr87 at the start, we can use that ratio as the y-axis for a plot. However, different minerals within the sample will acquire different quantities of Rb87, and we can use the ratio of Rb87 to Sr86 to form the x-axis of the plot. If our initial values are:

P = amount of Rb87 at the time of stratum formation
D(1) = amount of Sr86 at the time of stratum formation
D(2) = amount of Sr87 at the time of stratum formation

then we plot an x-y plot consisting of:

x = P/D(1), y = D(2)/D(1)

the axes therefore correspond to:

x = increasing enrichment of Rb87 in the sample with increasing value
y = increasing enrichment of Sr87 in the sample with increasing value

Now, the global composition of the melt, from which the stratum eventually forms, will have a given point value on this plot. As the melt cools, and minerals crystallise out, different minerals will migrate along a straight line in this plot, as all the minerals will inherit the same value of y (= D(2)/D(1)), but inherit different values of x (=P/D(1)). The result will be, at zero age, a horizontal line connecting the points for those minerals in the plot.

Now, as the Rb87 decays in each mineral, it will produce S]87. Therefore, over geological time, the data points will move upwards and to the left.

Now, because decay occurs in a proportional manner, courtesy of the decay law derived above, when 20% of the Rb87 has decayed in one mineral, then 20% of the Rb87 will have decayed in all the minerals present in the stratum. This means that all the points will move upwards and to the left of the plot. This means that those points corresponding to the minerals with the greatest initial Rb87 concentration will move the farthest, and the movement will be such that all of the points will remain on a straight line. Indeed, those familiar with Monte Carlo simulation methods can produce a computer simulation that reproduces this exact result. As a consequence, any stratum containing the appropriate minerals will yield, for a given age, a line of points whose slope increases with time, and the slope of that line can be used to determine the age of the sample.

Note that we don't need to know the initial amounts of any of the elements present in the sample in order for this to work. All we need to know is the present-day ratios of those elements. And, from that data, we can reconstruct the original composition of the melt.

Now, here is the fun part. If the sample suffered any transport, then this will become immediately apparent because the points will deviate significantly from a straight line plot. This is because the minerals containing the various elements will undergo transport differentially. For example, if the minerals lost Rb87 due to various processes of aqueous chemistry, then this would shift all of the points to the left, but because different minerals are involved in the process, each with a different chemistry, and a different response to the aqueous processes that could remove Rb87 from them, the amount of x-shift will be different for each mineral, and as a consequence, straight line correlation will be destroyed. Immediately scientists see this, they know that something unusual has happened to the sample after formation, and that dates obtained from it are unlikely to be reliable.

Indeed, if the Earth were only 6,000 years old, not only would ALL isochron plots involving minerals with long half-lives be flat, horizontal lines, but random loss or gain of the parent nuclide would not affect those results. If the Earth were only 6,000 years old, any "contamination" that creationists assert would be present that would render radionuclide dating methods invalid, would not even be noticeable on a purported "young Earth". Contamination would only ever be noticeable if the Earth was old. Which means that far from "invalidating" radionuclide dating, detectable contamination in a sample via the isochron method actually reinforces an old age for the Earth.

Worse still, from the creationist standpoint, the known possibilities for systematic alteration of an isochron plot, that results in modification of the data points such that they remain collinear, result in an underestimate of the age of the sample - in other words, the isochron plot records them as being younger than they actually are, not older. Complete homogenisation of the stratum with respect to the content of Sr87 will reset the isochron 'clock' to zero, and partial homogenisation will result in a line of lower slope than previously, causing the technique to underestimate the true age.

Once such a plot is complete, any strong correlation to a straight line (as yielded by regression analysis, which will give us an indication how much we can trust a date from the plot, and what value of error to apply to the plot), will yield the following values:

[1] the y-intercept of the line is the value of D(2)/D(1) at solidification;

[2] the slope of the line is equal to ΔP/(P - ΔP), where ΔP is the amount of Rb87 lost to decay, and thus allows us to determine the age of the sample, given the known half-life of Rb87 (we can back-calculate using the decay law to determine what value of P was initially present to produce the observed result).

There is a body of technical literature on the subject of isochron dating, and, needless to say, it requires a fair amount of work to plough through, but for those who have acquired the relevant scientific and mathematical background, it is well worth exerting this effort, not least in order to prepare oneself for the inevitable quote mining of the scientific papers that will arise in creationist circles.

And now, I'd like to turn attention to this:

Purported "Exceptions" To The Decay Law

One of the more interesting findings of recent years was that rhenium-187, a radionuclide that undergoes decay by electron capture, can have its half-life altered under laboratory conditions. However, the mechanism of alteration offers no hope to anyone entertaining fantasies about a 6,000 year old Earth, for the following reasons:

[1] The mechanism only applies to isotopes that decay via electron capture, and both α decaying and β- decaying isotopes are unaffected by this mechanism;

[2] The mechanism only has a small effect upon the half-life of Re187 unless extreme conditions are applied (and the scientists had to resort to extreme measures to determine this);

[3] The conditions required to produce this mechanism in Re187 atoms on Earth are physically unreal.

What the relevant scientists did, was to take Re187 atoms, and subject them to ever more extreme levels of ionisation. In order to do this, they had to resort to a particle accelerator, and use large amounts of energy to ionise the Re187 atoms to the required amount. As any student of basic physical chemistry understands, it takes a certain amount of energy to remove one electron from a neutral atom, but, once that electron is removed, it requires more energy to remove a second electron, because that electron is now being removed from a positively charged ion, and more energy is needed to overcome the additional electrostatic attraction now present. Consequently, as one removes yet more electrons, more energy is needed for each subsequent electron. In order to speed up the decay process of Re187, scientists stripped all of the electrons from the Re187 atoms, making them extremely highly ionised. Extreme states of ionisation of this sort only occur in nature within the confines of extremely hot incandescent plasmas, with temperatures well beyond that required to turn elements such as rhenium into gases, and rhenium has the highest boiling point of all the elements, at a whopping 5,600°C (courtesy of Kaye & Laby again). Even this temperature isn't enough to strip 75 electrons off a rhenium atom, and the temperature required is more likely to be of the order of 65,000 Kelvins or beyond, which means that trying to invoke this mechanism as a means of "accelerating" nuclear decay involves heating the Earth's crust to temperatures more normally associated with the chromospheres of supergiant O class stars.

Apart from the fact that this mechanism requires ludicrously absurd conditions to have occurred in the Earth's crust in order for it to happen, and apart from the fact that this mechanism is useless for U238 and several other important isotopes used in radionuclide dating, because they do not decay via electron capture, it's actually a waste of time trying to argue against the constancy of the decay law under normal conditions, because this one exception requires such extreme conditions that the Earth would not have remained a solid planet if they had been present. Plus, the mere fact that the half-life for Re187 is of the order of 4.16 × 10^10 years, means that the presence of any detectable Re187 in the Earth's crust means that the planet is ancient. If by some bizarre freak of physics, Re187 decay had been sped up by this mechanism without vaporising the Earth's crust, the anomaly would have been so immediately detectable alongside the other radionuclides, that scientists would have noticed something was amiss long ago. That word 'consilience' is back to haunt those who prefer mythology to reality.

