## Archive for the ‘Weird Stuff’ Category

### Mind Reading In 30 Seconds

Sunday, December 11th, 2011

I want to try a little experiment, if you have a minute.

Think of a two digit number between 1 and 50. Both digits should be odd, but not the same number. Don’t scroll down until you’ve picked a number.

I’m starting to see it now…

I saw this on a TV magic show a long time ago. A guy was doing this to random people on the street, and there were only two different reactions. Either he’d be wrong, and they’d wonder why anyone would even try such a dumb trick, or he’d be right, and they’d be amazed.

Although it might seem that there are many possible numbers that fit the given conditions, there are only eight (13, 15, 17, 19, 31, 35, 37, 39). And for whatever reason, people pick 37 far more than its fair share – the show claimed it was more than half the time.

So the trick doesn’t always work, but when you guess someone’s number with complete confidence, it’s hard for them not to be impressed.

We know that “people don’t do random,” even when it comes to meaningless things like picking a number. I’d wager that 35 is a common choice and 13 is not, though I couldn’t really tell you why. I actually picked 37 the first time, and changed it to 39 only because I realized that 37 was too obvious.

People have wonderful abilities of intuition and pattern recognition, but a downside of this is the tendency to see meaning when it’s not there. Sometimes a random number really is 19, despite our desire for it to be 37.

Oswin Craton has a nice article about extrasensory perception, and how he was able to make many people think they had some degree of ESP with a test involving questions like the 37 thing.

(However, beware of the straw man argument – out of all the people I know who say they’re psychic, none of them claim to be mind readers.)

### Should Vegetarians Enter Hot Dog Eating Contests?

Sunday, June 12th, 2011

Most people would say that someone has the right to be a vegetarian, since it’s a personal choice. But most people would also say that their choice doesn’t give them the right to enter a hot dog eating contest and demand that the rules be changed to accommodate them.

That’s an extreme case, but there are other cases that aren’t so clear-cut. When can an organization be expected to accommodate individual beliefs and practices, and when does the individual have to either comply or go home? What would you say in the following situations?

1. The Muslim weightlifter

Kulsoom Abdullah dresses for competitions the same way she always dresses in public – with her entire body covered, except for her face and hands. But she won’t be able to do that if she wants to participate in competitions governed by the International Weightlifting Federation.

The rules say that the elbows and knees must not be covered, so that judges can verify that the joints are locked and that the competitor is not wearing anything that gives them an advantage. But Abdullah was happy to hear that the IWF is willing to discuss the issue at their next meeting, and possibly allow some kind of exemption.

On the one hand, it’s probably possible to figure out a way to cover her elbows and knees while also allowing the judges to do their job. On the other hand, why should the burden be on the IWF and the judges?

What if the competition was during Ramadan (when Muslims fast between sunrise and sunset), so she wanted to compete at 5 AM instead of the scheduled time of 5 PM? What if someone’s religion requires them to wear thick clothing that makes it impossible to verify that their joints are locked? What if someone’s religion forbids them from touching metal?

2. The Marine at airport security

In the movie Taking Chance, Kevin Bacon plays a Marine Corps officer. As he approaches airport security in his service uniform, the TSA agent asks him to remove his medal-clad coat so it can go through the x-ray. Kevin refuses and asks to be taken to a private room and wanded down.

The TSA agent is annoyed and asks not to be told how to do his job. As the growing line becomes increasingly impatient, the agent again asks that the coat be removed. Kevin says he will not desecrate his uniform by running it through the x-ray, and demands to be wanded down in a private room. The agent allows this, but he isn’t happy about it.

This situation is similar to the previous one. He’s perfectly capable of removing his jacket and making it easy for everyone, but doing so conflicts with his beliefs. The biggest difference is that airports are already set up to allow private screenings – it’s not like the TSA has to debate whether they should allow this.

But suppose that for whatever reason, granting this request was difficult (maybe the person who usually does these things wasn’t on duty at the time). Does Kevin have a reasonable right to refuse to take off his coat, or does he give up that right by choosing to fly?

While we’re at it, what if he believed that planes should just drive on the roads instead of flying? What if he wanted to salute with his left hand?

