Photo by http2007

This is my 200th post. Thus, I can now say I’ve written hundreds of posts, instead of dozens. It will take 1,800 more posts before I can say I’ve written thousands, so this is a nice milestone!

I heard about this puzzle from @marelisa on Twitter, and I found a related but harder version on Wikipedia. It’s known as either Einstein’s Riddle, or The Zebra Puzzle. Albert Einstein allegedly created it as a boy, and he said that only 2% of the world’s population could solve it.

While it’s not clear whether it was actually created by Einstein, the 2% figure seems about right, especially because most people haven’t tried a puzzle like this before. But if you’re feeling up to it, I’ll give both versions of the puzzle, followed by some tips on how to do it.

Here’s the version of Einstein’s Riddle that Marelisa found. (Note there’s no zebra in this one.)

- In a street there are five houses, painted five different colors.

- In each house lives a person of different nationality.

- These five homeowners each drink a different kind of beverage, smoke a different brand of cigar, and keep a different pet.

Einstein’s riddle is: Who owns the fish?

Necessary clues:

1. The British man lives in a red house.
2. The Swedish man keeps dogs as pets.
3. The Danish man drinks tea.
4. The Green house is next to, and on the left of the White house.
5. The owner of the Green house drinks coffee.
6. The person who smokes Pall Mall rears birds.
7. The owner of the Yellow house smokes Dunhill.
8. The man living in the center house drinks milk.
9. The Norwegian lives in the first house.
10. The man who smokes Blends lives next to the one who keeps cats.
11. The man who keeps horses lives next to the man who smokes Dunhill.
12. The man who smokes Blue Master drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next to the blue house.
15. The Blends smoker lives next to the one who drinks water.

Here’s the version of The Zebra Puzzle in Wikipedia. This is the first known publication of the puzzle, from 1962. While similar to the version above, it’s significantly harder. As far as I can tell, it requires making a guess from multiple possibilities, then looking ahead to see how it pans out, and backtracking if it doesn’t work.

1. There are five houses.
2. The Englishman lives in the red house.
3. The Spaniard owns the dog.
4. Coffee is drunk in the green house.
5. The Ukrainian drinks tea.
6. The green house is immediately to the right of the ivory house.
7. The Old Gold smoker owns snails.
8. Kools are smoked in the yellow house.
9. Milk is drunk in the middle house.
10. The Norwegian lives in the first house.
11. The man who smokes Chesterfields lives in a house next to the man with the fox.
12. Kools are smoked in a house next to the house where the horse is kept.
13. The Lucky Strike smoker drinks orange juice.
14. The Japanese smokes Parliaments.
15. The Norwegian lives next to the blue house.

Now, who drinks water? Who owns the zebra?

(In the interest of clarity, it must be added that the five houses are in a row, each is painted a different color, and their inhabitants are of different nationalities, own different pets, drink different beverages, and smoke different brands of cigarettes.)

Here are some tips.

I can’t imagine solving these puzzles without using a chart to keep track of what you know. Most people would use a chart like the following, where it starts off blank and you fill in the words as you learn what’s in each house.

This is how the chart would look near the very beginning, after applying the clue that milk is drunk in the middle house.

But this is what I did. I started with a chart listing all the possibilities. For example, each of the drink cells started off with “Water Tea Orange Milk Coffee,” which I abbreviated here as “WTOMC” so it fits. Then I began deleting options that were impossible.

Below you can see how it looks after learning that milk is drunk in the middle house.

This way is more cumbersome, and I would only do it on a computer, not on paper. But I think it makes it easier to keep track of what you know, and therefore easier to solve the puzzle. That’s because you can track every possibility you rule out, instead of only writing something down after you’ve ruled out all other possibilities.

One more tip: cross out clues after you no longer need them. As the list of clues shrinks, you fill in the details, and eventually find out who owns the fish or the zebra.

Photo by AMagill

The Matrix trilogy presents a number of yin yang pairs, one of which is seen in the Oracle and the Merovingian. Although they take on the form of humans in the matrix, they’re actually computer programs. And they’ve been designed to specialize in different kinds of logic.

The Oracle is gifted with foresight based on inductive reasoning. Although she’s not actually psychic, she was specifically created for the purpose of understanding humans, and this gives her amazing powers of prediction. She can effectively see into the future, up to the point where free will presents a choice. She says nobody can see past a choice they don’t understand, thus showing her limitations.

The Merovingian is gifted with hindsight based on deductive reasoning. Believing that everything is determined by cause and effect, he thinks that someone’s power is based on their understanding of why events unfolded the way they did, and he understands this quite well. But his ability makes him overconfident, because he really doesn’t know everything. For example, he didn’t know that his wife would turn against him, because he saw no cause that would create that effect.

