The loose version of this principle says “After placing n pigeons into m compartments, if n is greater than m, you will find that some compartment must contain more than one pigeon.”

Seems obvious, and perhaps it is, but at least in the world of data compression it must be trotted out from time to time in order to bludgeon dreams back to reality.
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A term meant to convey a person’s inability to make sense of the numbers that run their lives. Innumeracy was coined by cognitive scientist Douglas R Hofstadter in one of his Metamagical Thema columns for Scientific American in the early nineteen eighties. Later that decade mathematician John Allen Paulos published the book Innumeracy. In it he includes the notion of chance as well to that of numbers.

The example of innumeracy found in this post is somewhat more interesting than most, because it comes from a source that really should know better: Discover Magazine.
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American Express Needs YOUR Feedback!

Dear American Express Blue Cardmember:

American Express would like your feedback. We would like you to participate in a survey about your Blue card from American Express. Your participation will provide us with valuable feedback and help us tailor card benefits to better meet your needs.

As a token of our appreciation, you will receive $5 from American Express*. Please note that this survey will be running for a limited period of time. To increase your chances of receiving the honorarium, please complete the survey at your earliest convenience.

The web address for the survey is shown below. To begin the survey, simply double-click on the address to go directly to the questionnaire. However, if you are unable to double-click on the address, please copy and paste the text below into your browser’s address bar.

Well, I need five bucks, and a little bit of checking gave me moderate insurance that this was really from American Express, not a phisher. The survey was being outsourced to Confirmit, a real company, and they don’t seem to be on any malware site lists. Furthermore, as things went on, there was an enormous amount of content in the survey and seemingly no payoff for phishers, so it seems unlikely that this is a scam.

However, right off the bat there was some cause for concern. Double-click on the address? How many browsers do you use that need a double-click before they follow a link? If Confirmit is a real company, they clearly didn’t assign their top copywriter to this project.

The real fun started when I actually started the survey. The classic “make a good first impression” rule that your mother taught you is just as true for web pages as it is for anything else. And the first page of the American Express survey was the equivalent of showing up for your first date with a big gravy blotch on your tie:
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From this we know two things: The Anchorage airport runs their flight listings on Windows PCs, and they aren’t using any anti-virus software. Homeland Security, what do you think?

The world is full of people making miraculous claims for video compression. For example, the hucksters at Euclid Discoveries have been leading their investors on with tales of incredible video compression for years now. No doubt that somebody, someday, might make a quantum leap in video compression, but for the past 25 years it’s been just hard work with slow and steady progress.

A lot of the people who have made these claims in the past are either crackpots or criminals, so I found myself kind of annoyed when Robert X. Cringely popped up with a miracle compression claim in his June 24, 2004 column. Robert isn’t crazy, and he’s not a criminal. He spends a lot of time talking to smart people and trying to synthesize their ideas into frameworks that he can deal with, and he’s pretty good at it.

In this case, he asserted (without references) that the bandwidth of the optic nerve was in the 100Kbps range - thereby implying that we ought to be able to cook up a compression scheme that uses a model of the human eye to provide full bandwidth video at 100 Kbps. It’s not the first time Bob has wandered down this alluring path, he got hyped up in 2002 about Foveating Codecs. (Seen any deployed recently?)

Anyway, the point of all this Bob background is just to point to this paper in which some Penn researchers assert that the bandwidth of the human optic nerve is around 10 Mbps - a bit different from the Cringely numbers. What’s interesting is this means that present coding schemes that provide decent representation of video are operating in the ballpark of that number, which might mean the whole thing kind of adds up.

It’s easy for people to get caught up in a whirl of excitement about impossible video compression, and it happens all the time - just ask the hundreds of innocents who have busted open their piggy banks to buy shares in Euclid. I’ll close with a quote from Bob showing how compelling the idea can be - compelling enough to make people overlook the basic facts:

Oh, and there’s another little side benefit — the end of blindness.

And it is doable, the algorithms have already been worked out and are running today in Matlab.

That was two years ago, so I guess the algorithms are still stuck in their Matlab jail.