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The Original "Thinking Outside the Box" Puzzle!

March 6, 2009 in Blogs, Psychology Today by Psychology Today

Let me first introduce myself and this blog, which is titled Total Brain Workout. I am a professor of anthropology at the University of Toronto, and one of my main areas of cultural research is puzzles. I have also been teaching an undergraduate course on puzzles (their history and cultural meaning) at the University for many years. It is one of the most satisfying courses I have ever taught because, by the end of it, the students not only develop puzzle-solving skills (which they may have thought they didn’t have at the start), but also come out of it with a better perspective about the role of puzzles in human life. This blog is modeled on puzzles that I put together for my recent book, The Total Brain Workout: 450 Puzzles to Sharpen Your Mind, Improve Your Memory & Keep Your Brain Fit, published by Harlequin Books. It will contain one or two puzzles, and (if relevant) the history behind them, to tease your brain and thus keep it fit. As I indicate in the preface to that book, it would seem that such apparently “trivial amusements” foster brain growth, by stimulating logical and creative thinking regions of the brain. Research has come forward to suggest (although not prove beyond a shadow of a doubt) that puzzles sharpen the mind, improve memory, and keep the brain fit throughout life, and especially later life. As a boomer myself, and a puzzle addict since my childhood, I welcome this news. If puzzles are to the brain what physical exercise is to the body, then let’s do puzzles-not just for fun, but more importantly for brain fitness. And even if the research is not exactly what it is claimed to be, so what! Doing puzzles cannot hurt. Puzzles are as old as human history. They are found in all cultures throughout time. One of the first documented puzzle-and still one of the most famous-is the Riddle of the Sphinx. According to myth and legend, when Oedipus approached the city of Thebes he encountered a gigantic sphinx guarding entrance to the city. The menacing beast confronted Oedipus, posing the following riddle to him, and warning him that if he failed to answer it correctly he would die instantly at the Sphinx’s hands: What has four feet in the morning, two at noon, and three at night? The fearless Oedipus answered (paraphrasing his statement somewhat): “Humans, who crawl on all fours as babies, then walk on two legs as grown-ups, and finally need a cane in old age to get around.” Upon hearing the answer, the astonished sphinx killed itself, and Oedipus entered Thebes as a hero for having gotten rid of the terrible monster that had kept the city in captivity for so long. Ironically, by solving the riddle the devastating prophecy, which Oedipus tried to elude-that he would kill his father (which he did unwittingly on the way to Thebes) and marry his mother, the widowed queen of Thebes-came true. Why are we so intrigued by stories such as this one which revolve around puzzles? The answer might lie in the origin of the English word puzzle itself, which comes from the Middle English word poselen “to bewilder, confuse.” And indeed, puzzles generate bewilderment and confusion, because they cannot be solved by applying any formula or method mindlessly. They always require a dose of creative, unconventional thinking, which psychologists call “insight thinking.” This is essentially an intuitive grasp of a pattern or twist concealed by the puzzle. Given their appeal, some puzzles have given origin to commonly-held ideas, such as the one that life is comparable to the three main parts of a day (the