By the Principle of the Long Run, a coincidence is always deemed to be a chance event, no matter how tiny the odds. If paranormal coincidences exist, the normal scientific approach means that they would be mixed in with chance events and made invisible.

Science rules out of existence the very phenomenon that it should be investigating: that some coincidences may be caused by an undefined non-chance process, X.

This assumption that coincidences must always created by chance means that the conventional criterion for statistical significance does not work for coincidences. Null hypothesis significance testing (NHST) is not applied.

P < .000000000001 Not Significant, says the accepted scientific view

The standard criterion for rejecting a null hypothesis H0 is p<.05 or p<.01. For coincidences, however, this probability can be as low as p<.000000000001 (10-12) or even smaller and the occurrence is accepted as falling within chance levels.

This double standard in evaluating the statistical significance of coincidences is interesting: no matter how improbable the outcome, the event is said to be consistent with the null hypothesis.

How can we escape this paradox? I wish to suggest a hypothesis that my totally skeptical friends and readers will find apocryphal. To avoid miscounting paranormal events as chance events, and defining them out of existence, it is necessary to hypothesise two populations of coincidental events, those due purely to chance, and those that have a putative paranormal source.

Imagine a coincidence with an odds of 10 to the minus 12. This is one chance in a million million. Consider the  possibility that there is an alternative to the normal, null hypothesis, which we can call the ‘paranormal hypothesis’:

H0: The null hypothesis – what occurred was purely chance

H1: The paranormal hypothesis – what occurred was too improbable to be caused by chance

Plausibility of events with different odds with a duplex of distributions for normal (chance) and paranormal (non-chance) coincidences. The shape of the distributions is normal and, speculatively, the dispersions are set to provide a cross-over point with odds of 10-12  where the Bayes factor is one (thin vertical line). Events with odds to the left of this line have Bayes Factors < 1.0 and to the right of this line, Bayes Factor > 1.0. The two dotted lines indicate events with odds of 10-6 and 10-18 where the Bayes factor is .20 and 5.0 respectively.

According to this hypothetical framework, a cross-over point with a Bayes Factor of 1.0 occurs with an odds value of 10-12. In order to specify the form of these distributions it would be necessary to collect large numbers of data points with exact odds values.The hypothesised existence of a separate population of paranormal events places N Theory and P Theory on an equal footing as explanations and avoids a double standard.

Is the theory correct?  It is impossible to say.

# Improbability and Impossibility in Nature

## The Science of the Impossible

#### Yet William Hyde Wollaston and Joseph von Fraunhofer independently discovered that the spectrum of the Sun contained a great many dark lines which, by 1859 had been shown to be atomic absorption lines. Each chemical element present in the Sun could be identified by analysing the lines, making it possible to discover what a star is made of.

Another example is teleportation.

## Teleportation

This word was coined by Charles Fort in his book Lo! and was subsequently copied by legions of science fiction writers including the “transporter” in Star Trek. Thanks to entanglement, physicists have achieved teleportation  Particles that are entangled behave as if they are linked together no matter how wide the distance is between them. If you change the “spin” of one entangled electron, the spin of the twin electron will also change.

Entangled particles therefore  “teleport” information. In 2002 a theoretical way of entangling  large molecules, was described. “Classical teleportation” even occurs when a beam of rubidium atoms disappear in one place and reappear in another. This method transmits all the information about the atoms through a fibre optic cable so that they can be “reconstructed” elsewhere.

Yet entangled particles, it can be argued, are part and parcel of ‘one thing’ and teleportation may not be valid in this context. If by unfortunate accident somebody severs a finger from their hand, the finger is still a part of their hand. A severed finger can survive for 12 hours or more in a warm environment and up to a couple of days if refrigerated. It can be re-attached to the hand by reconnecting the arteries and restoring the blood flow. So the finger and the hand remain a part of one body.

## Precognition

Julia Mossbridge and Dean Radin (2018) review the evidence for precognition or ‘prospection’  in a recent paper  http://dx.doi.org/10.1037/cns0000121 As they point out, scientists generally consider prospection involving influences from the future to be ‘flatly impossible’. They present empirical evidence challenging the assumption. If this evidence can be replicated using preregistered designs and analyses, then the consequences would be profound.   Such replication studies are keenly awaited.

My review of the literature shortly to be published suggests that we may be waiting in vain if we are looking for evidence inside the laboratory.

## Impossible Today, Possible Tomorrow?

The paranormal is the investigation of phenomena that are thought, on current knowledge, to be IMPOSSIBLE.  Yet some of those very things may be possible in the future. The question is which ones?

The field of the paranormal has changed enormously in the last half-century with a massive growth in numbers of investigators and publications on extra-sensory perception, psychokinesis, precognition and homeopathic medicine (Figure 1).

FIGURE 1. Growth in numbers of research publications about specific topics within the paranormal in 20-year periods, 1960-2019.

## What is Here

The ‘Anomalist Psychology’,  ‘Paranormal’ and ‘Coincidence’ sections of this blog site present authentic, first-person accounts of anomalistic phenomena and their often compelling nature along with laboratory studies, research syntheses, and critical analyses.

This blog site covers the entire field of Anomalistic Psychology – ESP, psychokinesis, precognition, ganzfeld, dissociative states, out-of-the-body experiences, near-death experiences, hypnotic trance,  and their relevance to theories of consciousness.  Many of the same psychological processes are involved in these different areas, i.e. the will to believe, magical thinking, subjective validation, confirmation bias, expectation and placebo effects, and many more.

The blog site is supported by a new book, Psychology and the Paranormal, to be published in 2020.

Some of the most common obstacles in teaching students in this field are: readiness to believe almost anything without sound reasons, misunderstanding of laws of chance and probability, lack of statistical sophistication or understanding of scientific methodology. The critical tools necessary for scientific appraisal of the paranormal are not generally available.

On the surface paranormal phenomena all appear to defy rational explanation. The blog encourages readers to acquire the critical skills to appraise scientific claims for the paranormal.  After reading both ‘sides of the story’, readers should be in a position to express informed opinions and have the tools and methods for critical thinking about the paranormal and scientific claims more generally.

The blog is geared to the needs of teachers, researchers and students interested in Anomalistic Experience, Parapsychology and Consciousness. These are exciting, challenging and fun areas on the fringes of mainstream science.

## The Requirement of Impartiality

Here I do not take a fixed believing, sceptical or disbelieving stance on the paranormal. I offer a neutral gaze which seeks the evidence both pro and con. This approach keeps the door open to whatever conclusions the evidence leads.