3. The handicapped golfer

Casey Martin has a birth defect known as Klippel Trenaunay Weber syndrome, which requires him to constantly wear two rubber compression stockings and makes it painful and dangerous to walk long distances. He wanted to use a golf cart in the PGA Tour, but the rules say that everyone walks, as the fatigue from walking is part of the game.

His lawyers submitted videos showing the severity of Martin’s condition, in which his leg turned gray as the blood tried to push its way up. They argued that walking would risk fracturing his leg, which would lead to amputation, and that using a cart would not give him an advantage over his competitors who had to walk.

Martin’s request to use a cart under the Americans with Disabilities Act was initially denied by the PGA Tour in 1997. In 2001 the case went to the Supreme Court, who ruled 7-2 in favor of Martin.

Since this situation involves a disability rather than a personal choice, it might be easy to say that of course he can have a cart. But does that give him an unfair advantage over people who have to walk several miles in the hot sun?

If we’re going to say that walking isn’t part of the game, then anyone should be able to use a cart. If we’re going to say that giving him a slight advantage is an acceptable compromise to allow someone with a disability to play, then what constitutes a disability?

What about a sprained ankle? What about narcolepsy? What if someone who can’t swim for medical reasons wants to enter a triathlon?

### A Briefer History Of Time

Sunday, March 13th, 2011

What do we really know about the universe? How do we know it? Where did the universe come from, and where is it going? These are some of the questions addressed in A Briefer History of Time by Stephen Hawking and Leonard Mlodinow.

This is a 2005 rewrite of Hawking’s 1988 classic A Brief History of Time, which amazingly remained on the best-seller list for four years despite attempting to explain complex mathematics to a general audience.

Although the original book contained only one equation (E = mc2) and lots of illustrations, the inherent complexity of the subject matter made many readers say “Well, we love it, but we don’t understand it!”

Therefore, this rewrite removes the purely technical stuff while focusing on a simplified (though certainly not simplistic) treatment of the core concepts. Read it for an entertaining but not overly taxing explanation of curved space, the big bang, black holes, wormholes, relativity, and quantum gravity.

What’s the point of it all? We’re hopefully moving closer and closer to discovering a unified theory, which would basically give us the answer key to the universe. As Hawking says, ”If we find the answer to that, it would be the ultimate triumph of human reason–for then we would know the mind of God.”

### Unless You’ve Been Living Under A Rock…

Friday, February 18th, 2011

Unless you’ve been living under a rock, you know that 99.999% of the planet is living under a rock. At least, that’s the only conclusion I can come to, based on how far we’ve lowered the bar for using this opener.

The bad news? As cultured and sophisticated as you are, you can virtually be assured that you are living under a rock. The good news? It’s apparently a really big rock, and there’s lots of company here.

So how can you find out for sure if you’re a resident of this vast world under the rock? I did a search to determine the criteria. At first, I found a few suggestions that it only takes minimal awareness to separate yourself from these people:

• “Unless you’ve been living under a rock for the last decade or so, you are familiar with the concept of the internet.”
• “Unless you’ve been living under a rock, you’re aware that America is in the midst of a recession.”
• “Unless you’ve been living under a rock, you’ve probably heard of Justin Bieber.”
• “Unless you’ve been living under a rock, there’s a good chance you’ve already heard of Susan Boyle.”
• “Unless you’ve been living under a rock, you know that Michael Jackson died.”
• “Unless you’ve been living under a rock you are almost certainly familiar with Facebook.”
• “Unless you’ve been living under a rock, you’ve probably heard of The South Beach Diet.”
• “Unless you’ve been living under a rock for the past month or so, you know that today is Election Day.”

OK, this is pretty reasonable. Maybe there was room for me above ground. Or so I naively thought. When I looked deeper, I saw that being a surface dweller requires an impossibly diverse knowledge base:

