Can 20 People Stand on a Wing? Can a Conspiracy Theorist Be Stupid?

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I’m sure you’ve all heard about the airplane that ditched in the Hudson last week. (Just 30 blocks from my office!) When it happened, after we found out more about what caused the plane to ditch, I wondered how long it would take before the 911 Truthers came up with a conspiracy theory about it.

Not long. Via SkepticBlog comes news of a conspiracy theorist claiming that the ditching doesn’t make any sense. Brian Dunning at SkepticBlog does a good
job explaining what’s so stupid about this, but there were two things about
it that I thought were particularly interesting from the point of view of a math and computer science geek.

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Apples vs Orchards: Comparing Inauguration Costs

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People keep sending me links to this, so I’ll make a short post about it.

In the hubbub surrounding the Obama inauguration, there’ve been all sorts of incredulous press pieces discussing the supposed outrageousness of the costs of this inauguration compared to others. I’ve personally heard this reported on the BBC world service, CNN, Fox, and MSNBC. In these
reports, the cost of the Obama inauguration is generally reported as
between 150 and 160 million dollars. When they provide a contrast, they talk about how Bush’s second inauguration cost $40 million.

The problem is, this is a metric error. They’re comparing apples to orchards.

When they cite the Bush inauguration cost as $40 million, they’re talking
about the cost of the inauguration parties – that is, the cost of the festivities themselves. That cost does not include security. It does
not include the cost of paying police to shut down the city streets. It doesn’t include the cost of cleaning up after the crowds. It’s just
the cost of the parties.

The Obama figure of $150-$160 million includes everything – police, security, setup, and cleanup.

A fair comparison? If you exclude the security costs, Bush’s second
inauguration cost $42 million; Obama’s is expected to cost around $45 million. If you include the security costs, Bush’s second inauguration
cost somewhere around $155 million. (The exact figures are still not public
knowledge; Bush and company treated it as a “national security matter” which
did not need to be disclosed.)

Yet another fake controversy brought to you by the supposedly liberal-biased media.

Excuse the brief interruption…

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Just a brief note, to let you all know why there’s a lack of new posts.

Once again, I managed to kill my laptop. The machine died suddenly, with no warning. I’m currently waiting for a replacement, and once I get it, I’ll need some time to set everything up to my liking. I also had three posts in progress on the machine; I’m not sure whether they were backed up or not, and won’t be able to find out until I get a new machine.

Things will be back to normal as soon as possible, but don’t expect much for the next couple of days.

Blaming Bush: This time, it wasn't his fault.

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And now for a short gripe from the other side of the political spectrum.

Normally, I like Media Matters. I personally think that the whole “left-wing media” thing
is a crock. The media has become so sensitive to the accusation of left-wing bias that they actually shy away from even dreaming of criticizing a conservative, and attack liberals with great fervor as a way of showing that they’re not being unfairly nice to them. In general,
I find Media Matters does a good job of showing how the modern press really works.

But the fact is, they are a biased organization, and you need to be very careful
to look at the details of what they write. Just like right-wing media-watch organizations,
they do look for interpretations of facts that support their bias, even if it requires
significant abuse of those facts to make the interpretation fit.

This morning, they provided an excellent demonstration of that. President Bush gave his final press conference this morning. The people at the conference showed a lot of deference to him, and let him get away with a lot. But one thing that Media Matters focused on
touches on math, and it’s bad.

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Social Security vs Ponzi Schemes

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Naturally, since this friday was the first time that the SB server has really been down since I start blogging (planned downtime, as it happens, for a major system upgrade), there
was spectacularly bad math in the local news here in NYC friday afternoon.

I’m not sure how long this has been the case, but Mayors of NYC have a radio show. It’s a mixture of them spouting off about whatever they feel like babbling about, and call-in questions. I don’t generally listen, but once in a while, if the mayor says something either particularly interesting or particularly insane, I’ll hear the segment repeated on the local NPR station.

In this friday’s show, he sprung a really shockingly stupid line. The supposed
topic was Bernard Madoff and his pyramid scheme. Bloomberg responded by saying
that “Madoff’s isn’t the biggest ponzi scheme ever. If you really want to see the
worlds biggest ponzi scheme, just look at social security.” He continued along
those lines for a few minutes.

