The driver of Apple’s comeback was the staggering success of the iPod. It was a device that changed how we listen to music, and it was (is?) ubiquitous. What’s amazing is that the iPhone has made that success look positively anemic. The iPod’s best year ever was 2008 with 54.8 million devices sold and its best quarter was Q1 2009 with 22.7 million devices sold.*

Q1 2012 saw Apple selling 37 million iPhones and 15.4 million iPads. Tim Cook, Apple’s CEO, said they sold 62 million iOS devices in the quarter. That means iOS is nearly 3 times more successful than the iPod at its peak. For the calendar year 2011, Apple sold 93.1 million iPhones – more than 2007, 2008, 2009, and 2010 combined – and nearly double the iPod’s most successful year.

*Apple’s Q1 is actually calendar Q4 (the holiday season). They start their fiscal year in October.

(as an aside, there is a great story called “The Riddle Of The Universe, And It’s Solution” in Douglas Hofstadter and Daniel Dennett’s anthology ‘The Mind’s I” about what might happen if you could come up with a fallacy so dense that you could not eject)

The simple logical loop is created by a statement such as “This sentance has threee errors”. There are only two obvious errors (the two typos) which means that the sentence is wrong, but the fact that the sentence has miscounted means that there are actually three errors and thus the sentence is correct, however that means that the third error no longer exists and once again the sentence is incorrect. And so on, and so on. Another good example is the statement “I cannot assert this sentence.” If you agree that you cannot assert the sentence then really the sentence is wrong since you can assert it, but that means the sentence is right that you cannot assert it, and so on, and so on.

More fun, is when the concrete field of math comes into play. I remember when Mort Anderson, my AP calculus teacher in high school was frustrated with our class one day. We were distracted and not paying attention. He put the following on the board and then just sat at his desk while we tried to figure out what he had just done. Follow this factorization if you will (you’ll need to recall some algebra for this one):

X = X (take two numbers)

X2 = X2 (square them both)

X2 – X2 = X2 – X2 (subtract the square from both sides)

(X + X) * (X / X) = X * (X / X) (factor each side)

(X + X) = X (divide both sides by (X – X))

now, replace X with 1 and you just proved that 1 + 1 = 1.

Every step in that equation appears to be legal algebraic maneuvers but the result is impossible. The reason is simple. When you divide both sides by (X – X) you’re forgetting that X – X is actually 0 and you cannot divide by 0. Now you know why you can’t divide by 0 – addition ceases to function and the universe will begin to cave in on itself.

Probability is a great area for logical traps. I love the old statistics joke “How do you ensure that a terrorist doesn’t bring a bomb onto your plane? Bring your own bomb! The probability that your plane has two bombs on it is so remote it could never happen!”

That joke relies on an inversion of the base rate fallacy. It assumes that the probabilities are linked when, in fact, they’re not. For example: if you flip a coin, the likelihood of getting heads is 1/2. If you flip a coin twice, the likelihood of getting heads on both flips is 1/2 * 1/2 or 1/4. You can figure out the probability of getting X number of heads in a row by calculating 1/2^X (e.g. X = 4, 2^4 = 2 * 2 * 2 * 2 = 16, therefore getting heads 4 times in a row has a 1/16 likelihood). So getting heads 100 times in a row is astronomically unlikely. However the likelihood that you get heads on the hundredth flip is still 1/2 because that flip doesn’t know that there have been 99 before it. So too does the terrorist not know that there is already a bomb on that plane so the likelihood of his act taking place is not affected by yours.

Recently, my friend Dewitt Clinton posted the following on Google+:

According to this, our galaxy has 100,000,000,000 planets. And there are at least 100,000,000,000 galaxies in the observable universe.

Which averages out to over 10,000,000,000,000,000,000,000 planets in total (all things being equal).

Which means that even if there’s just a .00000000000000000000001% chance of life on any given planet (about 3 quadrillion times less likely than you being eaten by a shark this year), then there’s life on at least one more out there. = )

I realized there was an implication with that probability that I wasn’t entirely comfortable with:

Since I’m 99.9% certain that there is other life in the universe, and it’s 3 quadrillion times more likely that I’ll be eaten by a shark this year then, by the transitive property, I am absolutely certain to be eaten by a shark this year.

Sonofabitch.

The likelihood is so high, in fact, that if I sat in a hut in the middle of the sahara, a shark would spontaneously appear from thin air and eat me. An event that would be deeply unfortunate for me and incomprehensibly surreal for any by-standers.

This is an example of an appeal to probability. In fact, just because something could happen, does not mean it will. If I were living in a hut in the sahara, the likelihood of being eat by a shark would approach 0 (there is still some chance, just not much…).

What are your favorite fallacies?

I’ll leave you with a recent XKCD cartoon that shows the unsustainability of using the word sustainable at current rates. Enjoy:

That’s kind of awesome.

The funny thing is, no one’s really hiding the secret of how to make awesome online communities. Give people something cool to do and a way to talk to each other, moderate a little bit, and your job is done. Games like Eve Online or WoW have developed entire economies on top of what’s basically a message board. MetaFilter, Reddit, LiveJournal and SA all started with a couple of buttons and a textfield and have produced some fascinating subcultures. And maybe the purest (!) example is 4chan, a Lord of the Flies community that invents all the stuff you end up sharing elsewhere: image macros, copypasta, rage comics, the lolrus. The data model for 4chan is three fields long – image, timestamp, text.

Now tell me one bit of original culture that’s ever come out of Facebook.

The glitch, which struck at around 11AM, was affecting online services for consumers all over Europe, the Middle East and Africa. All are served by a RIM data centre in Slough.

Slough?

Where have I heard of that place before?

Oh yeah, it’s the place where this guy works:

David Brent from Slough

Coincidence? You decide….

The man has no internal logic. Or at least, no sense of irony.

Cheney vigorously defends the Iraq fiasco and the failed nation-building effort there as a success but then there is this:

[Cheney] also offers a cautionary tale about the unintended consequences of government regulatory overreach in the private sector, a key issue in the 2012 election. In 1971, he was assistant director of operations for the Cost of Living Council, which imposed wage and price controls in part to lower inflation. Instead, the controls sparked rising inflation, marketplace chaos and food shortages. The experience “confirmed my innate skepticism about what government could and couldn’t do.”

His message to Americans today: “When something as big and ham-handed as the federal government tries to run something as complex and dynamic as the American economy, the result is sure to be a train wreck.”

So if it’s impossible for the federal government to run something complex then how did he think the federal government could run Iraq?