The Merovingian and the Oracle are opposites in this regard, and he dismisses her as a silly fortune teller. He laughs at Neo and his friends for visiting him just because the Oracle advised them to, when they didn’t really know why they were there or what they expected to happen. They were just blindly following orders, without knowing the answer to that all-important question: why?

But despite his mocking, the Merovingian secretly desires the Oracle’s powers of induction to complement his powers of deduction. And understandably so, when you consider what one could do with both of them.

This post is fairly long and complicated, but it’s virtually guaranteed to boost your reasoning skills. Read it once, then enjoy the benefits of improved logic for a lifetime.

Inductive reasoning

The Oracle inductively knew that Neo was coming, and she was ready with cookies in The Matrix (1999).

With inductive reasoning, you reach a conclusion that is believed to be true but not guaranteed. Specifically, you use observations of particular cases to make a generalization. While this may not seem logical, we do it all the time.

Here’s a common example:

“The stock market has averaged 10% annual returns in the past, so it’s reasonable to expect that it will continue to do so.”

Statements like this are often followed with an admission that 10% returns are not guaranteed. As they say, past performance does not guarantee future results.

However, predicting 10% returns based on available data seems preferable to ignoring the past, and deciding that returns of 10%, -100%, or 1,000,000% are equally probable. In other words, we naturally want to make a prediction, so we should make one that fits the pattern.

The card game Mao is based on inductive reasoning. New players are not told what the rules are, because the point of the game is to figure out the rules. Players have no choice but to observe the game, make many mistakes, and slowly piece together the rules by induction.

Here are some examples of so-called strong induction:

“Mary always hates horror movies, so she’ll hate this horror movie.”

“I’ve never seen a green canary, so your canary is probably not green.”

“Technology has changed a lot in the last 100 years, so it will change a lot in the next 100 years.”

“White eggs have a hard shell, so brown eggs must have a hard shell.”

“Five channels are showing static, so the cable is out.”

“Penicillin killed these bacteria, so it will kill other bacteria.”

“Pi does not terminate or repeat after the first million digits, so it never terminates or repeats.”

This is called strong induction because the conclusion is likely to be true, assuming the premise is true.

However, these statements could be stronger if the wording were more specific. What does it mean that “Mary always hates horror movies?” Which ones, and how similar are they to the one you’re predicting she’ll hate? You could also say she’ll probably hate the movie, to acknowledge the possibility that she might not.

Here are some examples of what’s called weak induction:

“I could run fast 60 years ago, so I can run fast now.”

“I always sleep until noon, therefore everyone always sleeps until noon.”

“I made a wish and it came true, so all wishes come true.”

This is weak induction because the arguments aren’t very convincing at all. There’s a very weak link between the premise and the conclusion.

However, what one person considers weak induction, someone else may consider strong induction. For example, Isaac Newton induced his theory of gravity from observing the motions of planets and falling apples. This theory was undoubtedly met with varying degrees of resistance, depending on how strong someone considered the induction to be.

Any induction, particularly weak induction, carries the risk of overgeneralization, which can lead to prejudice and delusion.

Rejecting inductive reasoning

On the other hand, if you don’t generalize at all, that’s a problem too. If you know how to drive a Camry, it would be crazy to say that you don’t know how to drive a Corolla because it’s a different model. We have to generalize to survive.

I know a baby who rejects inductive reasoning. When he gets hungry, he cries. Most babies will stop crying when you start feeding them, but not him. He knows that just because baby food satisfied his hunger last time, there’s absolutely no guarantee that it will satisfy his hunger this time.

So he keeps crying, while mom shovels food into his mouth as fast as she can. He doesn’t stop crying until he actually feels full, and therefore has proof that his hunger was satisfied. And he’s a big baby, so this takes two jars.

You can imagine how his mom feels. She inductively reasons that since he’s done this every time, he’ll continue to do so for a while. Wouldn’t it be nice if her baby used inductive reasoning to determine what was likely to happen, instead of insisting on a guarantee?

Deductive reasoning

The Merovingian deductively believes that every cause and effect has already been determined, so he just sits back and enjoys himself in The Matrix Revolutions (2003).

With deductive reasoning, you apply known rules to given data to prove a conclusion. Unlike inductive reasoning, deductive reasoning lets you arrive at a guaranteed conclusion, as long as your reasoning is sound. This is what we usually think of as “logic.”