The best evidence from studies and meta-analyses across a wide range of areas are reviewed. A particular focus will be studies from the post-2000 period up to and including 2019 as other books adequately review the history of the field (e.g. Caroline Watt: Parapsychology. A Beginner’s Guide).

There are instances where the evidence is so strong that I have changed my own position over recent years. For half of my life I was a dyed-in-the-wool ‘skeptic’ or, to put it more plainly, a disbeliever. That situation changed. I steadfastly maintain the neutrality of the dispassionate scientist, neither believing nor disbelieving, attending to the evidence. I hope that other ‘skeptics’ will strive to keep their minds untainted by prejudice and show the moral courage to go where the evidence takes them.

I humbly encourage every reader to avoid being ‘intellectually whipped’ into any fixed view of the truth. Comfortable though it may be to have a fixed view, that view could well be misplaced, and, unwittingly, lead into a cul-de-sac.

Be aware of the streetlight effect or drunkard’s search principle, the bias that occurs when we search only where it is easiest to look:

A policeman sees a drunk man searching for something under a streetlight and asks what the drunk has lost. He says he lost his keys and they both look under the streetlight together. After a few minutes the policeman asks if he is sure he lost them here, and the drunk replies, no, and that he lost them in the park. The policeman asks why he is searching here, and the drunk replies, “this is where the light is”.

Looking where it is easiest to look

We must learn to look where the evidence is, not where it is easiest to look.

This blog provides critical analysis and motivation to challenge, defend and justify scientific claims of the paranormal.

If the evidence is there to guide you, changing your mind is a strength not a weakness.

Let’s stop acting like the drunk who is looking where the light is brightest; let’s look with sobriety in the cold daylight where there might be something significant to be discovered.

# Under the Wallpaper

One never really knows what might be under the wallpaper. Redecorating reveals secrets, a veritable archeology of habitation. When my parents sold up and bought a house about 50 years ago, they left few traces.  I often look down the street from the main road as I go past, to see if the place is still there, but only once have I walked to the house to see it at close quarters. One day when my nostalgia got the better of me I visited the building to take a closer look at our former dwelling, a ground-floor maisonette in Landport, Portsmouth.

## Three bright orange murals

Quite fortuitously, the owners were redecorating. I took the opportunity to knock on the door, but nobody was home.  Curtains were down, ladders were up,  paint cans, brushes all around, and – surprise, surprise –  peeled back wallpaper. I couldn’t resist taking a quick peak through the window at the bedroom where my brother Jon and I slept and dreamed over a ten-year period (see red arrow).

On Jon’s side of the room, as bold as brass, I could see three bright orange paintings – a trumpet, a bugle and a banjo. Immediately I knew these paintings were Jon’s. I knew how Jon would doodle and sketch things. Jon loved jazz.  If Jon painted anything, it would have to be these. I was seeing them for the very first time.  Jon must have done them after I had moved north in September 1966, shortly before Jon had moved to London as a professional jazz musician.

## Odds

What are the odds of seeing Jon’s musical murals on my only visit to the building in 50 years?

A) We need to estimate how likely it was that Jon had ‘received approval’ to do these paintings in the first place. It is difficult to put a hard-and-fast figure on this, but it is unlikely to have been more than one in 10.

B) Next, we need to make an assumption about how often the walls were repapered. I expect on average around once every five years, which would be 10 times in 50 years.  The probability that the wallpaper was peeled off on any particular day over 50 years (18,250 days) = 10/18250 = .000548 = 5.48 x 10 to the minus 4

C) Next, we need to calculate the probability that I would pay a visit on any particular day over the 29.5 years (10,767 days) that I was living in Britain over this 50-year period, which is  1/10767 = .0000928 = 9.28 x 10 to the minus 5

The odds for P (A +B+C) = 1/10 x (5.48 x 10 to the minus 4) x 9.28 x (10 to the minus 5)           = 50.85 x 10 to the minus 10 = 5.08 x 10 to the minus 9

or

5 chances in one billion

# Reality or Illusion?

I have provided accounts of five striking coincidences over my lifetime. The five events individually have odds in the range 10-9  to 10-18.  What are the odds that all five coincidences could happen to one individual?

To determine the probability of five independent events, A, B, C, D and E, all occurring, we need to multiply the probabilities of the individual events:

P(anB and C and D and E) = P(A)×P(B) x P(C)×P(D) x P(E)

The five coincidences, which were independent of each another, are as follows:

A) The Chiswick Coincidence: P=10-18 = one chance in 1,000,000,000,000,000,000  = one in one quintillion (a million, million, million)

B) Coincidence or Luck?: P = 10-10  = one chance in ten billion.

C) Citizen 63 – Marion Knight: P= 4.5 x 10-10  = 4.5 chances in ten billion

D) The Flying Horseshoe:  P = 1.3 x 10-12 = 1.3 chances in a million, million

E) Under the Wallpaper:   P = 5.08 x 10-9 = 5 chances in a billion

The combined probability of the five events is :

P =   10-18 x 10-10 x 4.5 x 10-10 x 1.3 x 10-12  x 5.08 x 10-9

P = 3 x 10-58

This is one of the smallest probabilities imaginable.

Yet, according to the accepted scientific theory, coincidences are chance events, and so there is nothing extraordinary here.

# The Flying Horseshoe

## A Mysterious Horse Shoe

It is one of our cultural beliefs that horseshoes are lucky. Almost everybody knows it. Many respect it. There is a cottage industry around it. Almost every “olde worlde” pub and inn in Europe displays one or more horseshoes. Almost anybody who has had contact with horses, and many who have not, keep a horseshoe on the mantle shelf, on a wall, or hanging on a door, myself included. Although skeptical about astrology, the Loch Ness monster, and leprechauns (to name but a few) I am today as capable of superstitious behaviour as anybody when it comes to horseshoes. Let me explain why.

One day I was clearing the junk out of my garage with the help of a local odd-job man, Bert, who had called by one day to see if I needed any assistance. After a couple or so years of neglect the garage was neck-high in newspapers, boxes, and various other recyclables. Bert and I set about the task and spent the better part of a morning cleaning it out very thoroughly.

Before Bert set off with a fully loaded van, he pointed to a rusty old horseshoe lying on the garage floor. I had certainly not been consciously aware of it and, presumably, the previous owners had left it there. “Look,” Bert said, “what’s this doing on the ground? You should hang it up. It’ll bring you luck.” I was surprised that he took this old rusty horseshoe quite so seriously, but, without further ado, Bert placed the horseshoe outside on the garage window sill next to the door. That was the last I thought about the horseshoe for two or three years.

