We’ve all experienced a highly improbable event in our lives. Probably many, in fact. Some of us more than others, some more seemingly improbable than others. There is such a thing as the Law of Large Numbers that explains these coincidences and “miracles”.

The Law of Large Numbers simply stated (sans math): with a large enough sample many odd coincidences are likely to happen.

Coincidence: an occasion when two or more similar things happen at the same time, especially in a way that is unlikely and surprising.

Miracle: an unusual and mysterious event that is thought to have been caused by a god, or any very surprising and unexpected event.

~

On a side note, I was disappointed with Dictionary.com’s listing on these words so I thought I’d go to the Cambridge Dictionary. The definition above is from the Dictionary of British English. Out of curiosity, I looked up the word miracle in the Cambridge Dictionary of American English:

Miracle: an unusual and mysterious event that is thought to have been caused by God, or any surprising and unexpected event.

A very subtle but telling difference! I think I’ll be using the British version from now on.

~

Anyway, I digress, again! I like how the definition of miracle is either caused by god, or (moving the goalposts) unexpected. Those are two very different kinds of events. One is something supernatural, manipulated by god’s hand. The other is something merely surprising. And yet the definition combines them, basically rendering it rather meaningless.

So let’s get to the numbers that Michael Shermer shared in his article. He says:

I cannot always explain … specific incidents, but a principle of probability called the Law of Large Numbers shows that an event with a low probability of occurrence in a small number of trials has a high probability of occurrence in a large number of trials. Events with million-to-one odds happen 295 times a day in America.

Shermer quotes CERN physicist Georges Charpak and University of Nice physicist Henri Broch from their book, Debunked!: ESP, Telekinesis, and Other Pseudoscience:

In the case of death premonitions, suppose that you know of 10 people a year who die and that you think about each of those people once a year. One year contains 105,120 five-minute intervals during which you might think about each of the 10 people, a probability of one out of 10,512 — certainly an improbable event. Yet there are 295 million Americans. Assume, for the sake of our calculation, that they think like you. That makes 1/10,512 × 295,000,000 = 28,063 people a year, or 77 people a day for whom this improbable premonition becomes probable. With the well-known cognitive phenomenon of confirmation bias firmly in force (where we notice the hits and ignore the misses in support of our favorite beliefs), if just a couple of these people recount their miraculous tales in a public forum (next on Oprah!), the paranormal seems vindicated. In fact, they are merely demonstrating the laws of probability writ large.

So, for example if 23 random people are asked their birthdays, there is a 50% chance that at least 2 of them celebrate the same birthday. It may seem like an amazing coincidence, but it’s not amazing at all.

Then Michael Shermer refers to a review of the above book by another physicist, Freeman Dyson. He talks about Littlewood’s Law of Miracles:

“In the course of any normal person’s life, miracles happen at a rate of roughly one per month.” Dyson explains that “during the time that we are awake and actively engaged in living our lives, roughly for eight hours each day, we see and hear things happening at a rate of about one per second. So the total number of events that happen to us is about thirty thousand per day, or about a million per month. With few exceptions, these events are not miracles because they are insignificant. The chance of a miracle is about one per million events. Therefore we should expect about one miracle to happen, on the average, every month.”

So a miracle is basically a one in a million event, according to Littlewood who was a University of Cambridge mathematician. And we all have about a million little events in our lives every month. So we all get a miracle a month, or thereabouts (actually 35 days). See how cool math is? Of course, a miracle a month is rather commonplace, isn’t it?

Then, when observing and reporting events, there is the ever present loom of confirmation bias and anecdotal evidence, which is not very reliable, if at all.

One thing I’ve never understood is when people see Jesus or Mary in bird poop or a pizza pan or a stump. (Basic everyday pareidolia, of course). Nothing special happens except that they recognize a face in a random pattern. But before you know it a shrine is constructed and people are kissing the bird poop and praying at the stump. Not being religious, I find this completely silly, but they are True Believers. Does the miracle follow the sighting? I never hear about anyone claiming a bonifide miracle from one of these sightings. (Then again, no true miracle has ever been verified, not scientifically). And Mary needs a better agent if she’s reduced to showing up in bird poop, but that’s just my humble opinion.

Other resources:

• Coincidences: Remarkable or Random?

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One important tool is going to be Occam’s Razor: “entities must not be multiplied beyond necessity” (entia non sunt multiplicanda praeter necessitatem). That’s it in a nutshell right from William of Ockham, a Franciscan monk and English philosopher, theologian and logician in the 14th century.
Another way to put it is: The simplest explanation is usually the correct one. But don’t get confused by the term, simple. It means: The hypothesis with the fewest assumptions is usually the correct one. When giving explanatory reasons for something, don’t posit more than is necessary. Or, don’t make any more assumptions than you have to.

