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Amazing Graphic – All the Biases October 4, 2017

Posted by Ubi Dubium in Brain Glitches.
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My spouse put me on to this image:

This is a chart of ALL the known cognitive biases, grouped into rough categories.  This is one of my favorite subjects to learn about, because it really helps me understand why people do inexplicable things.

What are cognitive biases?  (I also like to call them “brain glitches.”)  They are the ways humans mess up when thinking, making consistent sorts of mistakes and being illogical in predictable ways.

In a way, it makes sense that we have some of these glitches. We simply do not have enough brain capacity and brain power and speed to completely think through everything in our lives.  We can sit down and ponder through a few things logically, but that’s tiring and often too slow.  Most of the time we function on “rules of thumb” and mental shortcuts, and for most of human history those worked well enough, usually.  But maybe not so well in our complicated modern world.

But some of these just seem to be idiosyncrasies of the way our brain is wired.  And we are all subject to them, to some extent.  But understanding these has certainly been helpful for me, both in catching myself thinking sloppily, or understanding why other people behave the way they do.

To see a full size image that you can actually read, please go here.

(And once I finish with sporking the Mormon guidebook, I think I might start a blog series based off this graphic, looking at sets of biases in the way they are grouped together in the chart.)

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Inner Demons January 19, 2017

Posted by Ubi Dubium in Books, Brain Glitches, Responses.
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Still reading Steven Pinker’s The Better Angels of our Nature.  I’ve just finished the chapter on what it is about human brains that leads us into violence that ought to be avoidable.  Again, this chapter really could be a whole book on its own.

He sums up at the end of this chapter by re-listing five “inner demons” and I think his list is a good summary.  He didn’t number the list, but I’m going to here:

  1. People, especially men, are overconfident in their prospects for success; when they fight each other, the outcome is likely to be bloodier than any of them thought.
  2. People, especially men, strive for dominance for themselves and their groups; when contests of dominance are joined, they are unlikely to sort the parties by merit and are likely to be a net loss for everyone.
  3. People seek revenge by an accounting that exaggerates their innocence and their adversaries’ malice; when two sides seek perfect justice, they condemn themselves and their heirs to strife.
  4. People can not only overcome their revulsion to hands-on violence but acquire a taste for it; if they indulge it in private, or in cahoots with their peers, they can become sadists.
  5. And people can avow a belief they don’t hold because they think everyone else avows it; such beliefs can sweep through a closed society and bring it under the spell of a collective delusion. (pg 570)

The chapter has a really detailed examination of each of these points.  This is a really interesting book, and I wish it was required reading for every politician before they were allowed to take office.

Self-delusion January 14, 2017

Posted by Ubi Dubium in Brain Glitches, Questions, Responses.
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I’m reading Steven Pinker’s The Better Angels of Our Nature.  It’s an enormous and thorough work on the decline of violence.  Each chapter could really be a book on it’s own, and it’s taking me a really long time to work through it.

A day or so ago, though, this sentence jumped out at me.  It’s in a section where he’s discussing why humans tend to think they are more competent, smarter, and luckier than they actually are:

“… Positive illusions are a bargaining tactic, a credible bluff.  In recruiting an ally to support you in a risky venture, in bargaining for the best deal, or in intimidating an adversary into backing down, you stand to gain if you credibly exaggerate your strengths.  Believing your own exaggerations is better than cynically lying about it, because the arms race between lying and lie detection has equipped your audience with the means of seeing through barefaced lies.” (pg 512)

Hmm.  I’ve been looking for reasons why humans tend to be so good at self-delusion, and this idea could factor into the explanation.  But its validity would hinge on humans being reasonably good at detecting lies.  I’m not convinced that they are, especially given recent politics.

What do you think?

Answers to “A Question for Atheists” August 14, 2016

Posted by Ubi Dubium in Questions, Responses.
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Godless Cranium linked to a post at flyinguineapig, with two longish questions for atheists. Flyinguineapig appears to be a strongly christian blogger, but these questions aren’t really the typical “gotcha” questions that I would expect to see on a blog of that sort, so I’ll go ahead and tackle them. Rather than try to answer in the comments at either of those blogs, I’ll post my answers here, and link back to them.  Also, I prefer to write my own answers before I read through everybody else’s answers.