Riddle of the Sphinx). Others are the source of everyday expressions. Here is a brainteaser that gave origin to the expression “thinking outside the box.” Many readers undoubtedly know it: Without letting your pencil leave the paper, can you draw four straight lines through the following nine dots? Those who may not have come across this puzzle before might tend to approach it by joining up the dots as if they were located on the perimeter (boundary) of an imaginary square or flattened box. But this reading of the puzzle does not yield a solution, no matter how many times one tries to draw four straight lines without lifting the pencil. A dot is always left over. It is at this point where creative thinking comes into play: “What would happen if I extend one or more of the four lines beyond the box?” That hunch turns out, in fact, to be the relevant insight. One possible solution is as follows: Can you find the others? It should now be obvious why this puzzle gave rise to the expression “thinking outside the box,” which entered the English language around the middle part of the twentieth century when people in business and education started referring to it as a prototypical example of what creative or “lateral” thinking is all about. It continues to be cited by psychologists as an example of how the mind tends to impose unnecessary limitations upon methods of attacking problems. Who invented the puzzle? I have looked into several sources and have been able to trace it as far back as 1914, in the first edition of puzzlist Sam Loyd’s (1841-1911) Cyclopedia of Puzzles. But the principle it embodies is probably older, as Martin Gardner indicates in his 1960 edition of Loyd’s work (titled The Mathematical Puzzles of Sam Loyd). The Nine-Dot puzzle is a 3 × 3 version of what can be called generally a Dot-Joining puzzle. Can you solve the Sixteen-Dot (4 × 4) and Twenty-Five Dot (5 × 5) versions? Again, you just connect the dots without lifting your pencil. How many lines are required in each of these two cases? Do you detect a correlation between number of dots and number of connecting lines? Sixteen-Dot Version Twenty-Five-Dot Version As a final word on Dot-Joining puzzles, I should mention that, as with any puzzle genre, once the general principle involved in solving them is deciphered, the genre starts losing its appeal. However, like any good joke, Dot-Joining puzzles can be played on others over and over to great effect. I await your answers, solutions, discussions, anecdotes, etc. for this particular puzzle, including any general formula for solving any general version (n × n) of the puzzle (if there is one). I also welcome suggestions for future puzzles on this blog. This is going to be fun!  (Scroll down for the answers)                           Answers Each of the following constitutes only one possible solution. Sixteen-Dot Version Six lines are needed for this version of the puzzle. As mentioned other solutions are possible. All involve six lines. Twenty-Five-Dot Version Eight lines are needed for this version of the puzzle. Other solutions are possible. Can we generalize? By making the Nine-Dot puzzle as complex as we desire (increasing the number of dots to 16, 25, 36, 49, etc.), a pattern seems to emerge through inspection. This pattern can be charted as follows: Dots    Lines Required 3 × 3    (3 + 1) = 4 4 × 4    (4 + 2) = 6 5 × 5    (5 + 3) = 8 6 × 6    (6 + 4) = 10 …    … n × n    n + (n – 2) = 2n – 2 I should point out that I have not tested this pattern beyond a 6 × 6 version of the puzzle. As with all inductively-derived formulas, there is no way to be sure that the formula works all the time. It thus can be called, simply, a working formula.  

