Simple - Isn't
If in other sciences we should arrive at certainty
without doubt and truth without error,
it behooves us to place the foundations of knowledge in mathematics.
Opus Majus, bk. I, ch .4 Roger Bacon c.1214 - c.1294
The simple believe everything, but the clever consider their steps.
March 21, 2000 CNN.com
Federal Investigators' Comments: The witnesses were on land, sea and air. Some were surfers. Many may have been influenced by news media reports about the explosion.
March 21, 2000 CNN.com
NTSB comment in its Witness Group Study report: FBI witness interviewing was focused on the possibility that a missile had been used against the accident airplane. This focus may have resulted in bias on the part of some of the interviewers. The NTSB witness reports conclude that the cause of the explosion cannot be determined through eyewitness accounts alone.
In case the "FBI biased them" explanation might not be believed the NTSB considered floating an idea that the eyewitnesses were all suffering from "perceived memories". Elizabeth Loftus of the University of Washington, perhaps the world's greatest expert in manipulation of perceived memories, was scheduled by the NTSB to appear at the Baltimore hearings to help in the presentation of witness "perceptions" of the TWA Flight 800 disaster. Her presentation was canceled by joint FBI/NTSB agreement. Tom Shoemaker asked Dr. Loftus: "Can you please share with me what your presentation was going to include?" Dr. Loftus replied, "Basically, to address the question of why people thought they saw missiles when there weren't any." Apparently the NTSB supplied Dr. Loftus with information proving to her that no missile(s) were seen by eyewitnesses, regardless of what they thought they saw on July 17, 1996.
The equation is as follows:
Probability of Event (P) = [1-(U^N) ] X
Percent Probability (P) equals one minus the Unreliability (U) raised to the power of the Number of Participants (N) all multiplied by one hundred.
For example: If you give a coin to one person and ask them to flip it and you hope to see a "head" what is the probability that you will get it?
What if we give two people a coin each and ask both to flip their coins and we hope to have one "head" show up, the probability that we will get it is now 75%.
With three people the chances that we can get at least one head is 87.5% and with four people it is 93.75%.
Another way to look at these probability outcomes is as follows:
Assume that one has identical pieces of equipment which need to operate for a set period of time but each can do so with only 50% reliability.
How many pieces of equipment do we need to operate simultaneously to ensure with 99.9% probability that we will get the job done?
Now if a witness is "right" in an observation only 10% of the time (or another way of putting this is that the witness is unreliable in 90% of his observations) then if one had 50 such witnesses what is the probability that what they said happened, actually happened?
The solution is shown below:
Accuracy of Witness Groups at Ten Percent Reliability
No of Witnesses Probability that Event Happened
1 10.00 % (N=1 and U=0.9)
5 40.95 % (N=5 and U=0.9)
15 79.41 % (N=15 and U=0.9)
20 87.84 % (N=20 and U=0.9)
35 97.50 % (N=35 and U=0.9)
50 99.48 % (N=50 and U=0.9)
Suppose an Eastbound red car collides with a Southbound blue car at an intersection controlled by green-yellow-red traffic signals on all 4 corners. There are 100 witnesses. Fifty of the witnesses contend that the signals controlling Eastbound traffic were green when the red car entered the intersection and the other 50 witnesses contend that the traffic signals for Southbound traffic were green when the blue car entered the intersection. Both drivers were alone and both were killed. Which driver ran the red light?
100% of the witnesses contend that one of the cars entered the intersection when the traffic light controlling it's direction of travel was green.
Was it the red car?
Was it the blue car?
1) First we must assume that the 100 witnesses are all independent i.e. they did not discuss the crash among themselves.
2) They are each 10% reliable as the table above assumes i.e. there is only a 1 in 10 probabality that any one of them saw the correct color of the lights.
Then you have a 99. 48 % probability that both sets of 50 eyewitnesses were in fact correct.
So how does one rationalize this?
What it means is that I can come to fully informed conclusion that there is a 99.48% probability that the traffic lights were indeed showing green in both directions at the same time.
We need no further analysis of the eyewitnesses by the police or their explanation of what they think happened.
We need to go and check out the traffic lights!
With the TWA 800 eyewitnesses we need no further explanation from the FBI, the NTSB, or the CIA of what they think happened.
We need to go and find the people who fired the missiles!
Simple. Isn't it?