On Sunday, November 1, 1998, I was making a hurried attempt to tidy up my back garden. I noticed the horseshoe lying on the ground. I hesitated for a few seconds, but decided not to pick it up, and left it on the ground. I remember consciously thinking to myself, What on earth are you doing almost taking this silly lucky horseshoe stuff seriously!? As usual in those days, I was fairly busy. After sending off a batch of edited manuscripts to the next issue of the Journal of Health Psychology on Monday, giving a lecture to the fifth-year medical students at Cambridge University on Tuesday, I was off to Milan on Wednesday to visit two research project leaders in northern Italy.

I was accompanied by my colleague Catherine Sykes. Following the two visits, Catherine and I had spare day on Saturday, November 7, to do some sightseeing. We were staying in Breschia, and decided to take a train to nearby Verona to spend a few hours there before returning home to London.

## A Mysterious Horse Show

After arriving at Verona train station, we discovered that centre of the city was a bus ride away. We walked out of the station and across the plaza to a bus stop with a mob of excited people, many of whom were foreign (i.e. non-Italian)  clearly in a hurry to go somewhere. Almost as soon as we arrived at the bus stop, a bus arrived and everybody crowded on, us included.  Mistakenly we assumed the bus was going to the town centre. It was absolutely crammed full of people like sardines in a can. After a minute or two of pushing and shoving to get a position in the jam, we asked one of our fellow travellers where exactly the bus was going. “Why, to the horse show, of course!”

So here we were being swept along by a chance decision to a horse show in Verona that we didn’t know existed until that moment! The bus was absolutely buzzing with people excitedly anticipating what – for them, and also for me – was to be a very special event.

Rather than get off at the next stop, we decided to stay on board and see what all the fuss was about. It was, we discovered on arrival at the show grounds, the 100th Fieracavalli, Verona 5-8/11/98.” This was certainly no ordinary horse show.

We were directed to the entrance gate for foreign visitors to discover hundreds of people crowding around with their passports. All foreigners with valid passports were to be admitted free of charge. After a few minutes we managed to get to the front of the line and were given our admission tickets. We entered the stadium and found thousands of people walking around many dozens of stands and marquees with every imaginable equine thing on display. There were saddles, riding gear, horse feed, anything that horses and riders could possibly want. Catherine and I strolled around the park with no real sense about what to look for, deciding to spend an hour there and leave…

## A Flying Horse Shoe

After a few minutes of exploration, we came to a large marquee. We could hear applause from an audience inside and we ventured in to find a few hundred people viewing a pony and rider contest from the tiered seating. We found some spare seats near the top of a tier in the second row from the back, and sat down. We observed a contest of skill and speed. Each pony and rider entered the arena and galloped at full speed around a small course marked out by posts, then raced to the exit. We watched three pony and rider teams. Then a fourth pony came into the arena and began its gallop through the course.

Suddenly, without warning, we became aware of a fast-spinning object flying through the air. In a split-second it became apparent that it was hurtling straight toward us. Catherine shouted out, instinctively I ducked, and like a huge bullet, the fast-flying object passed a few millimetres above my head. I felt its slip stream across my hair.

The object hit a man seated directly behind and above me squarely in the body. His wife screamed, but he was unharmed, the padding of his coat having protected him. It was a flying horseshoe!

Had I not quickly lowered my head beneath the horseshoe’s trajectory, I quite possibly would not have survived. At best I would have received a serious head injury. At worst it could have been fatal.

I thought immediately of the horseshoe lying in my garden. I had faltered over it but picked it up. I couldn’t stop myself from thinking that I should have picked the horseshoe up and put it back where it belonged, on the windowsill.

We left the stadium is a state of mild shock. As we discussed the incident, the ‘take-home message’ was clear: Horse shoes are lucky.  Handle with respect!

The next time I was in the garden I immediately put the horseshoe back ‘where it belonged’ – on the shed windowsill.

What would you have done?

## Odds

We can calculate the odds of the flying horseshoe events as follows:

A) Find a horseshoe in the garden shed – 10 to the power -1 = 1/10

B)  Find the horseshoe lying on the ground immediately before visiting Italy, faltering, and finally leaving it there – 10 to the power -2 = 1/100

C) Following a crowd on a bus in Verona – 10 to the power -1 = 1/10

D) Discovering the horse show — 10 to the power -2 = 1/100

E) Entering a particular marquee – 10 to the power -1 = 1/10

F) A horseshoe flying precisely toward me. There are 360 degrees horizontally and 360 half-degrees vertically – 1/(360 x 360) = 1/129600 = 1.3 x 10 to the power minus 5

The combined probability of above A – E,  P = 1.3 x 10 to the power minus 12.

This represents odds of 1.3 in one million, million.

This coincidence was originally published in: Marks, D. F. (2000). The Psychology of the Psychic (2nd ed.), pages 248-250.

# Citizen 63 – Marion Knight

## What I Missed Seeing

It was 1963. I had played a minor role in a BBC documentary film “Marion Knight’ but had missed seeing it because I was travelling abroad. This was an era without video recorders or YouTube. If you missed something, you missed it, and that was that.

The ‘Citizen 63’ series received critical praise. The series was described as “One of the most significant TV shows of 1963“. Five individuals had been shown dealing with their everyday lives, their pressures, problems, beliefs and values: a businessman, a police inspector, a shop steward, a scientist and a ‘rebellious’ teenage schoolgirl, Marion knight.  The director, John Boorman, was working for the BBC in Bristol.  He later directed other documentaries, such as The Newcomers (1964). A few years later he was in Hollywood (Point Blank, 1967, Hell in the Pacific, 1968). Boorman returned to the UK to make Leo the Last (1970), Deliverance (1972), Zardoz (1974) and Exorcist II: The Heretic (1977). He became more famous for Excalibur (1981), The Emerald Forest (1985) and Hope and Glory (1987) which brought a second Academy Award Nomination.

Commenting on Citizen 63, one reviewer wrote: “1963 was very much the coming-of-age for those children born in the aftermath of the Second World War. Free of the threat of war and no longer constrained by National Service and of the austerity years that followed there was a new found hope for the future that manifested itself in pop, fashion and a rejection of Victorian values and the social taboos that Britain had been steeped in since the turn of the century…Citizen 63 is an extraordinary record of a transitional period when conventions were being challenged at the very point when youth culture was about to explode in a way that would define the whole era.”

