James A. Choury
WorldVenture missionary to North Brazil
[Leia este artigo em português]
One common misconception regarding probability is that enough time makes even highly improbable events almost certain. This misconception may be a result of confusing two different types of circumstances. These circumstances are known as independent and dependent events. To illustrate this difference we can use coins and cards since this makes possible fairly simple mathematical calculations.
Two events are independent when the result of one has absolutely no effect on the other. Tossing one coin twice or tossing two coins at the same time are independent events. Drawing one card from a deck and replacing and shuffling the deck and then drawing the second card are two independent events. The odds remain unchanged when dealing with independent events. For example, the odds of tossing a head on any given toss of a coin are 50%. If I have tossed the coin three times and never have gotten a head the odds on the fourth toss of getting a head are still just 50%. This is a simple example of how our natural tendency is to think that the odds get better when, in fact, they do not.
However, drawing one card from a deck and not replacing it definitely affects the odds on the next draw of a card. The deck has been modified! This is an example of dependent events.
The odds of drawing a spade from a deck of cards on the first draw are 13/52 or .25000 or 25%. If the first card was not a spade, and the card is not replaced, the odds of drawing a spade on the second draw are 13/51 or .25490 or 25.4%. Note that the odds improved. After drawing 8 cards and never getting a spade and not replacing the cards the odds of getting a spade on the ninth draw would be 13/44 or .29545 or 29.5%. If no spade is drawn in 39 draws and the cards were not replaced then the odds of drawing a spade just before the 40th draw would be 13/13 or 1.000 or 100% because at that point there would only be spades in the deck and drawing a spade would be a certainty.
In discussions concerning the origins of the universe and of life, we can begin talking of independent events where the odds remain the same with each new “trial” (i.e. they never improve) and slip into treating the independent events as though they were dependent. From there it is easy to conclude that the desired event must eventually occur because the odds continually improve until becoming a certainty.
One example might be the thought that life originated when lightning struck a pool with slime in it. (Seldom is the question of where the slime came from addressed). Lightning strikes the pool. The odds of life being formed in this way are highly unlikely and in this case nothing happens. (By the way, it is much more probable that any “incipient” life be extinguished in this way than produced). But some time later another pool of slime is struck by lightning. Again nothing happens but sometime later another pool of slime is struck by lightning, etc. Clearly these are independent events and the odds never improve. Yet we are tempted to think that given billions of years it has got to happen eventually. Given enough time it becomes a certainty. Actually the probability never gets any better. (Perhaps it would improve the odds if lightning were to strike the same pool of slime many times but that only brings in more highly unlikely events).
When discussing issues dealing with probability we must remember that if the events are independent the odds do not improve with time.
Here is a less controversial example to illustrate the point. Let’s imagine a large tray with 50 coins in it. The odds of all the coins being “heads” by chance are 1/250 or 8.88 to the negative 16th power. There is only one way all the coins can come up heads. There are 1,125,899,907,000,000 ways for the coins to come up not all heads. If the tray were “bumped” every second allowing the coins to fly into the air and land again in the tray they would never “by chance” come up all heads because the odds never improve. The odds at each trail would still be 8.88 to the negative 16th power against it. It is ever more probable that at least one coin will be “rebellious” to our wishes and insist on coming up tails.
In discussions of the origin of the universe and of life we are often encouraged to think that given enough time it would have to happen simply by chance. Understanding the difference between independent and dependent events helps us see the error of this way of thinking. The point is the odds never get any better no matter how much time is allowed.
In this brief, four part, study of logic and probability we have seen that the debate concerning the origin of life and of the universe quite naturally and of necessity falls into two camps, i.e., chance or intelligent design. The Law of the Excluded Middle forces the debate into those two, mutually exclusive, options. We have also seen though our rapid lesson on probability that joint, complex, interrelated and highly improbable events are extremely unlikely so as to border on the impossible. These logical and mathematical realities should lead the unbiased inquirer to conclude that the universe and life itself came into being by means of intelligent design.
Why then do so many cling so tenaciously to the “by chance” explanation of the origin of the universe and of life? One reason may be the Law of the Excluded Middle combined with rejection of the concept of a designer. Remember, if it wasn’t by chance then it must have been by “not chance”. But “not chance” is equivalent to saying design and that means intelligent design. One must either accept intelligent design or insist that everything that exists and life itself happened by chance. Those with a philosophical commitment which excludes design are left with chance as the only logical choice available to them. The problem lies in that often this philosophical presupposition is believed to be science and is proclaimed as science. The actual scientific evidence and logic lie on the side of intelligent design.
Unfold the Evangel before your eyes!
Are you worn out?
Are you overwhelmed?
Are you rational?
Only rational, non-dogmatic persons can understand and accept this message. Give yourself a try. Nothing will be like before, I promise!
terça-feira, novembro 07, 2006
James A. Choury