My first question is more general. I see this among atheists and my agnostic friends. People deny the possibility of any deity’s existence because of the lack of some kind of proof. It occurred to me that I have no idea what kind of proof you’re looking for. Furthermore, it seems to me that, in many cases, not just in the case of spirituality, what constitutes proof is at least somewhat subjective. I would love to get a few different perspectives, so my question is, what would prove to you that God exists?

Let me start with this part of the question: “People deny the possibility of any deity’s existence…”  Most atheists I know don’t actually do this, so the question is starting out with rather of a strawman assumption.

The difficult part of this assumption is – how do you define a god?  It’s a really nebulous term.  I know what the christians mean when they talk about their god, but the question here is “any deity”.  What characteristics would a being need to have in order for us to consider it a god?  Let’s look at a few examples: (more…)

The King who Rained Confirmation Bias January 9, 2016

Posted by Ubi Dubium in Brain Glitches.
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One website I love is called “You Are Not So Smart”, written by David McRaney, which looks into all the different ways that we delude ourselves. Great stuff. He’s migrated it into a podcast now, but the original articles are still on the website.

One of the most important topics he covers is confirmation bias.  After you read this, go read his article:

http://youarenotsosmart.com/2010/06/23/confirmation-bias/

Here’s how he opens that article:

Have you ever had a conversation in which some old movie was mentioned, something like “The Golden Child” or maybe even something more obscure?

You laughed about it, quoted lines from it, wondered what happened to the actors you never saw again, and then you forgot about it. Until…

You are flipping channels one night and all of the sudden you see “The Golden Child” is playing. Weird. The next day you are reading a news story, and out of nowhere it mentions forgotten movies from the 1980s, and holy shit, three paragraphs about “The Golden Child.” You see a trailer that night at the theater for a new Eddie Murphy movie, and then you see a billboard on the street promoting Charlie Murphy doing stand-up in town, and then one of your friends sends you a link to a post at TMZ showing recent photos of the actress  from “The Golden Child.”…

He goes on to talk about how that first reference primes us to notice and remember those other references, which otherwise we would have ignored.  How what appears to us to be a significant pattern is really nothing of the sort.

I just have one problem with this article.  I’ve never seen “The Golden Child”!  I don’t really care for Eddie Murphy movies, never noticed this movie on TV or Netflix, so this example just doesn’t resonate with me.  But I’ve been having a very similar experience over the last few days that I want to talk about.

A week ago I was remembering back to the TV shows from my childhood, and how some child actors just showed up everywhere.  I was specifically remembering how Johnny Whitaker was in everything, so I went looking on YouTube for clips from the old version of Tom Sawyer that he did.  (And found them, and I had forgotten that a very young Jodie Foster played Becky Thatcher.)  But that reminded me of a version of The Littlest Angel that he had done in the late 60’s:

Littlest angel

I found the full version on YouTube.  I remembered liking it as a kid, but going back to watch it now, it was really bad.  Really, really stupid and bad.  Fred Gwynne could actually sing, though, who knew?  But overall it was cheesy, poorly written and just painful to watch.  (Priming accomplished.)

A few days later, I was bored, and so asked Wikipedia for a random article.  What came up?  The entry for the really old TV show Car 54 Where Are You?  That was pretty cool, because some years back I had caught some reruns of this show, and so I was familiar with it, and even remember how the theme song went.  Here’s the stars:

Car 54

Are you seeing the pattern here?

Now we’re up to lunch Thursday.  My spouse and I were at a little restaurant near my office, and it had background music on, the usual fairly current pop stuff, but nothing too distracting.  Then they played something that I couldn’t help but listen to.  It turns out to be Fall Out Boy’s song Uma Thurman.  I had to look that song up, because I couldn’t catch any of the words at the time.  What caught my ear about it was the old song that they had sampled.  (That was the only thing that caught my ear about the song.)

What had they sampled?  The very distinctive theme song to The Munsters!  So what pops into my head – this guy of course!

Herman Munster

I only noticed this “pattern” because my brain was already primed to notice it from the awful video I watched a week ago.  Otherwise I would probably never have noticed it.  Confirmation bias in action.

(The title of this post comes from one of the children’s books written and illustrated by Fred Gwynne, which I also remember from my childhood.)

King who rained

48 Sure-Fire “gotcha” questions for Atheists! (part 2) June 17, 2015

Posted by Ubi Dubium in Questions, Responses.
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Previous post in this series.

