-- Probability --

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This post has sort of been percolating in my mind for 2-3 years! (a bit pedantic) so may as well just toss it out there, since I don't foresee a lot of news to report in the next few months....

S'pose you roll a normal die (dice) 10 times.... which of the following 2 sequences would be more likely to occur:

6 2 2 4 3 5 6 1 2 1  or

1 1 1 1 1 1 1 1 1 1

Typically people will say the first sequence is more likely.... BUT, statistically they are wrong. BOTH sequences are equally likely, out of the 6¹⁰  possible outcomes they each have one chance of occurring. Sometimes it helps to think of it in simpler shorter terms.... which of these is most likely:

4 3 5  or

1 1 1

There are only 216 possible outcomes for three numbers and each of the above have 1 in 216 chances of occurring. No matter how much longer you make the strings, all have equal probability of occurrence.

Probability is a quirky area within mathematics, even some professional mathematicians have problems with it (the famous Monty Hall Puzzle was an example of a simple probability riddle that tripped up even degreed mathematicians).

A different sort of example:

S'pose I flip a presumably fair coin 4 times in a row and get all heads, and ask you to predict the next (5th) flip. There are 3 main ways of approaching it: 1) we are overdue for a tail, so predict a tail (this is the so-called 'gambler fallacy,' that somehow the previous outcomes have some sort of an influence over the next outcome, which is actually completely independent), or 2) assume it must NOT be a fair coin and will thus come up heads again, or 3) realize each possibility still has a 50/50 chance and randomly pick either heads or tail.

The human mind instinctively looks for patterns even imposing patterns where none may exist. This all borders on what I often call the fallacy of over-generalization. People look at a subset of examples and then extrapolate (or generalize) to all possible examples. 

Mathematics takes matters to the opposite extreme, where no amount of examples can "prove" the general case:

Many of you likely are familiar with the Collatz Conjecture in mathematics. A famous and fun conjecture that has been verified as true for the first 2.8 quintillion integers. There are several math conjectures/hypotheses verified for trillions of numbers (including perhaps math's most important conjecture, the Riemann Hypothesis); they are stiiiiiill just unproven conjectures!, NO AMOUNT of individual numbers tested can confirm their truth. 

I bring all of this up because ultimately the arguments over the Ivory-billed Woodpecker distill down to arguments over probability. I'm rarely persuaded  by attempts to apply mathematical probability to the case of the IBWO -- the number of interactive factors/variables/contingencies are just too many to be sufficiently accounted for, and soooo many assumptions must be made along the way (but humans are always impressed with themselves when they are able to slap numbers onto things!). Still, even if 900 IBWO claims were easily shown to be Pileateds, it simply does NOT mean or guarantee that the 901st such claim is automatically a PIWO. Each case must be adjudged on its own merits, credibility, description, details, etc., NOT based on past mistakes no matter how many. Past mistakes are "evidence" of what can happen, but NOT necessary evidence of what happens with a new instance. So, we are always left with a residue of a few claims that can't be easily dismissed -- the location is good, the observer is knowledgeable/experienced, the description/details are on the mark -- there is no basis for discounting it, EXCEPT by relying on all past mistakes... which in fact do NOT necessarily bear on the current claim. I'll grant that there exist some further reasons for making such extrapolations, but skeptics must understand the enormity of their automatic dismissal of ALL such instances (at the very same time that they readily accept the ID results of 100s of bird counts and bird atlases every year -- did Jimmy really see 15 Northern Cardinals in Area 14 just because it seems plausible?). ALL the arguments that skeptics make over and over and over and over again for why the IBWO couldn't possibly persist DO HAVE counterarguments (which I won't re-hash here, and which no one is forced to accept), but granted the further passage of time without yet better evidence will add weight to their view.

Donald Rumsfeld famously said, "There are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don't know we don't know."

Skeptics (and most people) like playing with the "knowns" and even dabbling from time to time with "known unknowns," and then think they reach certainty, but too often they fail to acknowledge the "unknown unknowns".... and if the Ivory-billed Woodpecker persists at all, that is the realm where it will be found....

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