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The Original "Thinking Outside the Box" Puzzle!

Did Casey Kill Caylee?: Could There Be an Insanity Defense Coming?

March 6, 2009 in Blogs, Psychology Today by Psychology Today

Since my two previous postings on this case several months ago, the skeletonized remains of little Caylee Anthony were discovered by a county meter reader a mere hundred yards or so from her home. Now we know that Caylee is in fact deceased, and that, according to authorities, was the victim of premeditated murder. Police have been zeroing in on the Anthony home as the possible site of Caylee’s killing, linking to that location many of the forensic clues found at the grisly scene where dismembered bones and a tiny human skull with duct tape still covering the place where the mouth and lips once were. Meanwhile, Casey remains incarcerated. Her brother, Lee, was deposed recently by lawyers representing supposed “nanny,” Zenaida “Zanny” Gonzalez, who denies having ever even met Casey let alone being the regular babysitter for Caylee Anthony. Grandparents Cindy and George are refusing to participate in the Gonzalez defamation law suit depositions, citing as their reason psychological fragility. The judge in that case has given them twenty days to produce psychiatric documentation to support this claim. Since George Anthony, Casey’s father, reportedly became despondent and actively suicidal following the discovery and identification of his granddaughter’s remains, being sequestered for almost two weeks in a psychiatric hospital, such documentation may indeed be forthcoming for him, if not for his wife. One curious and possibly telling comment made by Casey’s brother Lee during his deposition for the civil suit last week was his recollection that Caylee’s alleged abductor, “Zanny,” had, according to Casey, commandeered her personal password at myspace.com, changing it to “timer55,” and directed her via the internet and text messaging to go to certain locations, threatening the lives of family members if she refused. He recalls Casey telling him that she believes Caylee was taken by Gonzalez “to teach her a lesson.” What lesson might that be? And why? Lee Anthony reiterated under oath: “I believe everything my sister tells me.” Lee himself seems to believe that “timer55″ holds some sinister, secret numeric meaning. What might this say, if anything, about brother Lee’s state of mind? And possibly Casey’s? I do not know whether Ms. Anthony is guilty as charged and have had no direct involvement in this matter. Nor can I speak definitively to her state of mind past or present or that of her family without having interviewed them directly. However, as I mentioned previously , this case brings to mind a clinical syndrome called Shared Psychotic Disorder or folie a deux , trois , or perhaps quatre . This unusual phenomenon typically involves a primary person or “inducer” becoming delusional and others close to her or him to differing degrees adopting that distortion of reality. Of the four immediate family members, George, a former homicide detective, may be the least in denial about what happened, which could explain his suicidal reaction: some studies suggest that depressed individuals perceive reality more clearly than non-depressed people. But it would appear that both Lee and his mother, Cindy, if not consciously covering up, may still be under the spell–despite having been separated for months from Casey. If Casey could be depicted to a jury as having been clinically paranoid at the time she allegedly killed her daughter Caylee– as opposed to being perceived as merely selfish, immature and manipulatively lying to escape responsibility and punishment for this evil deed– might this be the basis for a forthcoming insanity defense ? Meanwhile, prosecutors have for now apparently decided not to reinstate the death penalty in this case, influenced in part by a legal brief by a former member of the defense team which hypothesizes that Casey could have been depressed and manic around the time of the alleged crime. In my first posting , I raised this same question, which, without extensively evaluating such a defendant, is impossible to answer. Could Casey possibly suffer from bipolar disorder ? If it were convincingly shown that the alleged crime occurred during a severe manic or depressive episode–either of which can sometimes include delusions–this could conceivably support an insanity defense. In the unlikely event there were to be an insanity defense in the Casey Anthony case, her attorneys would need to prove that Casey could not differentiate between right or wrong at the time of the alleged crime, or did not appreciate the nature and quality of her evil deed. The insanity defense is quite difficult: Less than 1% of jury trials attempt to prove legal insanity. Of those, only about one-in-four succeed. The finding of Not Guilty by Reason of Insanity (NGRI) is generally a hard-sell to juries. The defendant may be demonstrably mentally ill, or, here in California, clearly in a state of diminished mental capacity at the time of the crime, yet still not technically legally insane. Legal insanity is a high bar. The mere presence of serious mental disorder or psychosis does not necessarily meet the stringent standard for legal insanity. Nor does the diagnosis of a personality disorder alone or having been under the influence of or addicted to some licit or illicit substance when committing the crime. Florida’s insanity defense law, like California’s, allows defendants to acknowledge that they committed the act for which they have been charged, but argue that they should not be found guilty because they have a mental illness or defect. The defendant’s mental state must have been so severe as to prevent her from knowing what she was doing or the consequences of her crime when committing the crime. Alternatively, the defendant may have understood what she was doing and the consequences of her actions, but can still invoke the insanity defense if she did not understand that her actions were wrong. As in California and most other states, the Florida insanity defense is based on the M’Naghten rule , named after a mid-nineteenth century British case in which a severely delusional man, Daniel. M’Naghten, attempted to assassinate the Prime Minister, mistakenly killing instead the Prime Minister’s secretary. He was found not guilty by reason of insanity, but due to public outcry, the so-called M’Naghten standard was established, requiring that for such a defense, the defendant, due to a “defect of reason,” must be proven to have not known the nature and quality of his or her actions or that those actions were wrong. Controversial as it is, the insanity defense goes to the very heart of the notion of personal responsibility : Are we always fully responsible for our actions? Are there certain disorders, diseases, syndromes, dangerous states of mind, or mitigating circumstances that can negate or reduce personal responsibility? If so, what are they? And where do we as a society draw that line? These are precisely the sort of complex existential, philosophical, psychological and legal questions Casey Anthony’s defense team would have to persuasively address were they to decide to invoke the rare and risky insanity defense.    

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Did Casey Kill Caylee?: Could There Be an Insanity Defense Coming?

