Archive for June, 2010

The 7 Deadliest Martial Arts

Monday, June 28th, 2010

The Shaolin Temple in China

The Shaolin Temple is considered the birthplace of kung fu (which is a generic name for the Chinese martial arts). From its humble origins, kung fu eventually developed into literally thousands of different styles.

Combined with all the other martial arts that have been developed around the world, there are a virtually endless number of possible ways to beat your enemies senseless. But some ways work better than others. Out of all the different martial arts, which are the deadliest?

Let me be clear that I’m not necessarily talking about the “best” martial arts, only the most practical. Swimming is a great sport, but it will never be as fast as running. Likewise, a martial art heavy on flashy high kicks and choreographed forms may be a great art, but not as deadly as the ones that appear below.

Also, I consolidated similar arts – no need to include judo when BJJ is on the list, Wing Chun when JKD is on the list, etc. Finally, while the arts below are numbered, they are not ranked.

1. Boxing

You’re probably going to say that boxing isn’t really a martial art. While I’d tend to agree (even though I’m not exactly sure why), this list wouldn’t be complete without it.

Despite its apparent simplicity, boxing incorporates a number of elements critical to successful combat, such as timing, footwork, reading your opponent, and putting your weight into your strikes. Not to mention that the training is very practical, with a heavy dose of sparring against resisting opponents.

Advantages:

  • Your hands are fast, accurate, and a short distance from your opponent’s head.
  • Because of its simple style, emphasis is put on practical application rather than showy display.

Disadvantages:

  • If your attacker won’t limit themselves to just using their hands, why should you?
  • Anyone who attacks you is likely to be stronger, so trying to outpunch them is a losing proposition.

Notable practitioners: Muhammad Ali, Sugar Ray Robinson

2. Muay Thai

Known as the Art of Eight Limbs, Thailand’s national sport uses punches, kicks, knees, and elbows for eight points of contact. It is generally considered the deadliest type of kickboxing, and is a staple of MMA fighters.

Advantages:

  • A Muay Thai roundhouse kick has been compared to being struck by a baseball bat. Instead of using a chamber and a snap, the whole body is thrown into the kick, and contact is made with the rock hard shin.
  • An elbow or a knee thrown from the clinch can easily end a fight, which is why they are sometimes banned in competitions in other sports.

Disadvantages:

  • The only reason they can kick with their shins is because they’ve kicked enough heavy bags or bamboo trees to build up a thick layer of scar tissue. Do you really want to do that to yourself?
  • No attention is paid to the ground game.

Notable practitioners: Saenchai Sor Kingstar, Anderson Silva

3. Brazilian Jiu-Jitsu

This derivative of Japanese judo is a form of grappling, using chokes and joint locks rather than strikes, leverage and technique rather than strength. It rose to instant prominence in 1993 at the first Ultimate Fighting Championship, where different martial arts were pitted against each other in a contest with minimal rules. BJJ practitioner Royce Gracie won easily, dispatching his three physically superior opponents in a total of five minutes.

Advantages:

  • Most fights end up on the ground, where someone who only knows kicks and punches will be outmatched by someone who knows sweeps and armbars.
  • When fighting a larger opponent, you take away much of their strength advantage by grappling up close instead of opposing their force directly.

Disadvantages:

  • Since many people have now learned how to defend against takedowns, and since fights never start on the ground anyway, ground fighting can never replace stand-up fighting.
  • The gi they wear makes it much easier to be grabbed and choked. It represents the suit that all Japanese men would have worn when judo was invented, but today you can’t assume that your attacker will be wearing something that sturdy.

Notable practitioners: Hélio Gracie, BJ Penn

4. Krav Maga

This is another one that people generally don’t consider a martial art, but we have to include it. This eclectic close combat system of the Israeli Special Forces uses wrestling, grappling, and striking to neutralize threats (even weapons) by any means necessary, often by attacking the body’s most vulnerable points.

Advantages:

  • It teaches how to make weapons out of everyday objects, which are probably all you’ll have when you’re attacked.
  • It teaches what to do in life or death situations.

