Permutations, Probability and the Existence of God

Photo courtesy Wikipedia

One evidence for the existence of God is the existence of life itself.

The popular scientific theory (which is taught in schools) that life happened by accident is widely professed by scientists, professors, etc. But strictly by the numbers, the probability of the existence of life in the entire universe is extremely low. In fact it would be crazy to think of it as anything but a miracle. I will attempt to show a short proof in the following article.

To understand the argument we need to cover some definitions:

Probability

Example:

Let's say we have a dice with six sides numbered one through six.
What is the probability that you will roll a "1"?
The answer is 1/6 or 16.67%.
 
The formula:

Probability　＝	Number of things that actually occur
	Number of things that are possible

Permutation

Example:

Let's say you have two six-sided die. What are all the possible permutations for rolling the dice where order matters (e.g. 2,1 is considered distinct from 1,2)?

1,1	1,2	1,3	1,4	1,5	1,6
2,1	2,2	2,3	2,4	2,5	2,6
3,1	3,2	3,3	3,4	3,5	3,6
4,1	4,2	4,3	4,4	1,5	4,6
5,1	5,2	5,3	5,4	5,5	5,6
6,1	6,2	6,3	6,4	6,5	6,6

There are 36 or 6² possible unique orderings or permutations.

What if we add a third die?

1,1,1
1,1,2
1,1,3
. . .
6,6,4
6,6,5
6,6,6

There are 216 or 6³ possible orderings or permutations.

Here's the formula:

Permutations in an ordered set = n^m
Where n is the number of possible values per element.
Where m is the number of elements in the set.

Putting Permutations and Probabilities Together

We can answer some interesting questions using permutations and probabilities.

Example:

What's the probability of picking 6 random letters from the alphabet; say from 6 bags with letter tokens; and randomly spelling the word CHEESE?

First, we calculate the number of possible outcomes:

26⁶ = 308,915,776

Next write down the number of correct outcomes; There's only one way to spell CHEESE that I know of.

Finally, calculate the probability:

1/308,915,776

Supposing you could draw and test the 6 letters once per second. How long could it take you to randomly draw and spell the word cheese correctly under these terms?

It could take: 308,915,776 / (60x60x24x365.25) = 9 years, 288 days

DNA is necessary for life

DNA is like a blueprint for a plant or an animal. If DNA base pairs are not in the correct sequence, it cannot be used to create life. In this light, it is safe to say that one of a number of correct sequences is necessary for life as we know it.

Below is a partial breakout of the human genome that I got from wikipedia.
http://en.wikipedia.org/wiki/Human_genome

Chromo-some	Length (mm)	Base Pairs	Valid Variations
1	85	249,250,621	4,401,091
2	83	243,199,373	4,607,702
3	67	198,022,430	3,894,345
4	65	191,154,276	3,673,892
5	62	180,915,260	3,436,667
6	58	171,115,067	3,360,890
7	54	159,138,663	3,045,992
8	50	146,364,022	2,890,692
9	48	141,213,431	2,581,827
10	46	135,534,747	2,609,802
11	46	135,006,516	2,607,254
12	45	133,851,895	2,482,194
13	39	115,169,878	1,814,242
14	36	107,349,540	1,712,799
15	35	102,531,392	1,577,346
16	31	90,354,753	1,747,136
17	28	81,195,210	1,491,841
18	27	78,077,248	1,448,602
19	20	59,128,983	1,171,356
20	21	63,025,520	1,206,753
21	16	48,129,895	787,784
22	17	51,304,566	745,778
X	53	155,270,560	2,174,952
Y	20	59,373,566	286,812
mtDNA	0.0054	16,569	929

Each DNA strand is made up of 4 base-pairs, which can be put in any order, although there are specific rules such as each chromosome is made up of some number of genes, each gene is made up of a sequence of proteins which are made of sequences of base pairs. The gene is typically ordered with a protein called a "start codon" and ends with a "stop codon". There are a lot of other details which won't be covered here. but needless to say, DNA sequencing is pretty complex and specific.

So if I was to test the probability of finding a correctly ordered sequence for say, chromosome #22 "at random" I would proceed as follows:

First, calculate the number of possible combinations of base pairs:

4^51,304,566 = 3.6395x10^30,888,426

Now take the number of valid sequences and divide by the possible values to get the probability:

745,788 / 3.6395x10^30,888,426 = 2.0491x10^-30,888,421

This number is so small as to be unfathomable by the human mind. Happening upon even one sequence of this size in the correct order, is in and of itself a miracle.

A Simple Proof that Life is not an Accident

But we're talking about life, not evolution right? Nobody's saying that man "suddenly appeared". You're jumping the gun. Right. So after the "big bang", these things are supposed to have happened "very slowly" over a long, long period of time. Plus there are zillions of stars and planets in the universe, life was bound to happen on one of them eventually... Right? Right? Let's consider this point of view.

According to wikipedia, the smallest known cellular organism (as far as DNA goes) is Candidatus Carsonella ruddii, with only 160,000 base pairs. But scientists also lean toward the possibility of much smaller organisms as the first form of life. The smallest known quasi-living things are called circoviruses, which apparently can have as little as 2,000 base pairs. Whether they are alive is debatable, but for this argument, to make it interesting, we'll base our proof on a tiny DNA sequence like that of the circovirus.

Many theories base the origin of life on having the right ingredients in the right place at the right time and then adding energy in the form of electricity such as lightning, or direct sunlight, or thermal energy. Many experiments have been done with ambiguous results. For our approach we don't care where the ingredients or the energy comes from just that the perfect and ideal conditions already exist.

Modern estimates put the number of planets in the universe to about 10²⁴, but for argument's sake, let's say you have 1 centillion (10³⁰³) planets in the universe. Additionally, let's say that you have 1 centillion "hot-spots" on each planet already with DNA particles in place, energy, etc., simultaneously trying 1 centillion DNA permutations per second. Furthermore, the only goal you have is to produce one circovirus DNA set with 2,000 correctly-ordered base pairs.

The math looks like this:

4²⁰⁰⁰ (possible base pair permutations) / [10³⁰³ (planets) ｘ 10³⁰³ (hot spots) ｘ 365.25x24x60x60 (seconds/year) ｘ 10³⁰³ (permutations per second) ] = 4.144x10²⁸⁷ years

Given that the current estimated age of the universe is 13 billion (1.3x10¹⁰) years, even with the insanely contrived conditions I just proposed, the universe isn't remotely old enough to have "spontaneously" produced life in this manner. So, unless you believe in miracles it is very, very, very (add about 10²⁸⁷ "very"s here) unlikely that DNA-based life could have spontaneously occurred in our universe.

There is also one very important point I haven't made yet. Assuming that somehow all of the right ingredients for DNA landed in the right place at the right time (however improbable), AND in the perfect environment (nutrients, heat, moisture, etc.) AND all of the DNA sequences just happen to be in the correct order (very unlikely, refer to the treatment above); Even if you had ALL that, can you really say that life would occur? Would a million lightning bolts be enough to do it?

In other words, without God, the chance that life has occurred "by chance" is ludicrous.