So continuing on with this set of thoughtful answers to stupid questions.

9. Do you know that Jesus loves you?

No, because he doesn’t.  He’s dead, so he doesn’t love anybody.  Dead people don’t feel emotions, it’s one of the major side effects of being dead.  I know that his fan club says that he’s alive and he loves people.  But then some members of Elvis’s fanclub still think Elvis is alive.  They know because they saw him shopping down at the Piggly-Wiggly.

10. If Christianity is false, then why is it popular?

Ah – the old argument ad populum, if it’s popular it must be true.  For hundreds of years bleeding was the most popular medical treatment. That didn’t mean it was effective.  Power Balance bracelets were so popular that the company had the money to buy naming rights to a stadium!  But the bracelets turned out to be overpriced rubber bands with a big campaign of deceptive marketing behind them.  There’s plenty of things that are popular that are still complete rubbish.

And you also have to consider the availability heuristic, which is a fancy phrase that means we give too much importance to the information we see right around us, and ignore other factors.  If you live in the US Bible Belt, it’s easy to think that christianity is the most popular, because it’s what’s around you every day.  But only about 1/3 of the world’s population is christian, the rest are muslim, hindu, buddhist, etc etc.  If christianity were so obviously true, you’d think it would be more popular.

11. If you say Christianity is not true, then why do hundreds of people continue to become saved every day?

Now we need to talk about confirmation bias.  We pay attention to and remember things that are different,  interesting, or that agree with the opinions we already have.  We ignore information that is ordinary,  boring, or that contradicts our opinions.  So hundreds of people are becoming “saved” every day?  How many are quitting?  You don’t actually know.  Your church doesn’t pay attention to those numbers, or at least they don’t tell you if they do, and you don’t notice when somebody stops showing up, unless it’s a friend.  Can you imagine if a church had an announcement in it’s bulletin that said “Well this week we saved two souls for jesus, and five other people stopped believing”?  Yeah, they don’t print that part.

So how do we know whether christianity is gaining or losing converts overall?  Here’s a chart, made with information about the US gathered from the Pew Forum, showing the religion people were raised with, and their current religion.  There’s a lot a switching, but it’s apparent that  a lot more people are switching out of religion than are switching into it.

religion switching

This second graphic shows that all US christian groups declined in membership from 2007-2014, but the numbers of unaffiliated increased dramatically.

religious landscape

So at least in the US, you are not converting more people than you are losing.  Sorry.

12. Why do we not see half trees and half carrots, fronkeys, and crocoducks if evolution is real?

Because that’s not the way evolution works, and this question shows a refusal to even try to understand the basics of it.  If we saw crazy things like that, instead of slow stepwise modifications over time, it would be evidence that our theories about evolution were totally wrong, and we’d have to rethink things.  But we don’t see those.

13. Why is Richard Dawkins afraid to debate Ray Comfort?

He’s not afraid, a debate with Comfort just isn’t worth his time.  There’s several reasons for that.

  • He’s a famous and accomplished biologist and science communicator, and engaging Comfort in a debate would indicate that he thought Comfort was a worthy adversary and raise Comfort’s perceived status.  To paraphrase Dawkins’ comment on this (in American English) “It would look better on his resume than on mine.”
  • Comfort offered $10,000 as a challenge.  That’s much less than Dawkins’ usual speaking fee for a regular appearance.
  • Comfort is not an honest debater.  Matt Dillahunty once accepted a debate with Comfort, agreeing on the format and subject matter ahead of time.  But once the debate started, Comfort declared that he didn’t care what the subject of debate was, he was just going to preach, and launched into his usual soapbox spiel.  I listened to this entire debate, and Comfort was rude and dishonest about his intentions from the beginning.  Matt has said he would never accept another debate with Comfort, and I don’t see any reason why anybody else would want to either.
  • Debates are not a good format for arriving at truth or changing minds.  There are better ways to go about it.

14. Did you know Christopher Hitchens was saved before death?

No, because he wasn’t.  You don’t get to make stuff up and claim it’s true.  He was very definite about not believing, right up to the end, and had harsh words for the people that he knew would try to propagate a fiction like that. This is called “lying for jesus” and it doesn’t make you look like someone who should be listened to and trusted.  If making up stories like that is the best you’ve got to support your religion, then give up now.

