“Show Your Work!” Do you remember seeing those words at the top of an exam? It was not enough to give an answer, even the right answer. You had to show how you arrived at your conclusion. This demand to show your work wasn’t just true in subjects like math or physics where there is only one right answer, it was also there for essays. You were told to take a position on an issue and then provide sound reasoning for your stance. And if you wanted to do well on the writing portion of a college entrance exam, “showing your work” was imperative.
I wonder, however, how many have ever shown their work regarding the question of God. When I say God I mean an eternal Creator who has revealed who he is, called us to walk in his way, and will judge us according to our response to him. The question is: do you believe such a God exists? Many today enthusiastically raise their hand to answer, and do so with an emphatic yes or no. But my question is can they show their work. Do you they have sound reasons for their position? Do you?
If the question at hand were relative to whether Nike shoes were better than New Balance, the inability to show one’s work could be dismissed. The consequences of one’s position on the shoe matter are minimal at most, and, furthermore, one can hardly be expected to maintain a well thought out answer to all of life’s mundane questions. But the question of God, at least as I have presented it, is not of an inconsequential nature. If there is a God who will indeed judge us for the way we respond to his self-revelation, then we ignore him at a great price. If there is not such a God, we can go on our merry way.
Showing our work can be a bit trickier than we think regardless of where we stand on the question of God. I say this because our first response may be to provide reasons why we want God to exist or not to exist, but wanting something to be true falls short of supporting its validity. Thomas Nagel, prominent atheist philosopher, writes: “I hope there is no God! I don’t want there to be a God; I don’t want the universe to be like that.”  Sorry, Dr. Nagel, but dismissing God based on your personal desire wouldn’t fare too well on an exam. On the other hand, a died-in-the-wool believer might say something like, “I don’t know what I would do without my belief in God.” That might be so, but could not a child with an imaginary friend say the same thing about that which we know is not real?
These days, it seems like most people are pretty firm on their answer concerning God. They even proudly raise the flag for one side of the question or the other. I don’t decry that. I like it when people have a strong sense of what they believe. But it’s hard to take people too seriously if they can’t show their work.
 Thomas Nagel, The Last Word (Oxford University Press, 1997), 130.
This month my oldest son graduates from Princeton University in Mathematics. This is written in honor of him, albeit it does not contain anything near the math that he works with.
Proponents of Darwinian evolution generally argue that at some point in the universe’s history inorganic matter combined in such a way as to create amino acids which in turn created proteins to allow for the development of the universe’s first cell. From this original cell, reproduction occurred and over time mutations and natural selection brought about the biological world as we now know it.
Mathematics would suggest, however, that believing in such a chain of events is simply not plausible. In fact, so implausible is such a scenario that if one were to stake their belief in the origins of life on such, it is quite certain that she would also have to believe any assertion put forward throughout history. Let me explain.
The living cell is made up of whole host of parts. Among these are DNA, RNA, amino acids, and proteins. Proteins have very specific functions in the cell and must be made by an exact combination of amino acids. This exact combination is guided by a very specific sequencing of the bases in the DNA, which is then transcribed by the RNA, so that protein development can occur.
The number of amino acids used to build even a simple protein is significant (about 150) and these amino acids must be in a perfect sequence in order for a protein to become functional. In a series of articles published between 1996 and 2004 in the Journal of Molecular Biology, Biochemistry and the Proceedings of the National Academy of Sciences, Douglas Axe was able to substantiate the odds of such sequencing at 1 in 10^74.
Compounding these odds is the unlikelihood of only peptide bonds occurring between the amino acids and of the amino acids all being of the “left handed” variety (all of which is necessary for the process to work). The odds of each of these two factors occurring are each 1 in 10^45. All together then the odds of amino acids creating a simple protein are 1 in 10^45+45+74, or 1 in 10^164. To give a sense of just how large this number is, consider that there are only 10^80 elementary particles in the universe. This means that you would have a trillion, trillion, trillion, trillion, trillion, trillion, trillion, trillion greater chance of picking a single lottery-winning atom in the universe than you would of seeing amino acids form a single protein.