• “Unless you’ve been living under a rock for the past year or so, you are aware of the Bokeh effect.”
• “Unless you’ve been living under a rock, you know that Microsoft finally signed off on Visual Studio 2005 and that it’s available now (or soon) to MSDN subscribers.”
• “Unless you’ve been living under a rock, you’re aware by now that an endocrine disrupting chemical known as Bisphenol-A (BPA for short) has been popping up in all manner of consumer goods.”
• “Unless you’ve been living under a rock for the past few months, you know that I have been busy developing a library that will, hopefully, make OpenGL development as painless and fun as possible.”
• “Unless you’ve been living under a rock, you’ll know that one of the Skrull infiltrators (and the Empress herself) in Marvel’s Secret Invasion is none other than Spider-Woman.”
• “Unless you’ve been living under a rock for the past month, you know that the VMA’s advanced mixed choir, Powerhouse, was invited to perform on the Oprah Winfrey Show, for a special Glee episode.”
• “Unless you’ve been living under a rock, you’ve heard about The Audience Conference, taking place in NYC on Friday, November 6th at the Hudson Theater.”
• “Unless you’ve been living under a rock, you know that Katie Holmes performed a tribute to Judy Garland on Fox’s dancefest competition So You Think You Can Dance last night.”
• “Unless you’ve been living under a rock for the past six months, you’ve heard of US interaction designers and strategists ZURB.”
• “Unless you’ve been living under a rock, you’ve seen pictures of the beautiful all-new 2011 Cadillac CTS and CTS-V Coupes.”
• “Unless you’ve been living under a rock, you’ve already played Madden NFL 09.”
• “Unless you’ve been living under a rock, you know that Lars von Trier is the premier author of the Danish Dogme 95 manifesto.”
• “Unless you’ve been living under a rock for the last week, you’ll have noticed that Google’s App Engine now lets you run Java web apps.”
• “Unless you’ve been living under a rock for the last couple of weeks, you’ll know that the big news this month has been the launch of the ATI Radeon HD 6850 1GB and the ATI Radeon HD 6870 1GB.”
• “Unless you’ve been living under a rock, you’ve seen the blogosphere cooking and baking their way through Dorie Greenspan’s gorgeous new cookbook Around My French Table.”
• “Unless you’ve been living under a rock, you are well aware that Bora Zivkovic left ScienceBlogs 24 hours ago.”
• “Unless you’ve been living under a rock, you’re aware of the controversy over CW Skimmer.”
• “Unless you’ve been living under a rock lately you then know Dead Space 2 hit shelves this week.”
• “Unless you’ve been living under a rock, you’ll have heard about the Andy Gray & Richard Keys kerfuffle/scandal.”
• “Unless you’ve been living under a rock, you have heard the recent brouhaha over Microsoft’s Windows Genuine Advantage (WGA) Notifications update to Windows.”

Give yourself a pat on the back if you were aware of most of these things. But remember, all it takes is one gap in your knowledge to banish you to a subterranean prison. I hope there are enough cavefish for all of us.

### Did Your Zodiac Sign Change?

Friday, January 14th, 2011

“What’s your sign?” has become a very volatile question to ask today. Millions of Scorpios are terribly upset to have possibly metamorphosed into Libras or even Virgos overnight. And there hasn’t been this much heavenly hubbub since Pluto was demoted from planet status in 2006.

If you don’t know what I’m talking about, it appears that the astrological community suddenly realized today that the stars have moved over the last few thousand years, and the zodiac has been given a long overdue realignment. As a result, most people have shifted back one sign, the long lost sign of Ophiuchus is now back with a vengeance, and Scorpios have been placed on the endangered species list.

I’m not sure if the new system will stick, or whether horoscopes are purported to be based on tropical zodiac signs or the actual position of the constellations, or whether the Chinese lunar calendar will have to restate quarterly earnings. Fortunately, I’m still a Taurus in the new system, so I’ve been spared from the potential identity crisis.

Questions for you: Do you believe in astrology at all? If you don’t, does your sign still matter to you, and why? Do you think some people will deliberately change their personality to fit their new sign? Are horoscopes dangerous?

(Below are the date ranges of the signs under three different systems. The tropical zodiac is the one you know and love; the IAU definition gives the new dates that everyone’s talking about. Dates are not set in stone, but vary each year depending on the timing of the vernal equinox, etc.)