For example:

“The sum of the angles of every triangle is 180 degrees. In this triangle, two angles are 45 degrees, so the remaining angle must be 90 degrees.”

We like deductive reasoning for a couple of reasons. One, we’re so used to thinking of it as the definition of logic. Two, it’s a lot more certain than inductive reasoning, and people like certainty.

However, it also gives us false certainty. Suppose you’re looking at an animal, and want to prove that it can fly. So you use this logic:

“This animal is a bird. All birds can fly. Therefore, this animal can fly.”

There are a couple of problems here. Most importantly, the claim that all birds can fly is false. For example, penguins can’t fly. We call an argument like this valid because the deduction was logical, but not sound because it’s based on a false premise.

Also, how can you confirm that it’s a bird? On a math test, you’re given all the information you need. But in the real world, a problem won’t necessarily be set up so conveniently.

The problem with deductive reasoning is that it’s like an insurance policy that guarantees to pay off, but only if a particular set of conditions is met exactly. And you’d better read the fine print. It’s easy to be far more confident in the outcome than your logic warrants.

The deduction above is relatively simple, but verifying the preconditions is extremely difficult. How do you know it’s a bird? Because it looks like other birds you’ve seen? That’s inductive reasoning. What’s the definition of a bird anyway?

Is it true that all birds except penguins can fly? What about chickens? They can fly a little, or can they? What’s the definition of flight? What about injured birds? What about birds that are afraid to fly?

Math is logical, but filled with assumptions

Math makes heavy use of deductive reasoning, but it’s a lot less solid than we might think. Think back to your high school math. You learned how to deduce many things, but it was all based on a set of axioms that we just assumed to be true.

Some of these axioms seem obvious, like “all right angles are congruent.” Of course they are. How could they not be? But that’s an assumption that can’t be proven. Some axioms seem stupidly obvious, like “if A and B are true, then A is true,” or “x = x.” It hurts your head to even imagine them not being true, but we need to make these assumptions to support everything else.

In geometry, we even have three undefined terms: point, line, and plane. This goes beyond unproven – they’re not even defined!

For over 2,000 years, Euclid’s assumptions of geometry seemed so obvious that no one questioned them. Today, we need to specify “Euclidean geometry” when referring to the version that seems obvious to us, because there are different versions where these assumptions are violated.

Far from being an unquestionable universal truth, Einstein suggested that Euclidean geometry is a good model of physical reality only if the gravitational field is not too strong.

Yes, math is very logical, and you can say that A is definitely true, if you assume that B, C, D, E, F, G, and H are true. But in that case, what have you really proven?

An attempt at inductive reasoning in math

Say we have a function f, where

f(x) = x⁶ – 15x⁵ + 85x⁴ – 225x³ + 274x² – 120x

OK, but what is this, really? What’s f(0)? You plug it in and see that f(0) = 0. OK, what about f(1)? That’s also 0. You try f(2), f(3), and f(4), and they’re all 0 too. Looks like a pattern is emerging.

You try f(5) and get 0 again. Now you’re getting tired of this. Obviously, f(x) = 0 for all whole numbers x, right?

Nope, because f(6) = 720.

This is the problem with inductive reasoning. You can observe as many specific cases as you want, but you’ll never prove a generalization from observation unless you observe all possible cases.

However, our observations are still helpful, because we can apply deductive reasoning to them. The fact that f(0) = 0 means that x is a factor of f(x). The fact that f(1) = 0 means that x – 1 is a factor of f(x), and so on. By factoring everything out, we find that

f(x) = x(x – 1)(x – 2)(x – 3)(x – 4)(x – 5)

This form is much simpler, and now we can see exactly why f(x) = 0 only when x is 0, 1, 2, 3, 4, or 5.

So while our inductive reasoning failed, our observations turned out to be fuel for deductive reasoning.

Let’s try another one.

Mathematical induction

Let’s say you want to prove that 1 + 2 + 3 … + n = n(n + 1) / 2 for all natural numbers n. This seems far from obvious. How would you even get started?

Well, let’s plug in some numbers and check. It’s true for n = 1. Also 2, 3, 4, 5, 6, 7, 8, 9, 10…

But we saw in the last example that just because something is true for ten or a thousand or a million cases, that doesn’t guarantee that it’s true for all cases. So what can we do?

Think about when you set up a bunch of dominos to knock down in a chain reaction. It works like this:

If (1) all the dominos are set up in such a way that if one falls down, the next one falls down, and (2) the first domino falls down, then they all fall down, right?

Let’s use that same idea to prove that 1 + 2 + 3 … + n = n(n + 1) / 2 for all natural numbers n.

First, let’s check that it’s true for n = 1. Yes, it is.

