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In various forms, the probability argument against the randomness of Darwinism—in which odds are computed or estimated—has been made by many different scientists since Darwinism was first proposed. One way to make the probability argument is to use the known structure of major organic molecules such as DNA and protein., For example, the probability p of getting in one trial an exact sequence of N links, when there are C different equally likely choices for each link, is:
Applying this equation to DNA, where C is 4—or to protein, where C is 20—quickly gives infinitesimally small values of p as N increases. For example, consider the DNA needs of the first self-reproducing bacterium (until self-reproduction enters the picture, Darwinian natural selection has nothing to work with). In an effort to raise p: assume that the DNA needed to code the bacterium is only 10,000 links (this is enough to code a small number of proteins, totaling about 3,300 protein links); assume that at any DNA link, any two of the four bases will be adequate in coding the DNA for that link, because, presumably, there are many DNA sequences for our 10,000-link DNA that would adequately code a usable set of proteins for the first self-reproducing bacterium (this assumption lowers C from 4 to 2); assume that the number of trials done, which is multiplied by p, is a million trials per second (106) for the estimated age of our Milky Way galaxy (15 billion years is roughly 1018 seconds) for each elementary physical particle in the visible universe (estimated by physicists at roughly 1080 particles); and assume that nothing else is needed, other than this DNA strand, to make the first self-reproducing bacterium (a very generous, albeit ridiculous assumption). With these assumptions the probability of the first bacterium arising by chance is:
||×106 ×1018 ×1080 ≈ 10–2,906|
In other words, the odds are roughly 102,906 to one, against.
 Each molecule of DNA is a long molecule composed of chemical units called bases. These bases are strung together like links on a chain. There are four bases. Thus, there are four choices for each link.
The sequence of bases in an organism’s DNA is very important, because this sequence is the means by which DNA stores information, which is known to include the structure of individual proteins. A bacterium—the simplest organic life that can reproduce itself without the need to parasitize other cells—typically has many strands of DNA, containing altogether hundreds of thousands or millions of bases.
 A protein is a long folded molecule. Just as DNA is composed of a sequence of smaller building blocks, so is protein. However, whereas the building blocks of DNA are four different bases, the building blocks of protein are twenty different amino acids. Although a protein has more choices per link, a protein rarely exceeds several thousand links in length.
A bacterium has several thousand different proteins. The average length of these different proteins is somewhere in the hundreds of links.
 Any self-reproducing machine in the physical universe must meet certain theoretical requirements. A self-reproducing machine must have a wall to protect and hold together its contents. Behind this wall the self-reproducing machine needs a power plant to run its machinery, including machinery to bring in raw materials from outside the wall. Also, machinery is needed to transform the raw materials into the components needed to build a copy of the self-reproducing machine. And machinery is needed to assemble these components.
All this transport, transformation, and assembly machinery, requires a guidance mechanism. For example, there must be some coordinated assembly of the manufactured components into the new copy of the self-reproducing machine. Thus, the guidance mechanism cannot be too trivial, because its complexity must include a construction plan for the entire self-reproducing machine.
The requirements of a wall, power plant, transport machinery, transformation machinery, assembly machinery, and a guidance mechanism—all working together to cause self-reproduction—are not easily met. Consider the fact that there are no man-made self-reproducing machines.