So let’s say you have 2 competing hypotheses that are basically equal in most respects. Then this principle would suggest that you choose the hypothesis that makes the fewest assumptions while still sufficiently answering the question. In science Occam’s Razor is used as a rule of thumb (a heuristic) to help researchers develop good models.

In your life it can help you make decisions and choose what to think and what to believe (or not believe). You can use it as a heuristic as well, a great rule of thumb in your Critical Thinking Toolkit.

Sometimes atheists use Occam’s Razor to argue against the existence of god since everything can be explained through natural means without complicating it with the supernatural.

Another example: Crop circles. There used to be 2 competing ideas for where crop circles came from. One was that flying saucers from an alien world made them. Another was that a person  (or people) used some type of instrument to make the designs in the grass. Since there is no evidence for the flying saucers from outer space, and given how complicated and how many assumptions need to be made to make that argument work, Occam’s Razor would suggest that the simpler explanation would be that humans did it with instruments. That is the argument that makes less assumptions.

Of course, the second argument could be wrong, but until there was more information, it was the preferable hypothesis. Then 2 guys admitted to the crop circle hoax in the 1990′s. So that ended that debate for most people.

A quote by Carl Sagan is appropriate here: Extraordinary claims require extraordinary evidence. When it comes to the supernatural, Occam’s Razor is a very valuable tool indeed.

Sources:

• The Skeptic’s Dictionary
• Wikipedia
• 2Think.org

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If there is one gift you can give to a child or anyone else, it is to teach them to think for themselves. The educational system doesn’t teach this important skill. It teaches rote memorization and focuses on test taking. Therefore it’s up to you to learn it for yourself.

Unfortunately, I’m self taught and have no formal training in this realm. Which means sharing it with you is harder. So instead of putting it off even longer, I thought maybe we could explore the subject together and develop a plan for sharing with others in our lives or on the web. First, let’s define it.

Here is a quote: [Critical thinking is a] desire to seek, patience to doubt, fondness to meditate, slowness to assert, readiness to consider, carefulness to dispose and set in order; and hatred for every kind of imposture. ~ Francis Bacon (1605)

Here is the short and sweet definition:

Critical Thinking: n: the mental process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and evaluating information to reach an answer or conclusion.

But I’ve found that there are many different interpretations for this concept. You can see a whole page of them here.

Here’s another one:
“Critical thinking is best understood as the ability of thinkers to take charge of their own thinking. This requires that they develop sound criteria and standards for analyzing and assessing their own thinking and routinely use those criteria and standards to improve its quality.” Elder , L. and Paul, R. “Critical thinking: why we must transform our teaching.” Journal of Developmental Education, Fall 1994.

What makes a critical thinker? Here are some attributes:

• asks pertinent questions
• assesses statements and arguments
• is able to admit a lack of understanding or information
• has a sense of curiosity
• is interested in finding new solutions
• is able to clearly define a set of criteria for analyzing ideas
• is willing to examine beliefs, assumptions, and opinions and weigh them against facts
• listens carefully to others and is able to give feedback
• sees that critical thinking is a lifelong process of self-assessment
• suspends judgment until all facts have been gathered and considered
• looks for evidence to support assumption and beliefs
• is able to adjust opinions when new facts are found
• looks for proof
• examines problems closely
• is able to reject information that is incorrect or irrelevant

Just about anyone can learn to think more critically. Even more importantly, you can use it in nearly every aspect of your daily living. You already think all the time, but if you are not consciously trying to think critically, your thoughts will be more biased, distorted, partial, uninformed and prejudiced. You’ll make decisions based on your emotions and feelings, you’ll rely on your “intuition” and your gut instinct, which can sometimes be useful but can often be quite flawed.

One way that flawed thinking is noticeable is through Logical Fallacies, which we talk about here at HDC.

Here are some other resources that you might find useful:

• Critical Thinking on the Web
• Foundation for Critical Thinking

Well, that is enough to get us started. Do you have any great resources for learning to think critically that you would like to share?

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I know not all of you like to listen to podcasts. So I went through it and transcribed a good chunk of what Luke said in his lecture, the parts that I thought were most important. I have a few thoughts afterward. By the way, I missed the beginning for reasons I can’t remember (this took me a couple of days to make it all make sense) but this is a lecture about Dr. Ernest Becker and Terror Management Theory.

Partial transcript:

…This is where we get neurotic about death. It’s the ultimate inferiority complex. Our lifespan is limited. We realize we must die but in striving to overcome that, it creates more problems. We put a lot of energy into denying death.

One way to summarize Becker’s theory: It’s good to have a brain that can plan for the future and be self-aware, but the problem is that when we become scared of our own mortality it sets up a defense against that. Part of the defense involves symbols. We think symbolically and so our symbols set up a barrier. These symbols can be religious, political, symbols of our mastery over the world, symbols of making money, etc.

