Thursday, June 30, 2011

Revisiting the Watchmaker - Bayes' Theorem

I have previously explained the watchmaker argument and the inherent circularity, but I thought I would expand my objections with a bit more mathematical rigor.

As a brief review, the watchmaker argument involves a cute little story about finding a beautiful gold watch in the middle of nowhere and, how silly it is to conclude that the watch was not manufactured by some intelligent being.
The main thrust of this argument is this:  the likelihood of the existence of a complex universe containing life is very small if there is no intelligence to deliberately create it.

Now I will briefly explain Bayes' theorem.
If P(A|B) is the probability of A given B
and P(A) is the independent probability of A (not given any other variables),

Then P(A|B) = P(B|A)*P(A)/P(B).

Now, let's look at the watchmaker argument.  We have two propositions:
G = God Exists
L = Life Exists (in a complex universe)
(Not G is written ~G)

We are to assume, from the argument, that P(L|G) is much, much larger than P(L|~G).  This is debatable, but there are some arguments in favor of this.
The watchmaker argument would have you believe that P(G|L) is large because P(L|~G) is so small, that is, if there is life, god likely exists because life is so unlikely to exist without god.  Essentially, the statement is that P(G|L) = 1 - P(~G|L) = (approx) 1 - P(L|~G).

However, inverse probabilities are not so simple as this naive argument would have you believe.  In reality:
P(G|L) = 1 - P(~G|L) =  1 - P(L|~G)*P(~G)/P(L).
What we don't know here is the relative magnitude of P(L|~G)*P(~G)/P(L), because the likelihood of god's existence (independent of other variables) is unknown.  Therefore, no conclusions can be drawn.  If P(L|~G)*P(~G)/P(L) is close to 1, then P(G|L) is actually very small, close to zero.

Now, I think I've made my point, but I'd like to venture into the realm of speculation now, so take this as you will.
Does god count as life?  If so, then P(G) < P(L) assuming that life besides god can possibly exist.
If that is the case, then P(G)/P(L) < 1, so P(G|L) = P(L|G)*P(G)/P(L) < P(L|G).
This gives us the rather minor conclusion that life must give god's chance less of a boost than god give's life's chance.  Thus, the watchmaker argument is inherently weaker than it purports to be.

Sunday, June 26, 2011


I haven't been writing much at all lately.  To be perfectly honest, things have been changing rapidly in the last few weeks.

I'm happier, for one thing.  I have motivation once again to get things done,  and I can take satisfaction in my work, something that seems pretty novel after months of deep depression.
I'm on good terms with my family, and I'm open about how I feel about religion.  I am actually trying to be friendly at church... if I'm going to remain more or less active for my wife's sake, I guess I'd better start learning to be comfortable in the community.

My political views have been evolving as well.  I have actually been thinking a lot about libertarianism and the role of government lately... something I have avoided doing out of sheer horror at the obnoxiously-uninformed rhetoric of the teabaggers.  Not that I'm becoming libertarian, but I feel that it's healthy to seriously consider views other than those I've become accustomed to holding.
To be perfectly honest, I've actually become more pessimistic, politically.  I don't feel like there is anything that can be done at this point to save our civilization... our society is consuming resources and energy at ever-higher rates despite the decreasing cost-effectiveness of all of our resource-gathering operations.  But I suppose all civilizations must fall.
I may write more about all this later... I'm still considering a lot of things.

I have been taken by surprise at how quickly things seem to change.  I'm almost afraid of the feelings of hope and contentedness that I have recently begun to experience... like I can't trust them.  Maybe I can't, maybe life sucks and I'm only in denial if I feel otherwise.  I'm still not convinced that life can have any meaning... but at least I'm enjoying it a little, now.  Perhaps what I'm most afraid of is a loss of objectivity... I have no desire to simply become caught-up in my own affairs to the point at which I'm not thinking constantly and thoroughly about the state of the world around me.
I'm still not completely convinced that a healthy mind is a sane mind.