Sign Tropical Zodiac Sidereal Zodiac IAU Definition
Aries 3/20 – 4/20 4/14 – 5/1 4/19 – 5/14
Taurus 4/20 – 5/21 5/14 – 6/1 5/14 – 6/21
Gemini 5/21 – 6/21 6/14 – 7/31 6/21 – 7/21
Cancer 6/21 – 7/23 7/14 – 8/1 7/21 – 8/11
Leo 7/23 – 8/23 8/14 – 9/13 8/11 – 9/17
Virgo 8/23 – 9/23 9/13 – 10/30 9/17 – 10/31
Libra 9/23 – 10/23 10/14 – 11/13 10/31 – 11/21
Scorpio 10/23 – 11/22 11/13 – 12/30 11/21 – 11/30
Ophiuchus N/A N/A 11/30 – 12/18
Sagittarius 11/22 – 12/22 12/14 – 1/2 12/18 – 1/21
Capricorn 12/22 – 1/20 1/13 – 2/1 1/21 – 2/17
Aquarius 1/20 – 2/19 2/12 – 3/2 2/17 – 3/12
Pisces 2/19 – 3/20 3/14 – 4/1 3/12 – 4/19

### A World Without Time

Sunday, October 10th, 2010

Buckminster Fuller thought it was important to describe the world as accurately as possible, in order to avoid clouded intuition and maintain a good grip on reality. To do that, he used language in unusual ways. For example:

• Because we now know that the world is not flat, the word “worldwide” doesn’t make any sense. He said “world-around.”
• Since we now know that the sun does not revolve around the earth, it doesn’t make sense to talk about “sunrises” and “sunsets” as if we’re still and the sun is moving. He called them “sunsights” and “sunclipses” to describe them from our perspective as the earth rotates.
• “Up” and “down” are awkward because they refer to directions in a plane that moves around with you. If someone at the South Pole goes “upstairs” (relative to them), would someone at the North Pole say the other guy was going “downstairs?” That’s why Fuller said he was walking “outstairs” or “instairs,” referring to his motion relative to the center of the earth.

I wonder what Buckminster Fuller would have said about “next weekend.”

People fall into two groups in terms of what “next weekend” means to them:

1. Those who say “If I meant this weekend, I would have said this weekend.”
2. Those who say “But this weekend is the next weekend.”

This became an issue for me a few weeks ago on a Tuesday, when my friend said she’d be in town “next weekend.” That Friday, she again said that she’d be in town “next weekend.” While technically correct, I thought it was odd that she’d say “next weekend” instead of “tomorrow.”

Had she forgotten that it was Friday? Or was she pushing her plans back a week? Or was she just talking weird? I called to ask, and found out she’s in group 1 and I’m in group 2.

I always knew group 1 people were out there, but I didn’t know I actually knew one. And thus began a long and painful investigation into the matter. Short answer: almost everyone is in group 1, but they can’t say why.

Despite my best efforts to understand how “next weekend” could mean two weekends from now, I’ve still come up blank. The best I can come up with is that “next weekend” could be interpreted as “the end of next week,” except that (1) I didn’t say “the end of next week,” I said “next weekend,” and (2) the weekend does not come at the end of the week (although personally, I think Monday should be the first day of the week).

Here are some points of confusion that come up when “next” can potentially mean either “next” or “next next” depending on who you’re talking to:

• If someone says “Our next meeting is next Friday,” almost everyone thinks that means that one meeting from now is two Fridays from now. Why doesn’t it mean that two meetings from now is one Friday from now, or one of the other combinations?
• If someone calls you on the phone and says “I’m going to kick your ass the next time I see you,” does that mean this coming time or the following time?
• If someone says “I’m going to turn into a werewolf at the next full moon,” does that mean this coming full moon, the following one, the full moon of the next calendar month, the full moon of the next lunar month, or what?

(Notice that all of this confusion is avoided if “next” always means “next.” Just sayin’.)

I actually think that the confusion is mainly around the meaning of “this” rather than the meaning of “next.” After all, if today is Saturday, everyone agrees on what “this weekend” and “next weekend” mean.

But what if today is Wednesday? In that case, “this weekend” makes no sense at face value. You can’t say “Are you having a good time so far this weekend?” But we say “this weekend” as a shortcut for “this coming weekend,” and then it makes sense.

On the other hand, on a Monday, many people think that “this weekend” means “this past weekend,” and a few of them think that “last weekend” means the weekend before that.

Could you ask, on a Monday, “Did you have a good time this weekend, and will you have an even better time this weekend?” Does “this Arbor Day” mean Arbor Day of this year (possibly in the past), or this coming Arbor Day (possibly next year)? Don’t even get me started on the linguistics of time travel.