Now as fantastic as those odds are, we are only just beginning. The simplest cell needs about 250 different kinds of proteins to carry out its functions. This means that one must take the number 10^164 and multiply it by itself 250 times in order to calculate the odds of a single cell coming into existence, which when completed amounts to 10^41000. Remember there are only 10^80 elementary particles in the universe, making the odds of 1 in 10^41000 unfathomable.
It’s at this juncture in the argument that proponents of evolution often argued that given the age of the universe there are so many opportunities for amino acids to combine in just the right order that the odds of 1 in 10^41000 really aren’t that insurmountable. But let’s see if that is the case.
According to physicists the transition of physical entities from one state to another can only happen so fast. That is, transitions cannot happen any faster than light can travel through the so-called Planck length of 1/10^33 centimeters. Given the speed of light and the gravitational constant, the shortest time in which any physical effect can occur is a mere 1/10^43 of a second.
Considering that we have a good idea of the number of particles in the universe (10^80), the amount of time since the Big Bang (10^18 seconds) and the number of possible interactions per second (10^43), it is easy to calculate the number of possible interactions that could have taken place since the creation of the universe: 10^80+18+43, or 10^141.
So then, let’s put our two numbers together. The number of possible interactions in the universe is 10^141 while the odds of a single cell coming into existence are 10^41000. That means that even though there have been a huge number of chances for interaction among particles since the universe began, the odds of a single cell coming into existence by chance is still only 1 in 10^41000-141, or 1 in 10^40859. These kinds of odds, of course, still make the belief in an evolutionary process rather ridiculous as it calls us to believe in something as “fact” that only has a 1 in 10^40859 chance of having even started.
But that is not the whole story. In calculating the odds of 1 in 10^40859 of a single cell coming into existence, we made a lot of assumptions. And these assumptions would stretch the odds even more that evolution is responsible for the biological diversity we have today, as well as the existence of humans. These assumptions include the idea that at every possible expanse of time in the universe in which interaction between elements could have taken place all of the elements in the universe were indeed interacting with one another. They also include the idea that none of the combination of elements along the way would be harmful to the single cell that was produced or that chemistry could actually take place at a speed approaching Plank-time. Or consider the assumption that the atmospheric conditions of the universe were even conducive to creating a single amino acid in the first place. Contrary to the much touted Miller-Urey experiment, the Earth’s early atmosphere simply does not give us confidence that many if any amino acids could have randomly been created in the first place. Furthermore, while the odds of a single cell coming into being are truly absurd, they only account for the development of a single cell. What then are the odds that from that single cell all of today’s complex plant, animal, and human life evolve in the relatively short life of the Earth?
I wonder what your reaction is to all this math. I find that it saddens me. It saddens me because it reveals the lengths to which people will go to deny the reality of a supreme intelligent being. For over a century now our children have been forced to learn that the best explanation (indeed the only “factual” and “scientific” explanation) for the origin of life is one that at best has only less than a 1 in 10^40859 of being possible. To understand the utter ridiculousness of this sort of education, consider what would happen if every theory and idea we thrust upon our children only needed to have a similar probability of being right. No doubt we would be forced to teach our kids that that Ronald Reagan was a myth, that grizzly bears once lived on the moon, and that you only imagined that you read this even though you think you did.
Please understand that what these numbers imply is not a new finding. Within little more than a decade of the discovery of DNA, the world’s best mathematicians, engineers, and physicists recognized the outrageous odds of random chemical activity generating the biological information needed for life. In 1966, many of them met at the Wistar Institute in Philadelphia to discuss the problem. The conference was titled “Mathematical Challenges to Neo-Darwinism” and there it was recognized that because of the sheer number of possible bases and amino acids the random formation of a new gene or protein is not plausible. As the decades have gone by there has been nothing new discovered that would give reasons to throw out their conclusion. In fact, the more we know about DNA and cellular activity, the more certain one can be that the odds of life by chance is not even worthy of a moment’s consideration.