Disadvantages:

  • It’s just a bunch of eclectic crap thrown together. When you know a million techniques, it’s hard to quickly decide which one you need now.
  • It can be very hard to find a good school.

Notable practitioners: Jason Bourne, Jack Bauer (well, can you name a real one?)

5. Jun Fan Jeet Kune Do

There’s always a lot of confusion surrounding Bruce Lee’s Way of the Intercepting Fist. People love to discuss what JKD is and is not, and how it is what it isn’t, and isn’t what it is. But here, I’m simply referring to his signature style without any of the philosophy.

Jeet Kune Do is a hybrid system that borrows heavily from several arts, especially Wing Chun, boxing, and fencing. But unlike most hybrid systems, it absorbs what is useful while casting off what is useless, arriving at the bare combat essentials. Movements are direct, straightforward, and non-classical.

Advantages:

  • By training in four different combat ranges (kicking, punching, trapping, grappling), the practitioner becomes well-rounded.
  • It stresses simplicity and efficiency, conserving time and energy in all movements.

Disadvantages:

  • Although it’s theoretically very effective, it’s fairly obscure and hasn’t been tested very much.
  • Good luck finding a decent school where you live.

Notable practitioners: Bruce Lee, Ted Wong

6. MMA

Mixed martial arts was originally a sport that saw people competing with very different styles. However, when it became apparent what was effective and what was not, a new hybrid style emerged, and this is what I mean by “MMA.” This style may be customized by each fighter, but generally combines boxing, Muay Thai, and Brazilian Jiu-Jitsu.

Advantages:

  • Combines stand-up and ground skills to produce a well-rounded fighter.
  • The effectiveness of this style has been tested and proven more than any other.

Disadvantages:

  • It’s only been tested and proven for a particular set of rules. The game changes when you allow 12-6 elbows, small joint manipulation, eye gouging, biting, groin strikes, headbutts, rabbit punches, etc.
  • What works best on another MMA fighter is not necessarily what will work best against your attacker.

Notable practitioners: Fedor Emelianenko, Randy Couture

7. To be determined

Let’s hear it. What is YOUR choice for the deadliest martial art?

Meat Is More Than Murder

Sunday, June 20th, 2010

What is the Meatrix?

“We are like you; the thought pressed into his mind. We did not mean to murder, and when we understood, we never came again. We thought we were the only thinking beings in the universe, until we met you, but never did we dream that thought could arise from the lonely animals who cannot dream each other’s dreams. How were we to know? We could live with you in peace. Believe us, believe us, believe us.”

- The Formic hive queen, Ender’s Game

Eating animals is wrong. If you think that statement is hypocritical coming from a meat eater, you would be correct (I’ll come back to that later). But that doesn’t make it any less true.

I certainly don’t expect to convert anyone to veganism with this post, but I hope to at least lead some people to the unavoidable conclusion that eating animals is wrong, even if they choose not to act on it. If someone has a convincing argument for the opposing side, I’d love to hear it (no sarcasm meant there).

For a long time I never understood why vegetarians had such a moral objection to eating meat. Sure, it would be great if we were powered by wind or sunlight. But since we’re not, some other life forms have to be on the losing end of the food chain, right? Does it make that much of a difference who eats whom?

Granted, the rules for what animals are OK to eat don’t exactly make sense. Pigs, for example, are smarter than dogs, more affectionate than cats, and cuter than horses. Why don’t we put them on the same pedestal? Who decides these things? I don’t even know all the rules. Is it OK to eat snakes? Dolphins? Hippos? Gazelles? Giraffes? Lions, and tigers, and bears? Oh my!

But let’s say we all agreed on which animals were most expendable. We’ve identified some species that are delicious, sanitary, have the right number of legs, and are cute enough, but not too cute. What then, is the problem with these crazy vegetarians?


Photo by Create For Animal Rights

When I looked into it, I quickly saw that the issue (for me, at least) isn’t whether meat is murder. Of course it’s murder, but I’d have no problem if it were only that.