Now, let’s check that if it’s true for some arbitrary number x, then it’s also true for x + 1, i.e., that 1 + 2 + 3 … + x + (x + 1) = (x + 1)(x + 2) / 2.

OK, if 1 + 2 + 3 … + x = x(x + 1) / 2, then 1 + 2 + 3 … + x + (x + 1) = x(x + 1) / 2 + (x + 1) = (x² + x + 2x + 2) / 2 = (x + 1)(x + 2) / 2. Done. And so the dominos all fall down.

This is called mathematical induction, yet it’s technically a form of deductive reasoning, because the conclusion is guaranteed if you do it right. However, it’s similar to inductive reasoning in that you’re taking a finite number of observations and generalizing them to an infinite number of cases.

But wait a minute. How do we know that the principle of mathematical induction, the “domino trick,” is true? Well, it’s usually taken as an assumption! It can only be proven if you make certain other assumptions, such as (1) the natural numbers are well-ordered, (2) every natural number is either 0 or the successor to another natural number, and (3) n + 1 > n for all natural numbers n.

Wow, we sure need to make a lot of assumptions in order to “prove” anything! Which brings up another point. Even if you manage to prove something, how can you prove the proof? Fermat’s Last Theorem was “proven” many times by reasoning that was ultimately revealed to be flawed.

Abductive reasoning

Deductive reasoning is often used in math, because they’re trying to prove things from a known starting point.

Inductive reasoning is often used in science, because they’re trying to discover things, not prove them.

And there’s another type of reasoning, called abductive reasoning, that’s often used by detective types, because they’re trying to explain things, not discover or prove them.

It works like this. A patient has certain symptoms, and goes to the doctor. The doctor knows that appendicitis will cause those particular symptoms. There are other possible causes, but appendicitis is far more likely, and therefore considered the best diagnosis based on the known information.

In some countries, doctors have been known to remove the appendix without actually testing for appendicitis. They thought it was better to occasionally be wrong than to consistently take the time and money to run a test to confirm a rather obvious diagnosis.

Now, using the method of your choice, possibly abductive reasoning, can you determine the point of this post?

Photo by stephend9

In the comments on The Birthday That Never Arrives, some people requested another lateral thinking puzzle. Here you go!

This one comes from Encyclopedia Brown, a series of children’s mystery books published from 1963 to as recently as 2007. These books star Leroy “Encyclopedia” Brown, the 10-year-old know-it-all supersleuth son of the chief of police. (For the members of generation Y, an encyclopedia was something like Wikipedia, but in books!)

This story has been reconstructed from what I remember.

Mr. Diamondthief is invited to a party at a friend’s house. Because the house contains things that people would like to steal, all arriving guests are frisked to make sure they aren’t carrying any weapons and such. Mr. Diamondthief is clean, so they let him in.

But Mr. Diamondthief has sinister motives. He’s really there to steal a diamond. And he’s been in this house before, so he knows exactly where it is. Upon entering the foyer, he goes up a narrow staircase, down a long hallway, into the fourth room on the left, where the diamond is. He takes the diamond.

Because he knows he’ll be frisked on the way out, he can’t just take the diamond out with him. So he looks around, trying to find some way to get the diamond out of the house. He comes across a bow and a quiver full of arrows. Perfect! He ties the diamond to an arrow, opens the window, and shoots the arrow into a tree down the street. He closes the window, puts the bow back where he found it, and wipes off his fingerprints.

He then walks out the front door. They frisk him, and he’s clean. The arrow with the diamond is stuck in a tree down the street, but he decides it’s too risky to get it now. Another party guest might see him walking down the street instead of getting into his car, or the cops might search the homes of all the party guests. He decides to come back for the diamond another time.

The next day, the owners of the house notice the missing diamond, and call the police. Police chief Brown calls all the party guests back to the house for questioning, and to search for the diamond. The assumption is that the diamond is probably still in the house, since all guests were frisked on the way out. Of course, Chief Brown takes his son Encyclopedia with him, since he’s the one with the best detective mind.

Encyclopedia thinks Mr. Diamondthief looks suspicious, but there’s no evidence against him. Encyclopedia starts exploring on his own, and finds the bow and quiver of arrows, noting that one arrow is missing. He sees the window, and realizes how the diamond was stolen.

As Encyclopedia comes down the stairs, he hears Mr. Diamondthief saying “Chief, this search is pointless. Even if the diamond is still here, this house is huge. We’ll never find it!”

Encyclopedia says, “Don’t worry, Mr. Diamondthief. The diamond is just an arrow flight away.”