Does “this light” mean the light a few feet in front of you, and so “the next light” means the following one? Or does “this light” make no sense because we’re not at a light, so “the next light” is this one a few feet in front of us?

Anyway, once I realized how ambiguous something as simple as “next weekend” can be, that changed everything for me. The language we use shapes our thinking, for better or for worse. If I can’t say “this” and “next” because of the potential confusion, then how can I express concepts of time? And if I can’t express them, how can I perceive them?

Two years ago, Glen Allsopp left this comment on my post Don’t Label Me:

“I watched a film by Eckhart Tolle recently in which he asked you to imagine the world if you didn’t have a name. Close your eyes and try it, it’s quite interesting.”

When I imagine a world without names, I get the sense that the separation of you and me is an illusion. There is no “me,” because I am you. When I imagine a world without time, I get the sense that the separation of past and future is an illusion, or at least not accurately represented by a one-way absolute dimension.

As Christian Shephard said on LOST, “There is no ‘now,’ ‘here.’” Or as some guy at the National Institute of Standards and Technology said, “Our clocks do not measure time. Time is defined to be what our clocks measure.”

This post was published on Metric Moment, 10/10/10 10:10:10.

Photo by fdecomite

### Everything’s An Illusion: A Glitch In The Matrix

Friday, June 4th, 2010

In The Matrix, Neo sees a black cat walking by. A second later, an eerie feeling creeps over him as the same cat walks by again, making the exact same movements. He finds out that a déjà vu is usually a “glitch in the Matrix,” meaning that their digital reality has been reprogrammed and is now misfiring.

They give a better example of a glitch in the Matrix in Beyond, the first short film in the Animatrix series. Some kids have found a “haunted house” where glass bottles shatter and reassemble, rain falls from a clear sky, broken light bulbs flicker, shadows aren’t attached to the objects that cast them, and they can jump from a height and stop before impact. (A team of “rodent exterminators” clears everyone out and repairs the glitch.)

Neo himself is also a glitch. The Architect tells him: “Your life is the sum of a remainder of an unbalanced equation inherent to the programming of the Matrix. You are the eventuality of an anomaly, which despite my sincerest efforts I have been unable to eliminate from what is otherwise a harmony of mathematical precision.”

When I talk about a glitch in the matrix, I’m not necessarily talking about Neo’s Matrix, but any kind of system that gives a certain perception of reality. The glitch is what shatters that perception, making you realize that the whole thing was an illusion.

During a lucid dream, you’re conscious, but at first you don’t know that you’re dreaming because your brain makes everything so real. However, it doesn’t get everything exactly right. If you just get the idea to test the dream world, you can easily find some glitches: lights that stay on when you flip the switch off, books and clocks that change when you look away, people who say things that don’t make sense, etc. Discovering one glitch tells you it’s all a dream.

Isaac Newton worked out a theory of gravity that held up well to the observations people could make at the time. However, his theory had a rather large glitch that he just swept under the rug. He was forced to assume that a gravitational field propagated at infinite speed. He hated this, but without a theory of relativity, he had no choice.

It was more than 100 years before before observations of Mercury’s orbit showed a glitch, paving the way for a new theory of gravity. Similar things are happening today, as theories of quantum mechanics are being developed to address glitches in classical mechanics at the subatomic level.

### Life, the universe, and everything

What is the universe? Essentially, it’s just a very sophisticated program.

This program is made up a number of rules. Things such as “for every action, there is an equal and opposite reaction,” “F = ma,” “E = mc^2,” and so on. But the rules alone don’t do anything. They need some objects to act on. Objects such as you.

Human DNA consists of 3.2 billion pairs of nucleotide bases, with four possibilities for each. This caps the maximum number of genetically distinct people at 4^3,200,000,000 (and in fact far less, since most combinations won’t work).

At conception, your DNA was determined from one of these possibilities. Perhaps you were model #62,085,423,678,990,876,543,357,896,534,567,897,634,524,790,043,446,854,568,987,434,543.

But your DNA didn’t fully describe you, even at such a young age. There were many other factors, such as where and when you were born, what your family was like, etc. But regardless, you were just an object described by a handful of variables.