And now, it's time to deal with carbon dating specifically, as this is subject to much peddling of lies by creationists. in particular, I'll deal with the drivel that was posted back in 2011 by Arsewater In Genesis (I won't bother with a link as I don't want to give these verminous scumbags any traffic if I can help it, but the diligent will find this page with ease if it hasn't been taken down). Let's examine the lies peddled by ideological stormtroopers for creationist masturbation fantasies, and dismantle them piece by piece, shall we?

Let's take a look at this shall we? As usual, personal pronouns directed toward the original author, in this case the hilariously named Mike Riddle.

Scientists use a technique called radiometric dating to estimate the ages of rocks, fossils, and the earth. Many people have been led to believe that radiometric dating methods have proved the earth to be billions of years old. This has caused many in the church to reevaluate the biblical creation account, specifically the meaning of the word “day” in Genesis 1. With our focus on one particular form of radiometric dating—carbon dating—we will see that carbon dating strongly supports a young earth. Note that, contrary to a popular misconception, carbon dating is not used to date rocks at millions of years old.

And right out of the gate, you admit that C14 dating is not used for such dating purposes! Therefore how can a dating technique that is NOT used for dating extremely old material be used to "prove" your fatuous young Earth nonsense? The ONLY way in which you could establish a recent age for the planet is if techniques that ARE used to date ancient material routinely returned young ages. A schoolboy would be able to see through the faulty logic you are using above.

Oh, and once again, why do propagandists for supernaturalist idiocy always fail to understand the distinction between proof, which is a formal procedure in mathematics, and evidential support, which is the process that the physical sciences rely upon?

Before we get into the details of how radiometric dating methods are used, we need to review some preliminary concepts from chemistry. Recall that atoms are the basic building blocks of matter. Atoms are made up of much smaller particles called protons, neutrons, and electrons. Protons and neutrons make up the center (nucleus) of the atom, and electrons form shells around the nucleus.

The number of protons in the nucleus of an atom determines the element. For example, all carbon atoms have 6 protons, all atoms of nitrogen have 7 protons, and all oxygen atoms have 8 protons. The number of neutrons in the nucleus can vary in any given type of atom. So, a carbon atom might have six neutrons, or seven, or possibly eight—but it would always have six protons. An “isotope” is any of several different forms of an element, each having different numbers of neutrons. The illustration below shows the three isotopes of carbon.

This has to be a first. A statement of scientific fact in an AiG screed that isn't wrong. Though you would have to be a complete numpty to mess this one up.

Some isotopes of certain elements are unstable; they can spontaneously change into another kind of atom in a process called “radioactive decay.” Since this process presently happens at a known measured rate, scientists attempt to use it like a “clock” to tell how long ago a rock or fossil formed.

No, scientists DON'T "attempt" to use it as such, they DO use it as such, and successfully, precisely because the process of radionuclide decay obeys a precise mathematical law that is dependent upon time as the sole independent variable. When a precise mathematical relationship exists between the behaviour of a system and the time over which this behaviour takes place, you have a clock by definition.

There are two main applications for radiometric dating. One is for potentially dating fossils (once-living things) using carbon-14 dating, and the other is for dating rocks and the age of the earth using uranium, potassium and other radioactive atoms.

WRONG!!!!

C14 dating is NOT used to date fossils!

Why?

Because ... wait for it ... fossils that are millions of years old contain no carbon!

ALL the organic material in a sufficiently old fossil is regarded, certain interesting exceptions notwithstanding (and I've covered the Mary Schweizter paper in full elsewhere), to have been replaced by inorganic minerals. Which is why other dating techniques are used for the relevant strata. Of course, in the light of Schweitzer's work and that of one or two other scientists, we may have to revise the view that organic material is always replaced wholesale, but the circumstances in which said replacement does NOT take place are considered unusual, given that the preponderance of fossils found thus far DO display wholesale replacement of organic material with minerals, a process known to geologists as permineralisation. Furthermore, if scientists re-evaluate the view that permineralisation occurs in all instances as a result of the work of Schweitzer and others, they will do so because reality tells them than such re-evaluation is warranted. Science modifies its theories to fit the real world, in contrast with religions, which seek to modify the real world to conform to doctrinal assertion.

Plus, in rigorous and precise work, what happens is that strata above and below the fossils in question are dated, thus providing a time range within which the fossils must necessarily have been formed. Then, if the stratum containing the fossils is itself amenable to dating, that stratum itself is dated, in order to verify that its date lies between the bracketing dates obtained from the bracketing strata.

Carbon-14 (14C), also referred to as radiocarbon, is claimed to be a reliable dating method for determining the age of fossils up to 50,000 to 60,000 years. If this claim is true, the biblical account of a young earth (about 6,000 years) is in question, since 14C dates of tens of thousands of years are common. [1]

In other words, reality says that your book of myths is wrong. In the world of science, this means that reality wins.

When a scientist’s interpretation of data does not match the clear meaning of the text in the Bible, we should never reinterpret the Bible.

In other words, you merely erect here the blind assertion that when reality and doctrine differ, reality is wrong and doctrine is right. I suspect you are too addled by supernaturalist delusion to realise how absurd this notion is.

God knows just what He meant to say, and His understanding of science is infallible, whereas ours is fallible.

Mere blind assertion. When did anyone, in 5,000 years of trying, present any substantive evidence to support the existence of any of the numerous species of invisible magic man that human imaginations have invented over time? So, you've moved from stating known scientific fact to stating rectally extracted blind mythological assertion, and presenting said blind mythological assertion as if it constituted fact. Sadly for you, in the real world, assertions such as this, bereft of genuine, substantive evidential support, do not constitute established fact. FAIL. That's before we consider the number of assertions in your sad mythology that are knwon not merely to be wrong, but to be fatuous and absurd. Which I'll leave for another time.

So we should never think it necessary to modify His Word.

In other words, once again, when reality and doctrine differ, you assert that reality is wrong and doctrine is right. Fatuous drivel.

Genesis 1 defines the days of creation to be literal days (a number with the word “day” always means a normal day in the Old Testament, and the phrase “evening and morning” further defines the days as literal days).

Which means that it's horseshit. Because once again, to those of us who paid attention in a science class, reality wins every time in a contest against blind ex recto mythological assertion.

Since the Bible is the inspired Word of God

Another blind ex recto assertion. Which, since supernaturalists have never provided substantive evidential support for the postulate that your magic man actually exists in the first place, merely constitutes ex recto assertion on top of ex recto assertion.

we should examine the validity of the standard interpretation of 14C dating by asking several questions:

Except that scientists have already done this and verified that the dating technique is valid, using several independent checks. I'm tempted to ask here the famous question "why do the curves agree?" that is familiar to some of the more long-standing stalwarts of other forums I'm a member of, but I digress ...