Psychology and Taxes on Capital

March 5, 2009 in Blogs, Psychology Today by Psychology Today

President Obama’s proposed budget includes an increase in taxes on capital. That won’t be very useful in generating tax revenue in the short-run. But it will also make fixing the broken economy even harder. Taxes on capital include taxes on interest income, dividend income, and capital gains. First, let’s get real, people aren’t receiving much interest and dividends these days. Interest rates are at historic lows and companies have slashed their dividend by half, 90%, even 100%. And with stocks and real estate falling so much, who has capital gains these days? You are not going to raise much revenue here for quite awhile. Increasing taxes on capital now will discourage capital from coming into our markets at this critical time. As an illustration of this, consider the proposed energy cap and trade program. This program seeks to tax carbon emissions above a certain level (the cap). A business under the cap can sell those credits to other businesses (the trade) that are over the cap. The purpose of this program is to tax pollution in order to discourage it. They seek to encourage companies to invest in low emission technologies. Note that taxing the carbon emissions discourages producing carbon emissions. The same principle applies to capital. We need capital to come into the marketplace. We need it for buying homes. We need it going into the stock market (so my 401k can recover!). We need it in our banks so that the government can stop providing it. We need new capital, so why are we discouraging it by increasing taxes on it? Increasing taxes on capital right now has no benefits because it won’t raise significant revenue. However, it has severe disadvantages because it signals those with capital to go somewhere else (for example, China has no taxes on capital gains). I encourage politicians to avoid their ideological stances and think clearly about what new policies actually achieve and what incentives they create.  

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Psychology and Taxes on Capital

by Vaughan

Rewiring the brain for fun and profit

March 3, 2009 in Blogs, Mind Hacks by Vaughan

Wired has just published an excellent two part article on neuroengineering, the practice of altering the brain with electronics or optics. It looks at a number of interesting projects, from light controlled neurons to magnetic brain stimulation, and focuses on the work of talented neuroengineer Ed Boyden who I had the pleasure of doing a joint talk with at a SciFoo conference. In fact, TMS gets electricity into the brain peacefully, without either cutting it open or shocking it with millions of volts. The target area of the brain is treated like the coil in a generator, subjected to rapidly changing magnetic fields until electricity begins to dance across its neurons. Unlike the optical switch developed by Boyden and Stanford’s Dr. Karl Deisseroth, TMS doesn’t reach the deeper regions of the brain, but there are a lot of important and interesting areas in the cortex where TMS delivers its current. It’s also far less precise than the optical switch, although TMS seems positively surgical when compared to the imprecisions of the pharmaceuticals we pump into our bodies. The second part is probably the highlight, discussing the possibilities of having these technologies more widely available so your average garage hacker can tinker with them (and themselves), and what ethical dilemmas this might cause. Link to ‘Inside the New Science of Neuroengineering’. Link to ‘How Neuroengineering May Change Your Brain.

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Rewiring the brain for fun and profit

by Vaughan

Junk food marketers rediscover the Crockus

March 1, 2009 in Blogs, Mind Hacks by Vaughan

The following is from a recent New York Times article on how snack food company Frito-Lay have based their latest women-focused campaign on ‘neuromarketing’. Parts of the article nearly made with weep with despair. [Advertising agency] Juniper Park used neuromarketing in a slightly different way. Ms. Nykoliation began by researching how women’s brains compared with men’s, so the firm could adjust the marketing accordingly. Her research suggested that the communication center in women’s brains was more developed, leading her to infer that women could process ads with more complexity and more pieces of information. Hang on a minute. Communication centre larger in women? She doesn’t mean… the crockus by any chance? A memory and emotional center, the hippocampus, was proportionally larger in women, so Ms. Nykoliation concluded that women would look for characters they could empathize with. Stop sniffing the TipEx. And research Ms. Nykoliation read linked the anterior cingulate cortex, which processes decision-making and was larger in women, to feelings of guilt. (Experts differ on how directly functions or feelings are associated with various parts of the brain.) Ms. Nykoliation then asked NeuroFocus to review her assumptions and, as Juniper Park developed ads, to test the ads to verify that women liked them. We should have guessed a ‘neuromarketing’ company would be involved. Neuromarketing is an interesting research field looking at the neuroscience of buyer decisions but so far there is not a single scrap of data that shows neuroscience can better predict buyer decisions that plain old ‘marketing’. In other words, if you’re wanting to actually market a product, it’s a huge waste of money. However, that hasn’t stopped various ‘neuromarketing’ companies from springing up and selling their sweet nothings to large corporations for hard cash. I say a huge waste of money, but it did get them a feature in The New York Times who also posted their commercial online, so maybe it’s not such a daft move after all. Link to NYT article.

