Proteins, DNA and RNA are extremely complex organic molecules that are essential for life.  These molecules could not have originated through evolution.  Natural selection requires living cells that are capable of replication, and living cells could not exist until these molecules were already in existence.[1]   The only alternative materialistic explanation is that these molecules must have originated by random molecular combinations, but when you do the math, it turns out that this is extremely unlikely—far less likely, in fact, than many things we regard as being impossible.
 

The Proteins Needed for Life.

Proteins, for example, consist of long chains of 400 or more amino acids in a specific sequence.  Each of the amino acids in the sequence is one of 20 different kinds, and if the sequence is altered slightly, the protein will not be functional.  Moreover, 19 of the 20 kinds of amino acids[2] come in two forms—a left-handed and a right-handed form—but living things consist only of left-handed molecules.  Outside of living things, amino acids occur only in a 50-50 ratio of right-handed and left-handed forms.  Even if we artificially create a sample where one form or the other predominates, the sample will, with time, return to a 50-50 ratio through a process called racemation.

The odds of 400 left-handed amino acids linking up by chance is less than (0.5)³⁸⁰, and, since the simplest cell would need over 120 proteins, the combined probability would be less than (0.5)^380x120 = 1.08x10^-13,727.  This is an impossibly small probability, and we have not yet accounted for the specific sequences of amino acids needed, which would reduce the probability far more.[3]

Now suppose that, once every nanosecond for 15 billion years, one billion attempts were being made in every cubic millimeter of seawater on a trillion trillion earthlike planets throughout the universe, to create these 120 proteins.  Would there be time enough to obtain this at least once?

Just do the math:  There are about 10²⁷ nanoseconds in 15 billion years.  Earth's oceans have a volume of approximately 1.3x10⁹ cubic kilometers, or 1.3x10²⁷ cubic millimeters.  For a trillion trillion similar planets, this would be 1.3x10⁵¹ cubic millimeters of ocean water.  If a billion attempts were made every nanosecond in each cubic millimeter of these oceans for 15 billion years, the total number of attempts would be about 6.15x10⁸⁶.  The probability of getting just one set of the needed proteins in all these attempts would be (6.15x10⁸⁶)(1.08x10^-13,727) = 6.64x10^-13,641, which hardly makes a dent in the original vanishingly tiny probability of forming the needed proteins.
 

Can We Improve the Odds?

Our assumptions are already unrealistically generous, but lets see how much we gain by pushing them way past the limits of credibility. A "googol" is the number written as 1 followed by 100 zeros—we write it in concise form as 10¹⁰⁰. Let's upsize each of our assumptions to a googol or so:

1) instead of 15 billion (1.5x10¹⁰) years, make it 1.5x10¹⁰⁰ years.
2) instead of a trillion trillion (10¹²x10¹²=10²⁴) earthlike planets, make it 10¹⁰⁰ earthlike planets.
3) instead of a billion (10⁹) attempts every nanosecond (10^-9 seconds) make it 10¹⁰⁰ attempts every 10^-100 seconds.
4) instead of a single universe, suppose this were occurring in 10¹⁰⁰ universes.

10^(100-10) = 10⁹⁰ to account for the increased number of years
10^(100-24) = 10⁷⁶ to account for the increased number of planets
10^(100-9) = 10⁹¹ to account for the increased number of attempts per nanosecond
10^(100-9) = 10⁹¹ to account for the increased sample rate (formerly nanoseconds)
10¹⁰⁰ to account for the increased number of universes

This increases our original number of attempts from 6.15x10⁸⁶ to 6.15x10⁵³⁴, and the probability of ever getting the needed proteins increases to a grand total of  6.64x10^-13,193. This is still vanishingly small, and to obtain such "favorable" odds, we had to make some ridiculously generous assumptions.
 

Winning the Lottery.

To put this in perspective, let's compare these odds with some that might be more familiar to us.  Suppose a lottery prints 100 million tickets, but only one of the tickets is the winning ticket.  Suppose you buy just one ticket.  What is the likelihood that you purchased the winning ticket?  The answer:  1 in 100 million, or 10^-8.

Now, suppose this continued every year for 50 years—each year 100 million tickets are printed, and only one of them is the winning ticket, and each year you buy only one ticket.  What would be the odds that you would hold the winning ticket year after year for 50 years in a row?  The answer:  10^-400.

Suppose now that it was not you, but your next door neighbor who keeps winning the lottery year after year after year.  The first year, you might think he was just the lucky guy who happened to buy the winning ticket.  But the second year, it's starting to look pretty fishy.  By the third year, the police are carrying him away on fraud charges.  If he kept winning 50 years in a row, no one would think that he's just a really lucky guy.  It is virtually certain that someone had been cheating.

There are some who argue in return that "Well, someone has to hold the winning ticket. Perhaps there are infinitely many universes, and our universe just happened to get the winning ticket."[4]

Like most naïve probability arguments, this one sounds pretty good if you haven't done the math.  Already, we have considered what the odds would be, given an unimaginably huge number (10¹⁰⁰) of universes of unrealistically long ages, churning away at unrealistically incredible speeds.  The improvement in probabilities doesn't even begin to show up on the radar!!

Besides this, there's no guarantee that any universe would have the "winning ticket", even if there did happen to be an infinite number of them.  To demonstrate this, I am thinking of an infinite set of numbers—what is the probability that one of the numbers in my set is equal to 1?