1. Is the explanation of the data derived from empirical, observational science, or an interpretation of past events (historical science)?

Ah, this specious dichotomy rears its ugly head again.

Exactly what do you call subjecting a sample to direct measurement to determine the ratios of radionuclide to daughter nuclide other than direct empirical observation?

This is empirical, observational science. Your specious attempt to characterise it as something other is precisely that - specious.

2. Are there any assumptions involved in the dating method?

No. The method has been subject to independent checks using other dating techniques that rely upon vastly different physical phenomena. Once again, "why do the curves agree?" looms large on the horizon. Those checks include such phenomena as: lake varves, coral growth rings, ice cores from Greenland and Antarctica, tree rings ... which, oddly enough, ALL AGREE WITH EACH OTHER DESPITE BEING FORMED DUE TO DIFFERENT PHYSICAL PROCESSES. I wonder why that is?

3. Are the dates provided by 14C dating consistent with what we observe?

Yes. See above with respect to the other dating methods that AGREE WITH C14 DATING.

4. Do all scientists accept the 14C dating method as reliable and accurate?

Yes. At least, real scientists do.

All radiometric dating methods use scientific procedures in the present to interpret what has happened in the past. The procedures used are not necessarily in question. The interpretation of past events is in question.

Except that we have NO evidence to support the notion that physical laws were different in the past, which is what is required here in order to support your absurd thesis. I'm reminded here of SN1987A.

The secular (evolutionary) worldview interprets the universe and world to be billions of years old. The Bible teaches a young universe and earth. Which worldview does science support?

If you have to ask this question at all as a purportedly functioning adult, then your education is sadly lacking. Either that, or you're engaging in the usual duplicitous apologetics for which AiG is infamous.

Can carbon-14 dating help solve the mystery of which worldview is more accurate?

Your problem here is that it's not just C14 dating you have to worry about. Indeed, C14 is the least of your worries. The fact that dating methods used to date far more ancient material routinely yields ancient ages for that material, and that this is consilient with astrophysical observations such as SN1987A, is a far bigger worry for your doctrine than C14.

The use of carbon-14 dating is often misunderstood.

You got that right. You misunderstood its proper use above. It isn't used to date true fossils because, wait for it, true fossils contain no carbon! The carbon they once contained has all been replaced by inorganic minerals!

Carbon-14 is mostly used to date once-living things (organic material).

Only when that material has NOT been subject to permineralisation.

It cannot be used directly to date rocks; however, it can potentially be used to put time constraints on some inorganic material such as diamonds (diamonds could contain carbon-14).

Oh, you're going to erect this specious canard again are you? The "radiocarbon in diamonds" canard has already been addressed. One source addressing this canard is this one.

Because of the rapid rate of decay of 14C, it can only give dates in the thousands-of-year range and not millions.

So why are you raising objections to this technique, and not other techniques that DO give dates of 10^6 to 10^9 years and beyond? Might this have something to do with the fact that you would have to rewrite the whole of physics to do this? Not that this has stopped creationists in the past.

There are three different naturally occurring varieties (isotopes) of carbon: 12C, 13C, and 14C.

Guess what? C13 has biological implications as well. I'll let you sweat over that one.

Carbon-14 is used for dating because it is unstable (radioactive), whereas 12C and 13C are stable. Radioactive means that 14C will decay (emit radiation) over time and become a different element. During this process (called “beta decay”) a neutron in the 14C atom will be converted into a proton. By losing one neutron and gaining one proton, 14C is changed into nitrogen-14 (14N = 7 protons and 7 neutrons).

Strange how your 3,000 year old book of myths never mentioned any of this, isn't it?

If 14C is constantly decaying, will the earth eventually run out of 14C? The answer is no. Carbon-14 is constantly being added to the atmosphere. Cosmic rays from outer space, which contain high levels of energy, bombard the earth’s upper atmosphere. These cosmic rays collide with atoms in the atmosphere and can cause them to come apart. Neutrons that come from these fragmented atoms collide with 14N atoms (the atmosphere is made mostly of nitrogen and oxygen) and convert them into 14C atoms (a proton changes into a neutron).

The process is actually a little more sophisticated than described above, but the above is not essentially wrong. I advise the interested reader to look up cosmic ray spallation.

Once 14C is produced, it combines with oxygen in the atmosphere (12C behaves like 14C and also combines with oxygen) to form carbon dioxide (CO2). Because CO2 gets incorporated into plants (which means the food we eat contains 14C and 12C), all living things should have the same ratio of 14C and 12C in them as in the air we breathe.

Not quite correct. The transport of C[14 into living organisms depends upon their environment. The above account is only strictly correct for terrestrial organisms. The same is not necessarily true of marine organisms, and indeed, determining this was one of the first tasks that scientists set out to perform. Which is why scientists use other techniques for dating marine material of abyssal ocean origin, or else use different calibration techniques to those used for terrestrial organisms, because they have determined experimentally that such different calibration is required. Once again, this is merely a case of scientists doing their job properly, namely paying attention to reality.

Once a living thing dies, the dating process begins. As long as an organism is alive it will continue to take in 14C; however, when it dies, it will stop. Since 14C is radioactive (decays into 14N), the amount of 14C in a dead organism gets less and less over time. Therefore, part of the dating process involves measuring the amount of 14C that remains after some has been lost (decayed). Scientists now use a device called an “Accelerator Mass Spectrometer” (AMS) to determine the ratio of 14C to 12C, which increases the assumed accuracy to about 80,000 years.

Actually, my understanding is that 60,000 years is the current upper limit, though I haven't read the very latest literature. It's possible that advances have pushed the boundary further back, but I've yet to see this documented in the primary scientific literature. Speaking of which, have you read any of it?

In order to actually do the dating, other things need to be known. Two such things include the following questions:

Ah, cue canard erection in 3 ... 2 ... 1 ...

1. How fast does 14C decay?

The half-life of C14is 5,730 years. Source: Kaye & Laby's Tables of Physical & Chemical Constants.

2. What was the starting amount of 14C in the creature when it died?

And here I can smell the canard being erected already. Which has been addressed courtesy of calibration curves.

The decay rate of radioactive elements is described in terms of half-life. The half-life of an atom is the amount of time it takes for half of the atoms in a sample to decay. The half-life of 14C is 5,730 years.

Looked up the same tables, did you?

For example, a jar starting with all 14C atoms at time zero will contain half 14C atoms and half 14N atoms at the end of 5,730 years (one half-life). At the end of 11,460 years (two half-lives) the jar will contain one-quarter 14C atoms and three-quarter 14N atoms.

And why can't we use this phenomenon as a clock, given the above?

Since the half-life of 14C is known (how fast it decays), the only part left to determine is the starting amount of 14C in a fossil. If scientists know the original amount of 14C in a creature when it died, they can measure the current amount and then calculate how many half-lives have passed.

And guess how they determine this? By performing C14 dating upon material of known age. Not just once, but for thousands of samples across a range of known ages. This data can then be used to produce the calibration curve.

