Saturday, July 13, 2013

Objectivity and Bayes Theorem


I'm still pondering objectivity - so I have to at least skirt the topic of how I’d arrive at a “most likely explanation” using a “thinking tool” like the abbreviated version of Bayes Theorem above. This formula (often referred to as “BT”) represents

“the probability (P) that a hypothesis (h) is true given all the available evidence (e) and all our background knowledge (b)”

Ptolemy got it wrong That’s actually a pretty simple way to choose between alternatives. Many of us apply this instinctively every day, although we don’t think about it in such formal terms. However, when we start to examine things from a more objective, less emotional point of view, we must be more honest and rigorous. How might we then use this formula for assessing the likelihood that causes of phenomena in the real world are what we think they are? I won't explain BT here, because I’m not an expert, but I can still use it as a pattern to help me assess whether something is more or less likely to be true.

Imagine that I’m an ancient human observing that the sun moves across the sky once a day. What are the possible reasons this happens? It could be any of the deities Ra, Surya, Freyr - or several others. It could be that the sun circles the earth on its own - as Ptolemy thought.There could be some other plausible explanations entirely. Since I assume that shit doesn’t just happen for no reason, I feel there is a explanation for the sun crossing the sky. Now, being honest and rigorous, I have to admit that, in this example, although the sun-god Ra is my choice as the real explanation for why the sun moves across the sky once a day, alternative explanations for this phenomena exist. Some alternatives I’m aware of, some, I’m not. Seeing as how I haven’t done a legitimate investigation into why the sun moves across the sky once a day, I probably need to assign each alternative an equal probability of being true, and then do some testing to raise or lower their individual probabilities based on the outcome of each test.

In probability speak, the sum of all probabilities for an explanatory hypothesis is 1 (or in gambler-speak: 100%). And since there is always more than one plausible explanation, then each alternative has a non-zero, non-one probability.

At this point, I can also say that, of the tens, or hundreds or thousands of plausible explanations, there may be millions or billions of implausible explanations that, although easy to dismiss, are not logically impossible, so they also have a non-zero probability. And they all contribute to that total of exactly 1.

Therefore, with the limited set of proposed explanations for the sun traversing the sky, my initial calculation ought to be:

  1. Ra did it = .2
  2. Surya did it = .2
  3. Freyr did it = .2
  4. Ptolemy was right = .2
  5. All other explanations = .2
... so that we then have a total probability of 1 - a 100% chance that our 5 hypotheses cover all possible explanations.

This is a key point - that every possible alternative that is not impossible should be considered to have a non-zero probability before you start gathering evidence. And that there are explanations that we don’t know about that we must acknowledge - here I group them as “All other explanations”.

When all of the hard work of investigating is done, it turns out that Ra and the gang were not the cause for the sun traversing the sky. It was the earth turning on it’s axis that made it appear the way it did.

We can approach the question of whether God exists the same way. We might even arrive at a similar conclusion.

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