Mr. Diamondthief says, “Well then, go outside and look for it.”

Encyclopedia says, “Dad, arrest him!”

How did he know Mr. Diamondthief was guilty?

As a kid, I thought the answer was a little cheesy. I actually like it much better now, though my preferred answer is slightly different from the official answer.

If you’ve heard it before, don’t blurt out the answer – let’s give a chance for other people to guess.

Salvador Dalí’s The Persistence of Memory

Marelisa Fabrega wrote about lateral thinking and gave us some interesting logic puzzles to play with. In the spirit of promoting lateral thinking, I’ve come up with a puzzle of my own. Be the first to solve it, and win a prize.

A guy wakes up early in the morning, happy because it’s his birthday. Because he’s very precise about time, he wants to jump up and shout “Woo hoo!” at the exact time of his birth.

He looks at the clock and sees that it’s not time yet, so he waits and twiddles his thumbs. But after a while, he suddenly realizes that it will never be the right time. Why?

If you think you know the answer, leave a comment and tell us. If you’re the first one to get it, I’ll leave a comment on your blog and give you a stumble. Hey, I didn’t say it was a big prize!

Photo by elginwx

Tehy say taht you can sbmarlce the ltreets in a wrod, and it wlil slitl be pfltceery utslbadnrnadee as lnog as you keep the fsrit and lsat lrtetes in the rhgit pcale. So tehn why do we feel all tihs pusersre to ccehk our snileplg?

Jim Gdeuat petiond out to me a tpyo in Gntseares Wutohit Gienes. I’m gald he chguat it elray, but I htae tpoys. Waht was I sspopeud to do? Did I hvae to gvie eynorevn tiehr menoy bcak and be ozecarstid form the ctmnimouy?

But wehn I rbreemmeed taht silneplg d’nseot acefft cpsihrenooemn vrey mcuh, I flet a lot bteetr. In fcat, I mhgit tnihk auobt ornfefig sblmearcd vsnireos of my eokobs at a dcnusoit.

Scnie the fsrit and lsat lrteets hvae to be in the rghit pacle, a wrod has to hvae at lsaet fuor ltretes in oedrr to srbalmce it. And eevn tehn, it wn’ot cgnahe if the mdldie of the wrod is a pdmorinlae, lkie “keep.”

I hvae to wdenor if smelbarcd wdros are awyals rblazoigcene, lkie suoicoiudlaipxecitslgaflacepiirris or asnairatnemilbatsesiditnishm. And mbyae tihs wnd’luot wrok on a rmusee, lkie “dreeisd srlaay: 17,93$5.”

But waht do you tnihk? Can we ralex our sdradnats for sniplelg and not wrroy auobt it so mcuh?

One day back in April, I was in a Quiznos, staring out the window, and eating the worst sandwich in America. I was thinking about quitting my job because it had just gotten to the point where I was dreading every day. The problem was that I was completely dependent on my salary, so quitting my job would have been irresponsible.

Without a job, how would I pay the mortgage and the rest of the bills? And what about the future? Being unemployed for any significant length of time would mean serious delays for getting my Lamborghini Gallardo. This had always been my “someday” car, because with a price tag as low as $190,000, it was “the poor man’s Lamborghini.”

But I really wanted to quit my job, so I thought that I’d have to just scrimp and save, and put my ridiculous fantasies on hold indefinitely. I said to myself, “Well, I guess I’m not getting my Lamborghini anytime soon.”

Not five minutes later, a shiny white Lamborghini Gallardo drove right past me.

OK, was this some kind of joke? If I had thought of a Honda S2000 or a BMW Z4 I could just pass it off as coincidence, but this was a Lamborghini! There’s not a whole lot in that shopping center either, so the owner had just swung by for something like a haircut, or kabobs, or Taekwondo lessons. It’s not like there was an auto show going on.

And what made this even weirder is that this was the day after I posted about synchronicities. So was this just a coincidence, or a sign from the universe? I have no idea.

There were a couple of problems though. One is that the color was wrong. I was thinking about a green car, and this one was white. More importantly, I was thinking about owning it, not just watching it drive by. Oh well. I guess the universe is sometimes a tease.

I ended up not quitting my job then, but six months later the company shut down, so I’m currently on a mini-retirement. I haven’t seen any more signs since then, but if I happen to come into possession of a Lamborghini, you can be sure I’ll post about it.

Yeah, I know, there’s no such thing as genies. What can I say though? Beliefs don’t have to be reasonable.

Image from The Matrix Reloaded (2003)

In one scene of Enter the Matrix, Trinity asks Ghost if he really believes that Neo will fulfill the prophesy of him ending between the war between the humans and the machines.