The objects plus the rules make the system, and now the program is running. But like all programs, it has glitches.

### A simple glitch in Doom

I recently stumbled across this page about a bug with the “picked up a medikit” message in Doom. In their rush to revolutionize the first-person shooter genre, id Software apparently didn’t have time to test everything (or retest everything after last-minute changes).

When you pick up a “medikit,” you get an extra 25 health points, and you see a message saying “Picked up a medikit.” If your health was below 25 when you picked it up, the message was supposed to say “Picked up a medikit that you REALLY need!” However, since the code does the < 25 check after adding the 25 health points, the “REALLY need” message will never be displayed:

```case SPR_MEDI:
if (!P_GiveBody (player, 25))
return;

if (player->health < 25)
player->message = GOTMEDINEED;
else
player->message = GOTMEDIKIT;
break;```

The authors of that web page helpfully posted a corrected version of the code. Ironically, the corrected version is much worse than the original:

```case SPR_MEDI:
if (player->health < 25)
player->message = GOTMEDINEED;
else
player->message = GOTMEDIKIT;

if (!P_GiveBody (player, 25))
return;
break;```

If this had been done, the “Picked up a medikit” message would have been displayed even if it wasn’t actually picked up (like if you already had 100% health). The correct fix would have been to simply change 25 to 50 in the original code.

This is just meant to show how easy it is to introduce a glitch. In this case, it’s an easy fix, and it could be made without any complications. But it’s not always that easy.

### A more complicated glitch in Pac-Man

Pac-Man theoretically has an infinite number of levels, with no ending. But because of a bug in level 256, it’s impossible to go any further.

The current level is stored as a single byte (8 bits), and therefore can’t get any higher than 255. When it tries to increment to 256, it rolls over to 0. But this actually doesn’t cause any problems, except for one big one with the fruit-drawing routine.

Normally, 0 to 7 fruits are shown at the bottom right, depending on what level you’re on. But when the level counter goes back to 0, the game attempts to draw 256 fruits, corrupting the right half on the screen and leaving an insufficient number of dots to finish the level.

How is this glitch different from the Doom glitch? First, it was much harder to catch. Who would think they needed to test 256 levels of Pac-Man? What player would spend enough quarters to even get close to that point? Why stop at 256? Why not 1,000 or 1,000,000? What about testing what happens when other high numbers get high, like lives, points, or time?

Second, there’s the question of how to fix it. When the level counter goes back to 0, you know it’s really level 256. But there’s no way to know the difference between levels 1 and 257. So how do you know whether to draw 0 fruits or 7? Or should they draw more than 7 fruits at the higher levels? Should they use two bytes to store the level?  Then they’d have the same issue at level 65,536. Should they use another bit to indicate the level is 256+, and just leave it at 7 fruits? Should they end the game after level 255? Whatever change they make, they have to retest it.

### You can’t fix every bug

But the Pac-Man glitch is still a relatively small issue. Come on, it’s just about drawing a few pieces of fruit. But when programs grow in complexity, they rapidly become more difficult to fix.

In a software engineering class I took, we learned a surprising fact about fixing bugs in a sufficiently complicated program. The number of bugs starts high, and when you start fixing them, the number of course comes down. But the number of bugs can only get so low. Past a certain point, continuing to fix bugs causes the total number of bugs to increase.

I’m not exactly sure what explains this counter-intuitive result. It’s partly because of workarounds that people put in place to accommodate known bugs, which suddenly become bugs themselves when the original bugs are fixed. And it’s partly because people who use the program will come up with new requirements that aren’t properly implemented.

Anyway, since you can’t fix all the bugs, you get to a point where you either have to decide to keep putting out fires, live with the bugs you have, or start over. Starting over isn’t as bad as it sounds: Microsoft wrote Windows NT from scratch to greatly improve a buggy Windows 3.1. And the Architect wanted Neo to start over by rebooting the Matrix and repopulating the Earth from 23 people.

### A self-referential trap

In 1998, two companies called Google and Amazon.com were all the rage. Google was a new search engine that we all used because we heard it was the best, but didn’t really know why. And Amazon.com was an online bookstore that claimed to have a book about everything.