The real problem is that meat is torture. More specifically, raising animals for food in the way we do is torture. Our demand for animal products has just grown far beyond our ability to supply them humanely. We no longer just kill the animals; we do things to them that I doubt you would be willing to do personally.

I’m not going to go into a lot of details here, but the video Cruelty to Animals: Mechanized Madness gives a good look at how animals are raised for food. It’s pretty graphic. For a much milder and more entertaining version, watch the two cartoon movies at The Meatrix.

“Power tends to corrupt, and absolute power corrupts absolutely. Great men are almost always bad men.”

- Lord Acton

People seem to be hardwired with an “us vs. them” mentality. What happens when one group is bigger, stronger, or technologically superior to another? They trample the rights of the weaker group, or even consider it to at their disposal. That torturing a weaker group is wrong seems to be a lesson the human race needs to keep relearning.

Manifest destiny, the belief that the European settlers were under a divine mandate to conquer North America, fueled them to do unspeakable things to the poorly armed Native Americans. Ditto for African American slaves, as well as the many examples of slavery in other countries. The Holocaust, women’s rights, gay rights, there always seems to be another group to discriminate against, despite the lessons of the past.

And for God’s sake, this is just a matter of accepting that people are people. We’ve got a long way to go before everyone acknowledges that animals are entitled to basic dignity as well.

Murder and torture become much easier with distance. It’s not too hard to send a drone to kill people without remorse. It’s a lot harder to pull the trigger yourself. And it’s even harder to actually twist a knife into them.

Would you be able to go Jack the Ripper on a little piglet while it squeals in pain? (See the Cruelty to Animals video above.) Probably not, but we have no problem paying thugs to do our dirty work for us. There’s so much distance between us and the animals, it’s easy to ignore what goes on.

You only like your sausage because you don’t have to watch it being made. And if you wouldn’t be willing to make it yourself, you have to admit that it’s wrong.

“Marge, kids, the things I saw. It makes me never want to eat meat again. Just fish, chicken, burgers, veal on Fridays, deer, but only in season, and if necessary, the sweetest meat of all: human.”

- Homer Simpson

Now, to address some anticipated objections:

1. “But we’re supposed to eat meat.”

I do think that we evolved to eat meat. We also evolved to lose our teeth, our eyesight, and die in our twenties, but we’ve managed to make some improvements on that. Our bodies may have evolved without ethical considerations, but that doesn’t mean our brains can’t do better.

Anyway, we weren’t meant to eat nearly as much meat as we do. Many of our health problems are a direct consequence of dietary problems, one of which is excessive meat consumption. Our closest relative, the chimp, eats mainly plants.

2. “But you can’t get enough protein from a vegan diet.”

Tell that to a 400-pound gorilla as it munches on leaves, fruits, and shoots. Or a 110-ton vegan Argentinosaurus, the largest land animal that ever lived. Or any of the vegan athletes out there. Maybe there aren’t that many, but you can start with Carl Lewis.

3. “But vegans are at risk for a vitamin B12 deficiency.”

Isn’t it just a little ironic for someone to brag about their adequate intake of vitamin B12 while they march down the path to diabetes, heart disease, and cancer? I don’t happen to know where vegans can get B12 from, but this seems like a minor issue.

4. “But it doesn’t do any harm to consume animal products, if you’re not actually eating the flesh.”

It may not seem so, but it does. See this Undercover Investigation at Hy-Line Hatchery for the shocking impact of eating eggs. (Does it remind anyone else of when Itchy sent all the Scratchys from the cloning machine to the killing machine?) There are similar issues with drinking milk.

5. “But animals aren’t entitled to the same rights as people.”

No one’s saying that pigs should be able to vote. But since they’re smarter than three year old children, maybe we shouldn’t castrate them without anesthetics. Just sayin’.

6. “But where do you draw the line? You can’t end all animal abuse. Look, you just stepped on an ant.”

We can’t prevent all homicides either. That doesn’t mean we might as well declare open season. Don’t worry about where the line will ultimately be drawn, just start moving towards it. Currently, we’re far less compassionate to animals than their natural predators are. We have plenty of room before we reach the line.

7. “But I just like the taste of meat.”