Since no one was there to measure the amount of 14C when a creature died, scientists need to find a method to determine how much 14C has decayed. To do this, scientists use the main isotope of carbon, called carbon-12 (12C). Because 12C is a stable isotope of carbon, it will remain constant; however, the amount of 14C will decrease after a creature dies. All living things take in carbon (14C and 12C) from eating and breathing. Therefore, the ratio of 14C to 12C in living creatures will be the same as in the atmosphere. This ratio turns out to be about one 14C atom for every 1 trillion 12C atoms. Scientists can use this ratio to help determine the starting amount of 14C.

Actually, no they don't. What they do is gather together large numbers of samples of material of known age and analyse the ratios in those samples in order to provide the calibration baseline. It's not as if we don't have plenty of such material to hand. Apart from tree ring samples from ancient trees, we have plenty of entombed human corpses of known age to perform the requisite tests upon. Corpses that were buried and whose date of burial was recorded and chronicled. So before you erect the canard that the starting amount cannot be known, the above tells anyone who paid attention in a science class that the amount CAN be known.

When an organism dies, this ratio (1 to 1 trillion) will begin to change. The amount of 12C will remain constant, but the amount of 14C will become less and less. The smaller the ratio, the longer the organism has been dead. The following illustration demonstrates how the age is estimated using this ratio.

Originally, I reproduced the table in question at this point in a previous exposition, but this board doesn't support the tags required (sigh). I'll have to let everyone track down the table for themselves on the Arsewater in Genesis page, if it's still extant.

A critical assumption used in carbon-14 dating has to do with this ratio.

WRONG!

There is NO assumption involved. Because scientists have performed dating tests upon thousands of samples of material of known age in order to determine what the outcome should be for material of a given age. And, they have used this real world data to calibrate the dating technique. When said calibration is performed, they then test said calibration against other dating techniques relying upon different physical phenomena (e.g., lake varves, tree rings, you get the picture?) in order to ensure that they all agree.

It is assumed that the ratio of 14C to 12C in the atmosphere has always been the same as it is today (1 to 1 trillion).

WRONG!

This is NOT ASSUMED AT ALL. Why do you think scientists went to the trouble of testing thousands of samples of known age? To ELIMINATE this assumption from the picture!

If this assumption is true, then the AMS 14C dating method is valid up to about 80,000 years. Beyond this number, the instruments scientists use would not be able to detect enough remaining 14C to be useful in age estimates. This is a critical assumption in the dating process.

WRONG!

This is NOT a "critcal assumption" AT ALL. Once again, scientists tested thousands of samples of known age across a broad age range spectrum in order to determine how to calibrate C14against real world material of known age.

If this assumption is not true, then the method will give incorrect dates.

But when scientists have access to thousands of data points obtained from material of known age, this "assumption" is NOT NEEDED. Because they have real world data from samples of known age with which to compare samples of unknown age. Which means that your assertion above is totally WRONG.

What could cause this ratio to change? If the production rate of 14C in the atmosphere is not equal to the removal rate (mostly through decay), this ratio will change. In other words, the amount of 14C being produced in the atmosphere must equal the amount being removed to be in a steady state (also called “equilibrium”). If this is not true, the ratio of 14C to 12C is not a constant, which would make knowing the starting amount of 14C in a specimen difficult or impossible to accurately determine.

Which is why scientists tested material of known age specifically in order to REMOVE THIS VARIATION from the dating method.

Dr. Willard Libby, the founder of the carbon-14 dating method, assumed this ratio to be constant.

Oh really? Let's see what Willard Libby himself said in his Nobel Lecture in 1960, shall we? For those interested, Willard Libby's full Nobel Lecture is available here for download. Let's take a look at it shall we?

Radiocarbon dating had its origin in a study of the possible effects that cosmic rays might have on the earth and on the earth’s atmosphere. We were interested in testing whether any of the various effects which might be predicted could actually be found and used. Initially the problem seemed rather difficult, for ignorance of billion-electron-volt nuclear physics (cosmic ray energies are in this range) was so abysmal at the time and incidentally fourteen years later still is so abysmal, that it is nearly impossible to predict with any certainty the effects of the collisions of the multibillion-volt primary cosmic radiation with air.

However, in 1939, just before the war, Professor Serge Korff of New York University and others discovered that the cosmic rays produce secondary neutrons in their initial collisions with the top of the atmosphere. The neutrons were found by sending counters, designed to be sensitive to neutrons, up to high altitudes and they were found to have an intensity which corresponded to about two neutrons being generated for each square centimeter of the earth’s surface per second. Whereas it was extremely difficult to predict the types of nuclei that might be produced by the billion-volt primary cosmic rays, the neutrons being secondaries were in the million-volt energy range and therefore subject to laboratory tests. So at this point the question was : "What will million-electron-volt neutrons do if liberated in the air?" The answer to this question was already available - in fact, Professor Korff noted in one of the papers announcing the discovery of the neutrons that the principal way in which the neutrons would disappear would be to form radiocarbon. The reaction involved is a simple one. Oxygen is essentially inert to neutrons but nitrogen is quite reactive. Nitrogen-14, the abundant nitrogen isotope, reacts essentially quantitatively to form carbon-14 with the elimination of a proton. It also reacts about one percent of the time to produce tritium, radioactive hydrogen, which is another story leading to a method of dating water and wine.

To return to radiocarbon dating - knowing that there are about 2 neutrons formed per square centimeter per second, each of which forms a carbon-14 atom, and assuming that the cosmic rays have been bombarding the atmosphere for a very long time in terms of the lifetime of carbon-14 (carbon-14 has a half-life of about 5,600 years) - we can see that a steady-state condition should have been established, in which the rate of formation of carbon-14 would be equal to the rate at which it disappears to reform nitrogen-14. This allows us to calculate quantitatively how much carbon-14 should exist on earth (see Fig. 1); and since the 2 atoms per second per cm^2 go into a mixing reservoir with about 8.5 grams of carbon per cm2, this gives an expected specific activity of living matter of 2.0/8.5 disintegrations per second per gram of carbon.

The mixing reservoir consists not only of living matter which dilutes the radiocarbon, but of the dissolved carbonaceous material in the oceans which can exchange carbon with the atmospheric carbon dioxide and thus dilute it. In fact, the ocean is the larger part of the diluting carbon reservoir (see Table I). For each square centimeter of the earth’s surface, there are about 7.25 grams of carbon dissolved in the ocean in the form of carbonate, bicarbonate, and carbonic acid, and the biosphere itself contains about 0.33 gram per square centimeter of surface. Adding all the elements of the reservoir, we get a total of 8.5 grams of diluting carbon per cm^2, and the 2.0 carbon-14 atoms disintegrating every second should be contained in 8.5 grams of carbon. Thus, the specific activity of living carbon should be that number. We find this to be the actual value observed to within about 10 percent (see Table 2). Of course, the times for mixing of all parts of the reservoir must be short compared to the average lifetime of radiocarbon, 8,000 years. The time for mixing of the oceans is the longest, about 1,000 years on the average.

