# Faith and Reason: Existence and Uniqueness

## Existence and Uniqueness

This Faith and Reason video presents an argument for the existence of God that is like no other. Here, I employ statistical methods, like those used for scientific evidence, to establish the existence of God with a 5 sigma level of significance, using four separate measures.

To begin, we shouild note that the **Bell Curve** arises naturally whenever a myriad of factors is summed; this is illustrated in the video with the sum of three dice. This fact is known as **The Central Limit Theorem**, and it is a fundamental result in statistics. It explains why Bell Curve distributions arise almost everywhere in nature. The Central Limit Theorem justifies why the Bell Curve is used so often in statistics and why it makes sense to use it here.

Every Bell Curve can be specified by two parameters: **mean** and **standard deviation**. The mean is the average value, and it lies at the center of the Bell Curve. A change in the mean translates the distribution horizontally. The standard deviation describes how spread out the values are. Varying the standard deviation changes the width of the distribution.

The mean and standard deviation are represented by the Greek letters mu and sigma, respectively. Sigma is used to measure distance from the mean as well as the width of the curve. This is convenient since sigma captures the probabilities of the curve perfectly. For example, the region that is 2 sigmas above the mean is approximately 2 percent. So, the chance of getting a value that is 2 sigmas above the mean is about 1 in 50.

The chance of getting a value that is **3 sigmas** above the mean is about 1 in 741. The chance of getting a value that is **5 sigmas** above the mean is about 1 in 3.5 million. A result in the 3 sigma range is called "Evidence" in science, while a result in the 5 sigma range is called an "Observation" in science.

Incidentally, 5 sigma is the level that was used to determine the recent observation of the Higgs Boson. Note that there was no direct evidence for the Higgs Boson. That is, the particle was not observed directly, rather the particles that are thought to result from its decay were observed instead. A recent YouTube video from Fermilab explains 5 sigma and the discovery of the Higgs Boson; it influenced my thinking in this video.

Much like the Higgs Boson, which is sometimes called the "God Particle," God is never directly observed either. However, like the decaying particles, we can detect the presence of God in the World via his influence. To this end, I present four measures by which God may be observed at the 5 sigma level or beyond.

### Measures of God's Influence

- Number ofAdherents
- Length of Belief
- Length of Empire
- Book Sales

The first two measures compare the God Abraham to the gods of other religions. The last two compare the God of Abraham to secular entities. These form the measures of uniqueness and existence for which this video is named.

First, we look at the number of adherents. Using statistics from the 2010 CIA World Book, we have that 33.3% of the World is Christian and 21% is Muslim. Together they sum to 54% and represent the largest group of worshippers for any god in the World. Much of the rest of the world worships a variety of gods or none whatsoever.

In the video, I have given two sets of numbers: One that is realistic and another which is a gross overestimation. For the realistic numbers, we have a mean of 5 million and a standard deviation of 1 million. With this, the God of Abraham is an astronomical 3000 sigma above the mean. For the gross overestimate, we have a mean to 1.5 billion and a standard deviation of 300 million. Even with this, the God of Abraham is more than 5 sigma above the mean.

For the length of belief, we have roughly 3000 years since the Bible was written and people began to worship the God of Abraham. Most other religions, like that of Greek Mythology, have arisen dissolved with their respective empires. For this, I first set mu to 500 years and sigma to 100 years to estimate that God is 25 sigmas above the mean. In the second case, I uesd the large overestimate of mu as 1500 years and sigma as 300 years to get that God is beyond the 5 sigma level.

The length of empires is a comparison to secular entities. For this, the only sensible comparison is the Catholic Church, which has a line of succession 266 rulers long, beginning with St Peter and continuing through the recently elected Pope Francis. In the secular realm, we have the Roman Empire, the Greeks, the British, etc. This comparison was inspired by Father Robert Barron's Catholicism Series, where toward the end of the first episode he gives a brilliant reminder of how the Catholic Church has outlasted the Roman Empire.

Most of the world empires have lasted much less than a thousand years, while the Catholic Church is approximately 2000 years old and still going. For numbers, I gave a mean of 1000 years and a standard deviation of 200 years, if we include only the successful empires. If we include the less successful ones, then we have a mean of 500 years and a standard deviation of 300 years. Eiter way, the Catholic Church is beyond the 5 sigma level.

For the last comparison, I used a list of book sales in the last fifty years that was compiled by James Chapman. Here, the Bible is given to have 3.9 billion in sales. Realistically, there is no way to get anywhere near 5 sigma. So, I used the obvious overestimate of 150 million as the mean and 25 million as the standard deviation. In this case, the Bible is still 150 sigmas above the mean. Of course, this mean is larger than all but three of the books on the list. So, it is an enormous overestimate.

All of these statistics could reasonably be tested with greater accuracy, but suffice it to say that my overestimates will hold in any case. The longevity of belief and the Church, along with the widespread influence that I have shown, serve to underscore the eternal and omnipotent nature of God. All of that is measurable.