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Junk food marketers rediscover the Crockus

Men, their perception of women, and their tools [Dr. Joan Bushwell's Chimpanzee Refuge]

February 17, 2009 in Blogs, Brain & Behaviour by BrainAndBehaviour

Research out of Princeton University and noted at this past weekend’s annual AAAS meeting gives weight to an idea that cognitive and social scientists have tentatively considered for years: Given sufficient provocation, men view women as sex objects. Men are more likely to think of women as objects if they have looked at sexy pictures of females beforehand, psychologists said yesterday. Researchers used brain scans to show that when straight men looked at pictures of women in bikinis, areas of the brain that normally light up in anticipation of using tools, like spanners and screwdrivers, were activated. Scans of some of the men found that a part of the brain associated with empathy for other peoples’ emotions and wishes shut down after looking at the pictures. Susan Fiske, a psychologist at Princeton University in New Jersey, said the changes in brain activity suggest sexy images can shift the way men perceive women, turning them from people to interact with, to objects to act upon. This makes perfect sense, given that when males view pictures of NASCAR events, daffodils, and human waste, anecdotal evidence suggests that they are inclined to think of not only various power tools, but also limitless varieties of copulatory activity. In the study, Fiske’s team put straight men into an MRI brain scanner and showed them images of either clothed men and women, or more scantily clad men and women. When they took a memory test afterwards, the men best remembered images of bikini-clad women whose heads had been digitally removed. This is merely a symbolic leveling of the playing field. If men in lust-struck states are operating without benefit of their brains, then it is only just that the objects of their lust be rendered similarly decerebrate. In the final part of the study, Fiske asked the men to fill in a questionnaire that was used to assess how sexist they were. The brain scans showed that men who scored highest had very little activity in the prefrontal cortex and other brain regions that are involved with understanding another person’s feelings and intentions. “They’re reacting to these women as if they’re not fully human,” Fiske said. “Not fully human” is as likely to mean “superhuman” as “subhuman,” correct? Looks like further research is needed . Read the comments on this post…

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Men, their perception of women, and their tools [Dr. Joan Bushwell's Chimpanzee Refuge]

Francis Collins will be so disappointed [Pharyngula]

February 16, 2009 in Blogs, Brain & Behaviour by BrainAndBehaviour

Collins has argued that one piece of evidence for god is the human moral sense, which he claims could not have evolved. I guess we’re going to have to call monkeys our brothers and sisters then, since researchers have found that monkeys have a sense of morality . (Let me guess; he’ll just push the magic moment of ensoulment back another 30 million years.) Furthermore, they have explanations for how altruism could have evolved. Some researchers believe we could owe our consciences to climate change and, in particular, to a period of intense global warming between 50,000 and 800,000 years ago. The proto-humans living in the forests had to adapt to living on hostile open plains, where they would have been easy prey for formidable predators such as big cats. This would have forced them to devise rules for hunting in groups and sharing food. Christopher Boehm, director of the Jane Goodall Research Center, part of the University of Southern California’s anthropology department, believes such humans devised codes to stop bigger, stronger males hogging all the food. “To ensure fair meat distribution, hunting bands had to gang up physically against alpha males,” he said. This theory has been borne out by studies of contemporary hunter-gatherer tribes. In research released at the AAAS he argued that under such a system those who broke the rules would have been killed, their “amoral” genes lost to posterity. By contrast, those who abided by the rules would have had many more children. It’s a little glib and speculative, but it’s enough to shut down the claim that morality couldn’t have evolved. I also have deep reservations about some of the claims in the article. Other studies have confirmed that the strength of a person’s conscience depends partly on their genes. Several researchers have shown, for example, that the children of habitual criminals will often become criminals too – even when they have had no contact with their biological parents. Ugh. Criminality is too flexible and too easily influenced by the environment — strip me of my income and throw me on the streets, and I’ll become a criminal, too, if it keeps me and my family from going hungry. But then, I suppose anyone could claim those are just the genes of my roots in the lower socioeconomic classes. Read the comments on this post…

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Francis Collins will be so disappointed [Pharyngula]

Beta-blocker drug erases the emotion of fearful memories [Not Exactly Rocket Science]