This is interesting, for it means the following : The present intensity of the cosmic radiation (unless there have been canceling errors in our calculations) corresponds to the average intensity over the last 8,000 years, the average life of carbon-14. It says also that the ocean is mixed nearly perfectly to its bottom depths in 8,000 years. This we know because we included all of the dissolved carbon in the sea. Also, direct measurement of the carbonate and bicarbonate in deep ocean water confirms this. These conclusions could be false if errors in the very different quantities - the intensity of the cosmic rays and the mixing rate and depths of the oceans - should happen just to cancel one another. Being so unrelated, we believe this to be very unlikely and conclude that the agreement between the predicted and observed assays is encouraging evidence that the cosmic rays have indeed remained constant in intensity over many thousands of years and that the mixing time, volume, and composition of the oceans have not changed either.

In other words, Libby set out right at the start to TEST the "assumption" that the production of C14 was effectively constant, and according to the best measurements available at that time, arrived at the conclusion from the real world data that this was a safe view to hold.

Moving on, Libby says this:

We assimilate cosmic-ray produced carbon-14 atoms at just the rate that the carbon-14 atoms in our bodies disappear to form nitrogen-14. At the time of death, however, the assimilation process stops abruptly. There is no longer any process by which the carbon-14 from the atmosphere can enter our bodies. Therefore, at the time of death the radioactive disintegration process takes over in an uncompensated manner and, according to the law of radioactive decay, after 5,600 years the carbon that is in our bodies while we are alive will show half the specific carbon-14 radioactivity that it shows now. Since we have evidence that this has been true for tens of thousands of years, we should expect to find that a body 5,600 years old would be one-half as radioactive as a present-day living organism. This appears to be true. Measurements of old artifacts of historically known age have shown this to be so within the experimental errors of measurement.

Oh look. Libby explicitly states that tests have been performed on artefacts of historically known age. In other words, NO "assumptions" involved!

His reasoning was based on a belief in evolution, which assumes the earth must be billions of years old.

Rampant bullshit, as Libby's own words from his Nobel Lecture, quoted in full above, clearly demonstrate. Libby did NOT "assume" an old Earth in advance, instead he tested his dating technique upon material of known historical age in order to determine that his dating technique was valid.

Furthermore, this has nothing to do with the theory of biological evolution, which is NOT a "belief" but a valid scientific theory supported by massive amounts of real world data, and no "assumption" about the age of the Earth is involved, because the vast mass of scientific evidence from multiple lines of inquiry supports an old Earth, including astrophysical data.

Assumptions in the scientific community are extremely important. If the starting assumption is false, all the calculations based on that assumption might be correct but still give a wrong conclusion.

Except that science is in the business of testing assumptions to destruction, unlike religion, which dares not do so. This is precisely what happened here - Libby explicitly states in his Nobel Lecture that material of known historical age was tested in order to determine the validity of the dating technique.

In Dr. Libby’s original work, he noted that the atmosphere did not appear to be in equilibrium.

Actually, if you read his work, you will find that he dealt with this issue by testing material of known historical age, which could then be used to calibrate the dating technique. The construction of calibration curves has been an essential part of chemistry for decades. Indeed, on pages 600 through to 603, Libby presents a list of historical artefacts that were subject to testing, one of which was a linen wrapping used to wrap one of the Dead Sea Scrolls, the scroll in question containing the text of the Book of Isaiah, which was dated as being approximately 2,000 years old.

Also, Libby himself says in his Nobel Lecture that he was aware of instances of changes in the ratio of C14 to C12 in the atmosphere, viz:

It has been observed that fossil carbon dioxide from the combustion of coal and oil beginning at about 1870 began to dilute the biosphere and to reduce the radiocarbon content until 1954, when the explosion of atomic devices reversed the trend. The carbon-14 introduced by the neutrons produced in the explosions more than compensated for the reduction by the fossil carbon, which at that time had amounted to about 3 percent in the Northern Hemisphere as compared to the primeval level extending as far back as has been possible to measure by tree rings. Hl. de Vries and Hans E. Suess have been particularly active in research on this point. Dr. Suess, in fact, discovered the fact that fossil carbon dioxide was reducing this specific activity in recent biospheric material as compared to the general level prior to 1870. Broecker and Olson have made careful studies of the carbon-14 content of ancient woods as well. And the general result is that prior to 1870 there appeared to be only very minor variations on the order of one percent or less in the radiocarbon content of living matter. The recent perturbations are of no great concern for present living archeologists and geologists. Of course, in the future it will be difficult to correct for the period when these perturbations were active; i.e., 5,000 years from now there may be some difficulty in understanding why for the period of a century or so, beginning in 1870, the radiocarbon level was so perturbed. However, the written records may well explain the anomaly. And, in fact, radiocarbon dating as such may not be needed to establish historical fact.

And, of course, the reason that those perturbations are of no great concern is precisely because of the existence of thousands of data points obtained from samples of known historical age that can be used to calibrate the dating technique. Note also that tree ring data began to assume importance with respect to the business of calibration very early in the days of the development of the technique.

This was a troubling idea for Dr. Libby since he believed the world was billions of years old and enough time had passed to achieve equilibrium.

Poppycock. He didn't seem troubled in his Nobel Lecture above. What was it he said again? Oh yes:

"And the general result is that prior to 1870 there appeared to be only very minor variations on the order of one percent or less in the radiocarbon content of living matter. The recent perturbations are of no great concern for present living archeologists and geologists."

In other words, the real world data led him to conclude that the technique was sound.

Dr. Libby’s calculations showed that if the earth started with no 14C in the atmosphere, it would take up to 30,000 years to build up to a steady state (equilibrium).

Let's assume that this isn't a misrepresentation of Libby's work (which I suspect). This was a problem how, precisely? Especially in the light of the above?

If the cosmic radiation has remained at its present intensity for 20,000 or 30,000 years, and if the carbon reservoir has not changed appreciably in this time, then there exists at the present time a complete balance between the rate of disintegration of radiocarbon atoms and the rate of assimilation of new radiocarbon atoms for all material in the life-cycle. [2]

Ah, quote mine time. Wondered when this would happen. :)

Sadly I don't have Libby's book in front of me, so I can't determine how egregious a quote mine this is likely to be. But, given AiG's track record, that this IS a quote mine would not surprise me in the least. Reference [2], for those who wish to track this down, and determine if this IS a quote mine, is Libby's book Radiocarbon Dating, from the University of Chicago Press in 1952.

Plus, Libby was merely devising, in the above, the simplest set of conditions that would lead to equilibrium, given a zero C14starting point. More complex models have since been devised. I notice none of those are being addressed.

Dr. Libby chose to ignore this discrepancy (nonequilibrium state)

BLATANT LIE. As the above reproduction of Libby's words clearly demonstrates. Which above all, demonstrates that he determined that the solution to any variation in C14/C12 ratios lay in the generation of a body of data obtained from samples of known historical age that could then be used to calibrate the dating technique. Libby "ignored" NOTHING. This is a scurrilous attack upon the reputation of an honest, hard working scientist, a Nobel Laureate no less, and is typical of the duplicity that ideological stormtroopers for doctrine engage in.

and he attributed it to experimental error.