I know. This sounds like the weakest reason, and yet it’s the one that stops everyone from making a change (along with other practical issues like wanting to fit in, or difficulty finding vegan alternatives in some situations).

I’ve gone vegetarian or vegan for several weeks at a time on a few occasions, but I’ve always come back to eating meat. It’s just too easy to forget what the animals go through, and too easy to remember that I like chicken burritos.

I know that eating animals is wrong, but this is a really tough habit to break. I just don’t feel enough of a repulsion enough of the time to want to make much of a change.

So why the hell am I writing this, and why don’t I get off my high horse? Because it’s not an all-or-nothing thing. Every little bit counts, and some changes are very easy to make.

I ditched milk with no problem at all. That’s a few more cows who won’t be injected with hormones and have their babies killed while they get sucked dry. I’m mostly off pork. That’s a few more pigs who won’t be crammed into disgusting cages and butchered alive. And I’ve cut way back on red meat in general. More cow friendliness.

If even these things are too much to give up now, what else can you try? Can you refuse to eat foie gras? You probably don’t eat it anyway, so it should be pretty easy to take a stand against it. There’s a big continuum here, so if you can’t jump to the other side, just take whatever steps you can.

Many people wonder, if there’s a god, then why does he let bad things happen? They think that if they were god, there would be no suffering. But guess what? Compared to animals, you are god. What will you do with that power?

When Do You Judge Someone?

Thursday, June 10th, 2010

A Florida woman makes three 911 emergency calls to report that her local McDonald’s ran out of McNuggets. We call her “a frivolous waste of taxpayer money.”

A Washington man argues for a national boycott or lawsuit because Wendy’s charges 70 cents more to upgrade a double cheeseburger to a combo meal than to upgrade a fish sandwich to a combo meal. We call him “a loser with nothing better to do.”

A South Korean couple spends 10 hours a day at an internet cafe raising a virtual child, while their real baby starves to death at 5.5 pounds. We call them “criminally negligent.”

Yes, it’s very easy to judge them. But are these people really any different from us?

I know you want to say yes (I sure do), but what exactly makes them different from you? If you had been given the same genes and the same experiences, wouldn’t you have made the same decisions? If nature and nurture are the same, what else can be different?

Effort seems to be a big factor in how we judge others. We expect them to exercise discretion in matters we think they should be able to control, while giving them a pass on things they can’t help. Which of these judgments do you agree with?

  • “It’s not his fault he’s epileptic; we can’t blame him for striking someone during a seizure.”
  • “It’s not his fault he’s ugly; we can’t blame him for looking like that.”
  • “It’s not his fault he’s weak; we can’t blame him for not being able to lift much weight.”
  • “It’s not his fault he’s crabby; we can’t blame him for not smiling much.”
  • “It’s not his fault he’s addicted to food; we can’t blame him for overeating.”
  • “It’s not his fault he’s stupid; we can’t blame him for thinking you can take fireworks on a plane.”
  • “It’s not his fault he’s lazy; we can’t blame him for sitting back and doing nothing.”
  • “It’s not his fault he’s evil; we can’t blame him for being a serial killer.”

But who decides what we should be able to control? Maybe it’s naturally easy for one person to be friendly, another person to be honest, and another person to be brave. How much credit can you get for just doing what comes naturally?

Calvin (Hobbes’ six-year-old buddy) said that Santa’s naughty and nice list is unfair, because Santa doesn’t judge people on a curve. Susie likes performing good deeds, but Calvin hates them, so he has to work a lot harder. Shouldn’t one of his good deeds count as much as ten of hers?

Do you judge people by their house, their car, their clothes, their job, their looks, their intelligence, their personality, their friends, their family, or anything else? Of course you do. We all do. But why?

Photo by Sudhamshu

Everything’s An Illusion: A Glitch In The Matrix

Friday, June 4th, 2010

Agents, in Matrix code

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.

Neo stopping bullets

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.

42 - the Answer to the Ultimate Question of Life, the Universe, and Everything

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 Split Screen

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.

The logical labyrinth guards
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?