To quote Philip Larkin's poem:  "Sexual intercourse began In nineteen sixty-three (which was rather late for me) - Between the end of the Chatterley ban And the Beatles' first LP."

‘Marion Knight’ was screened on 11th September 1963.  Marion was depicted as a so-called “rebellious girl” from a secondary-modern school in Portsea.  Marion was a follower of the trad jazz scene and dismissive of the pop music explosion that was erupting at the time. Selected for “her feisty, opinionated approach to life…with qualities of “leadership and grace”, Marion was the girl-friend of my school mate, Nigel Banister.

John Boorman – Director and Narrator opened with the comment: This film is about one person, you may admire her, you may dislike her but from her we may learn something about ourselves, for she is part of our society – a “Citizen ’63”.

Still from Marion Knight (1963) with Nigel Banister (left) and Marion Knight

## What I Finally Saw

On 24th October 2005,  I was napping in front of the TV.  This was not a casual nap.  It was a definite mini-sleep, fully prone on the sofa.  When I opened my eyes, astonishingly, there on the TV was a B & W film showing two people I knew, Nigel and Marion, riding a motor bike. In one of life’s circles, this was the opening scene of ‘Marion Knight’, the film I had missed seeing in ’63.

#### What caused me to wake at that particular moment, I will never know.  I thought I must be dreaming. As I opened my eyes, this is what I saw: my two teenage friends Marion and Nigel, on a film made 42 years earlier.

The clip was included in a BBC2 documentary  The Battle for Britain’s Soul  about the decline of the Christian church in 1960s Britain.  The BBC website states: “Angels over battlefields, the birth of the welfare state, US evangelism and a revolution in sexual freedom are all factors in the evolution of today’s largely secular society.”  The film was presented by the ‘Hippie Vicar’, the Rev Peter Owen-Jones.  According to Peter Owen-Jones, Marion Knight’s comments about free love among teenagers were emblematic of the ‘sexual revolution’ that is alleged to have taken place in the 1960s, when church congregations went into  a sharp decline.

## What Were the Chances of Seeing This Clip?

I obtained copies of both programmes from the BBC Preservation Services Department. The Marion Knight clip lasted 40 seconds.  I normally watched TV during the evenings for around three hours. With four channels, I need to calculate how much television content was available for the whole time I lived in Britain in the 29 years from September 1986 to August 2015.  Removing holidays or trips abroad would reduce this time by about six months, leaving 28-and-a-half years.

The calculation follows:

ACTUALLY VIEWED (AV) 180 minutes a day for 28.5 years = 180 x 365 x 28.5 =  1,872,450 minutes of TV. Multiplying by 60 gives 112,347,000 seconds.

Bearing in mind that the total amount of evening television across 4 channels over this time would have been a lot more than this. Let’s say an evening lasts for 6 hours from 18:00 to 24:00.  Then the total evening TV content would have been:

TOTAL TV CONTENT AVAILABLE (TA) 6 hours = 360 minutes a day for 28.5 years = 360 x 365 x 28.5 x 4 = 14,979,600 minutes of TV which is 898,776,000 seconds.

The probability that the clip would have occurred in the TV content I actually saw would have been: AV/TA = one-eighth ( .125).

The clip lasted only 40 seconds. What are the chances of seeing this 40-second clip at the precise moment that I awakened?  Bear in mind the entire amount of TV I had actually viewed over the 28.5 years was 112,347,000 seconds.  The answer is:

40/112,347,000 = .0000003560

To allow for the fact that I only saw one-eighth of the total evening TV available, we must multiply this figure by 1/8, which gives: .00000004450

or 4.45 x 10 to the minus 8.

## A Boundary Condition

There is another factor to consider. The only possibility to view this clip was dictated by the fact that the producer of the 2005 BBC documentary ‘The Battle for Britain’s Soul’ decided to include this particular clip from the 1963 BBC film ‘Marion Knight’.  The chances of this event are difficult to estimate.  In round figures we could guess that it would have been be in the region of one in a hundred (10 to the minus 2).

This would put the combined probability of seeing the clip at around:

4.45 x 10 to the minus 10

or

4.45 chances in ten billion.

# Coincidence or Luck?

How many striking coincidences can we expect in a single lifetime? Setting the bar high, let’s define ‘striking’ as a probability of less than one in a billion. I list here a few of my own. The first set of coincidences was an incredible run of luck while travelling as a student. I feel entitled to count these as coincidences because, in each case, whatever we set our minds to, happened a few minutes later. It was a case of coincidence combined with luck. I estimate the probability of each of the four events as we go along, and give a final probability estimate at the end.

## 1) No Money in Cologne

In August and September 1963 I went travelling with a school friend Graeme Locke.  We travelled through the UK, Scandinavia and the two Germanies.  The trip of 2000+ miles took us over land by road and rail, and over sea ferry routes. For the road parts, we couldn’t hitchhike the whole time but we did so whenever we could. In East Germany, we travelled by train from Berlin to Cologne, one of the few approved routes available.

On arriving at Cologne station, we had a slight problem – we still needed to get back home in Portsmouth but were completely out of money. I say ‘slight’ problem, because it was soon resolved. We started a ‘porter service’ for people in need of help with their luggage. We stationed ourselves at the taxi drop-off point and, within no more than 3 minutes, arrived an elderly lady in furs with a luxurious set of four suitcases.

Möchten Sie eine Hand mit Ihrem Gepäck?

Sure enough, the dear lady needed some help to take her considerable luggage set to platform 13. We took it over, about three minutes work. Thanking us, the lady gave us a tip – a very large tip. From memory, is was 40 Deutsch marks – four of these:

In today’s money, it must have been worth at least €60, enough to buy our train+ ferry tickets to Dover, plus some change for a slice of pizza  [p = 10 to the minus 4].

## 2) No Money on the Ferry

OK, so far so good, we were aboard the Calais-Dover ferry, but now we were skint once again. In those days, before health and safety regs took over everyday life, people would be crammed into every available space on board the ferry. On every deck from aft to stern and from port to starboard, passengers were sitting cheek by jowl.

We got chatting to a Turkish student squatted next to us on his way to Fresher’s week at Newcastle University. He had a lot of questions because this was his first visit to England.

The bell rang for the first sitting of lunch. C’mon he said, let’s go for lunch. We explained our predicament, and instantaneously he just said, no worries, lunch is on me. We enjoyed a fulsome lunch with our new found Turkish friend [ p = 10 to the minus 2].