Bullshit. As the above reproduction of Libby's Nobel Lecture clearly demonstrates. Once again, this is a blatant lie.

However, the discrepancy has turned out to be very real. The ratio of 14C /12C is not constant.

But when scientists have access to thousands of data points from material of known historical age with which to calibrate the dating technique, this does not matter. The ratios could fluctuate to a far greater extent than has been established by actual measurement, and this would not be a problem provided that we had access to a large enough data set from material of known age with which to produce the relevant calibration curve.

The Specific Production Rate (SPR) of C-14 is known to be 18.8 atoms per gram of total carbon per minute. The Specific Decay Rate (SDR) is known to be only 16.1 disintegrations per gram per minute. [3]

And where did the creationist who wrote the above obtain his data? Because reference [3] above is another creationist screed.

What does this mean? If it takes about 30,000 years to reach equilibrium and 14C is still out of equilibrium, then maybe the earth is not very old.

Poppycock. Libby explicitly stated in his work above that fluctuations in production rates need not be a problem when we have access to data obtained from material of known historical age to act as a basis for calibration.

Other factors can affect the production rate of 14C in the atmosphere. The earth has a magnetic field around it which helps protect us from harmful radiation from outer space. This magnetic field is decaying (getting weaker).

Ah, another creationist canard, one moreover that arises from the discredited tax dodger and convict Kent Hovind. Addressed here.

The stronger the field is around the earth, the fewer the number of cosmic rays that are able to reach the atmosphere. This would result in a smaller production of 14C in the atmosphere in earth’s past.

Except that "magnetic field decay" is a canard. I point everyone to the reference above.

The cause for the long term variation of the C-14 level is not known. The variation is certainly partially the result of a change in the cosmic ray production rate of radiocarbon. The cosmic-ray flux, and hence the production rate of C-14, is a function not only of the solar activity but also of the magnetic dipole moment of the Earth. [4]

Oddly enough, Reference [4] above is Suess's work, cited by Libby in his Nobel Lecture. Once again, I smell quote mine, given that Libby explicitly stated above that Suess had engaged in active research involving tree rings along with de Vries, and had alighted experimentally upon past variations in tree rings that again, can be used to calibrate the dating technique.

Though complex, this history of the earth’s magnetic field agrees with Barnes’ basic hypothesis, that the field has always freely decayed.... The field has always been losing energy despite its variations, so it cannot be more than 10,000 years old. [5]

Reference [5] is from Russell Humphreys, the creationist who fiddled his zircon data to fit his creationist presuppositions, and is entirely specious. The TalkOrigins link I provided earlier dealing with Hovind's erection of the decaying magnetic field bullshit covers this base.

Earth’s magnetic field is fading. Today it is about 10 percent weaker than it was when German mathematician Carl Friedrich Gauss started keeping tabs on it in 1845, scientists say. [6]

Quote mine time!

Reference [6] is this news article. Which, when read in full, says something a little more sophisticated. Let's read on from that first paragraph shall we?

If the trend continues, the field may collapse altogether and then reverse. Compasses would point south instead of north.

Not surprisingly, Hollywood has already seized on this new twist in the natural-disaster genre. Last year Tinseltown released The Core, a film in which the collapse of Earth's magnetic field leads to massive electrical storms, blasts of solar radiation, and birds incapable of navigation.

Entertainment value aside, the portrayal wasn't accurate, according to scientists who say the phenomenon of Earth's fading magnetic field is no cause to worry.

"The field has reversed many times in the past, and life didn't stop," said Gary Glatzmaier, an earth scientist and magnetic field expert at the University of California, Santa Cruz.

Glatzmaier is keeping an eye on our planet's weakening magnetic field as he tries to learn more about how Earth's geodynamo works. The geodynamo is the mechanism that creates our planet's magnetic field, maintains it, and causes it to reverse.

Magnetic Shield

Earth's geodynamo creates a magnetic field that shields most of the habited parts of our planet from charged particles that come mostly from the sun. The field deflects the speeding particles toward Earth's Poles.

Without our planet's magnetic field, Earth would be subjected to more cosmic radiation. The increase could knock out power grids, scramble the communications systems on spacecraft, temporarily widen atmospheric ozone holes, and generate more aurora activity.

A number of Earth's creatures, including some birds, turtles, and bees, rely on Earth's magnetic field to navigate. The field is in constant flux, scientists say. But even without it, life on Earth will continue, researchers say.

"There are small fluctuations, which lead to nothing, and large ones, which we know from the geologic record are associated with reversals," said Peter Olson, a geophysicist at Johns Hopkins University in Baltimore, Maryland.

When molten lava erupts onto the Earth's crust and hardens, it preserves a snapshot of Earth's polarity, much in the way that iron filings on a piece of cardboard align themselves to the field of a magnet held beneath it.

According to Earth's geologic record, our planet's magnetic field flips, on average, about once every 200,000 years. The time between reversals varies widely, however. The last time Earth's magnetic field flipped was about 780,000 years ago.

Oh dear. So much for a 6,000 year old Earth.

Oh, and by the way, the scientist interviewed in that piece, namely Gary Glatzmeier, has a web page devoted to the geodynamo and fluctuating magnetic fields here. On that page, Glatzmeier describes a supercomputer geodynamo simulation spanning 300,000 years of Earth core activity.

If the production rate of 14C in the atmosphere was less in the past, dates given using the carbon-14 method would incorrectly assume that more 14C had decayed out of a specimen than what has actually occurred. This would result in giving older dates than the true age.

But when scientists have data from samples of known age with which to calibrate the dating technique, this isn't a problem! What part of this elementary notion are you too stupid to understand, or too duplicitous to present correctly?

What role might the Genesis Flood have played in the amount of carbon?

None. It never happened. Your "global flood" is a fantasy. next?

The Flood

Which never happened. The fact that my tropical fish are alive and happily swimming in my aquarium spawning fit to bust provides evidence that your fantasy flood never happened.

would have buried large amounts of carbon from living organisms (plant and animal) to form today’s fossil fuels (coal, oil, etc.).

Crap. Coal and oil take long periods of time to form. And yes, TalkOrigins deals with creationist canards surrounding that too.

The amount of fossil fuels indicates there must have been a vastly larger quantity of vegetation in existence prior to the Flood than exists today.

Crap. How come the strata that coal comes from are frequently Carboniferous strata? Which date back to 300 million years? Indeed, the Carboniferous Era was so named precisely because many of its strata are coal bearing strata.

This means that the biosphere just prior to the Flood might have had 500 times more carbon in living organisms than today.

That would be one fucking crowded biosphere. But then you're one of these people who thinks that Noah was herding fucking Sauropods aboard his wooden barge. Here's a clue: The Flintstones is not a documentary.

This would further dilute the amount of 14C

Except that your fantasy crowded biosphere never happened, along with your fantasy flood.

and cause the 14C/12C ratio to be much smaller than today.

