Misconceptions about Me, Baye's, Rigor, Exodus, Evolution

[David Sklansky]

1. With few exceptions I make no effort at rigor. I consider rigorous mathemeticians, like the ones who wasted their lives figuring out how to eliminate the use of infintesimals, either obsessive compulsive, or so devoid of cleverness that they know this is the only way for them to contribute anything.

2. Any eight year old can understand Baye's Theorem. I explain it in a few pages in Getting The Best Of It. Anyone who hasn't read that book has no right to have an opinion about anything. Anyway here is an even shorter explanation. If an event may or may not occur, and if it does occur, there could be two or more explanations, then when it does occur you use the following technique to figure out the probability of a particular explanation. You form the fraction where the numerator is the original probability of the event occurring in that specific way and the denominator is the total probability of the event occurring.
If the probability that New York is destroyed is 5% because there is a one percent chance terrorists will do it, a 2% chance that nuclear war will do it and a 2% chance that an earthquake will do it, it means that if you are returning from Mars and see NY in ruins, it is 2/5 that it was an earthquake.

Slightly tougher one. There are ten coins in a jar. One is heavily weighted towards heads. 90%. You pick a coin and flip three heads. The total chances that could happen is 1/10 x .729 plus 9/10 x .125. DUCY .0729 + .1125 = .1854. So the the chances we picked the bad coin is .729/.1854

Notice that this technique works for events that have already happened as long as everyione agrees on the original probabilities.

3. Considering how simple I consider this comparing probability technique is, and the fact it was explained in my book, it is absurd to think I throw out the words Baye's Theorem to try to make my pronouncements seem more authoritive. I throw out those words as a substitute for the longer sentence "as any non moron can see this is simply a case of making the ratio of two probabilities".

4. This ratio of probability technique (ROP from now on) is the underpinning of the expression "extraordinary claims require extraordinary evidence". ROP is also the reason that the expression "Absence of evidence is not evidence of absence" is WRONG.

Many atheists make the horrible mistake of arguing against statements in the bible or comments by theists that do not directly pertain to miracles. This is silly on their part because the theist's evidence for their position is usually strong. Stuff like "does it make any sense the NO ONE would have stepped forward if they saw Jesus's body, (or if they realized that God wasn't talking to them in the desert).
These arguments would win the day if they were using them to persuade you of incidents that sometimes, though rarely occur. They lose only because they are trying to persuade you of the truth of something extraordinary. Something unheard of. Even more than unheard of. Something that there is good reason to believe is impossible. (Thus Pair The Board's comment that I base my probability of a miracle on its non occurence so far, is wrong. I also base it on the strong suspision that it can't occur. A subtle but important difference.)

The reason why the expression is an ROP problem works like this. Suppose I claim that I can see coins as they are flipped and caught and thus can call them with near perfect accuracy. Would you believe me if I did it five times in a row? You shouldn't if you thought that it was a million to one against me having that ability (even after I claimed it). You would need well over twenty accurate consecutive calls. But even that shouldn't suffice. Unless the only two explanations were that I got lucky or I had the ability. I could also be cheating. And even if that was a 1000-1 shot originally, it would still be, due to ROP, much more likely. So I would have to go to extraordinary lenghths to prove I wasn't cheating.

If my claim instead was that I had some gizmo in my shoe that saw the coin, it would be a less extraordinary claim and perhaps ten flips should convince you. See how that works?

BUT WAIT. Guess what. There really is at least one person who had this physical ability. They called him the Flipper. Now deceased. This changes everything. It shows that there is one example AND it shows that it is not an impossibility.
Because I know about this guy I actually would only need to see about six or seven accurate flips from someone else who claimed this ability before I'd bet on him. Just like I'd totally change my thinking about religion if I ever heard of ANY sort of CLEARLY supernatural event.

I don't have time to get to Evolution and Exodus and Absence of Evidence right now but I will shortly.

[djames]

Please apply your ratio of probability technique to exodus (including the miracle part) and the resurrection. You may have undefined quantities in the numerator & denominator...

[carlo]

[ QUOTE ]
Notice that this technique works for events that have already happened as long as everyione agrees on the original probabilities.



[/ QUOTE ]

Note that in the case of Exodus, Flood, Resurrection, or more considerably any historical event which is beyond a secretary recording the event(even this has the problem of a flawed secretary) the probabilities are definitely not evident. If the probabilities are agreed upon then you have a self fulfilling prophesy, the inherent bias of of the probability makers.This offers no comfort to to anyone hoping to find some semblence of truth, for in this type of approach the methodology becomes more important than the truth.

Its one thing to speculate on the probability of an event which is neuter as the rolling of dice but to bring this method to the world of religion, morality, or any matters which are important to the hearts and souls of men is without truth, beauty, or the good which is important to these very men.

[jay_shark]

You want P(bad coin | you flip 3 heads )

Call bad coin event A and flipping 3 heads event B .