## 3) No Money at Dover

Here we were in Dover, as skint as badgers, and so we started hitching again. A vehicle driver stopped within a couple of minutes offering to take us to Brighton. The driver kindly dropped us at Brighton station with a 10/- shilling note for our fares to Portsmouth [p = 10 to the minus 2].

## 4) Ten Bob in Brighton

No way were we about to waste ten bob on train fares!  Off we went to the A27 hitching the last remaining stage to Portsmouth.  Our final driver, in the first car that came along the road,  lived at Havant, a few miles east of Portsmouth. He kindly took us to his house, cooked us beans and poached eggs on toast, and drove us to our respective homes in Portsmouth.

After our 2000-mile journey, we arrived home with a crisp 10 shillings profit! [p = 10 to the minus 2].

## Probability of the Sequence

The four events are estimated to have the following probabilities:

1) Lady gives us 40 D-marks at Cologne station: p = 10 to the minus 4

2) Student buys our lunch on the ferry : p = 10 to the minus 2

3) Man gives us lift to Brighton and a 10 shilling note : p = 10 to the minus 2

4) Man cooks us a meal and takes us home: p = 10 to the minus 2

The combined probability of these four events is:

P = 10 to the minus 10 = one in a 10,000,000,000

or one in ten billion.

# Chilling

‘Murdered’ British backpacker Grace Millane, 22, made a chilling final Instagram post – featuring a skull painting and a quote about death.

Grace, an advertising graduate and talented artist, is believed to have been killed between December 1 and 2, court documents show. A few weeks before her death, Grace, had uploaded her last post to her Instagram art page – a watercolour of a human skull.

Grace had captioned the image “Two can keep a secret, if one of them is dead” – a quote from the theme song of the hit TV show, Pretty Little Liars, which follows the lives of four girls after their friend vanishes.

She captioned the post: “Two can keep a secret, if one of them is dead”
(Image: Instagram).

# One person’s coincidence another person’s yawn?

I recently came across the late Michael Thalbourne‘s  ‘A BRIEF TREATISE ON COINCIDENCE’.  Fascinating!

Especially notable in Michael’s account is the huge  gap that exists between the impact of a coincidence on the experiencer and an outsider perspective on the very same event.

This fact is revealed in his own experiences of sharing coincidences and witnessing other people’s reactions. This observation has been confirmed in laboratory research suggesting that one person’s amazing coincidence can bring on a yawn.

## Michael Thalbourne

Dr Michael Thalbourne (MT)  was born in Adelaide, South Australia, on March 24th 1955 and passed away on the 4th of May 2010. He was educated at the University of Adelaide and the University of Edinburgh. From 1980 until 1987 Thalbourne was employed at the McDonnell Laboratory for Psychical Research at Washington University in St Louis Missouri, USA.  In 1992 he returned to his hometown of Adelaide where he served as the President of the Australian Institute for Parapsychological Research and was the editor of the Australian Journal of Parapsychology.

## Survey of Beliefs about Coincidences

MT used a 10-item survey of attitudes towards, and experience of, coincidence with  24 people.  To  the statement “I have experienced truly astounding coincidences”, 25% reported “often”, 63% “now and again”, and 13% reported “rarely”; nobody reported “never”.

Another statement was:  “I experience many small coincidences which would probably not impress other people but which make life interesting for me”. 29% responded “strongly agree”, 58% said “agree”, while 8% were uncertain and 4% said “disagree”.

A third statement was “It takes a certain vigilance of mind to see subtle coincidences.” Sixty-seven percent agreed or strongly agreed, 17% were uncertain, and the same percentage said “disagree”. Thus, the majority agreed with the statement.

The causation of coincidences was included in the survey. MT asked: “Coincidences may be expected to occur from time to time just by chance or pure luck, and they never signify anything important or meaningful.”  MT reports that no one said “strongly agree”,  33% said “agree”, 21% were uncertain, while 29% disagreed and 17% strongly disagreed.

Another statement was “People who report many coincidences must be reading meaning into events which are just random.” Eight percent strongly agreed, 25% agreed, 38% were uncertain, 21% disagreed, and 8% strongly disagreed.

What is quite interesting is the strong link between having a positive attitudes towards coincidences and being much more likely to believe in experiences of the paranormal (r = .72, p < .001).

## Egocentricity – the ‘yawn’ factor

One problem in considering coincidences is the  “egocentricity” bias (Falk, 1989).  People consider their own coincidences to be surprising and worthy of note, but other people hearing those same coincidences tend to be dismissive of them, thinking they occurred purely by chance.

MT confesses that, following the Falk study, he became more reluctant to share his own personal coincidences with other people. As a person who recently shared a coincidence in print myself, I can well understand MT’s reaction.  But the large number of coincidences that he experienced seemed too great to be a chance effect, so he thought he’d carry on sharing them. I have also felt this way at times, and there is no fool-proof way of eliminating the paranormal hypothesis, as far as I am aware.

MT gives three detailed examples of what he took to be potentially ‘paranormal’ coincidences. I quote these here as part of a developing portfolio of published cases.

## MT Case 1

Thursday April 21st, 2005…

MT states: “I was deeply immersed in Liddell and Scott’s (1889) An Intermediate Greek-English Lexicon. In particular I was studying the preposition ΠΡΟ (i.e., PRO) to see whether it could mean “on behalf of”. I scoured the two-thirds of a column devoted to this preposition, but could not find the meaning I wanted. I had to give up at that point, because at 6:30 I was to go out to a fast food restaurant with a friend, for dinner.

Less than half an hour later, when we were at the restaurant, there passed by our table a young lad in soccer gear: on his shirt were the words, in Greek, ΑΣΠΙΣ ΠΡΟΝΟΙΑ (ASPIS PRONOIA). I for my part was astonished that he should be wearing, in Greek, even though as part of a longer word, the preposition ΠΡΟ. I knew that ΠΡΟΝΟΙΑ was a compound word made up of that preposition ΠΡΟ plus ΝΟΙΑ (from NOEEIN, to perceive), meaning something like “forethought”. (However, I was unfamiliar with the word ΑΣΠΙΣ, and I asked the boy what it meant, but he didn’t know. When I got home, I looked it up and discovered that it meant “a body of soldiers”. So the soccer shirt meant something like “a body of soldiers with forethought.”)

It seemed to me that the coincidence of having two quite unrelated instances of the Greek word ΠΡΟ within half an hour of each other was highly unlikely to occur by chance.