Bollocks. Your fantasy flood never happened. Neither did your fantasy crowded biosphere 6,000 years ago.

If that were the case, and this C-14 were distributed uniformly throughout the biosphere, and the total amount of biosphere C were, for example, 500 times that of today’s world, the resulting C-14/C-12 ratio would be 1/500 of today’s level.... [7]

Oh dear. Not Baumgardner's wibble. Another discredited creationist fantasist.

When the Flood

Which never happened because it was a mythological fantasy ...

is taken into account

In other words, is assumed to have taken place regardless of the large body of evidence that says it never happened ...

along with the decay of the magnetic field

Which is also horseshit, as the scientist whose web page I linked to above will happily tell you ...

it is reasonable to believe that the assumption of equilibrium is a false assumption.

And as I've repeatedly told you above, IT DOESN'T FUCKING MATTER WHEN SCIENTISTS HAVE LARGE AMOUNTS OF DATA FROM OBJECTS OF KNOWN HISTORICAL AGE WITH WHICH TO CALIBRATE THE DATING TECHNIQUE! Are you fucking stupid or what?

In 1997 an eight-year research project was started to investigate the age of the earth. The group was called the RATE group (Radioisotopes and the Age of The Earth).

Oh, not THESE wankers!

A thread covering the lunacy that is RATE was launched over at the now defunct Richard Dawkins Forums, a thread containing a whopping 8,611 posts, that debunks every piece of Flood bullshit in existence. I have the thread archeved, all 345 pages of it, which I don't propose to reproduce here, because it would take this post to about 3 million words.

The team of scientists included:

Get ready folks, for the list of wankers!

Larry Vardiman, PhD Atmospheric Science

Who is an integral member of the so-called "Institute For Creation Research", set up by arch-charlatan Henry Morris, the individual who told us that when reality and doctrine differ, reality is wrong and doctrine is right.

Russell Humphreys, PhD Physics

Ah, the man who couldn't label his rocks correctly! And who fiddled his data to fit creationist presuppositions. That epic 345 page thread I cited above, involved much merriment on the subject of Russell Humphreys and his wankery ...

Eugene Chaffin, PhD Physics

Who?

John Baumgardner, PhD Geophysics

Ah yes, another discredited fantasist. This was the man who erected the "runaway subduction" bullshit.

Donald DeYoung, PhD Physics

Who?

Steven Austin, PhD Geology

Again, should I know this person?

Andrew Snelling, PhD Geology

Oh, not THIS wanker. A man who has demonstrably lied for doctrine.

Steven Boyd, PhD Hebraic and Cognate Studies

Er, why would a group investigating the validity of radionuclide physics in dating need someone studying Hebraic studies ... ??? Well we hardly need to ask what religious bias is going to be determining the outcome of this lot's wibblings, do we?

The objective was to gather data commonly ignored or censored by evolutionary standards of dating.

Oh look, it's the tinfoil hat conspiracy canard again. Not to mention the massive amounts of projection involved. Only last time I checked with the real world, the people doing the "censoring" of data that didn't conform to presuppositions were creationists.

The scientists reviewed the assumptions and procedures used in estimating the ages of rocks and fossils.

Except that there ARE no "assumptions". See above. We can all see where this is leading can't we boys and girls?

The results of the carbon-14 dating demonstrated serious problems for long geologic ages.

Oh really? I wonder what canards are to be erected here?

For example, a series of fossilized wood samples that conventionally have been dated according to their host strata to be from Tertiary to Permian (40-250 million years old) all yielded significant, detectable levels of carbon-14 that would conventionally equate to only 30,000-45,000 years “ages” for the original trees. [8]

Crap. Dealt with here. This was more of Snelling's lies for doctrine.

Similarly, a survey of the conventional radiocarbon journals resulted in more than forty examples of supposedly ancient organic materials, including limestones, that contained carbon-14, as reported by leading laboratories. [9]

Oh look, Reference [9] is another creationist screed. This is beginning to look tiresomely familiar.

Samples were then taken from ten different coal layers

Yawn. TalkOrigins dealt with the coal bullshit too. Here you go everyone.

that, according to evolutionists

Oh not THIS canard again. Do I have to repeat myself yet again about the "evolutionist" discoursive elision?

represent different time periods in the geologic column (Cenozoic, Mesozoic, and Paleozoic).

And of course, even by your own admission earlier, C14 dating would not be used for Palaeozoic material!

The RATE group obtained these ten coal samples from the U.S. Department of Energy Coal Sample Bank, from samples collected from major coalfields across the United States. The chosen coal samples, which dated millions to hundreds of millions of years old based on standard evolution time estimates, all contained measurable amounts of 14C.

Ever analysed coal properly? Only it has a habit of containing other substances apart from carbon. Such as radioactive minerals. Uranium and thorium being two that appear in coal. Indeed, one of the reasons that coal burning has been discouraged is because the ash resulting from coal burning contains measurable quantities of radium. Indeed, coal fly ash constitutes a higher level of radiation hazard than some nuclear materials used in nuclear medicine. Consequently, some of the carbon in that coal can absorb neutrons emitted by these heavy radionuclides. This has been known to scientists for some time.

In all cases, careful precautions were taken to eliminate any possibility of contamination from other sources.

A likely story given the track record of creationist "experiments".

Samples, in all three “time periods”, displayed significant amounts of 14C.

And we know why. Generation of C14 due to the coal being in proximity to radiogenic materials such as uranium and thorium. More on this here.

This is a significant discovery.

Bollocks. Scientists have known about this for some time.

Since the half-life of 14C is relatively short (5,730 years), there should be no detectable 14C left after about 100,000 years.

Only if the carbon hasn't been anywhere near any other radionuclides. If it's been anywhere near granite, for example, it'll be exposed to plenty of radionuclides.

The average 14C estimated age for all the layers from these three time periods was approximately 50,000 years.

So even though the samples contained C14 of radiogenic origin, the values obtained were still close to the upper limit for C14 dating. Quelle surprise. If the planet was only 6,000 years old, why didn't they yield dates of only 6,000 years? For that matter, why has NO other dating technique yielded this precise age as the upper limit for ANY analysed sample?

However, using a more realistic completely fabricated pre-Flood 14C/12C ratio

Translation: a completely fabricated value concocted to conform to mythological bollocks ...

There, fixed for you.

reduces that age to about 5,000 years.

In other words, fiddling the data to fit your presuppositions. Russell Humphreys was good at that. Zircons, anyone?

These results indicate that the entire geologic column is less than 100,000 years old—and could be much younger.

Crap. What about all the other dating techniques such as U-Pb and K-Ar, which yield no such results? I suppose you're going to "ignore and censor" those, are you?

This confirms the Bible and challenges the evolutionary idea of long geologic ages

Poppycock. If your book of myths was right, every dating technique should be yielding a maximum age of 6,000 years for every sample analysed. For that matter, there should not even exist varve counts going back more than 6,000 years, or ice core camples with terminal material older than 6,000 years. Varves from Lake Suigetsu in Japan have been counted back to 40,000 years, and ice cores from Greenland and Antarctica go back as far as 700,000 years. This material simply should not exist on a young Earth.

