Tuesday, May 22, 2007

What is Astronomical?

My definition of astronomical is a number that is big enough to account for the size of the universe. It is something that reflects the number of possible events throughout time and space that could have occured from the postulated big bang until now. How big is this number?

If we poke around the net, we find that the age of the universe is guestimated at 15ish billion years. A nice number. Using computer notation, we have 15e9. There are 31,536,000 seconds in a year, giving 4.7e14 seconds since the big bang. If a computer were operating at 1 billion operations per second during this entire time, we would have 4.7e23 operations since the beginning of time.

This is just the beginning. Now what if each particle of the universe were a computer? How many operations could have been performed throughout all time? A "solar mass" is definied as 1.98892e33 kilograms and there are billions of stars in each of billions of galaxies. Astronomers have multiplied this all out and come to a range from 1e72 to 1e87. Taking the upper limit and multiplying by the number of operations, we have our upper bound: 4.5e110, which is 4.5 times 10 billion times a google. Wow! The mother of all computers could do a lot of arithmetic.

Now consider a sequence of 111 base-10 digits. What is the chance of picking a particular sequence? The answer is 1 in 1e111, which is more than the above definition for astronomical. In fact, for those who work in science, engineering and math, 1e110 isn't a particularly big number. A sequence of 111 digits is about as much information as 10 lines of software. If 10 lines have an error, a big chunk of the program will typically fail completely. A typical software product these days has on the order of 1 million lines of software which must be carefully engineered. Still more complex is a biological genome, which typically has 3 billion based pairs to encode the information.

The reason for this discussion is that I picked up "The Blind Watch Maker" to see if Richard Dawkins could form a rational argument. Having read the first 50 pages, I can't answer this yet because he hasn't argued anything. He has mentioned Paley and his awe at the designs of life. He has talked about how engineers do abstract reasoning and described some of the complexities of bats and eyes. He mentioned probabilitiess and billions of years, but only at an elementary school level.

Probabilities come in three forms. First there are the ordinary ones that we face everyday, like the chance of being struck by lightning or being abducted by space aliens(!). Second, there are the probabilities of statistical mechanics which do such an elegant job at describing the behavior of gases such as the air that we breathe. The third is design probabilities requiring specific sequences of characters or words. The probabilities of design problems having occured without a designer tend to be in a class that is completely different where astronomical is a very tiny number for expressing things. Dawkins has graped design. Reading up to this point, however, I am not sure that he has grasped numbers.

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