Friday, September 19, 2008

God & #’s

Once upon a time in the not too distant past, I had an atheist yell out, "Math rocks!!" while in his imagination he "refuted" something or other that I had written. Well, he's right, mathematics does rock; a mathematically precise universe even more so. While I enjoy philosophy and theology much much more, let's give math a go.

While admitting to the fact of our universe’s precise set of values, Bertrand Russel and like minded atheists claim that the constants and quantities that we observe were not made for us but that we adapted to and evolved “from” them. Let’s see. There are three numbers in particular that suggest atheists might be wrong about this. They are 1/10 to the power of 10 times(123), 10(162), and eπpi.
(Stupid blog - I can't even write these properly)

Oh well. The first number that Christians say points to God is 1 in 10 to the 10 to the 123. This number comes from astronomy. Oxford professor Roger Penrose discusses it in his book The Large, the Small, and the Human Mind. It derives from a formula by Jacob Beckenstein and Stephen Hawking and describes the chances of our universe being created at random. Penrose spoofs this view by picturing God throwing a dart at all the possible space-time continua and hitting the universe we inhabit. The Beckenstein-Hawking formula is too complicated to discuss here, but another approach to the same problem involves a Secular, Scientific term that atheists are coming to detest - the fine-tuning of the universe - and the existence of habitable planets.

The fine-tuning of the universe is shown in the precise strengths of four of roughly 50 basic forces.
. Gravity is the best known of these forces and is the weakest, with a relative strength of 1.
. Next comes the weak nuclear force that holds the neutron together. It is 10(34) times stronger than gravity but works only at subatomic distances.
. Electromagnetism is 1,000 times stronger than the weak nuclear force, and
. The Strong nuclear force, which keeps protons together in the nucleus of an atom, is 100 times stronger yet.
If even one of these forces had a slightly different strength, the life-sustaining universe we know would be impossible.

If gravity were slightly stronger, all stars would be large, like the ones that produce iron and other heavier elements, but they would burn out too rapidly for the development of life. On the other hand, if gravity were weaker, the stars would endure, but none would produce the heavier elements necessary to form planets.
The weak nuclear force controls the decay of neutrons. If it were stronger, neutrons would decay more rapidly, and there would be nothing in the universe but hydrogen. However, if this force were weaker, all the hydrogen would turn into helium and other elements.

The electromagnetic force binds atoms to one another to form molecules. If it were either weaker or stronger, no chemical bonds would form, so no life could exist.
Finally, the strong nuclear force overcomes the electromagnetic force and allows the atomic nucleus to exist. Like the weak nuclear force, changing it would produce a universe with only hydrogen or with no hydrogen.

In sum, without planets, hydrogen, and chemical bonds, there would be no life as we know it.

Besides these 4 factors, there are at least 45 others that require pinpoint precision to produce a universe that contains life. Getting each of them exactly right suggests the presence of an Intelligent Designer. Not to atheists mind you, but . . .

The second component to be considered when calculating the likelihood of this life-supporting universe is the presence of habitable planets. In addition to the fine-tuning of the whole universe, there needs to be a carefully specified place where life can reside. Life as we know it can only exist within certain limits. There are at least 45 parameters, from the size of our galaxy to the mass of the moon, which permit the presence of life on a planet. A huge galaxy erupts with too many stars and thus disturbs planetary orbits, but a tiny galaxy does not produce enough heavy elements for a planet to form. At the other end of the spectrum, too large a moon destabilizes a planet's orbit, while having no moon or one that is too small permits a planet to wobble as it spins and disrupts the planet's climate.

From these 45 planetary characteristics alone, Hugh Ross, in his chapter in Mere Creation, calculates there is less than 1 chance in 10(69) of habitable planets occurring at random. This is not a “religious” calculation but one that comes from the scientific field of probabilities. This is just one of the areas where atheists seem to arbitrarily ignore answers from science when they point in the wrong direction.

The fine-tuning of the four physical forces and the presence of one habitable planet are just two of the components that would go into a formula to predict the probability of a life-supporting universe. The first one to try to calculate this number was Frank Drake in 1961, when he listed fewer than ten factors. Coming at the same problem from a different direction by calculating the entropy of black holes, Penrose says the number is 1 in 10 to the 10 to the 123. This number is beyond human comprehension. 10 to the 10 to the 3 would be written as 10 followed by 999 zeros.
To write 10 to the 10 to the 123 in one line would extend beyond the bounds of the universe. If Penrose is right in calculating the odds of a life-supporting universe at 1 in 10 to the 10 to the 123, then a strong case for a Creator emerges. Not to atheists mind you, but . . .

The second number that points to God comes from the field of biology. William Dembski, in The Creation Hypothesis, suggests the following argument.
Darwin thought that all life, including humans, arose from a one-celled organism. Of course, at the time, Darwin didn’t know that that first cell had to come pre-loaded with DNA / RNA. Today’s atheists know this but this is another set of scientific information that they chose to ignore.

Regardless, to get from a one-celled organism to a human being with at least a trillion cells, there would have to be many changes. Daniel Dennett says that mutations don’t occur even once in a trillion “copyings.” And to get from one cell to us, we need not just any mutation but only helpful mutations which are so rare, especially outside the lab as to be nonexistent. However, with nothing but good judgment holding them back and projecting backward, atheists first point to Us and say, “See, we have evidence that helpful mutations must have occurred frequently, trillions upon trillions upon trillions of times over.”