February 16, 2009 in Blogs, Brain & Behaviour by BrainAndBehaviour

The wiping of unwanted memories is a common staple of science-fiction and if you believe this weekend’s headlines, you might think that the prospect has just become a reality. The Press Association said that a ” drug helps erase fearful memories “, while the ever-hyperbolic Daily Mail talked about a ” pill to erase bad memories “. The comparisons to The Eternal Sunshine of the Spotless Mind were inevitable, but the actual study, while fascinating and important, isn’t quite the mind-wiper these headlines might have you believe. The drug in question is propranolol, commonly used to treat high blood pressure and prevent migraines in children. But Merel Kindt and colleagues from the University of Amsterdam have found that it can do much more. By giving it to people before they recalled a scary memory about a spider, they could erase the fearful response it triggered. The critical thing about the study is that the entire memory hadn’t been erased in a typical sci-fi way. Kindt had trained the volunteers to be fearful of spidery images by pairing them with electric shocks. Even after they’d been given propranolol, they still expected to receive a shock when they saw a picture of a spider – they just weren’t afraid of the prospect. The drug hadn’t so much erased their memories, as dulled their emotional sting. It’s more like removing all the formatting from a Word document than deleting the entire file. Congatulations to Forbes and Science News who actually got it right. Kindt’s work hinges on the fact that memories of past fears aren’t as fixed as previously thought. When they are brought back to mind, proteins at the synapses – the junctions between two nerve cells – are broken down and have to be created from scratch . This process is called “reconsolidation” and scientists believe that it helps to incorporate new information into existing memories. The upshot is that when we recall old memories, they have to be rebuilt on some level, which creates an opportunity for changing them. A few years ago, two American scientists managed to use propranolol to banish fearful responses in rats. They injected the animals in their amygdalae, a part of their brains involved in processing emotional memories. The drug didn’t stop a fearful memory from forming in the first place, but it did impair the memory when the rats tried to retrieve it. Now, Kindt has shown that the chemical has the same effect in humans. Read the rest of this post… | Read the comments on this post…

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Beta-blocker drug erases the emotion of fearful memories [Not Exactly Rocket Science]

by Vaughan

Buck Rogers is not a blueprint

February 10, 2009 in Blogs, Mind Hacks by Vaughan

A quote from a recent Wired article that discusses a project to create a computer architecture based on the neurobiology of the brain. It sounds suspiciously like it’s based on Dr Theopolis from 70s TV series Buck Rogers in the 25th Century : In what could be one of the most ambitious computing projects ever, neuroscientists, computer engineers and psychologists are coming together in a bid to create an entirely new computing architecture that can simulate the brain’s abilities for perception, interaction and cognition. All that, while being small enough to fit into a lunch box and consuming extremely small amounts of power. Just because you didn’t mention Buck Rogers in the grant application, it doesn’t mean we don’t know what you’re up to. I mean, I’d love to recreate the magic of ‘Planet of the Amazon Women’ too, but you’ll need more than a fully conscious cognitively aware AI than runs off two AA batteries. If you’re completely mystified, and / or under the age of 30, you may want to check out this clip on YouTube. Dr Theopolis is the, er, lunch box like-AI on the table. He usually hangs round the neck of the annoying android Twiki. On a slightly more serious note, I just checked out Kwabena Boahen’s Stanford talk where he discusses exactly this sort of project to create neurally inspired computer chips. Definitely worth a look. Link to Wired article on cognitive computing. Link to Kwabena Boahen’s talk on neurally inspired chips.

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Buck Rogers is not a blueprint

by Vaughan

Looking into the mind of God

February 5, 2009 in Blogs, Mind Hacks by Vaughan

This week’s New Scientist has an interesting article summarising the current thinking on the psychology of religion. The research treats religion and belief in God or other supernatural entities as a natural consequence of how the brain works. This has taken two main strands in the research literature: the first is that these tendencies to believe in supernatural forces have evolutionary benefits for social cohesion and kinship, which is why they have been selected for. The other is that these beliefs are a side-effect of the actions of other useful cognitive processes we have developed. In other words, we have certain mental abilities, typically attributing intention and desire, which we unwittingly over-apply and hence attribute random uncontrollable events to mysterious but intelligent beings. The article is not particularly in-depth but is notable for its breadth of coverage and will give you a taste for the direction in which the cognitive science of religion is heading. Link to NewSci article ‘How your brain creates God’.

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Looking into the mind of God