I’d never seen the boy before, and have never seen him since, nor have I seen this Greek phrase (or any other Greek words) on another soccer shirt. However, those around me with whom I shared the coincidence dismissed it as chance (as perhaps the reader will too!) But the egocentric bias is strong for the experient of a coincidence as well as for the people to whom it is told. Thus, I continue to regard the coincidence (and many that I’ve experienced since) as being more than chance.”

## MT Case 2

“Saturday, December 11th, 2004, my family and I were gathered at the flat of my youngest brother to celebrate his 42nd birthday. Two coincidences occurred to me that day. First of all, my brother possesses a CD of the composer Monteverdi which he himself never plays but which he good-heartedly loans to me now and again. I spoke aloud the name of the composer, Monteverdi. I was misheard, and was asked “Verdi”? I said, “No. Claudio Monteverdi.” But the question got me thinking, “What is Verdi’s first name? Is it Giuseppe?”

I resolved to check my Webster’s Biographical Dictionary when I got home. Yes, p. 1515reveals that his name was indeed Giuseppe. The coincidence occurred a little later when I was watching the evening news, and a man was interviewed whose first name was given at the bottom of the screen as Giueseppe. (I in fact wondered if the station had spelt the name Giuseppe incorrectly.)”

## MT Case 3

“The …coincidence involved my father telling a joke about George W. Bush wanting to get into Heaven to talk with Moses. Bush tried several times, but on each occasion Moses told St. Peter to send him away. Finally, Moses said “The last time I talked with abush I ended up wandering in the wilderness for 40 years!” That evening, just after 8:30, I was watching a commercial station on which there was a movie called For Richer or Poorer with Tim Allen in it as an entrepreneur engaged in setting up theme parks. The character revealed his latest theme park inspiration, which he called “Holy Land”, and pointed out a bush “which bursts into flame every hour”. I know for a fact that my father was unacquainted with the movie and so he had no idea that the theme of the burning bush was to arise later that evening. It is interesting to me that when I told my father about what I’d seen and heard on TV that very night, sceptic that he was, his reaction was one of dogged silence, and certainly not the cry “How amazing!”, as he battled his cognitive dissonance. If he said nothing about the coincidence it would go away.”

## MT’s conclusion

MT  dismisses skeptical explanations based on chance “as a bottomless pit, able to swallow up each and every coincidence that does not already have a normal explanation.”

On the other hand, MT wisely states that “we must be ever cautious about the coincidences that we do evaluate as paranormal.”

The fact is, however, there is no fool-proof method to say one way or the other. It comes down to one’s own subjective evaluation.

What do you think?  Is pure chance the only credible explanation, or  are there hidden causes, or is something paranormal going on?

# ‘An obscure public-house on the Chiswick bank of the river’

Featured

## 23rd August 2018

At 30,000 feet on the midday flight from Marseille to Heathrow, I am thinking how to spend the afternoon. Unable to go straight home because an estate agent has arranged a viewing with a potential tenant, how would I fill this time?  I decide to go for lunch at one of my local haunts on the Thames bank, the City Barge.

Set aside for a moment the fact that the estate agent who had arranged the viewing was Chesterton’s, a family firm with connections to the writer GK Chesterton (1874 – 1936), ‘the prince of paradox’.  A few seconds after I made the  decision to go for a pub lunch ‘on the Chiswick bank of the river’, I open my kindle and make a fairly random decision to continue reading ‘The Man Who Was Thursday, a Nightmare by Gilbert K Chesterton (GKC).

I flip over the page to see in stark black and white a description of that very place which, moments previously, I had decided to visit, viz:

“”I think,” said Gregory, with placid irrelevancy, “that we will call a cab.” He gave two long whistles, and a hansom came rattling down the road. The two got into it in silence. Gregory gave through the trap the address of an obscure public-house on the Chiswick bank of the river. The cab whisked itself away again, and in it these two fantastics quitted their fantastic town.”

Coincidence is both puzzling and remarkable, a contiguity of events that appear to have no causal connecting principle between one another. A coincidence that seems to go way beyond the laws of chance can elicit a strong sense of the paranormal. I analyse here the ‘Chiswick Coincidence’ for the light it may shed on anomalistic experience.[1]  The correspondence between the free and voluntary thought of going to the pub on the Chiswick side of the river and Gregory’s choice to do the identical thing is particularly striking. This coincidence, like others that I,  or close family members, have experienced is multi-layered. I discuss here each of these 7 layers.[2]

## First layer

The ‘Chiswick Coincidence’ consists of two contiguous elements:

Element 1: My decision to go to the City Barge for lunch (because my flat was being viewed by Chestertons).

Then seconds later:

Element 2:  I read the line ‘an obscure public-house on the Chiswick bank of the river’ in the book by GKC.

Thus, the  first layer of coincidence is the fact that the estate agent and the author GKC are members of the same family.

## Second layer

The second layer is the fact that the decision to go to the Chiswick riverside pub was followed only a few seconds later by reading a piece of text referring to a ‘public-house on the Chiswick bank of the river’. My immediate reaction being “Wow!”, “Whoa!” “WTX!” in no particular order.

Historical records indicate that The City Barge has existed since 1484 when it was known as ‘The Navigator’s Arms’. Its first appearance in the licensing lists was in 1787 when it was the ‘City Navigation Barge’. As the ‘City Barge’ it was refurbished in 2014.  Historical sources point to at least 5 or 6 pubs on the Chiswick side of the river at the time of GKC’s story. The pub mentioned by GKC could have been any or none of these, perhaps only a figment of GKC’s fluid imagination. Two clues make the City Barge a good candidate however. Photographs of the City Barge from 1910, two years after the publication of TMWWTAN, show Thames barges actually tied up directly outside the City Barge. Also, when the two characters in GKC’s story, Gregory and Syme, leave the pub, they go out by the door and “close to the opening lay a dark dwarfish steam-launch”. This description fits the immediate riverside proximity of The City Barge perfectly.[3]

A kindle is a portable library. Mine is 1.33 GB of books, both fiction and non-fiction – the complete works of Shakespeare, Chaucer, Dickens, Joyce, Austen, Pepys, Swift, Zola and much more.  On the date in question, there were 498 works containing 146,817 pages [4]. With 350 words per page, there were around 50 million words on my kindle.  The odds of seeing the words “public-house on the Chiswick bank” on the first page I opened is around one-in-10 million (10-7).

## Third layer

I checked my diary for the days immediately following the date of this event (23rd August 2018). My diary says that I would be meeting my publisher Robert Patterson to discuss a new book on Psychology and the Paranormal.. Was I perhaps on the lookout for anomalistic experience at this time? If so, I had been presented with a brilliant example.

