Deep thoughts while nursing my baby
Monday, August 2nd 2010 @ 2:51 AM
I recently did a little math experiment. (This is one way I stay awake during those endless nursing marathons. Bear with me, even if you're not a math type, and of course, especially if you are. I will try to be very clear.)
I wondered, given 10 billion years, could a string of randomly generated letters of the alphabet, refreshing as a new permutation every second, eventually produce the classic novel War and Peace? (The English translation has around 560,000 words, and let's say there are an average of five letters per word, for a total of 2,800,000 letters.)
Now, 10 billion years is a very, very long time. Some scientists estimate that the universe is about 13 billion years old, right? Surely in 10 billion years, 2,800,000 random letters will at some point "write" War and Peace.
OK, now we do the math. First of all, how many seconds are in 10 billion years?
10,000,000,000 years = 3,650,000,000,000 days = 87,600,000,000,000 hours = 5,256,000,000,000,000 minutes = 315,360,000,000,000,000 seconds (315 quadrillion seconds).
That's 3.15 x 10^17. A huge number. Seventeen zeroes.
Now we need to know how many different permutations there are of a string of 2,800,000 letters (putting aside the complication of spaces between words for this calculation). There are 26 possible letters for each spot, so we have 26 x 26 x 26 x 26... (2,800,000 times), or in other words: 26^2,800,000 (26 to the 2,800,000th power) possible arrangements of letters in a string that's 2,800,000 letters long.
And that number is, for all intents and purposes, infinity. It has millions of zeroes. It's ridiculously large. Larger (by far) than the total number of atoms in the entire universe.
Let's think about this. If we spend 10 billion years randomly generating strings of 2,800,000 letters at the rate of one permutation per second, we can generate 315 quadrillion permutations.
The probability of one of those 315 quadrillion randomly generated strings being War and Peace is 3.15 x 10^17 / infinity (315 quadrillion divided by infinity), which is.... zero. No chance.
Now I'll tell you why this is important.
Think about the universe and everything that is contained in it. Even if we can perceive or conceive of only an infinitesimal fraction of the living organisms and nonliving things that make up the universe, we can certainly acknowledge that there is an infinite number of structures, systems, processes, etc. that are part of our world.
Everything from microscopic mitochondria doing their job in every living cell, to vast interconnected ecosystems, to mysterious astronomical phenomena—all have complex chemistries and moving parts that operate and interact seamlessly.
Let's take just one example as an illustration of what I'm talking about. How about human milk? According to scientists, we've had about 13 billion years for it to evolve into the perfect food to nourish an infant. And it certainly is incredible: it provides the ideal balance of every nutrient an infant needs, with proportions adapting to meet the baby's changing nutritional requirements during each feeding and as the baby matures into a toddler. Surely over the course of 13 billion years, Mother Nature has had enough time to work her magic through mutations and so on to create breastmilk. Right?
Now, how many "parts" go into mother's milk? It's not really quantifiable, but the "ingredients" would include the mother's diet—which means all of the various foods she eats, their sources in grains, fruits, vegetables, and animals, and the particular nutritional components contained in these foods, plus her entire digestive system, which has its own infinite "parts" that have had to evolve in order to accomplish its many tasks—plus the specific system of glands, ducts, and other chemical and physical structures that make the milk itself.
Then the baby's mouth and digestive system must be taken into account; how many "parts" in those? Don't forget the tastebuds and olfactory system that allow the baby to find its mother's milk appealing in the first place. Those had to get there somehow—right in the right place, at the right time, and working just right—otherwise the best milk in the world would be useless.
And this doesn't yet take into account the various "parts" that allow the baby to grow using the specific nutritional building blocks received through the milk. It also doesn't account for the hormonal processes that cause a mother of a newborn to begin to produce milk after she gives birth. And we're taking for granted that there is a baby (and a mother) in the first place.
How many tiny little parts would this add up to? Might it be at least 2,800,000?
And how many such systems are in our universe, all interdependent? Here are just a few random examples that, at least for me, give me food for thought and make me feel nothing less than awe for the infinite intricacy of our universe:
The water cycle. The circulatory system. Plants and animals exchanging oxygen and carbon dioxide. Skin that heals itself. Eggs hatching. Leaves decaying into the forest floor. Eyes. Colors. Seeds. Speech. Sap. Birds that fly and fish that swim.
It doesn't take long to realize that our universe is an infinitely vast collection of interconnected parts, microscopic and macroscopic, visible and invisible, living and nonliving, all working together in harmony.
Could this entire system, or even any one part of it (just our immune system, for example), have been generated through a series of hit-or-miss mutations over a very, very long period of time? Say, 13 billion years? Would there have been enough time to accomplish it? You do the math.
This is what I have concluded (and you are welcome to come to your own conclusion if you don't like mine): There is only one way the universe could have evolved itself into the beautiful, functional, self-perpetuating system that it is (instead of devolving into self-destruction through random mutations, most of which lead to bad outcomes), given only 13 billion years or anything less than an infinite number of years. And this one way can be understood as having three requirements:
Number one, many processes and systems would have had to be evolving simultaneously. Number two, every step would have had to happen with amazing efficiency, augmented by frequent quantum leaps in evolution to make up for the fact that there just is nowhere near enough time for it all to take place. Number three, Someone had to be directing the course of events.
In other words, there had to be a Creator, or it just couldn't be done. 13 billion years isn't nearly enough time. It's not enough time for one classic novel to be created randomly. And it's certainly not enough time for the whole universe to be created randomly.
Of course, once you realize there had to be a Creator, then you also no longer need 13 billion years (although you are welcome to use that paradigm if it's useful), since it was never enough time anyway. You could do it in six days, and then six thousand years. To G-d, it's all the same, and to us, we wouldn't know the difference, because we weren't here when it all began or when most of the real action took place. All we have are clues to an enormous cosmic mystery, and a Torah to help us see that scientific progress, while an amazing human achievement, can only take us part of the way to the truth. (Math, on the other hand, is another story!)
