Why did I make this proof?

People quite often state wrongly that "Absence of evidence is NOT evidence of absence." Why do they do that? Perhaps because they do not know better? And with this proof they get the possibility of knowing for sure that "Absence of evidence IS evidence of absence.", which is quite useful in many situations, such as these:

Absence of evidence for...
  • ...fairies, trolls, and ghosts...
  • ...weapons of mass destruction in Iraq...
  • ...crop circle aliens...
  • ...gods...
  • ...Microsoft patents in Linux...
  • ...miracle healings...
  • ...credentials...
  • ...CO2 from machines causing global warming...
  • ...UFO space ships...
  • ...telepaty, ESP, and telekinesis...
  • ...Linux stealing code from SCO corporation...
...means they get less likely all the time.
Buy a mug or shirt with the proof!

How to use it

How people react to the proof tells a lot about them.
Sane people think it is interesting and often useful.
Smart educated ones think it is fascinating.
Educated or accredited ones without smarts tend to wrongly claim there is something wrong with the proof, while misunderderstanding it.
Typical misunderstandings are of the axioms, what their logic mean, which logic system is used, missing that this is probability theory, etc.
And some use emotions against it, which of course is emotional and not sane.


This is the reason that faith is bad. Faith is the assumption of truth when evidence is absent. This absence of evidence is evidence of absence of truth. So faith in itself is evidence of falseness. Therefore, faith is not a road to truth, but instead a road to falseness.

Blindly following orders is also bad. The absence of a good reason for an order is evidence that the order is bad, since absence of good is bad.

Carl Sagan is often quoted as saying "Absence of evidence is not evidence of absence", but he meant it as an example of what fools mean, and has since been consistently misquoted as something he meant.
Correct quote by Wikiquote.
Misquote by Quotationspage.

One source of this confusion may be that "evidence" is a near synonym to both "proof" and "sign/indication" which are two different concepts. Using these words instead gives the two following correct sentences:

More serious is the American Statistical Association, who even sells a T-shirt with the wrong slogan on it. Being statisticians, they really should know better. Considering the large number of members who could have pointed out this error, it is rather telling that it is still there.

There was a previous version of this proof, but this new one is much shorter, simpler, and it also defines the concept of evidence, which is also very useful and absolutely necessary to understand what the proof is about, which many never did understand.

I have seen that the comprehension of this "absence of evidence" concept is one of the main differences between sensible and gullible people. Gullible people will not and cannot understand this concept.

A less proofy explanation:

For those of you who have not learned Bayesian inference yet, here is an explanation with words, examples, and analogies:

More women than men wear skirts.
Both women and men can use trousers instead of skirts.
Skirts for men are kalled kilts, and are usual in Scotland.
Thus there are 4 possibilites:

A man without a skirt
A woman without a skirt
A woman with a skirt
A man with a skirt

A skirt is evidence of a woman, because
there are more women than men wearing skirts.

So, if you see someone NOT wearing a skirt,
then it is more likely a man.

I get to use my shirt:

A Jehovas witness rang on my door, and I heard her coming, so I got my "Absence of Evidence" shirt on just in time to greet her.

This Jehovas witless was typical, babbling incoherently about Bible stuff. So I gently steered her toward evidence and proof, which turned out to be surprisingly easy, and she babbled happily away about biblical proof and the faith's proof for a while.

So I said to her "You do not know of what you speak, since you would not even recognize a proof if it was right in front of your nose!", while i put my chest closer to her face and pointed to the proof there.

She looked at me as if I were a devil, clammed shut, and went away with an arrogantly superior and offended expression. So I was obviously completely right about her.

Lastly, an anecdote from Roar Lauritzsen about Absence of Evidence:

"Suppose you are a programmer, and you are looking for bugs in a program. At first you cannot sleep at night because you are convinced that there must be a bug somewhere, you just haven't found it yet. To find the bug, you test the program to see if you find something that doesn't work as you expected. If you found something, it would be evidence that there was a bug. If you test the program a lot, and still find no evidence of a bug, this increases your confidence that there is no bug. In other words, it counts as evidence for the absence of a bug, and you are finally able to sleep better.

After a while, your program is thoroughly tested, and you still find no evidence for a bug. You begin to suspect that there might not be a bug after all. However, if there is no bug, you will have no purpose as a programmer. You feel as if your life depends on the existence of a bug. You are now looking for the Bug that will save you. You believe that there must be a Bug, so you test your program even more thoroughly. When you still cannot find any evidence for a Bug, you start to rationalize: Although I cannot find any Bug, that does not prove that there is no Bug. You are now a true believer in the Bug."

PS: A nice comment, in Spanish.

PS: A nice article, with pretty pictures.

2010-5-13: I am on Seth Robert's blog

2010-5-14: And then on boingboing