## Fourth layer

The idea of writing this book meant that I would soon be seeking new material. Although I was at the early stages when this incident happened, I can imagine no more suitable an illustration for a book on anomalous experience than this very incident. Reflecting back on this period, I can see how helpful the coincidence was in resetting my paranormal ‘Belief Barometer’.

## Fifth layer

Enter – or, I should say, re-enter – Martin Gardner.  Martin had kindly contributed Forewords to editions of my previous book on ‘psi’ (Marks and Kammann, 1980; Marks, 2000).[6]  Sadly, Martin died in 2010 leaving a huge legacy of 100s of literary and scholarly works with a readership of millions. I have copies of many of Martin’s books including Fads and Fallacies in the Name of Science (Dover, 1957), Mathematics, Magic and Mystery (Dover, 1956), The Annotated Alice. The Definitive Edition. Lewis Carroll (W W Norton, 2000).

In researching TMWWTAN I made the discovery that Martin had written a Special Annotated Edition of TMWWTAN (Gardner and Chesterton, Ignatius Press, 1999). Goose bump territory! How very strange. Discovering this Special Annotated Edition seemed enigmatic and enthralling in equal measure. The three-way connection between Gilbert K Chesterton, Martin Gardner and the very book I am writing does not end here.

## Sixth layer

As Chesterton noted, “hardly anybody who looked at the title ever seems to have looked at the sub-title; which was “A Nightmare,” and the answer to a good many critical questions” (Autobiography, Kindle Locations 1301-1303). Two key themes of TMWWTAN are free will and evil.  The Chiswick Coincidence triggered a change in my stance from disbelieving skeptic to neutral inquirer.  My eyes were opened to the genius of Gilbert K Chesterton, certainly a special writer and TMWWTAN is no ordinary book. It has been rated as one of the greatest works of 20th century literature. To quote from the American Chesterton Society website (https://www.chesterton.org/who-is-this-guy/):

“Gilbert Keith Chesterton (1874-1936) cannot be summed up in one sentence. Nor in one paragraph…But rather than waiting to separate the goats from the sheep, let’s just come right out and say it: G.K. Chesterton was the best writer of the 20th century…The reason he was the greatest writer of the 20th century was because he was also the greatest thinker of the 20th century… What was it he defended? He defended “the common man” and common sense. He defended the poor. He defended the family. He defended beauty. And he defended Christianity and the Catholic Faith.”

I was pleasantly surprised to read the above description that GFK defended the “common man”, common sense and the poor, my own values exactly.  Clearly, Gilbert Chesterton also made no secret of the fact that he believed in God, prayer and the afterlife.

## Seventh layer

Like GKC, and he also made no secret of it, Martin Gardner believed in God, prayer and the afterlife. In his autobiography, Martin stated he loved reading “anything by G. K. because of his never-ceasing emotions of wonder and gratitude to God, not only for such complicated things as himself, his wife, and the universe, but for such “tremendous trifles” (as he once called them) as rain, sunlight, flowers, trees, colours, stars, even stones that “shine along the road / That are and cannot be,” (Undiluted Hocus-Pocus.The Autobiography of Martin Gardner, 2013, p. 205).

GKC, together with the Basque philosopher and poet Miguel de Unamuno, were Martin’s two mentors. Martin’s autobiography mentions God no less than 128 times.[7] According to Martin Gardner (2013):

“Just as knowing how a magic trick is done spoils all its wonder, so let us be grateful that wherever science and reason turn they plunge finally into stygian darkness. I am not in the least annoyed because I do not understand time and space, or consciousness, or free will, or evil, or why the universe is made the way it is. I am relieved beyond measure that I do not need to comprehend more than dimly the nature of God or an afterlife. I do not want to be blinded by truths beyond the capacity of my eyes and brain and heart. I am as contented as a Carnap with the absence of rational methods for penetrating ultimate mysteries” (p. 341).

For a lot of different reasons, and in completely unexpected ways, the Chiswick Coincidence opened my eyes.  At a seventh layer, I find that the coincidence revealed another synchronicity: the shared values and beliefs of Martin Gardner, in many ways one of most precious mentors, and a man I could never have met, GKC, the author of the metaphysical thriller TMWWTAN.

## Combined Probability of Seven Layers

I give estimates here of the probabilities for each layer followed by a combined probability estimate.

Layer 1: The probability that the estate agent and GKC himself are from a single family is estimated to be 10-3. This estimate takes into account the number of West London estate agencies (500+) and the chance that the agent that I had selected would have a strong familial connection with GKC, the central character in this episode.

Layer 2: The probability that my plan to visit the Chiswick riverside pub would be followed a few seconds later by seeing the words ‘public-house on the Chiswick bank ’on the first page of my kindle is estimated to be 10-7. This estimate takes into account the huge quantity of kindle text (in excess of 50 million words) that I could have selected to read on this occasion.

Layer 3:The probability that on the same visit to London I would be meeting my publisher Robert Patterson to discuss a new book is estimated to be 10-1 . This accords with the frequency of such meetings which is approximately once a year.

Layer 4:Taking into account the fact that no contract for the paranormal book existed at the time, the probability that the Chiswick Coincidence would be useful material for this book is estimated to be 10-1

Layer 5:Taking into account of the fact that, before this incident, I knew almost nothing about GKC,  the probability that somebody I knew, somebody I regarded as a mentor, somebody who had written forewords to two of my  books, Martin Gardner, would also be somebody who had written a Special Annotated Edition of TMWWTAN is estimated to be 10-4

Layer 6: The probability that lifelong personal values, to defend the “common man”, common sense and the poor, I later discovered to be GFK’s values is estimated to be 10-1 [8].

Layer 7: The synchronicity in values and beliefs between Martin Gardner and Gilbert K Chesterton, author of TMWWTAN, is estimated to be a certainty. Martin loved GKC’s writing and shared his values and beliefs.

In addition, it is necessary to consider the boundary conditions. Sitting on an aeroplane on a short-haul flight, offers a variety of activities, viz: doing nothing, doing a puzzle, watching a film, listening to music, snoozing,  chatting,  looking out of the window, drinking a tea or coffee, reading a non-kindle item (newspaper, magazine or book), or reading a kindle. I estimate the probability that I would have chosen to read my kindle on this occasion as one-in-ten ( 10-1 ).

