On Communication

Communication is a tricky thing.

When we explain something to somebody we encode information, a concept, an idea.  You might think that what is important is the words that are chosen but that's only a small part of the picture.  How it is said, where it is said, facial expression and gestures actually contain a whole heap of extra information.  Once this encoding has taken place we're relying on all of it being decoded by someone else in a manner consistent with our intent.  That person is going to filter the complete encoded message through their senses, thoughts, feelings, values, needs and wants and come up with their own interpretation of what we're communicating.  So how can we ever know for sure that this inherently flawed process has worked the way that we intended?

One thing we can be sure of is that, regardless of our intent, the reality is we have to deal with the reality of how that message is perceived by the other party.  Moreover, undoing that initial perception can take a lot more work than what it took to create it in the first place.  Effective communication takes place when your desired effect is the result.  If you're not getting the result you want then it's a really good idea to try and work out what the barriers are.

So please, think carefully about what you say, what you ask and what your intended result is.  Spend some extra time making sure the message is clear and be accountable when its not.

Pareidolia and Apophenia

On 25 July 1976 the Viking 1 orbiter took a remarkable image of the surface of Mars.  It revealed what undoubtedly looks like a face in the region known as Cydonia.  You can see it in the picture below.  In fact, you cannot help but see it when you look at the picture.

Face on Mars - Viking 1 orbiter

When we find patterns in visual or auditory stimuli it's called pareidolia.  We cannot help but do it.  How many of us see the face in the image below? Does the cardboard box look surprised and unhappy?

A suprised and sad box :-(

This psychological trait is probably what lies behind many paranormal phenomena: seeing ghosts, electronic voice phenomena, seeing Jesus in a frying pan or Mary in toasted cheese sandwich to name but a few.

More generally, assigning meaningful patterns to meaningless or disorderly data is called apophenia.  Again it is something we all do without thinking.  This perhaps explains the gamblers fallacy and is likely to be behind the conspiracy theories relating to the assassination of JFK, the attack on the twin towers and so forth.  In a nutshell we're programmed to find patterns.  And this can be a problem if some of those patterns will mislead us.

Why is it important to know this?  Well, much of what we know of our reality comes from science.  Science relies on experiment and experiments rely on interpretation of data.  If we cannot completely trust our ability to identify meaningful patterns in this data we could not be sure of anything.  So, experiments must be repeatable.  Not just repeatable in the same way (but that's still important), but repeatable as a logical consequence of prior experiments.  If we only had a single low resolution picture of the Mars face we might still think it was a face.  Only by taking a higher resolution picture (repeating the experiment) can we conclude that it's just a mountain.  Want proof?  Here's the same area of Mars photographed by the Mars Reconnaissance Orbiter some 30 years later with the earlier image inset for comparison.

The real Mars face

But there's also another reason why its important.  Ramsey theory tells us that any sufficiently large set of data will contain a given feature of interest.  That's why there are patterns in the stars.  Remember that scene in A Beautiful Mind where John Nash asks Alicia to think of an object - from memory she chose an umbrella - and he finds it in the night sky?  Something similar exists in statistics.  When doing repeated tests at the same confidence level you increase the likelihood you'll find one that tests as significant when it's not.  To account for this we need to make adjustments to our tests.

To ignore this meaning-seeking propensity that we all have is to risk jumping to erroneous conclusions, indulging in conspiracy theories and, in extreme cases, I suspect it leads to paranoia.  Yet the same trait allows us to draw meaningful conclusions about survival and reproduction.  If we can't work out that the tasty animals will smell us when we're up wind of them we'll go hungry and the roll of the evolutionary dice will favour another species.  If we can't work out that girl is interested in us then our chances to reproduce go down.  So it's a double edged sword.  We need to know when we're being fooled and when we're not being fooled to make sense of the world properly.

Tools like Occam's razor can help with this.  Basically, this says that simpler theories should only be traded for greater explanatory power.  If I tell you that a ghost broke your favourite vase when you left it in my care, a simpler explanation would be that it was probably me that broke it.  You don't have to make the additional assumption about the existence of ghosts to understand what happened.  And...er...I'm truly sorry about the vase by the way.

If you're mind blown by the propensity of our minds to find patterns, think on this.  Somewhere, in the digits of pi, your entire genetic code is present as 8 bit words.  There is also is a full colour image of your face encoded in the digits.  Was it put there by someone or something? Or is a simpler explanation that Ramsey theory and the infinity of pi make it inevitable?

