Sunday, December 24, 2006

At What Point Does Randomness Become Ordered?

I have an mp3 song list of about 5200 songs and I always keep it on random shuffle. The other day i played a song and then hit next... it was the same song again (but with a different title because of a mistake). I replayed the previous song intro... yep sure enough.. those two were the same exact songs.

So I stepped back a little bit and it got me thinking. What are the odds of that happening...playing the same song sequentially like that? Well, assuming that there was only one duplication of the song the odds would be somewhere in the neighborhood of 1 in 27 million....Damn.. I could have just won the lottery but nooooooo had to play a stupid song twice...

Now using the Bayesian theorem the probability of A|B or A given B (where A = "I played both songs sequentially" and B = "I played the first of the two songs originally") the p value becomes much more reasonable once again (roughly .02% or 1/5199). In other words, if we take it for granted that I played the first song as a starting point, we have roughly .02% chance of playing the duplicate of that song (assuming that one exists and that I play at least two songs).

But now what if we didnt assume one existed? How could we figure out the probability of playing a duplicate among a remaining list of 5,199 songs? First you'd have to know how many duplicates there were.. Or to to put it more simply, how many different songs were represented in that list. Lets make things simple and just say we have a lot of duplicates - 199.. So we have 5,000 out of a possible... who knows how many millions are available to have on mp3. Of course, the liklihood would be dramatically increased (by an unknowable degree) because I already had the song once. That implies that the song probably something I like therefore its not terribly unlikely that I have downloaded or ahem, (burned it from a legitimate CD I purchased) twice by mistake. The fact that I already have the song makes it much more likely that I have a duplicate of it versus if you had a gigantic hat with all the world's songs written on different slips of paper and you pulled out one random song to see if I had that one in my list of 5200...

Nevertheless, this all goes to show that it would be utterly impossible to figure out any kind of actual probability in the grand scheme of things to duplicate that song. Suffice it to say it would be unlikely but probably not in extreme proportions (given that I had already played it once).

Hope I'm making sense so far because that was the easy part. Now taking it a step further in my thought process I just started to ponder this probability on a more.. removed and philosophical level (so to speak).

The question I asked myself was this: at what point do things cease being random and start being (apparently) brought about by intelligence? Because stepping back (far bacK) from the situation, we can see that a series of extremely complex sound waves (the song) just repeated themselves. You could not put a probability value on that happening without intelligence involved. Remember just playing 2 songs sequentially out of 5200 is 1 in 27 million and this would be like playing 10 million songs sequentially out of a possible 100 billion (and even that would be a gross underestimation).

But since in this case we have already admitted human involvement (I downloaded ... err..burned the songs on my computer and have a playlist of my own selection set up) we can see how it is not entirely unreasonable that this phenomenon occured. In fact, we have all seen it or something very much like it before. Sometimes I'll think of a song and somehow that song is played on my list at the next random shuffle.. Things like that happen all the time. But since we have a little human involvement, it doesnt seem too incredible to us. We take all that for granted.

Back to the question: from a naturalist perspective, ultimately all things must be random. If you go back far enough, everything came about from randomness (according to the naturalist cosmology). But at some point along the line, we stop thinking of occurances as random and start thinking of them as results of direct human (or intelligent) manipulation. The question I'm asking is: at what point is that? And, is there a way to legitimately quantify the cross-over?

Recently, Robert Fulford wrote an article about one of atheism's better apologists, Richard Dawkins in which he said:

G.K. Chesterton said he found it hard to believe in God but harder to believe that a swamp, if left alone long enough, will eventually build Chartres Cathedral;
And so that is really the issue I'm pondering. Because in essence, that is truly what naturalists believe in. It might be easier to understand just what is being said if you could look at the universe in a small crystal ball but as through one of those time lapse cameras where you're viewing in extreme - fast forward. You would see nothing at first, then you would see a tiny ball of light in the center that exploded and began expanding. As you focused in on the planet earth you would see it go from an asteroid chunk into a lush planet with vegetation and life springing up. It would turn green and eventually you would start seeing structures such as the great wall of China appear and later on, massive sky scrapers and cathedrals. It would cover the earth. Assumably eventually it would burn up or waste away or whatever but if you kept watching for long enough, all evidence of life would, in someway or another disappear.

The question is, was everything you witnessed purely random? Taking a look at it from that perspective and from the naturalist cosmology, any honest person would be forced to say yes. Looking from our very narrow perspective here on earth, it is easy to say "that cathedral isn't random because humans built it" but in fact, if not for divine creation of men it is random. It is the result of amino acids combining many millions of years ago in a swamp. In fact, taking it back further, it is a result of the big bang at which the universe began. Everything was necessarily set in motion at that time and nothing could be any different than it is now.

So while yes, humans did build the Pyramids, it was merely the product of billions upon countless billions of sequentially chemical and physical reactions which started with the random joining of amino acids in a swamp somewhere. The utterly incomprehensible complexity of this randomness set in a universe which has laws and rules (nevermind how or why they even exist), this randomness can appear to the untrained, uneducated and naive theist that some intelligence was involved in the universe since many things (such as the pyramids) don't appear to be results of complete randomness.

Well call me untrained, uneducated and naive.

Merry Christmas.


Jeff Miller said...

The randomness in the iPod is not truly random. It is based on a number used as a seed so you only get apparent randomness. Though there is a setting in iTunes to increase the apparent randomness and the unlikeliness of the same song being repeated.

TheGodFearinFiddler said...

I was actually using WinAmp but its probably the same thing. I know many 'random' numbers arent truly random. I think many of the random generators use the computer clock to generate 'random' numbers but anyway... The whole random shuffle thing is just what got me thinking. Thanks for the comments & merry Christmas!