The combined probability P of the seven synchronicities and the boundary condition is:

P  = 10-3 X  10-7 X  10-1 X  10-1   X  10-4   X 10-1  X 1 X  10-1   = 10-18

= one in 1,000,000,000,000,000,000

i.e. one in one quintillion (a million, million, million) [9]

These odds are so astronomical in scale, one must consider the possibility of a paranormal explanation. Not to do so would seem irrational and contrary to science.

## Explaining the Coincidence

How might this remarkable 7-layered coincidence, together with its impact and meaning, all be explained?  Let’s consider the explanations that are available from each side of the theoretical divide.

Hypothesis 1 – N Theory Explanation: Coincidences are bound to occur every once in a while purely by chance.

From the perspective of N Theory, I give the first type of explanation. The nugget of the Chiswick Coincidence lies within Layer 2:

Event A: choosing by free will to go to the City Barge for lunch.

Event B: choosing by free will to read, only moments later, a story, I would soon discover, that contains an incident about a  ‘public-house on the Chiswick bank of the river’.

When considered independently, neither event is in any way extraordinary. Only their near simultaneity appears extraordinary. If I had read the passage a few months, weeks or even days previously or sometime later, I would have noted that I knew just such a place but would not have blinked an eyelid.  Any Londoner is familiar with the experience of coming across familiar places in novels or movies.

It is necessary to consider the possibility of a hidden cause, something that might create the illusion of synchronicity when it isn’t really there. One possibility is that GKC may have been frequently mentioning things in and around Chiswick. In this case the coincidence might not be so odd after all.  It is possible to test this hypothesis relatively easily. It is said that Chesterton was one of the most prolific writers of all time. He wrote around 80 books, several hundred poems, 200 short stories, 4000 essays, and several plays. I downloaded the Delphi Collected Works of GK Chesterton onto my kindle. Using the kindle search function I found that there only 7 occurrences of the word “Chiswick” in GKC’s Collected Works. This fact makes the Chiswick Coincidence seem even odder than before.

Another possibility that must be considered is that I had already seen the crucial passage on a previous occasion. This possibility can be safely eliminated for two different reasons. Firstly, if I had already seen this passage, I would already noticed the connection between one of my favourite riverside haunts and GFC’s mention of it. In this case, seeing it for a second time would not have seemed the least bit remarkable. Secondly, a kindle automatically remembers the point reached at a previous reading and obligingly opens the selected book at that page.

The ultimate skeptical explanation is possibly the most accurate. It says that coincidences are just – coincidences!  A coincidence is a coincidence is a coincidence; a random, chance kind of thing. Something similar to the Chiswick Coincidence is occurring with someone somewhere almost every second of the day. When this extremely striking kind of coincidence occurs, it is bound to attract the experiencer’s attention. It is purely the wheels of chance turning and nothing else – once-in-a-blue-moon ‘Lady Luck’ and ‘Father Time’ jump into bed together and another coincidence sucker is born.

Hypothesis 2 – P Theory Explanation: Reverse causality by unconscious reading of the text triggers the decision to visit the pub on the Chiswick side of the river.

What of a paranormal interpretation? It is essential to air all possible explanations and the P Theory warrants a fair hearing.  The two key elements of the Chiswick Coincidence remain :

Event A: deciding by free will to go to the City Barge for lunch.

Event B: deciding by free will to read, only moments later, a story, which contains an incident about a ‘public-house on the Chiswick bank of the river’.

What about the possibility of reversed causality such that Event B occurs immediately before Event A.  This P Theory explanation goes like this: I read the part of the story about the Chiswick pub by an unconscious process of clairvoyance, clairvoyantly seeing the text about a ‘public-house on the Chiswick bank of the river’ inside my kindle.  Reading this text at an unconscious level triggers my decision to go to the City Barge for lunch. Afterwards, at a conscious level, when I switch on the kindle and actually read the text, I feel a sense of wonderment and surprise. This is no coincidence at all – reading about the Chiswick pub naturally and logically led to my plan to visit it.

If one is open to psi processes as scientific possibilities, then there should be no problem in accepting the P Theory explanation. In fact the P Theory nails it. If the skeptic demurs that there is no evidence for clairvoyance, unconscious perception or reverse causality and it just cannot be so, the P Theorist might well retort: “Normally, yes, but on this occasion all three happened.” There is no rational way of resolving the matter; which interpretation one accepts rests entirely upon subjective judgement.

## Summary and Conclusion

On a homeward journey, involving multiple free choices, a striking coincidence happened. The laws of chance suggest the odds against the Chiswick Coincidence are around one-quintillion-to-one.  Both an ‘N Theory’ interpretation and a ‘P Theory’ interpretation remain logical possibilities. There can be no definitive method of proving which explanation is the correct one. This incertitude requires a neutral stance and a degree of humility about one’s reaction to striking anomalous experience.[11]

My search for a scientific explanation was matched by an equally compelling realisation that there might not be one. Which interpretation is true cannot be decided by reason. Only personal preference –based on one’s a pre-existing bias – allows one to reach a definite conclusion.

Footnotes

[1] I freely acknowledge some readers may well view my ‘Chiswick Coincidence’ with skepticism.  If for no other good reason, ‘One person’s coincidence can be another person’s yawn’; https://wordpress.com/post/coincidences.blog/251

[2] The reader is encouraged to explore personal coincidences using this method of ‘layer analysis’.  Looking for layers of meaning enables one to grasp the full significance of a synchonicity.

[3] The City Barge is a 10-minute drive from Bedford Park, the “queer artificial village” of  ‘Saffron Park’, that features in GKC’s novel.

[4] With the settings on the kindle as they were at that time, there are 4-5 kindle pages to every printed page.

[5] To specify these distributions, a large sample of data points with exact odds values would be required.

[6] Martin Gardner (Foreword to the Second Edition, Marks, 2000) wrote: “It will rank as one of the strongest and best exposés ever directed at the more outlandish claims of parapsychology”(p. 13).

[7] By comparison, Chesterton’s autobiography mentions ‘God’ 62 times.

[8] I share GKC’s values as listed but not his religious beliefs.

[9] A quintillion is cardinal number represented by 1 followed by 18 zeros (US) and by 1 followed by 30 zeros (UK). Here I use the US definition.

[10] I adopt this response from Gardner (2013) The Whys of a Philosophical Scrivener (p. 235).

[11] Michael Thalbourne (2006) dismisses skeptical explanations based on chance “as a bottomless pit, able to swallow up each and every coincidence that does not already have a normal explanation.” The fact is, in regard to this coincidence, there is no fool-proof method to say whether the P Theory of the N Theory interpretation is correct. It comes down to making one’s own subjective evaluation.