“Do you believe that Neo is going to end the war?”

“Yes. I do.”

“So do I. But I can’t explain how or why.”

“Kierkegaard reminds us that belief has nothing to do with how or why. Belief is beyond reason. I believe because it is absurd.”

“You think it’s crazy to believe it?”

“To believe what? That a single man can defeat an entire race of machines, and end a war that has endured for over a hundred years? Of course! It’s complete lunacy. And that’s why we must believe it will happen. Faith by its very nature must transcend logic.”

I believe in global warming. I believe that it exists, that it’s caused by humans, and that it’s a big problem. You might think that I’m crazy to believe something like that with absolutely no evidence. It’s not like I’ve been measuring air and ocean temperatures, or analyzing greenhouse gas concentrations in the atmosphere.

Oh sure, there are supposedly some scientists who say the evidence is out there, but I’ve never seen it personally. I haven’t even met anyone who’s seen it. And in spite of that, I still choose to believe it.

Maybe global warming is too much of a stretch for you. Maybe you’d like to believe in something a little more certain, like gravity. But that’s a coward’s belief. You don’t believe in gravity, you know in gravity. If there’s no chance of being wrong, it’s not a belief, it’s a certainty.

A belief has to require a leap of faith in order to mean anything. And yes, that means you might be wrong. So put yourself out there and take a chance of being wrong. Don’t just sit on the sidelines playing it safe.

Image from The Matrix (1999)

In general, which is the greater mistake: believing something that turns out to be false, or not believing something that turns out to be true? People like to think that nothing is wrong with the second one, but aren’t they equally bad?

You can’t refrain from having an opinion, wait until incontrovertible proof arrives one day, and then decide to believe it and think you’re so smart for being sure not to be wrong. If you weren’t willing to go out on a limb one way or the other, you were wrong by default. We’re all going to be wrong a lot of the time no matter what, so you might as well hold beliefs that work for you.

I believe that I’ll ultimately make more money from this blog if I only promote products I like and present them fairly. Is that a sure thing? No, not at all. In fact, you kind of have to ignore logic a bit to believe it. But I think this belief serves me.

You can believe that people are fundamentally good, or that they’re fundamentally bad. You can believe in God, or believe in no God. You can believe that this is the worst time in human history, or that this is the best time in human history. Any reasonable belief will be true enough to defend, but you have to always ask if your beliefs serve you, because some can be detrimental.

Don’t be afraid to have beliefs beyond reason. Most of us believe a few things that we’ll admit don’t even make sense. And when you’re laughing at someone who won’t buy a house because the street number is 13, they’re laughing at you for not opening umbrellas indoors.

But it’s all about what works for you. If a belief feels right to you and leads you in the right direction, go for it, even though you might be wrong. That’s OK, and that’s why they’re called beliefs and not certainties.

But you know what? Even so-called certainties can be wrong. I’ve met lots of people who believed there was no such thing as a one-sided piece of paper, until I made them a Möbius strip.

Photo by David Benbennick

“Why not go out on a limb? Isn’t that where the fruit is?”

- Frank Scully

Steve and Erin Pavlina have just recorded the first podcast that they’ve done together. It’s called Being Psychic, and it focuses on Erin’s explanation of what being a psychic is all about. After falling off a kitchen barstool and splitting her head open at the age of 4, she started running around telling everyone she had ESP. Today she’s a professional psychic, in high demand and charging $295 for a 30-minute reading.

The podcast covers topics such as lucid dreaming, astral projection, spirit guides, what happens when you die, psychic impressions vs. emotions and imagination, what happens during a reading, how to develop your own psychic skills, and skepticism.

I don’t think it’s necessary to be a believer in order to enjoy it. If you’re at least somewhat open to the possibility of psychic phenomena, you’ll probably find it very appealing. It’s pretty long at 96 minutes, and the sound quality isn’t as good as Steve’s other podcasts, but it’s good enough.

I thought it was very interesting and entertaining, and I learned some things about Erin’s psychic journey that I didn’t know before. She seriously rocks, and now I’m even more appreciative that she picked my How To Be A Woman post as her third favorite of 52 submissions (and her #1 favorite by a guy).

Has anyone here ever gotten a reading from Erin?

Photo by aturkus

In The Matrix, Neo experiences some synchronicities, coincidences that are just so weird, so ironic, so impeccably timed, that despite his best efforts he can’t pass them off as being purely random.

A black cat walks by him, and then in a deja vu, another cat walks by, making movements that are absolutely identical to the first one. He gets an anonymous message on his computer saying “follow the white rabbit,” and then a few minutes later someone is standing at his door with a tattoo of a white rabbit on her shoulder.