When you did a search for something in Google, along with the search results, you’d get a list of books that Amazon.com had on that topic. Search for dogs, and Google said “Amazon.com has these books about dogs…” Search for magnesium phosphate tribasic, and Google said “Amazon.com has these books about magnesium phosphate tribasic…”

It was a little hard to believe. There was no way that Amazon had books about everything. But how could we catch them in a lie?

I figured that a self-referential statement would likely do the trick. I did a Google search for “topics that Amazon.com has no books about.” And Google then said “Amazon.com has these books about topics that Amazon.com has no books about.” Whether such books existed, I didn’t know, but I could be sure that Amazon didn’t have them. This was a glitch in the matrix.

### The system needs rules

Google’s problem in that case was that they put no restrictions on what you could type in. But every system needs rules, or it will crash.

A simple example is the liar’s paradox. Consider this sentence: “This sentence is false.” That sentence gives a contradiction, but that’s not really a problem. A consistent system just needs to consist of rules that don’t allow such a sentence to be constructed.

The so-called “naive set theory” in math has a similar flaw, as discovered by British philosopher Bertrand Russell in 1901. Russell’s paradox says this: Let S be the set of all sets that are not elements of themselves. Now, is S an element of S?

If you think about it, you’ll see that the answer is simultaneously yes and no. The paradox can be handled by using a set theory based on axioms that prevent us from forming sets like S. But this safety comes at a price.

Cartoon by xkcd

### Gödel’s incompleteness theorems

I’m about to get into a mathematical concept that’s easier to understand in a non-mathematical context. So to warm up, consider this:

- A government big enough to give you everything you want is big enough to take everything you have.
- If our brains were simple enough to understand them, we would be so simple we couldn’t.
- Every justice system either puts some guilty people back on the street, or some innocent people behind bars.

Makes sense, right? The fact that difficulties arise in social systems and our own brain is not surprising. What is surprising is that something similar happens in every mathematical system, where we theoretically have complete control.

In 1931, Austrian logician Kurt Gödel proved his two incompleteness theorems, which I’ve always seen as the best example of a glitch in the matrix. Unfortunately, it gets ridiculously complicated, so I’ll have to do my best to simplify.

In math, we construct things called formal systems. A formal system consists of a language and rules. Examples of formal systems include particular types of arithmetic, geometry, and set theory.

Formal systems can express statements in their language, such as “2 + 2 = 4″ or “Every integer is even.” Some statements are true, and some are false. Also, some statements can be proven, and some cannot.

Ideally, you’d like every statement to be provable if and only if it’s true. That is, you’d like your system to be both consistent (all provable statements are true) and complete (all true statements are provable).

What Gödel proved is that every formal system of sufficient complexity is either inconsistent or incomplete (or both). That is, it’s either too weak to prove everything it should, or it’s strong enough to prove something it shouldn’t. In other words, there’s a glitch in every matrix.

He did this by showing that you can always construct a statement G that essentially says “G is not provable,” but without explicitly referencing itself, and being constructed within the rules of the system. However, self-referential statements aren’t the only ones that can blow up.

Here’s the simplest example I have. Consider the statement “There is no set whose cardinality [size] is between that of the natural numbers and that of the real numbers.” We don’t know whether this statement is true. But we know that in ZFC set theory (the current standard), the statement can’t be proven either true or false.

We’ll eventually figure out whether it’s true or false by jacking out of the matrix and using a more powerful system, but either way, there’s a problem with ZFC set theory. We’ll have a true statement (either the one above, or its negation) that can’t be proven, and therefore ZFC is incomplete (and maybe inconsistent, too).

If there’s a glitch in every matrix, then what is real? How do you define real? Do you think that’s air you’re breathing now?

### Why Life Is Like LOST

Tuesday, May 25th, 2010

Do you remember what your life was supposed to be like? Most of us once had a certain destination in mind, and we were all set to go there. But something went wrong. Despite our carefully arranged plans, we ended up someplace else.

At first we’re very disappointed to end up in the wrong place. This isn’t the life we wanted. We might even call it a tragedy. After some time though, we start getting used to it.

We’re not sure whether this is a good place or a bad place, but it’s certainly interesting. Maybe it’s best to withhold judgment. And since this is where we’re going to be for a while, we might as well make ourselves at home, and take a look around.
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We find ourselves surrounded by people of all different backgrounds. We wouldn’t necessarily have chosen to be with these people, and we might think we have nothing in common with some of them. But when we learn their story, we probably find that we can actually relate to them. Eventually, we may realize that we need each other.

