Sunday, March 6, 2011

Three Brothers Bill

Once upon a time there were three brothers named Bill. They each had different fathers. The youngest, who had a weak stomach, was named Bill Abernathy, and his friends often called him Bill'aye in a mock English accent. The middle bill was named Bill Bartholomew, and his friends called him “BeeBee”.   The eldest was named Bill Charles, and the people he hung out with called him “BP” as he had developed a bladder problem in later years that forced him to spend large amounts of time in the bathroom.

One day BA got an invited to play on a game-show. His bothers excitedly watched him on TV from the living room of their split-level home.

The game-show host showed BA a series of doors, and told him that there was a fabulous prize behind one of the doors. The other two doors had amusing prizes of little value. He could choose any door, and if the fabulous prize was behind it he would keep it. BA was nervous, and almost threw up trying to make his choice, but he eventually chose door number one. Monty, the game-show host, thought for a minute, smiled, and then had his lovely assistant Vana open door number two. There behind door number two was a dented can of SPAM on an ornate pedestal. The audience laughed. Monty then turned to BA and asked him if he would like to stay with door number one, or switch to door number three. BA, unable to make another choice without vomiting, stayed.

BeeBee decided BA should have switched to door three, and silently cursed BA's week continence.

BP missed all this choosing because he was in the bathroom. He emerged just before the game-show host revealed what was behind the two remaining doors. BP asked what was going on, and BeeBee told him there was a marvellous prize behind one of the doors. BP randomly chose one of the doors, and they all waited to see who might have successfully chosen the correct door.

Which brother made the best choice? BeeBee reasoned that choosing door number one left a 2/3 chance of the awesome prize being in one of the doors not chosen. Eliminating one of those doors meant that there was twice as good a chance that the awesome prize was behind the remaining door.

BA could not change his mind, and BP was clueless. Did reasoning make for a better choice?

In order to test this I decided to create an empirical data set. I wrote the following PERL script:

# I'll run this ten million times

$door = 10000000; 
$choices = 0;
while ($choices <= $door) {
# lets put SPAM behind all the doors   
   @monty = ("SPAM" , "SPAM", "SPAM");
#then replace one can with Awesome   

   $monty[int(rand(3))] = "Awesome";
# BA chooses a door   

   $A = int(rand(3));   
   $billA = $monty[$A];
# Monty remembers what is behind the remaining doors   

   $t = 0;  
   $d = 0;  
   while ($t <= 2) {     
       if ($t == $A) {        
          $t ++;      
      } else {         
          $vana[$d] = $monty[$t];         
# and opens one of the doors that has a can of SPAM behind it        

   $open = int(rand(2));   
   $other = 1 - $open;
#BeeBee chooses the door Monty has not opened   

   if ($vana[$open] eq "SPAM") {     
       $billB = $vana[$other];   
   } else {     
       $billB = $vana[$open];   
# now BP chooses a door   

   $left[0] = $billB;   
   $left[1] = $billA;
   $billC = $left[int(rand(2))];
# see who won   

   if ($billA eq "Awesome") { $AC ++;}  
   if ($billB eq "Awesome") { $BC ++;}   
   if ($billC eq "Awesome") { $CC ++;}   
# lets print out the results and see who won most often
print "AC# $AC , BC # $BC, CC# $CC, #D $choices \n";

This program provided the following output:

AC# 3333932 , BC # 6666069 , CC# 5003653, #D 10000001

Which means that Bill'aye was right about 1/3 of the time, BeeBee was right 2/3 of the time, and BP was right 1/2 of the time.

It appears BeeBee's reasoning about the potential outcomes guided him towards potentially better results. However, BeeBee does not ever posses absolute knowledge about what the outcomes would be. Is his choice based in “faith”? Some people have argued to me that each of the brothers' answers were based in faith because they could not know what the correct answer was.

 “ faith is the substance of things hoped for, the evidence of things not seen” Hebrews 11:1 KJB

If choices about the unknown are, by definition, expression of faith, then what is the difference between the faith of the three brothers Bill?  BA's choice is based in fear; I have been told that fear is a lack of faith. BP obviously has the purest faith; his is not polluted by any foreknowledge. BeeBee's faith is guided by reason. BeeBee perpetuates doubt to manage his belief.

"I believe though I do not comprehend, and I hold by faith what I cannot grasp with the mind." --Saint Bernard

If this is faith, and is therefore of the same material as that which is used to create a belief in a god, then belief in a god is a malleable entity perfected by the application of doubt. If doubt leads one to the position that there is most probably no god then the person who declares themselves an atheist is the one with the most perfected faith.

The problem with the wise is they are so filled with doubts while the dull are so certain.-- Bertrand Russell

This is only where faith is defined as what we use to make decisions in the absence of knowledge. The more common type of faith is distinctly different. Faith used to create a type of certainty cannot be worked into a more desirable product. This type of faith is a cover for delusion; not ignorance. Ignorance can be cured with knowledge; delusion can only be cured by the decision to abandon the delusion.


Joe said...

Did Monty randomly chose the second door to open or knew ex ante it had the can of spam? Most of people get this statistical problem wrong (at 50/50) and thus are prone to be eating spam, but what else could they be wrong about? Will faith lead you to spamland?

adult onset atheist said...

Monty knows many things including which door has the awesomeness behind it. Many people find this intractable even after they have it explained to them, which is one of the reasons I included the empirical evidence. As far as Spamland…I know that there are many people who claim to have great faith who also forward lots of unwanted e-mails about jesus.