15. Are you aware Ray Comfort disproved atheism with a banana?

I’m aware that Comfort made a fool out of himself with a banana.  This is one of the questions that is so silly it makes me think this entire list is a spoof.  But for the benefit of those few people out there that still think this is a legitimate question, I’ll explain.

Ray (with Kirk Cameron) claimed that the shape and tastiness and convenience of bananas was evidence that god had designed them for us.

This is a wild banana.  If a god had designed bananas, this is what he designed.  It’s green and hard and full of seeds and really unappetizing and inconvenient.

Inside_a_wild-type_banana

Sweet yellow seedless bananas don’t happen in the wild.  They are the product of thousands of years of selective breeding by humans.  We selected for the traits we wanted, and over time produced a plant that suited our needs.  So of course it’s handy and tasty and  easy to peel and seedless.  (Duh.)

And how does Ray then explain a pineapple?  The best fruit in the world, hidden under a nasty hard rind that won’t peel off, with spiky leaves in your face.  Is that god saying “pppppbbbbbfttthhhh on you!” or what?

16.Why do people laugh at evolutionists?

It’s a defense mechanism.  Fundamentalist christians (unlike mainstream christians) have based their entire worldview around the literal truth of every single word of their book.  Anything that undermines any small part of that belief is a threat to all of it.  Ask a Presbyterian or a Methodist if the Garden of Eden was a real place and most will say “That’s obviously a myth, meant to teach a moral lesson.  Now lets sing some more happy songs about how great god is.”  They aren’t concerned about the literal truth of every word, so evolution is not a threat to them, and most of them are just fine with it. But for a fundamentalist, if you undermine even a small piece of their book their whole faith could come crashing down.

And another feature of christianity is that it puts mankind up on a pedestal as it were, insisting that the entire universe was created just for us.  We are the center of everything, we are special, we are different.  Everything we discover that puts us farther away from being the center of the universe must be fought tooth and nail. That’s why the catholic church fought so hard against Copernicus and Galileo when they proposed heliocentrism.  Not being in the center of everything made us seem less special, and they couldn’t have that.  Evolution likewise pushes us off that pedestal of specialness and puts us as just one animal among many.

So evolution tells us the bible is wrong and that we are not the pinnacle of creation.  Rather than face that possibility, fundamentalists make up nonsense “creation science” that doesn’t actually discover anything, and ignore inconvenient scientific findings, and tell themselves that all the professional biologists are making it all up.  And they laugh, and cover their ears, and say “LA LA LA!!  I can’t hear you!!” because if they didn’t they might actually learn something that would endanger their fragile belief system.

Next Post in this series.

Thoughts on “The Black Swan” March 8, 2015

Posted by Ubi Dubium in Books.
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I’ve finally finished plowing through The Black Swan.  No, not the movie about ballet dancers, this is the book by Nassim Nicholas Taleb about the influence of improbable events.  I’ve seen mentions in other books that the ideas in this book were influential on other thinkers whose work I really like.

As much as I was hoping that I could recommend this book as a good read, I really can’t.  There’s some important ideas in it, enough to fill a longish magazine article, or maybe a much shorter book.  But there’s not enough real substance to fill 300-ish pages, and it’s interspersed with digressions and ranting to the point that it interfered with my ability to follow his points, or stay absorbed in reading it.  It took me months of picking it up and putting it back down to finally get through it.

Black Swan

One of his main ideas is defining a “black swan” event.  The source of the name goes back to when people in Europe knew that all swans were white. The phrase “black swan” was used to mean something extremely unlikely.  Once black swans were actually discovered in Australia, this unexpected event changed that certainty.  However, Taleb uses “black swan” to mean an unforseeable event that has an unexpectedly large effect on society.  Something along the lines of 9/11, or a stock market crash or the rise of the internet.   (So, the discovery of black swans wasn’t actually a “black swan” event by his definition!)   This kind of event can’t be directly prepared for, since there’s no way to anticipate what the next one will be.

Another good concept he has is separating “mediocristan” from “extremistan”.  Mediocristan refers to situations where statistics fall into nice neat bell curves, and outliers are not of great influence.  As an example, suppose you were to take a random group of 1000 people, and chart their weight distribution on a histogram.  You’d probably get a nice bell curve distribution with only a few outliers.  Perhaps you might get one extremely heavy person in your sample, but if you look at the total weight of the group, that person would not represent a substantial fraction of the total weight of the group nor would their addition to the group throw off the averages very much.  There’s just limits on how much range of variability there can be for some measurements.