What Becker thought was that culture itself is a buffer against these threats to our self esteem. We set up our belief in culture and human culture really is an attempt to deal with threats to our own mortality and our self esteem. So first, what is self esteem?

Self esteem is not just a product of you, individually. What Becker thought was that self esteem was something you get a sense of only through other people. So you think of yourself as a valued person who has powers, who can act upon the world, but that is socially validated by parents, siblings, peers, a gradually expanding group of people. This gets more abstract and symbolic as the child grows up. So as a young adult you might latch onto ideologies. For many people this is religion. You join a church and get a sense of what you need to do to be good or bad from those groups too. The good thing is that these groups give you clear guidelines to derive your self esteem.

This can be positive or negative. So if you don’t get positive reinforcement, you’ll look for self esteem and validation in other ways. So this is why people join cults and gangs, etc.

Hero Striving System: whatever you use to seek pride and superiority. Everyone does this in different ways. The system is different for different people but it all boils down to wanting to feel worthwhile.

So cultural symbols can provide a buffer against our mortality fear. How can I transcend death? This is Immortality Striving. It all boils down to “the end is not the end.” This could also be more abstract. Your cultural striving could be symbolic striving against death. You believe your genes and your legacy will pass down even after you die through your children. You create something that will last after your death, like a pyramid, or a lot of money, etc. You’re saying, “I was here, I mattered.” This maintains your self esteem.

Here’s where the problem comes in. If you are so invested in these strivings, in these worldviews to drive your self esteem, that means any threat to those worldviews, to that symbolic system, if they are poked at, is not trivial. This will poke at your self esteem. This person is challenging my worldview. And someone doesn’t even have to be mean to threaten you, because there are different worldviews. Every time you encounter a different person, a different culture, you see the standards of normal differ.

What Becker thought was that being presented with a different worldview is inherently threatening. Because if that guy’s right, he has a different worldview, he seems perfectly happy with his system, and it’s contradictory to my system, there’s a problem for my system.

So a lot of war, strife and prejudice was really about more than just “you’re different, I don’t like you, you have funny gods”, but it’s a threat to our self esteem. So if he’s right, I’m not going to heaven, or there isn’t a heaven.

So an atheist’s world view is very different and therefore very threatening.

People, when confronted with different worldviews have to find a way to deal with it. You can denigrate people (call them stupid); try to convert them to your worldview (proselytize or missionary work) – which validates your worldview and your self esteem; assimilate people – neutralizes the threat by getting them to give up part of it (Native Americans, etc);  accommodation – declaw the other worldview by incorporating some of their elements into ours (like blue jeans, hippy symbols, etc) in a very sterilized sort of way; or annihilate the other worldview – genocide, stamping out everything about the American Indians, even their buffalo, don’t let them speak their own language, etc.

Here’s where Terror Management Theory comes in, with empirical testing. There are 2 main predictions to test:

1. If we threaten someone with mortality thoughts, if we remind them of death, that should result in compensatory response to bolster their worldview.

Mortality Salience Hypothesis (around the 30 minute mark)

2. If we poke at someone’s worldview and suggest that they may not be correct, we should see an increase in their death anxiety. They might become more fearful of their own mortality if their worldviews are challenged in some way.

From the clip of the video, Life and Death: Flight From Death: The Quest for Immortality (video on demand), Flight From Death – The Quest for Immortality (dvd)

The first component of TMT states that individuals need to sustain faith in a meaningful worldview.  The second component states that individuals need to feel as though they are value protected members, objects of significance within this worldview. This is self esteem.

Talk of politics and what kinds of leaders people will choose when their mortality feels threatened: (39 minute mark). (there is a polarizing effect)

There is a reciprocal relationship between threats and my own mortality and worldview.

49:00 – more religious studies: Here’s an interesting one. A group of high fundamentalists (believing in biblical literalism) were confronted with contradictions in the bible, they unconsciously thought about their own mortality more.

What does that mean? What’s at stake? It goes a bit deeper than they just want the bible to be perfect and literal, or that they want to preserve a belief in doctrine. When people are defending religious concepts, their worldview is at stake. When someone pokes at their belief and says your belief isn’t true, or here is evidence against your views, it’s more than just a contradiction of these facts, it’s an emotional reaction the person is going to have because that is their ticket to immortality. It raises fears of their own death when those are challenged.

52:30 – creation and evolution worldview studied with similar results. Creationists who had their worldview threatened had higher unconscious death fears.

Implications: why won’t people accept data on evolution? This study would imply that it’s not simple bullheadedness or dogmatism, it cuts deeper than that. From a TMT perspective, these people are defending their worldview. This is what keeps mortality fears in check. If someone comes along and pokes at that worldview it’s not just a matter of intellectual debate anymore, this is an actual threat to their sense of symbolic immortality.

