theology and probability, part2

In the following we shall finally consider one of the more serious issues.
Similar questions have bothered the serious thinkers for several centuries and perhaps I can finally make an important contribution.
What is the probability for the existence of the invisible pink unicorn?



It may be necessary to clarify a few terms first. With "invisible" we mean here that one cannot test or detect the supreme being with currently available scientific methods. With "pink unicorn" we mean that a true believer may (or may not) experience the supreme being through direct revelation as pink and a unicorn. It is obvious that this believe system is consistent [see footnote 1] and furthermore it seems to be reasonable as we shall see in the following.



It is also immediately obvious that an atheistic position (which assigns a probability p(i.p.u.) = 0 to the existence of the i.p.u.) is problematic and indeed inconsistent with the usual rules of reasoning.

In general one should not assign a zero prior to a consistent and eventually reasonable model, but furthermore
if one is certain that the i.p.u. does not exist, then there can be no facts directly related to the i.p.u. and thus no facts to make a rational decision that p(i.p.u.) = 0. [2]



The agnostic position, which assigns a probability p(i.p.u.) = A with
0 < A < 1 seems reasonable at first (the A stand for either agnostic or arbitrary), however, it really is problematic as well.

The obvious question is what value A to use, which does not have a good answer. But it gets much worse once we consider the fact that an agnostic (and only an agnostic!) must assign the same probability to the "invisible yellow dragon", the "invisible green parrot", the "invisible red herring" etc.
In other words, the agnostic has to deal with a discrete but obviously infinite set of possibilities, which are a priori equally likely, and assigning any probability A to one of them would mean that the sum

p(i.p.u.) + p(i.y.d.) + p(i.g.p.) + p(i.r.h.) + ... = A + A + A + ...

necessarily diverges instead of adding up to one [4].



This seems to leave us with the true believer, who assigns p(i.p.u.) = 1, as the only one with a consistent and reasonable position [3]. It is also the only one with a chance to gather real evidence through direct revelation.





-----------



[1] In order to better understand that believing in the "invisible pink unicorn" is perfectly consistent, we consider a model which assumes that the world around us with all its possible experiences is just the result of an elaborate computer simulation. The supreme being would then e.g. be the administrator of this simulation and she would be "invisible" to all
the beings in the simulated world. However, she may (or may not) choose to reveal her existence to true believers every now and then by programming the direct experience of a "pink unicorn".
Of course, to have true faith in the "invisible pink unicorn" does not include believe in this particular model and indeed a true believer would most likely understand it as heresy by limiting the potential mode of existence of the supreme being.



[2] If one makes the scientific statement that "pink unicorns do not exist", then it really means e.g. that a careful and exhaustive scientific search has not detected "pink unicorns" or that a particular well established theory excludes "pink unicorns". In other words "pink unicorns do not exist" is really a statement e.g. about the scientific search or the well established theory.

However, in the case of the "invisible pink unicorn" such a scientific search is meaningless
and no relevant theory can exist.

Furthermore, the fact that one did not experience the supreme being as "pink unicorn" through direct revelation is of course irrelevant, because such revelation requires true believe.



[3] True faith in the "invisible pink unicorn" sets the probability for all other possible supreme beings to zero, thus avoiding the problem of the agnostic.

Different to an atheist, the true believer in the "invisible pink unicorn" can indeed set the probability for the existence of the "invisible green parrot" etc. to zero, p[i.g.p.] = p[i.y.d.] = ... = 0, because she can use the fact of her own strong faith as justification; The atheist has no such fact available.





[4] added later 4/6/09

Yes, I am aware that a true Bayesian may use an improper prior in this case. (I also admit that I learned about it only two weeks ago and it was actually one reason to write this post.)

But how would she update this prior to get to real probabilities?
Notice that reports of revelation will only become available if true believers are around, but
this means Bayesian updating would depend on the existence of people not using the Bayesian method. How can one rely on the testimony of such irrational people?

One could also (try to) argue for a non-uniform prior. E.g. all invisible supreme beings are described as "the invisible X1 X2 X3 ... Xn" using n words X1, X2... , Xn.
It could make sense to weight the probability with the inverse of the complexity of the supreme being, approximated by n, e.g. such that p("the invisible X1 X2 ...Xn") = exp( -f(n) ) and f(n) is chosen so
that the sum of all probabilities converges. But there are a few problems with this.