In extremistan that’s not the case.  Instead of weight, let’s try charting wealth.  Again, take a sample 1000 people and you might get a nice bell curve, with a few poorer people, a few richer ones, and most falling in the middle, with only a few outliers.  But suppose that one of those outliers in your sample happened to be Bill Gates.  Now if you look at the overall total wealth of the group, or the average wealth, that one outlier has an overwhelming effect on the numbers.  Since the range of wealth doesn’t have the same constraints as a variable like weight, the same statistical methods aren’t applicable, because a single unexpected outlier can overshadow everything else.  A large part of the book is spent talking about how people, particularly statisticians and economists, act like we live in mediocristan instead of extremistan, and how we are blind to the possibility of unexpected, influential, outlier events.

He also spent a lot of time on logical fallacies and cognitive biases, which was certainly relevant to his subject. Although I have read better discussions of these elsewhere, I was glad to see them included.  Understanding that humans are naturally crappy statisticians, and prefer a good story to what the data actually says, helps explain why we are so bad at anticipating black swan events.

OK, good stuff so far.  I was hoping there would be a substantial part of the book devoted to “OK, now what?”  I wanted some discussion about the author’s proposals for the best ways to approach living in extremistan, and the best ways to structure society’s institutions so as to be able to bounce back from or adapt to the next black swan event.  But there was very little of this.  He talked about a specific investment strategy that he uses to guard against financial black swans, but otherwise largely ignored this important part of the discussion.  (A caveat on this point – I see that in the second edition of the book there is an additional 100-page essay that looks like it may cover these points.  That was not included in the e-book edition I read, so I can’t comment on its contents here.  It may resolve the problem I have with the lack of “now what?” discussion.)

Instead he spends a lot of the book railing against the economists and financial professionals who do not take his ideas seriously.  He calls financial forecasters, or anyone who uses a gaussian bell curve in their analysis, a bunch of dunderheads and idiots.  He laments that Nobel prizes in economics are only going to “experts” whose ability to predict market movements is no better than chance.  He seems to hold a lot of resentment toward those who are most respected in the field of finance and economics, and he lets it show.  He seems more concerned with people recognizing that his ideas are brilliant than he is in having brilliant ideas.  With this kind of arrogance in his approach, I’m not surprised that the industry would be slow to pay him much attention.   If you are trying to change someone’s mind, starting out by calling them “stupid” is a poor strategy.

Another drawback to the book is the way it jumped around from point to random digression to different point to – hey look, a chicken!  Reading this book was like listening to someone with ADD. (And a huge ego!) He would make conclusions that didn’t follow from his premises, use jargon that had yet to be defined, and refer to concepts that wouldn’t be discussed until later chapters. He could really have used a good editor to tighten this up and make it more readable.

There are books I have read and loved, that present innovative ideas and take the reader step by step logically and clearly to the author’s conclusions.  I would name On The Origin of Species, Relativity,  The Selfish Gene and Thinking Fast and Slow as wonderful books of this type.  And there are the few gems that do this while also enthralling and entertaining the reader.  Gödel, Escher, Bach is such a treasure of a book.  I was hoping that I would be able to add The Black Swan to this collection, but sadly it just doesn’t reach that level.

 

 

 

Use-Mention Errors, or, My Close Personal Relationship with Pinkie Pie February 5, 2015

Posted by Ubi Dubium in Brain Glitches.
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 I remember reading a discussion from Daniel Dennett some time ago about the idea of a Use-Mention Error.  I don’t remember where that was, or I’d link to it.  This idea has been whirling around in my mind lately because of several discussions I’ve seen.  The most recent was a lengthy attempt by a theist caller to philosophize a god into existence on a recent episode of The Atheist Experience, but I’ve also read many theist comments about how, even though some particular dogma doesn’t make sense, they still have a close personal relationship with god in their hearts.  And I just want to scream “BAD ARGUMENT!” at them.

The easiest version of the Use-Mention Error is when somebody confuses a thing with the term for that thing.   Daniel Dennett’s example goes something like this: (more…)

That one spooky thing (wrap-up) October 14, 2014

Posted by Ubi Dubium in Brain Glitches.
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Spooky-Moon-Morguefile-photo

OK, time to wrap the series up.

