A number to remember

In order to probe the assumption that random mutations are the basis for, or a factor contributing to, the theory of evolution, some people have used the argument of complexity (irreducible complexity; specified complexity): That is, they describe organisms that are too complex for having evolved by chance, or through random mutations.

A simpler approach we can use is the argument of limited time: That is, we can investigate the structure of the simplest organism that could develop randomly in a limited amount of time.
Whether form the Cambrian explosion, or from the formation of the solar system, or from the "Big Bang", time is limited.

What is a reasonable amount of time required for a minimal micro-organism to develop?

We will assume here that our minimal organism could have an impossibly simple "body" made of a sequence of only ten chemical compounds (such as amino acids, carbohydrates, proteins and other compounds), where the chemical in each specific position is chosen among 100 possible compounds.

We are being very generous here in this assumption for the simplest viable micro-organism: In reality, a micro-organism body would be much more complex, as it would have to include its DNA, RNA, cell membranes and all that is needed for it to survive, grow and reproduce.

For example, the smallest known bacterium, mycoplasma genitalium, which incidentally needs a host body, has 300 essential genes in its DNA (See: "How Simple Is Life?" - Discover Magazine, http://discovermagazine.com/2001/apr/featsimple#.UqBhR9JDtCo) and each gene has its own specific chain of organic compounds.

We also assume that the required complex compounds, including organic compounds, somehow developed before our micro-organism.
Finally, we assume that all the required chemical compounds are present in the same location in the universe, at the same time and in the same mix of 100 compounds, so as to be immediately available to our micro-organism.

An analogy

To use an analogy most people can relate to, let us consider the 10-character word "impossible", with each character chosen among a possible set of 100 characters.

Standard keyboards of desktop PCs have 101 keys, so let’s imagine one key being disabled in our keyboard, to have a round number of 100 keys.

random key input

The probability that a monkey (or a random process), pounding on our keyboard, will come up with the word “impossible”, without counting the quotes and without using uppercase characters, can be calculated as follows:

The probability for the monkey (or a random process) to hit the first character, an “i” on our keyboard is 1 out of 100.

The probability for the first two characters (“im”) to be hit, in the proper sequence, is 1 out of 100 x 100, or 1 out of 100² (or 10,000 or 10⁴). The probability for all the 10 characters in the word “impossible” to be hit, in the proper sequence, is 1 out of 100¹⁰ (or 10²⁰).

This number, 10²⁰, is much bigger than the age of the universe in seconds.

Within the time elapsed from the Big Bang, a random process simulating a key being pressed on a standard keyboard once every tenth of a second and checking the results once a second, cannot likely compose one specific 10-letter word.

Conclusion

The 10-letter word is an analogy for our micro-organism made of a specific string of ten chemicals, where each chemical in the string is chosen among a set of only 100 possible compounds. Note that all these compounds would have to be present at the same point in spacetime - this by itself a very unlikely event.

While in the analogy there could be several 10-letter words that make sense, there would be only one minimal organism that could possibly develop as fast as required. That is, by assumption, other organisms would be more complex and less likely to randomly develop within the available time.

Our organism would have had to "replicate" once a second, have done so for 100 billion years to finally have a (hypothetically) functional body.

There wasn't enough time since the Big Bang for even one such organism to likely develop, randomly, anywhere in the universe. We are completely "out of the ball park": Not one, but billions of organisms would have to exist for billions of years in millions of planets for a few to have a chance at starting an evolutionary process.

Thus random processes cannot contribute towards explaining the theory evolution.

But if the theory of evolution is not based on random processes, what is it based on?

How did organisms evolve?

More than a century after the evolution theory has been largely accepted in scientific circles and even as it is taught in elementary schools, scientists cannot answer its fundamental questions, nor have they been able to prove its validity.