Looking at Faith through Rose Criterioned Glasses, or, What is the SNR of God?

Earlier today, for reasons I do not know, I was thinking about Littlewood's Law of Miracles. It is a favored argument among skeptics--and by skeptic I mean not the suspicious or agnostic but the militant templars of doubt--against the presence of divine intervention in the world. It is, simply put, a statistical argument. If one assumes that a miracle is an event with a probability of one in a million, then, assuming we perceive one event per waking second, we will generally see miracles once a month--some we will consider significant, some we will ignore.

Now, I personally consider the argument flawed, if not practically autoreduction ad absurdum. However, quibbling over assumptions is a poor way to defend one's faith--if I argue in favor of one set of numbers, someone else can assume another and I cannot compel their presumptions. I would rather concede the law entirely, and continue from there. The soul of Littlewood's law is the Law of Large Numbers--that in a world of so many people, where so many events occur, our perceptions of probability will be challenged.

At this point, I will digress into talking about what I do for a living. One of the basic questions of medical imaging or nuclear medicine is how one detects a signal in the presence of noise. For example, even if one locks a Geiger counter into a room lined with lead, it will still detect an occasional radioactive event. This spurious detection is called the background noise. The weakest radioactive source you can detect in the presence of the background noise is called the minimum detectable activity (MDA). Now, this is a blog post and not a submission to a peer-reviewed statistics journal, so I will gloss over the calculations.

If we assume Littlewood's law, then miracles are a lot like radioactivity, mathematically speaking (i.e. they are both Poisson processes). I have to discuss a technical point here. It's the fairly obvious and intuitive statement that the longer you are measuring a signal, the easier it is to distinguish signal from noise. Basically, when you calculate an MDA, you have to specify the time period you are measuring over (and how sure you want to be, for that matter). This will be relevant in the next paragraph.

In analogy with the case of radioactivity, permit me to define the minimum detectable spirituality (MDS) as the minimum number of miracles that have to occur in a period of time for us to be 99% sure. Let as assume that you want to look at, say, 25 years of your life. The MDS is 1 miracle every 6 months (so that means a total of 14 miracles in a year). If you look back over 50 years, you would need 1 truly divine interaction a year to reliably notice it, even in the face of the other 12 you would expect to see from pure chance.

And what does this all mean? That depends on what you believe. I believe in miracles. I think God's signal is above the noise. And that means that, if someone should repeat Penn Gillette's quote about "luck is just probability taken personally", I can honestly and flippently respond that "just because I'm paranoid that doesn't mean they aren't actually out to get me."

UPDATE: I wanted to add a less flippant conclusions. The long and short of all of this is that Littlewood's Law tells you nothing about faith. Our lives are long, and given how little "spiritual activity" has to present for us to be able to distinguish it from the background noise, it's not irrational to claim to see the hand of God.