55:00 Dual nature to mortality salience. Studies show that if you show the positive aspects of a religion, for example, then expose them to mortality salience, the people end up defending a worldview that is more accepting. So religion and politics might contain mixed positive and negative messages. If the positive ones are primed and made more active, the person when under threat defends those more too.

So mortality salience isn’t all about doom and gloom and threats. What this would imply is that, it depends on what message is accentuated.

57:20 What about atheists, who don’t have a worldview of literal immortality? Does that mean that we’re immune from the effects of death threats because we’re not expecting to live for the resurrection, or be reincarnated? That is, we are probably not using that as a security blanket. Essentially Becker says it  doesn’t matter – “It doesn’t matter whether their cultural hero system is frankly magical, religious and primitive, or secular, scientific and civilized. It’s still a mythical hero system in which people serve in order to earn a feeling of primary value, of unshakable meaning. Civilized society is a hopeful belief and a protest that science, money and goods make man count for more than any other animal. In this sense, everything that man does is religious.” So there are just as many non-theistic, nonreligious worldviews that can be defended as religious worldviews. For example, the cult of Stalinism and Mao. Or other things people value like human rights, humanism, science: these things are also worldviews that are defended because they give our life meaning.

Somebody might not say, “I’m going to go to heaven, that’s the only thing that would matter to me”, but they might say that they support these values. That’s their ticket to immortality. So this has the same effect. If anyone pokes at the Bill of Rights, messes with Jefferson, or says that science doesn’t matter, to many people who have a naturalistic worldview that would be just as threatening as people who have religious worldviews. So these theories don’t just apply to people who have supernatural or religious worldviews.

1:00:00 What should people do with this information? The denial of death in our culture is particularly strong. So one way to deal with that is to learn to have a worldview that acknowledges mortality on a regular basis. Live more consciously with those reminders everyday, not in a negative or morbid sense, but in a sense that this is part of life. “This is going to happen to me, and I’m going to make life count now, instead of saying I can transcend and cheat death.”

Also, choose ideologies that don’t rely upon the strident defense of “that guy is threatening my worldview, I’m going to wipe him out”. Ideologies don’t have to be threatening to other people. Make the unconscious conscious. Recognize that this is a bulwark to my worldviews, to recognize when you see a commercial, a political package, or a doctrine that this is really more than what it says. It’s actually a worldview defense. If we make that conscious, we can recognize what it is that we’re doing when we do it. So then we can take a step back and say, “I’m going too far. I’m defending myself against my own sense of insignificance by doing this action.”

1:02:13 There are ways you can strive for immortality in a nondestructive way. It doesn’t necessarily mean you have to strive against other peoples’ worldviews. Find positive ways to find meaning for your lives through positive ways to defend your worldview; charity, supporting other people, etc.

~

If you’ve made it through the transcript and are still with me, congratulations. This isn’t the most fun topic, and this post is really long. But it does have huge implications and can really help us in understanding our own motivations as well as how other people are dealing with their own fears and thoughts.

I have a followup, also by Dr. Luke Galen and the rest of the Reasonable Doubts crew, that will give us some very practical advice in dealing with people and their dogmatic beliefs. But this post was plenty long enough, so I thought I’d save it for later.

I welcome your thoughts.

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-Richard Dawkins

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Pareidolia: a psychological phenomenon involving a vague and random stimulus (often an image or sound) being perceived as significant.

In psychology, the Rorschach test is a series of images used to invoke pareidolia to delve into the psyche of the patient. In religion and superstition, a vague stimulus is believed to be divinely sent. Here is a news story of Mary in bird shit. Notice how the people react to a random stimulus.

No matter how much I look at this picture, it looks like a face. The sink looks a bit shocked or frightened.

Carl Sagan hypothesized that detecting faces is a hard wired evolutionary advantage. This allows people to use only minimal details to recognize faces from a distance and in poor visibility but can also lead them to interpret random images or patterns of light and shade as being faces.

In 2009 a study was done to show that objects incidentally perceived as faces evoke an early (165 ms) activation in the ventral fusiform cortex, at a time and location similar to that evoked by faces, whereas other common objects do not evoke such activation. This activation is similar to a slightly earlier peak at 130 ms seen for images of real faces. The authors suggest that face perception evoked by face-like objects is a relatively early process, and not a late cognitive reinterpretation phenomenon.

Which would explain why everyone sees the following simple line drawing as a face:

This one, is of course, totally real. The Flying Spaghetti Monster is a holy visage mighty to behold! May you be touched by his Noodly Appendage!

Here’s a strange 6-legged sky pig.

This is the famous grilled cheese toast image. If you ask me, the face in there looks more like an actress from the 40′s than a religious icon.

And one more, for fun.

So, it’s nothing supernatural. It’s just the way our brains work to fill in information and make sense of the world as fast as we can.

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