Very Large Numbers
Paul V. Hartman
The largest numbers we are likely to use in daily discourse are in the billions. (It used to be the millions.) Examples: There are now 6 billion people on this planet; the solar system has been here about 4.5 billion years; the money spent by our government every year is in the billions; the number of stars we can see on a clear night is "billions and billions." Although these numbers are large, on a relative scale they are tiny in comparison to the breadth of the universe, or the time of its existence. The Really Large Numbers, breathtaking in their extent, numbing, in fact, go beyond simple comprehension.
Our language is not set up to handle them in any easy way. Scientists use a short hand for handling large numbers, called logarithms, such that the number 1,000,000,000 (one thousand million, or one billion) is represented by the figure 109, also called "10 to the ninth" or "10 to the ninth power," and it saves a lot of printed page when you get to the part about describing the size of the universe.
Yet everything we propose in terms of "odds" - such as when we say the "odds" for something happening are such and such - has much more to do with Really Large Numbers than it does with more comprehensible "billions." To say that something is possible or impossible only in relation to the numbers in the first paragraph, or in the life of a human, or in the time since the birth of our sun, is way short of reality.
Consider the notion of the spontaneous appearance of life on this planet. Many people, arguing their conclusions from many different directions, (i.e. the probability of a self-replicating strand of nucleic acid arising from carbon, hydrogen, and an electric spark) conclude that the odds Against are too large to be believed. (One popular analogy has to do with the odds of a tornado sweeping through a junkyard, assembling a 747.) But this conclusion ignores Very Large Numbers, and pays no obedience to the notion of a nearly infinite number of trials.
If you can conceive of a 747 being pulled together by a tornado PROVIDED there are an infinite number of chances to do so over an infinite length of time - if you can conceive that the "odds" of this are very low - but not zero, then you will understand the power of Very Large Numbers.
If the appearance of life where none existed previously were simply the lucky happenstance of the right conglomeration of certain ingredients in the right combination of circumstances, then Very Large Numbers tells us that the occasion WILL occur. It may take a very long time, but then we postulate that the universe is infinite, or very nearly so, and that the time of existence of the universe is infinite, or very nearly so.
That leaves plenty of room for the requisite Very Large Number of trials. The only way we could conclude that life could not appear spontaneously on this planet is to conclude that it could NEVER happen, not ANYWHERE, not under ANY SET of CIRCUMSTANCES, even with an infinite number of trials; that the odds against are, indeed, ZERO.
The fact is, no scientist in tune with Very Large Numbers has ever said those odds are zero; rather, they say the odds are too small to be believed. But look: the odds against winning a million dollars in a lottery is on the order of one in several millions, a true long shot. Yet people buy tickets. Why? The odds are not zero. Someone always wins. Always.
What is more, the fact that the odds for any event are very great does not mean that the event will occur at the end of a long time interval. An event that occurs once in a million tries is just as likely to occur on the first try as the last.
It can be argued that Time is not infinite, that the present universe appears to be about 20 billion years "old", and may have an "end." But the Big Bang Theory allows for the universe to be "created" over and over (Bang, Collapse, Bang - ad infinitum) and if that is true, then time is truly infinite, and we observe this universe rather than any previous one because it was in THIS go-around that chance favored the appearance of a life form that could understand the process.
Some will say that such calculations leave no place for God. But that is to settle for a shallow point of comfort rather than a deeper point, at a further remove, which can restore lost comfort, which is to acknowledge that although a scientific argument can be made for the appearance of life on this planet, with you and I acting as the proof of the theorem, there is no scientific theory for the Origin of the Origin of the universe. None. We have mentioned Big Bang. But that is an attempt to describe why everything in the universe appears to be moving "away" from some theoretical location, a theory based on "red shift", which appears to have proper pedigree, but is of no help to the larger question: how did the universe Begin?
Rather, the Theory is an effort to calculate the Bang back to a place in time when everything was at a "Point." But there is no science for what was going on at the Point, or for what constraint was on that Point, prior to the Bang. Do you understand that business about the Constraint? What is it? What releases it? What causes it to Return? This is mind-boggling stuff.
Big Bang is a mechanical theory, not an origin theory, because it does not start at the - well, the Origin.
Consider the origin of planet earth and its life forms as if it started 8,000 years ago (as the Old testament suggests but does not affirm) or 4.5 billion years ago. Why would either choice look necessarily different to us? The answer is we wouldn't know, we would have no way of knowing: anyone saying this way or that way would be expressing a mere opinion.
Okay, enough of this.
The religious establishment might be wise to change tactics: instead of arguing against spontaneous appearance of life on this planet - an argument which may never be settled for lack of good evidence either way - they should argue for God the Creator of the Universe. Creator and Initiator. Before the universe was, God was. From that perspective, Science will be obligingly silent.
Hey wait a minute! Isn't that what the Bible actually says?
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