Because the lifetime of C-14 is so brief, these AMS [Accelerator Mass Spectrometer] measurements pose an obvious challenge to the standard geological timescale that assigns millions to hundreds of millions of years to this part of the rock layer. [10]

Crap. I see the above reference is to that creationist screed again. Quelle surprise.

Another noteworthy observation from the RATE group was the amount of 14]C found in diamonds.

Haven't I already dealt with this bullshit? Oh yes I did, near the top of my post, where I said this:

Oh, you're going to erect this specious canard again are you? The "radiocarbon in diamonds" canard has already been addressed. One source addressing this canard is this one.

Secular scientists

In other words, scientists who pay attention to reality instead of worthless mythological assertion.

have estimated the ages of diamonds to be millions to billions of years old using other radiometric dating methods. These methods are also based on questionable assumptions

Bullshit. Blind assertion and a blatant lie all in the one package.

and are discussed elsewhere [11].

And surprise, surprise, the reference is a creationist screed.

Because of their hardness, diamonds (the hardest known substance)

Actually, it's only the hardest known naturally occurring substance. Humans have since manufactured harder substances, such as Borazon.

are extremely resistant to contamination through chemical exchange.

The link I provided earlier with respect to diamonds covers the contamination issue a lot more thoroughly than your above bland statement.

Since diamonds are considered to be so old by evolutionary standards, finding any 14C in them would be strong support for a recent creation.

Not if they were either [1] contaminated, or [2] obtained from a source in close proximity to a source of radionuclides.

The RATE group analyzed twelve diamond samples for possible carbon-14 content. Similar to the coal results, all twelve diamond samples contained detectable, but lower levels of 14C. These findings are powerful evidence that coal and diamonds cannot be the millions or billions of years old that evolutionists claim.

Bullshit. Addressed in the page I linked to earlier.

Indeed, these RATE findings of detectable 14C in diamonds have been confirmed independently. [12]

And what does Mike Riddle call "independent confirmation" here?

Reference 12 is, wait for it:

M. Riddle. Does Radiometric Dating Prove The Earth Is Old? in K. A. Ham (Ed.), The New Answers Book, Master Books, Green Forest, Arkansas, pp 113-124, 2006

Oh look. Mike Riddle's idea of "independent confirmation" is an article he wrote himself in a book edited by Ken Ham. Such is the nature of creationist "peer review"!

Carbon-14 found in fossils at all layers of the geologic column, in coal and in diamonds, is evidence which confirms the biblical timescale of thousands of years and not billions.

Bollocks. See above.

Because of C-14’s short half-life, such a finding would argue that carbon and probably the entire physical earth as well must have a recent origin. [13]

Oh look, it's another quote mine!

Unfortunately I don't have institutional access to the paper in question, but those who have, can chase up this reference and determine how egregious a quote mine this is:

Use Of Natural Diamonds To Monitor 14C AMS Instrument Backgrounds by R. E. Taylor and J. Southon, Nuclear Instruments and Methods in Physics Research B, 259(1): 282-287 (June 2007).

All radiometric dating methods are based on assumptions about events that happened in the past.

Crap. Go and learn some real physics. Some of which I've provided above.

If the assumptions are accepted as true (as is typically done in the evolutionary dating processes)

Blatant misrepresentation of valid science, and a blatant lie. There are NO "assumptions" involved. I've dealt with this bullshit above, with respect to dating methods in general.

results can be biased toward a desired age.

And guess whose "results" are thus biased? Creationist results! Quelle surprise ...

In the reported ages given in textbooks and other journals, these evolutionary assumptions have not been questioned

Bollocks. There are NO "evolutionary assumptions" involved. Go and learn some physics, dickhead.

while results inconsistent with long ages have been censored.

Bullshit. If these results were "censored", how come they appear in the scientific literature? Including that paper by Taylor & Southon I've just cited above? What a tosser you are.

When the assumptions were evaluated and shown faulty, the results supported the biblical account of a global Flood and young earth.

Poppycock. Oh have I got a surprise coming for you any moment now ...

Christians should not be afraid of radiometric dating methods. Carbon-14 dating is really the friend of Christians, and it supports a young earth.

Poppycock. A Christian publication rejects RATE's nonsense wholesale. The relevant article can be found here, and makes interesting reading. The relevant publication is the journal Perspectives on Science and Christian Faith, March 2008, pages 35-39.

Here's the last paragraph of that article:

The RATE team has honestly acknowledged that even if their technical claims were accurate, there remain unsolved problems that cannot be reconciled with any known scientific process. In his summary at the RATE conference in Denver on Sept. 15, 2007, Don DeYoung noted the need to invoke divine intervention in order to circumvent these problems. However, the oft-stated summary by the RATE team, that their results provide assurance of the biblical interpretation of a young earth, leaves the average listener with the mistaken impression that these problems are nonexistent, trivial, or soon to be resolved. Rather, the RATE team acknowledged overwhelming evidence for hundreds of millions of year’s worth of radioactivity [12] and admitted that compressing this activity into a few thousand years would generate more than enough heat to vaporize all granitic rock. [13] They state that no known thermodynamic process could dissipate such a large amount of heat. [14] Their expressed hope in solving heat dissipation by cooling via enhanced cosmological expansion [15] has not been realized and is not consistent with our knowledge of the expanding universe. [16] Thus, the RATE team has provided solid evidence that, scientifically, the earth cannot be thousands but must be billions of years old.

Oh dear. Looks like your screed is busted, and busted by a christian writer. Savour the irony, everyone!

The RATE scientists are convinced that the popular idea attributed to geologist Charles Lyell from nearly two centuries ago, “The present is the key to the past,” is simply not valid for an earth history of millions or billions of years.

Heh, even other supernaturalists disagree with you, and with RATE's bullshit. See above.

An alternative interpretation of the carbon-14 data is that the earth experienced a global flood catastrophe which laid down most of the rock strata and fossils....

Bullshit. Your fantasy flood never happened. My tropical fish are laughing at you.

Whatever the source of the carbon-14, its presence in nearly every sample tested worldwide

What, 14 diamonds equals "nearly every sample tested worldwide"? This is hilarious ...

Oh, what about the millions of samples in which this hasn't been found to be the case? Or are those going to be "ignored and censored"?

is a strong challenge to an ancient age.

Crap. See above.

Carbon-14 data is now firmly on the side of the young-earth view of history. [14]

Bollocks. Got any more apologetic arse water like this?

So, we have an apologetic screed by Ken Hambone's website of lies and bullshit, which openly and egregiously lied about Willard Libby's contribution to the carbon-14 dating technique, duplicitously accused him of fabrication (a nice, legally actionable piece of defamation), while parading as "scientific", a discredited morass of creationist fabrication that was genuinely exposed as fabrication.

Looks like the only thing that can't be trusted here is creationist assertion.

Game over.