There were things that we were so desperate to get back to, but now we can’t really remember why. Maybe we weren’t really supposed to be where we thought we were. Having left some parts of us behind, the past no longer matters. And looking ahead to the future is largely pointless, because there’s no way to predict it. All that matters are the experiences we have today.

A bunch of irrelevant crap will happen, sometimes for weeks at a time. We’ll often wonder, “What the hell does this have to do with advancing the plot?” Some of it will become significant later. Some of it won’t. What we think are our most important questions may never be answered, and we’ll get answers to questions no one asked. But the world wasn’t designed to answer your questions, and we can’t expect to be guided on a straight path from start to finish.

Bad things will happen to good people, and good things will happen to bad people. We’ll even lose track of who the good guys and bad guys are. We’re not sure what we’re supposed to do, what’s right and wrong, or even whether it matters. Are black and white really opposites?

We don’t really know what our part to play is. Are you supposed to learn to forgive yourself or others? Repair a relationship? Become a leader? Protect something? Get off drugs and act like a father? Stop torturing people? Kidnap people on a list? Shoot a polar bear? Set off a nuke? Push a button every 108 minutes? Study electromagnetism? Determine what happens to dynamite in 90+ degree heat? Turn into a smoke monster?

There’s really no one here to tell you what to do. And if someone is, you might not want to listen.

Many times, we’ll wonder whether this is all a test, whether our life has a purpose. Do we have free will? Do you believe in destiny? Are we here for a reason? You’ll probably be wondering right up until the very end, but you’ll never really know. Even after it’s over, everyone will still disagree about what it all means.

So, what then? Is life a hopeless chaotic jumble of teleporting islands, four-toed statues, doomsday numbers, mistranslated tattoos, sonic fences, magic boxes, invisible horses, fake beards, light and water wheels, and so on? Or is there a grand purpose to it all? I couldn’t tell you. But regardless, what can you do, other than making the most of each episode?

### Mesothelioma Lawyers, New York: The Movie

Sunday, May 9th, 2010

Feeling let down by Iron Man 2? Then give my movie script a try, and find out what awaits us in 2012.

Mesothelioma Lawyers, New York: The Movie is my 2010 Script Frenzy project. It’s a prequel to my novel of the same name, which was my 2009 NaNoWriMo project.

I suggest reading Mesothelioma Lawyers, New York: The Novel first, if possible. (Currently, the only option is to read it online page by page with all the ads, but I’ll make physical copies available on Amazon as soon as I can.)

The movie has none of the depth of the novel, the plausible 2012 theory, the end of the world drama, and so on. It’s basically just a dumbed down comedy. But it fills in the backstory of the novel, plus it has swordfights, drug-induced trances, sociopathic lawyers, Oompa-Loompas, and exploding kidneys.

Potentially starring:

Lindsay Lohan as Yvonne Dubois
Janeane Garofalo as Janice Goldwoman
Matthew Fox as Jack Crowley
Catherine Zeta-Jones as Milli Vanilli Chilli Willi
Glenn Close as Ivana Suyurass
and Leslie Nielsen as Count Voldemort Sidious Hitler the Terrible

### Mesothelioma Lawyers, New York: Insider Extras

Friday, March 5th, 2010

You know how sometimes you read or hear something, and you have the feeling that you’re missing an inside joke? People who read my novel Mesothelioma Lawyers, New York may have that feeling every few pages. While some of the Easter eggs are obvious, many are not.

As I had always planned to, I’ve updated the epilogue to point out the hidden references, symbolism that may have been overlooked, notes about the actual writing of the novel, etc.

Here are some of the questions that are answered:

• Where do the characters’ names come from?
• What is the significance of the photon with a wavelength of 400 nanometers?
• What is the meaning of Jack’s cryptic notes, which even he doesn’t understand?
• What blogger is referenced twice, though not explicitly named?
• What’s special about the exact time that Jack wakes up?

etc., etc. To get the full Mesothelioma Lawyers, New York experience, you need to read the epilogue – but it contains spoilers! (The full text of the novel is still freely available at the link above.)