Bayes Meets God

Bayes theorem is a remarkable bit of mathematics.  It encodes the rational, probabilistic reasoning we all do - even if we don't realise we're doing it.  Suppose I tell you that I spoke to a nice person on the train. In your mind they could be male or female with roughly equal probability.  If I tell you that the individual had long hair you instantly conclude that the person is more likely female than male.  We're doing math and not even realising it.  We consider our hypothesis \( H\) and consider the likelihood of any evidence \(E\) that we may have that supports the hypothesis.  In other words: the probability of the evidence if the hypothesis were true \(Pr(E \mid H ) \).  We also consider the complement of that hypothesis \( \overline{H} \) and the probability of the evidence if the hypothesis were false \(Pr( E \mid \overline{H} ) \).  We weigh this up and draw a conclusion very quickly. Mathematically we're computing:
\[ Pr( H \mid E) = \frac{Pr(H)Pr( E \mid H)}{Pr(H)Pr( E \mid H) + Pr( \overline{H})Pr( E \mid \overline{H})} \] In fact this math tells us why our reasoning works.

As an example, let's test the existence of god.  I may truly not know whether god exists or not so, to be fair, let's say the probability of his (or her or it's) existence before we consider any evidence is \(Pr(H)=0.5 \).  As a consequence of this we also know that the probability that there is no god is \(Pr( \overline{H} )= 1-Pr(H)=0.5 \).  These probabilities are called 'prior' probabilities and assigning the values to these such that all possibilities are equally probable is called a 'non-informative prior.'  Now, I may have a view on what these probabilities could be.  If that's the case I could assign other values to them. This is called an 'informative prior.'  However, if I do, I must be prepared to justify my reasons.

Now I have my prior probabilities set I can turn my mind to the evidence.  If there were a god he would reveal his existence when the faithful pray to him, so I might be particularly interested in whether the prayers of the faithful work.  After all, if there is a god he would answer their prayers right?  It says so in the bible:

"Therefore I say unto you, What things soever ye desire, when ye pray, believe that ye receive them, and ye shall have them." - Mark 11:24

Now, we have all heard of cases where there have been so called miraculous cures from terminal cancer.  It is true that not all such remissions can be explained by science.  The Cancer Council of Victoria state the following on their website.¹

"Spontaneous remission from an apparently terminal cancer is a rare but documented and unexplained phenomenon"

However they also state it may be easier to explain such cases as the science of oncology progresses.  Spontaneous remission in cancer patients has been estimated at 1 in 100,000.²  It does not happen often.  I am specifically interested in those cases where prayer was involved so it might be useful to look at studies on the efficacy of intercessory prayer.  Meta analysis of such studies have concluded that there is "no effect or a potentially small effect" and that "the most methodologically rigorous studies failed to produce significant findings."³  Now, this does not close the door to that possibility of an effect existing due to the potential for type II error in any statistical study.

Remember, at the beginning I said that I want to know how expected the evidence is if my hypothesis were true.  If a true believer prayed for 100,000 people the evidence is saying that 1 will experience a spontaneous remission because little to no effect has been found in studies.  That's shocking!  If god were real the bible tells me I should expect way more than that because prayer is supposed to work.  However, due the potential presence of type II error I'll assume that it's 1 in 50,000 instead.  After all that's doubling the chance of spontaneous remission when compared to studies. This gives me \(Pr(E \mid H ) = 0.00002\) .  It's like saying that god may choose to answer the prayers of the faithful occasionally - a small, but nonetheless significant, effect.

Now let me consider how expected the evidence is if my hypothesis were false.  If no god existed then it is not possible for prayers to be answered by him.  People that were prayed for would have a very small chance of spontaneous remission.  We have the evidence for that too.  The studies show that 1 person in 100,000 will experience spontaneous remission and that the rest won't.  So, how likely is the evidence if there were no god to answer the prayers of the faithful? Very likely - 99,999 people in 100,000 will not experience it so I can safely assert that \(Pr( E \mid \overline{H} ) = .99999\).  I now have all of the numbers needed to do the calculation.

\[ \begin{align*} Pr(H \mid E) &= \frac{Pr(H)Pr( E \mid H)}{Pr(H)Pr( E \mid H) + Pr( \overline{H})Pr( E \mid \overline{H})} \\ &= \frac{0.5 \times{} 0.00002}{0.5 \times{} 0.00002 + 0.5 \times{} 0.99999} \\ &\approx 0.00002 \end{align*} \]  
That number is pretty small right?  What happens if I add additional evidence such as the existence of a heliocentric solar system, the success science has had in explaining the mysteries of the universe, atrocities like slavery or the genocides committed in god's name and so on? What happens if I go through the bible and test each claim?  Clearly the evidence for god gets smaller and smaller and the places he has to hide start to shrink rapidly.  The more evidence like this we have makes the likelihood of a god approach (but not reach - if you want to cling to that) zero.

In order to overcome this it would be required that earth shattering, extraordinary evidence be produced of god's existence.  For now, the evidence is clearly not in his favour.

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1 http://www.cancervic.org.au/about/media-releases/2010-media-releases/october-2010/cancer-prayer.html^↩
2 Hobohm U (October 2001). "Fever and cancer in perspective". Cancer Immunol. Immunother. 50 (8): 391–6. PMID 11726133^↩
3 http://en.wikipedia.org/wiki/Studies_on_intercessory_prayer^↩