Neo has a feeling that these synchronicities mean something, but he can’t put his finger on it. To the people who have already been enlightened, it’s perfectly obvious that they mean something. They’re signs from the universe guiding him, showing him the path he’s meant to follow according to the grand design.

Sometimes I can’t shake the feeling that the real world works the same way.

Have you ever been thinking about someone, when suddenly the phone rang and you just knew it was them? Or have you ever had a song stuck in your head, when suddenly you heard it on the radio?

To be sure, a good number of strange coincidences are bound to happen just by chance. There are only a finite number of people, places, and things out there, so every once in a while two things will just randomly be in sync.

But sometimes so many unlikely things all happen at the same time, that it seems to be beyond chance. Let me tell you about a few recent examples in my life.

Bracelets for a Complaint Free World

On February 19th, my boss called me into his office, closed the door, and asked me “What do you think this is about?”

The answer was that I thought I was being fired for my attitude problem (long story short: I hate my job). But of course I wasn’t going to say that. Like when a cop asks you if you know why they pulled you over, you don’t say “Oh, that’s because I’m wanted in 48 states. You must have found the gun I threw into the river behind Fat Tony’s safe house two miles down the road.”

It’s a good thing I didn’t say anything, because it turned out that I was getting a bonus because of my “attitude and enthusiasm.” I have no idea where that came from, but it was so out of place I could barely contain my laughter. I took it as a sign that I got lucky this time, but I really needed to do something to fix my attitude ASAP, before it caught up with me.

I had heard about these purple complaint bracelets that Rev. Will Bowen was using to get people to go for 21 days without complaining. I had ordered some bracelets five months before, but I was still waiting. I knew they were really backed up, but were my bracelets eventually going to arrive, or had my order been lost?

On March 2nd, Pick The Brain announced that they were giving away 15 copies of Will Bowen’s book A Complaint Free World. All you had to do was leave a comment on their site that week, and you were entered into the competition. Hmmm, was I supposed to win?

On March 5th, I discovered Clay Collins at The Growing Life. Click on that link–do you notice something about his picture? Yup, he’s wearing one of those purple bracelets. So I left a comment asking him how long he had to wait to get them. To my surprise, he emailed me and offered to send me one of his extra bracelets! Are you kidding me?

On March 9th, I learned that I had won a copy of the book from Pick The Brain.

The message was clear: I really need to stop complaining. I can’t just ignore it anymore.

It Don’t Come Easy for Ringo Starr

On March 24, I wrote a post that briefly mentioned Ringo Starr as an example of someone who is mistakenly believed to have had an easy life.

The next morning, Catherine Lawson left a comment saying she didn’t realize that Ringo had a tough time on his way to the top.

A couple of hours later, as I was coming back from lunch, the last song on the radio was Ringo’s “It Don’t Come Easy.”

That evening, I watched an episode of The Simpsons. It just happened to be the one featuring that song, where Marge paints a portrait of Ringo.

The next morning, the radio had an interview with photographer Nancy Lee Andrews, Ringo’s former fiance.

That’s an awful lot of Ringo! But I don’t know what it means yet. I guess if I see him in real life, I have to follow him. Barring that, I don’t know what I’m supposed to do.

Kill Bill and Japan

On April 5th, my friend in Japan called me because I’m going to visit him soon. It was just by chance that he called on that particular day, because we hadn’t spoken in months. One of the things we talked about was whether we were going to make a trip to Tokyo. I had said that I wanted to go, but I didn’t realize it was going to cost $400 to get there. I didn’t mind paying that, but I didn’t want to obligate him and his wife to spend $800 if they didn’t really want to. After some discussion of the pros and cons, we decided that we’re probably going to go to Tokyo.

Right after our call, I went to Blockbuster to rent a movie. It was just by chance, because I don’t rent a lot of movies, and I wasn’t even supposed to be home that weekend.

I went through the new releases and didn’t see anything that seemed especially good. Then I considered action vs. drama, and decided to look through the action section, starting with the As. I got up to the Ks before I found something that caught my eye–Kill Bill. I didn’t know anything about it, other than it being a Quentin Tarantino movie, but I decided on it instantly.

I had no idea that half the movie was set in Japan! And I don’t think I’ve ever seen a movie set in Japan before. Even the version of Godzilla I saw was set in New York.

In the movie, Uma Thurman travels from the U.S. to Okinawa, and stays there for a month. Then, she goes off to kill Lucy Liu, the head of the Japanese crime world, who just happens to be located in…come on, you know this…Tokyo.