Well, actually, I was thinking of the set of even numbers.[5]   It contains infinitely many numbers, but it does not contain the number 1.  No member of my set holds the "winning ticket".  So much for the argument that, given an infinite number of universes, it is inevitable that one of them would produce life.

The atheist's rejoinder to this is "Well life exists—that proves that at least one universe held the winning ticket."  And, of course, it proves no such thing—one must adopt the atheist's presuppositions (i.e. that no deity exists who might have created life)—in order to conclude that there was a "winning ticket" and that our universe just got miraculously lucky and managed to beat the odds.

The reality is that the atheist believes in miracles but denies that there is a miracle-working God.  This truly requires a blind faith. The Christian God provides a rational basis for the origin of such complexity. The atheist's belief in random causes is pathetically inadequate to explain the origin of life.
 

We're just getting started.

So far, all we have is 120 chains of 400 left-handed amino acids. We don't yet have proteins—these amino acids need to be carefully sequenced in order to produce the specific proteins needed by a "simple" living cell.  It would not suffice to have 120 proteins all of the same kind, since different kinds of proteins fulfill different functions in the metabolism of a cell. We need 120 specific proteins, which means each of these proteins needs to have a specific sequence of amino acids.  The odds of randomly getting 120 proteins having just the right sequences is again so extremely unlikely as to be altogether impossible.

Okay, so for the sake of argument, suppose the impossible happened, and the correct 120 proteins somehow formed at the same time and all managed to come together in the same cell-sized droplet of organic soup.  We still would not have life.  We would also need …

• DNA—a molecule in the shape of a "double-helix" consisting of an extremely long sequence of base-pairs that encode the instructions needed to create a living cell.
• The correct instructions encoded in the DNA.  These instructions would need to contain volumes upon volumes of specialized information, describing how to build all the macro-molecular parts of the cell, how to sequence all the proteins and how to assemble these parts properly to form a living cell.
• RNA and other specialized molecules that 1) correctly decode the instructions in the DNA, and 2) follow these instructions to build a new cell.  In essence, this is a computerized factory made of extremely complex biological material.

All these separate parts and pieces—the 400 different kinds of proteins, the DNA with its pre-coded instructions, the RNA with its ability to decode and follow the instructions in the DNA, along with numerous other features—cannot just be dumped together.  They must be carefully assembled and interconnected in order to obtain a living cell—even the simplest living cell possible.

Truly, the odds of creating life by random molecular interactions over the life of the universe (or of a googol of universes, for that matter), may be considered totally impossible.  This fact has been acknowledged by evolutionists.  Marcel P. Schutzenberger, for example, said

... there is no chance (< 10^-1000) to see this mechanism [mutation-selection] appear spontaneously and, if it did, even less for it to remain...Thus, to conclude, we believe there is a considerable gap in the neo-Darwinian theory of evolution, and we believe this gap to be of such a nature that it cannot be bridged within the current conception of biology.[6]

It is our contention that if 'random' is given serious and crucial interpretation from a probabilistic point of view, the randomness postulate is highly implausible and that an adequate scientific theory of evolution must await the elucidation of new natural laws—physical, physico-chemical and biological.[7]

If there is any practical use for the word "impossible", surely it aptly describes the notion that all this complexity could ever have come into existence through random materialistic processes—no matter how much time, how many oceans or how many universes you throw at the problem.  If anything is impossible, this is it!
 

Footnotes.

[1] Theodosius Dobzhansky, a prominent evolutionist, stated:

"Natural selection is differential reproduction, organism perpetuation.  In order to have natural selection, you have to have self-reproduction or self-replication and at least two self-replicating units of entities ... I would like to plead with you, simply, please realize you cannot use the words 'natural selection' loosely.  Prebiological natural selection is a contradiction of terms."

T. Dobzhansky: The Origins of Prebiological Systems and their Molecular Matrices, Ed. S. W. Fox (New York, Academic Press, 1965), pp. 309, 310.

[2]  Of the 20 amino acids, glycine is the only exception.

[3]  Material in this paragraph is based on R. L. Wysong, The Creation-Evolution Controversy (Midland, MI, Inquiry Press, 1978), pp. 69-85.

[4]  It is ironic that atheists, who argue against the supernatural saying "You are only justified in believing what you can detect with your senses," will sometimes argue for "parallel universes" (for which they have no evidence) in order to explain away the impossible odds of forming life by random processes.  This demonstrates that atheism is a belief system and that it is self-contradictory—atheists violate their own arguments in order to defend their system.

[5]  There are infinitely many other examples that could be given.  For example, the set of all numbers larger than 100 would not contain the number 1.  Neither would the set of all numbers larger than 101, or 102, or 103, etc. If we allow fractions, then the set of numbers that lie between 2 and 3 is an infinite set, but these numbers are all larger than 1, so none of them holds the "winning ticket" either.

[6]  Marcel P. Schutzenberger, "Algorithms and the Neo-Darwinian Theory of Evolution", Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution (Philadelphia, Wistar Institute Press, 1967), p. 75.

[7] M. Eden: "Inadequacies of Neo-Darwinian Evolution as a Scientific Theory", Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution (Philadelphia, Wistar Institute Press, 1967), p. 109.