All of this explains why we are now being told to believe in multiple universe. Any scientist worth her salt knows that the only way to give evolution a reasonable chance is to come with more rolls of the dice so that the impossible odds of evolution aren’t so impossible. Thus, rather than casting aside evolution as a viable theory, proponents of evolution have come up with a multiverse theory, in which an infinitude of universes is proposed. This despite the fact there is no evidence of any other universes, nor is it plausible to imagine accessing knowledge about any of them. By adding universes, scientists then say, “We just happen to be in the universe where the dice were rolled in a perfect way, but considering all the universes, we could expect this to happen in at least one universe.” Can you imagine if we allowed such poorly supported theorizing to influence our courts of law? Let’s suppose a man is caught in the act of bludgeoning his wife with a club. His fingerprints are all over the club. Her blood is all over him, and the camera in the building recorded his violent act. In court, however, he argues that we live in the one universe where it only looks like he killed his wife and the evidence for his crime is illusory. Of course, acceptance of his alibi by our courts would be preposterous. And if it is considered preposterous, should not looking to multiverses as the alibi for Earth’s biological diversity be equally preposterous?
One might ask, “If the theory of evolution is so extraordinarily tenuous, why does anyone believe it?” I think there are two answers to this question. First, there are those who refuse to consider any other options. To do so would open up the door for the Divine, and this is not acceptable. As atheist Harvard biologist, Richard Lewontin, wrote:
We take the side of science in spite of the patent absurdity of some of its constructs, in spite of its failure to fulfill many of its extravagant promises of health and life, in spite of the tolerance of the scientific community for unsubstantiated just-so stories, because we have an a priori commitment, a commitment to materialism. It is not that the methods and institutions of science somehow compel us to accept a material explanation of the phenomenal world, but, on the contrary, that we are forced by our a priori adherence to material causes to create an apparatus of investigation and a set of concepts that produce material explanations, no matter how counter-intuitive, no matter how mystifying to the uninitiated. Moreover, that materialism is absolute, for we cannot allow a Divine Foot in the door.
Secondly, such an effort has been made by those who control the educational process to indoctrinate students from the youngest ages that for many the evolutionary explanation of Earth’s biological diversity has become a foregone conclusion without any real examination of the evidence. While a look at mathematics does not bode well for evolution, it is hardly the only damning evidence. One simply has to look at the fossil record to see a lack of transitional life forms and an explosion of phyla in a very short-period of time, the absence of a conducive “pre-biotic soup,” or the existence of human consciousness to recognize that something is seriously amiss with the theory of evolution regardless of the numbers.
© 2016 John Hopper
 Much of the scientific information in this article is from Stephen C. Meyers’ Signature in the Cell, chapters 9 & 10.
 Chemistry can't happen faster than atoms can move. Hydrogen is the most massive and fastest of the atoms. Since the vibrational frequency of a hydrogen molecule (which is made up of two hydrogen atoms) is only 1/10^14 seconds, it is probably safe to assume that the smallest period of time in which a chemical event could take place is not Planck time (1/10^43) but 1/10^14 seconds. This means that the number of possible interactions that could have taken place since the creation of the universe should probably only be 10^80+18+14, or 10^112, which further decreases the possibility of the evolutionary process beginning by giving less “rolls of the dice” so to speak. For the sake of simplicity, however, and to give evolution the best chance at happening, I stuck with Plank time in this argument.
 Richard C. Lewontin, “Billions and Billions of Demons,” The New York Review of Books (July 9, 1997).
 See, for example, Sarah Chafee, “Evolution in Kindergarten,” Evolution News & Views (April 16, 2016).
John likes to help people wrestle with the big questions of life in his work with Search Ministries. He served as a pastor in Houston for 16 years, earned his doctorate at Biola University, and is a contributing author of Reasons to Believe: Thoughtful Responses to Life’s Toughest Questions.