That settled it. I’m definitely going to Tokyo. I just don’t know why…yet.

The Karate Kid and Moving from New Jersey

Now that I think about it, I experienced another location-related synchronicity from a movie years ago. I was living in New Jersey, and I liked the area OK, but I didn’t like the career options that were available there, especially during the dot bomb days. My sister was trying to convince me to move to L.A. (where she lived) so I could do something more creative.

When we went to the beach that summer, she brought a movie for us to watch, The Karate Kid. Unbeknownst to her at the time, Daniel moves from New Jersey to L.A. before learning the secrets of karate from Mr. Miyagi. Yeah universe, real subtle. I didn’t move to L.A., but I did move to Virginia (which is where I got my black belt many years ago). Still working on doing something more creative, though.

Is This For Real?

Bear in mind that I’m not trying to convince you that any of this is more than coincidence. I’m just sharing some things that have happened to me, and suggesting that this might be worth thinking about. I do experience a lot of synchronicities, and they seem to happen more often the more I accept that they might mean something.

Could it all be in my head? Of course. But the more I think about it, the more I find it possible or even likely that some force is out there saying “Take the hint, moron” every time a sign appears. I really wouldn’t be surprised if I suddenly realized that life is just a dream, and everything happens because it’s supposed to happen.

What about you? Do you find that things happen to you that seem like they could be not just coincidence, but signs from the universe?

Image from The Matrix (1999).

“Have you ever had a dream, Neo, that you were so sure was real? What if you were unable to wake from that dream? How would you know the difference between the dream world and the real world?”

- Morpheus, The Matrix

For the last few months, I’ve been getting by on much less sleep than I used to. A nap in the early evening makes all the difference. However, I’m finding that I need at least 3 hours of sleep at night, or bad things happen. Bad things like barely being able to function in the morning, or oversleeping by 4 hours.

This morning was a new experience though. After getting 2 hours of sleep the night before, I lay down yesterday at 6:40 PM to take a 20 minute power nap. When I woke up, the clock said 5:30 AM. I was drawing a blank on what the heck was going on.

After a minute I remembered that I was supposed to wake up at 7 PM, so either I slept waaaaaaaaaay too long, or the clock was wrong. As I moved closer to check the clock, I noticed something very strange. When I moved my head, the clock of course stayed in place, but the numbers on the clock moved with me. They actually came off the clock! That’s when I thought that maybe this was my first lucid dream.

Ideally I would have written about lucid dreaming before, as there’s a lot to say about it. But for now, a short explanation will suffice. A lucid dream is a dream in which you’re aware that you’re dreaming. While technically asleep, you’re fully conscious, you have more or less complete control over your dream, and everything seems as real as it does when you’re awake. And don’t bother being skeptical, because scientific experiments have verified lucid dreaming.

I’ve heard that a good way to have a lucid dream is simply to intend to have one, or even to think about it. And since we had just been discussing lucid dreaming on Catherine Lawson’s blog, I thought maybe that had done it.

The numbers on my clock didn’t look right, but maybe that was just because I was groggy. I needed a bigger sign, so I got up and started looking for a “glitch in the matrix,” an imperfection in this fantastic simulation that would prove it was just a dream. But if you can’t wake from your dream, how would you know the difference between the dream world and the real world?

• Pinching yourself doesn’t work, because you can feel pain in dreams.
• First I tried to fly (not by jumping out the window, just from where I was). It didn’t work. If I could fly, then I’d know it was a dream. But not being able to fly doesn’t prove anything.
• Then I tried turning on the lights. Light switches rarely work in dreams. If they’re on, they stay on, and if they’re off, they stay off. The lights were off, and I flipped the switch. Nothing. But that didn’t mean anything, because I was just flipping the wall switch, and maybe the lamp itself was off. I tried another switch and a light came on. But that didn’t necessarily mean I wasn’t dreaming.
• Mirrors are my favorite reality check. Reflections in dreams often don’t look like they’re supposed to, and I often check mirrors when awake to make sure everything’s OK. But it looked right in this case. I was becoming more convinced that I was awake.
• Next, I tried reading things, looking away, and then reading them again. Very often, text will change in dreams. But it didn’t here. Darn. I was going to have to go to work in a couple of hours.
• Finally, I turned on my computer and starting checking email. Surely my subconscious mind wasn’t capable of emailing me or leaving comments on my blog, so I must have been awake.

All this just to find out that I had simply overslept and waken up disoriented. It was a bit disappointing, but also good practice for next time. In the meantime, I’ll have to start getting more sleep.