When you’ve deconverted from religion and superstition, and decided to live a life based in reality, what do you think about that one strange thing that might have once happened to you?  That thing that keeps you convinced that there’s a supernatural realm out there somewhere?

Before you can decide that it’s actually “supernatural”, you really need to consider the following alternate possibilities, which I’ve discussed in earlier posts:

  • It’s a natural occurrence that’s rare or unfamiliar to you (Part 1)
  • It’s technological (also Part 1)
  • It’s somebody deliberately tricking you (Part 2)
  • It’s a problem of faulty perception and/or faulty memory, perhaps combined with some of the above (Part 3, 3.1 and 3.2)
  • It’s “supernatural”

So, when you are thinking of that thing you once saw, before you conclude it was an actual “impossible thing”, first you need to run through a serious thought process about it.  Could you have mis-perceived it initially?  Or filled in mental gaps based on what you expected to see?  Did someone have something to gain by tricking you?  And have you embellished your memory over time, to the point where what you remember now really might not be what you saw initially?

Suppose that you have run through all those possibilities, and still have not come up with a plausible explanation.  Then you are left with two possibilities that I can think of.  Either it actually fell under one of the above categories but you couldn’t figure it out, or it was ‘supernatural”.  (Remember probability, which of those is most likely?)

So, finally, if you have still come to the conclusion that the thing you saw might actually  be supernatural”, we have the problem of defining that term.  Like “spirituality”, it’s a word that people throw around all the time, but when asked for a straightforward definition, they either can’t define it, or define it in terms of other vague undefined concepts, which isn’t helpful.  Here’s my working definition of “supernatural”:  We live in a four dimensional space-time universe  of matter and energy, governed by predictable physical forces.  That’s the “natural world”.  “Supernatural” would be something that is not that, either wholly or in part.

For us to detect something “supernatural”, it would have to have the ability to interact with our physical world in some way.  Even if that’s just deflecting some photons, or causing an EM disruption, or just planting a thought in somebody’s brain, all of those things are interactions with our physical world.  Any being that is completely unable to interact with our world would be totally undetectable and therefore irrelevant.

To be sure that something is really supernatural, you’d have to examine it in a way that eliminates all of the other possibilities we have already discussed.  Since the real world is so messy, the best way we can be sure is to do carefully controlled examinations, where we reduce the variables down to just the thing we are examining and eliminate cheating.  Of course, a fleeting “ghostly vision” isn’t going to be easy to catch in a lab experiment!   Lots of investigators have worked to pin down something “supernatural”, to where we could get a look at it, and actually say something coherent about it.  Alas, the better the controls are on your experiment, the more the “supernatural” aspect goes away.  The JREF has had a standing ONE MILLION DOLLAR prize to anyone who can demonstrate something supernatural under conditions controlled to eliminate cheating and wishful thinking.  So far no one has even passed the first round of tests.  Does this mean there isn’t any such thing?  Well, no, but given the results so far,  I’m not holding my breath.

Earlier posts in this series: Part 1 Part 2 – Part 3Part 3.1Part 3.2

That One Spooky Thing (part 3.2) July 17, 2014

Posted by Ubi Dubium in Brain Glitches.
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Continuing on…

I’ve been writing on the topic of how to think about that one thing lingering in your mind that might still make you wonder about the supernatural. As before, the possibilities that I have thought of are these:

•It’s a natural occurrence that’s rare or unfamiliar to you
•It’s technological
•It’s somebody deliberately tricking you
•It’s a problem of faulty perception and/or faulty memory, perhaps combined with some of the above
•It’s “supernatural”

So this time I’d like to talk about memory.  We like to think of our memories as video recorders, perfectly recording what happened and playing it back the same way every time.  But, sorry to say, this is not the case.  Our memories are buggy, subject to change, and just not very reliable, especially about details.

As I discussed in the last two posts, the first problem with memory lies in perception.  If we have misunderstood what we saw or heard, then we are remembering it incorrectly from the start.  So that’s one strike against us to begin with.  Let’s try a simple memory exercise before you read the rest of this post; take a pencil and paper and draw a simple line drawing of a bicycle.  Should be easy right?  Take a minute and give it a try.

(more…)