P(A|B) = P(AB)/P(B) = [1/10*(9/10)^3]/[9/10*0.125 +1/10*(9/10)^3] = 0.0729 / 0.1854 = 39.32% .

[Silent A]

[ QUOTE ]
The reason why the expression is an ROP problem works like this. Suppose I claim that I can see coins as they are flipped and caught and thus can call them with near perfect accuracy. Would you believe me if I did it five times in a row? You shouldn't if you thought that it was a million to one against me having that ability (even after I claimed it). You would need well over twenty accurate consecutive calls. But even that shouldn't suffice. Unless the only two explanations were that I got lucky or I had the ability. I could also be cheating. And even if that was a 1000-1 shot originally, it would still be, due to ROP, much more likely. So I would have to go to extraordinary lenghths to prove I wasn't cheating.

[/ QUOTE ]

Not really. I supply the coin. I do the flipping. Easy. [img]/images/graemlins/smile.gif[/img]

This reminds me of a common response I've gotten in the past from my replies to questions from Christains about "What would it take for you to believe in God/Jesus?" After I describe a test involving me telling God/Jesus what to do rather rather than God/Jesus doing something of their own choosing I typically get a response like, "how can you demand that God should do tricks at your beckoned call?"

The whole point is to minimize the chance that the claimant is cheating.

Also, I agree that bringing up Baye's Theorem isn't an argument from authority, unless we're talking about whose probability estimates we're using.

That's all I can say for now until you follow up on the details. Who else could get away with 1/2 starting a thread like this?

[bunny]

[ QUOTE ]
I explain it in a few pages in Getting The Best Of It. Anyone who hasn't read that book has no right to have an opinion about anything.

[/ QUOTE ]
I managed to get past the "rigorous mathematicians have wasted their lives" part, then I struck this and realised there's no point me reading further. Apparently, I'm not entitled to an opinion about anything.

[borisp]

[ QUOTE ]
I consider rigorous mathemeticians, like the ones who wasted their lives figuring out how to eliminate the use of infintesimals, either obsessive compulsive, or so devoid of cleverness that they know this is the only way for them to contribute anything.

[/ QUOTE ]
"Eliminating the use of infinitesimals" is an amazingly bad example to argue this point (the OCD part of which is likely spot on). It reveals your thorough ignorance of the rigorous mathematical community.

The notion of infinitesimal has been replaced by a rigorous notion, in more than one way. Some have been useful, others not so useful. One version is that an infinitesimal can be considered a compact operator on an infinite dimensional Hilbert space, and this interpretation is currently shedding some light on possible ways to unify quantum physics with gravity. Google "Noncommutative geometry" if you would like to know more. In any event, without this notion, our understanding of quantum mechanics would be not nearly what it is today.

There are people who need these techniques, to do real jobs, that may be boring and tedious to you, but nonetheless provide things like nuclear power to homes every day. To invent and develop techniques along these lines requires not only intelligence, cleverness, etc., but it also requires PATIENCE.

It is apparent to me that you lack this essential quality David, which is why your elementary school math contest genius has matured into a lazy old man's genius at rationalizing why you don't contribute to the body of academic knowledge in a nontrivial way. The reason why I make this assessment so readily is that I too was an elementary math whiz, and as I got older I saw more and more people "fall off the boat," simply because they could not study a problem that required sustained attention over weeks, months, years, etc. These folks had every skill but patience. Put them on Jeopardy, and they will shine. Ask them to do something real, to answer a question that no one has an answer to, whose answer may take hundreds of pages, and they say "I could, but I don't feel like it."

Although, I agree, it is easier to look at others and say "I could do that, but it is beneath me" than it is to admit that you are incapable of doing it. Which brings me to my second point, which is a response to your question in the earlier thread: the reason why most people don't understand simple Bayes arguments, etc. is that they don't have the patience to really understand the argument. Perhaps their emotional investment in being right is blocking their patience, whatever. You apparently were blessed with the ability to quickly grasp these concepts, which is an exceedingly rare trait among human beings. Patience is as well.

[borisp]

[ QUOTE ]
I managed to get past the "rigorous mathematicians have wasted their lives" part...

[/ QUOTE ]
Then you are a better person than I [img]/images/graemlins/smile.gif[/img]

[Subfallen]

boris---

Wait, are you saying that patience/dedication + high-but-not-genius-IQ can achieve non-trivial results in math/science?

I honestly did not know this was possible. (No sarcasm.) My impression had always been that essentially all important work was done by a few transcendent geniuses. Confirm/deny?

[djames]

Surely this is deniable. Perhaps this isn't the best example, but Wiles was able to build upon seemingly useless tools created by those with high-but-not-genius-IQ caliber mathematicians. Maybe the strides that take us to a strikingly higher level in our collective mathematical knowledge can only be taken by the truly elite (i.e. super high IQ and passionately motivated), but even these elite don't reinvent tools that others have spent their lifetimes constructing. Maybe you consider these intermediate steps to greatness trivial though, not sure.