Thursday, June 21, 2012

More on the Anthropic Principle

From a comment I made at Overcoming Bias, elaborated a bit:
Assume you have a display that reads "9", and a button that can be pushed to display a number; the only information you have is that the button was pushed at least once, pushing the button is the only way to change the display, and that the current display is "9".  What is the likelihood that, if pressed, it will display "9"?
You can assume 9 is possible.  That's it.  The problem you are solving asserts that 9 is currently the case; you don't know if it was pressed once or a billion times or a billion to the power of a billion times.  Because 9 is a given, it provides absolutely -no- information about the probability of 9 actually displaying, -except- that 9 is currently the case; for all you know, somebody who lived forever and really liked the number 9 pressed that button until it came up.  Every time you press the button yourself provides meaningful information about the display; the value it displayed when you came upon the display is meaningless.
The Anthropic Principle isn't a meaningless tautology, nor is it a fallacy.  It's recognizing that our existence is the equivalent of a display with the number 9, and a button.  The number 9 - our existence - is a given.  We cannot assign any probability to anything to do with our existence on the basis of our existence; it is part of the problem definition, NOT part of the information set pertaining to the problem.
It is a prior with a value of 1.0 - a prior which is guaranteed.  What are the odds of an individual in our problem scenario coming upon the display with the value "9"?  100%.  We've defined the problem so that this is the case within our scenario.
Similarly, the Anthropic Principle states that, for any condition necessary to our existence, the probability of that condition being the case in the universe we are examining the problem of the likelihood of our own existence in is 100% - we exist to examine the problem, therefore the condition must be true.  We're part of the problem definition; we add no information in terms of solving the problem, except to rule out 0% as part of the distribution.
The important thing in the relationship between these two is that the null hypothesis for the original display has a likelihood of 0%.  The null hypothesis of the Anthropic Principle contradicts itself; what would I assign to be the likelihood of my own existence, if I didn't exist?  This means it -is- a tautology - but a meaningful one.  A tautology is a statement which is implicitly true - either because it defines itself to be true "This statement is true", or because the null hypothesis is impossible "This statement is false".  It is important to remember that not all tautologies are fallacies.

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