It is obviously a very crude method to approximate the complexity of a supreme being in such a
way, e.g. some of the descriptions might be of the form "the invisible being which is ... but is
very simple indeed", etc.

Also, notice that the "invisible blue dolphin which likes yellow fish and ..." is known as
"iok Aum" in the Zaliwali language, so it would have a much higher probability than for an
English speaking Bayesian. But of course, probability is about subjective uncertainty 8-)

I guess there are many clever ways a Bayesian could "fix" this problem, but I am afraid from
my point of view it would only get us deeper and deeper into nonsense land.

a quantum of solace?

I cannot deny that the quality of this blog is declining rapidly (actually it is more accurate to say it did not improve as quickly as I hoped for). Thus I changed the title to reflect this sad fact.

In this spirit I shall write a few lines now about quantum gravity and the links I collected recently.



In her last post Sabine asks if quantum gravity has been observed by GLAST/Fermi in the gamma ray burst GRB 080916C. Interestingly, Lubos wrote about the same result(s) but with exactly the opposite conclusion. (Did I mention that the two don't like each other?)

Previously, Peter wrote once again about string theory being useless for ever predicting anything. At about the same time Lubos mentioned a recent paper about 'The footprint of F-theory at the LHC' and concluded that
the validity of string theory is a settled fact and indeed string theory is highly predictive. (Did I mention that the two don't like each other?)

Lubos also discussed Boltzmann eggs, mostly to attack a straw man used to stand in for Sean Carroll and his upcoming book. (Did I mention that the two don't like each other?)

CIP picked up on it and in comments to his post Lubos made some confusing or confused statements, which you may or may not find interesting.



--------------



And even more links.

John Ellis et al. also discussed the GLAST/Fermi and related results.

Craig Hogan proposes that excess noise observed at the GEO600 interferometric gravitational-wave detector could be direct evidence of holographic quantum gravity.

But Igor Smolyaninov thinks that this is unlikely.

Renata Kallosh found an argument why d=4 N=8 supergravity is finite for all loops.

Simon Catterall et al. put N=4 SYM on a 4d lattice (see also here).

Last, but not least, Aaron Bergman asks an important question about fretless guitars.

theology and probability

If you are a member of The Church of Bayes (*) I recommend you read this.

If you are a physicist considering to become a member I recommend you read that.



(*) Wikipedia: Thomas Bayes (1702-1761), British mathematician, statistician and religious leader



------------------------



I wanted to write about a nice illustrative example of Cosma's 1st exercise as the 2nd part to this post. But it has already been done before I could even begin with the typing (I was travelling) and I guess it is much better than what I would have achieved (but I would have left out the 'waterboarding', which is not that funny).

I recommend the comments to Brad DeLong's example if one is interested to see some members of the church argue (with each other). But then, perhaps you have something better to do...



The main lesson from all this is very simple. If the set of considered models does not contain the true model then Bayesian updating can go very wrong. But how does a Bayesian know that her process includes the true model without leaving the reference frame of her church?



Of course, we should not expect a true Bayesian to agree that there is a problem (e.g. in the comments to DeLong's post) - after all we know (now) that their procedure does not always converge on the truth...

Ikea chairs

In a review article about agent-based models Dietrich Stauffer once wrote

"Physicists not only know everything, they also know everything better."

In the spirit of "this indisputable dogma" Lee Smolin recently published his thoughts
about "time and symmetry in models of economic markets", advocating to formulate "economics in the language of a gauge theory".

If I would be in a generous mood, I would perhaps only point out that worse stuff has been published on the arxiv and in particular its econophysics section. But I am not and thus I will actually quote some of the deep insights of the author:

"..publishers have a simple motivation to cut costs by only printing the books that will sell,
but it seems very difficult to predict accurately which books will sell and which won’t.
One rule of thumb-to which there are exceptions-is that books that are not in book stores don’t
sell."

" Combining space, time and uncertainty, there is then a vast explosion in the number
of goods. Rather than having a particular model of Ikea made chair, we have a vast set of
chairs..."

"Consider the adage, well known to sailors, ”The two happiest days in
the life of a boat owner are the day they buy their boat and the day they sell it.”
Imagine coding this in a utility function." (*)



If one is interested in similar deep insight then this paper offers plenty of it.

If one is actually interested in the application of gauge theory in finance I would recommend
the book of Ilinski and this review.

But if one wants to read a well written critique of econophysics, I would recommend this essay instead.



(*) Actually, I can confirm the adage from personal experience as an obvious truth.