Darwin says these changes were produced at random, but they would have had to occur in the right order. It doesn't do any good to give an organism a leg until it has a nervous system to control it. Because trillions and trillions is too large a number for anyone to comprehend, let's reduce the number of necessary mutations to 1,000 and argue that half of these mutations are beneficial. That is a ridiculously impossible ratio, but atheists are proposing something ridiculous so let's spot them a billion point lead and see if they can catch up - Pfft - NOT!. Again, from the science of probabilities, the odds against getting 1,000 beneficial mutations in the proper order is 2 to the 1000. Expressed in decimal form, this number is about 10 to the 301.

10 to the 301 mutations is a number far beyond the capacity of the universe to generate. Even if every particle in the universe mutated at the fastest possible rate and had done so since the Big Bang, there still would not be enough mutations. Why? Well, based on the evidence of microfossils, scientists estimate that the time between the earth reaching the right temperature and the first emergence of life was only four hundred million years.

There are about 10 to the 80 elementary particles in the universe. The fastest they could mutate would be Planck time, or 10-42 seconds. Planck time is the smallest unit of time and can be approximated as the time it would take two photons travelling at 186,000 miles per second to pass each other. If every particle in the universe,10 to the 80, had been mutating at the fastest possible rate 10 to the 42 since the Big Bang about 15 billion years ago, or 10 to the 17 seconds ago, it would produce 10 to the 80 x 10 to the 42 x 10 to the 17 or 10 to the 139 mutations. But to have a chance at even 1,000 beneficial mutations takes 10 to the 301 tries, and that's using numbers that are easier to understand. Thus, the chance of getting 1,000 beneficial mutations out of all the mutations the universe can generate is 10 to the139 divided by 10 to the 301, or 1 chance in 10 to the 162.

For Darwin's theory to have a chance of being right, the universe would have to be a trillion quadrillion quadrillion quadrillion quadrillion quadrillion quadrillion quadrillion quadrillion quadrillion quadrillion times older than it is. Because the universe is so young, Darwin's argument fails, and William Paley's contention that design presupposes a designer becomes more persuasive. Not to atheists mind you, but . . .

The final number comes from theoretical mathematics. It is Euler's (pronounced "Oiler's") number: eπpi. This number is equal to -1, so when the formula is written eπpi+1 = 0, it connects the five most important constants in mathematics (e, πp, i, 0, and 1) along with three of the most important mathematical operations (addition, multiplication, and exponentiation).

These five constants symbolize the four major branches of classical mathematics: arithmetic, represented by 1 and 0; algebra, by i; geometry, by πp; and analysis, by e, the base of the natural log. eπpi+1 = 0 has been called "the most famous of all formulas," because, as one textbook says, "It appeals equally to the mystic, the scientist, the philosopher, and the mathematician."

The reason for this wide-ranging appeal is its utter serendipity. First, there is the ubiquitous number e, which pops up in the most unexpected places. It was first discovered in an attempt to make multiplication easier. In 1614, John Napier figured that adding exponents was easier than multiplying multi-digit numbers, so he (and others) calculated the logarithms of all integers from 1 to 100,000, expressing these numbers as powers of 10. Later mathematicians found it more convenient to express logarithms as powers of the natural log e, a number close to 2.71828.

This number also appears in banking, because it is the limit for growth of compound interest. Let's say one invested $1,000 in a very generous bank that paid an annual interest of 100%. If interest were compounded annually, at the end of the year, the money would have grown to $2,000. If, however, the bank compounded interest four times a year, the money would grow to $2,441.41. If the bank compounded interest continually, the deposit could grow to $2,718.28, which just happens to be the value of e times the original investment.

Finally, e turns up at the origin of calculus, where it is the function equal to its own derivative (if y = ex then dy/dx = ex), and it equals the limit of (1+ 1/n)n as n approaches infinity. e is irrational, so it can never be written exactly in decimal form, but it is a very useful and fascinating number in its own right.
When we combine e with πp, we are introducing the oldest irrational number. Two thousand years before Christ, the Greeks knew that πp was the ratio of the circumference of a circle to its diameter and that it could not be expressed as the ratio of any two integers. It is essential in geometry, but it also turns up in waves of air, water, electricity, and light, and it even helps actuaries calculate how many 50-year-old men will die this year.

The number i is a relative latecomer, proposed in the 1600s as an imaginary number and defined as the square root of -1. It was proposed to help solve equations like x2+ 1 = 0, but today it is useful in science and engineering. George Gamow, in his book One, Two, Three …… Infinity, even uses i to locate buried treasure with an outdated map.

The idea that these two irrational numbers should combine with an imaginary one to yield so utilitarian a result is breathtaking. It is like deconstructing a chemical necessary for life (salt) and finding that it consists of two deadly poisons (sodium and chlorine). That these three strange numbers with such diverse origins should work together to produce a result so basic to mathematics argues that there is a profound elegance or beauty built into the system. Not to atheists mind you, but . . .

The discovery of this number gave mathematicians the same sense of delight and wonder that would come from the discovery that three broken pieces of pottery, each made in different countries, could be fitted together to make a perfect sphere. It seemed to argue that there was a plan where no plan should be. Not to atheists mind you, but . . .

Because of the serendipitous elegance of this formula, a mathematics professor at MIT, an atheist, once wrote this formula on the blackboard, saying, "There is no God, but if there were, this formula would be proof of his existence."

Today, numbers from astronomy, biology, and theoretical mathematics point to a rational mind behind the universe. To be sure, they do not point to the personal God of the Bible as such. Yet they are not inimical to the biblical God, either. The apostle John prepared the way for this conclusion when he used the word for logic, reason, and rationality——logos——to describe Christ at the beginning of his Gospel: "In the beginning was the logos, and the logos was with God, and the logos was God." When we think logically, which is the goal of mathematics, we are led to think of God.

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