This is, to put it mildly, bullshit. Incredibly, stupid, rampant, bullshit.

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Cryptographic Padding in RSA

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Ok, away from politics, and back to the good stuff. When I left off talking about
encryption, we were looking at
RSA, as an example of an asymmetric encryption system.

Since it’s been a while, I’ll start off with a quick review of RSA.

Asymmetric encryption systems like RSA are based on computations that are easy to perform if you know the keys, and incredibly hard to perform if you don’t. In the specific case
of RSA, everything is based on a pair of very large prime numbers. If you know those two
primes, and you know the public key, it’s really easy to compute the private key. But
if you don’t know the two prime numbers, then even given the public key,
it’s incredibly difficult to compute the private key.

To be a bit more specific, in RSA, you get a pair of large prime numbers, P and Q. You
compute from them a totient of their product, which is the number
N=(P-1)×(Q-1). Then you arbitrarily pick a public exponent, E, which is
smaller than N, and which is prime relative to N. You can then compute
the private key exponent, D. If you know what P and Q are, it’s pretty easy to compute
D.

Once you’ve got D and E, your public key is the pair is (N,E), and the private key is the pair is (N,D).

If you’ve got a plaintext message M, then encrypting it with the public key
is done by computing ME mod N. If you’ve got a ciphertext C encrypted
with the public key, then decrypting it is done by computing CD mod N.

Encrypting a plaintext with the public key is exactly the same process
as decrypting a ciphertext produced with the private key. And vice versa.

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Circling Around The Speed of Light

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One of the many great things about my readers is how you folks keep me up to date with any new crap that springs up, so that I don’t need to spend so much time hunting down the real good stuff. There’s a beautiful piece of crap on youtube that was pointed out to me by one of you guys. It’s really a wonderful bit of circularity.

Circularity is something that I find beautiful in math. What I mean by circularity is that because numbers are closed, you can run around in circles playing games with that closure. Another post that I’ve got in progress is talking about RSA encryption, which is a beautiful example of circularity. You start with a message, encoded as a number, M. Then you take a particular set of three numbers, N, D, and E. If you raise M to the Dth power modulo N, you get a new number. M’. If you raise M’ to the Eth power modulo N, you get the original M. You’re never taking roots – but the two exponentiations cancel each other out modulo N. It’s beautiful, and astonishing, and yet it makes perfect sense.

That’s a complicated example of circularity. A simpler one, also involving modulo arithmetic, is to look at the tempered music scale. Let A=0, Bb=1, B=2, C=3, Db=4, D=5, Eb=6, E=7, F=8, Gb=9, G=10, Ab=11. Now, start at A, and follow through musical fifths – that is, go from A(0) to E(7). Then E(7) to E+7=14 mod 12 = 2 = B. Then B to Gb(9). Then Gb to Db(4). Then Db to Ab. Then Ab to Eb. Then Eb to Bb. Then Db to F. Then F to C. Then C to G. Then G to D. Then D to A. You’ve taken twelve steps of fifths, and wound up where you started. So by following through one of the natural musical elements of harmony, you’ve got a circle that visits each note exactly once. Looked at mathematically, it’s trivial. But it’s still pretty cool.

It’s pretty easy to trick yourself with circularity of you’re not careful. You can find what appear to be amazing numerical coincidences, because you don’t realize that you’ve created a circle.

The target of this posts isn’t an example of that. It’s a really trivial circle.

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Antisemitic Assholes, and Jewish vs. Israeli

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I’m working on more substantive, mathy posts, but in the meantime, I’m pissed,
so I’m making a quick off-topic post.

With the horrible things that are going on in Gaza right now, I’ve gotten a raft of antisemitic spam. Most of it has been through private mail, but some has been in comments on
the blog.

I’ve mentioned plenty of times on this blog that I’m Jewish. Not Israeli. Jewish.

I’m not a member of the Israeli military. I am not a citizen of Israel. I don’t get to vote in Israeli elections. I have no say in anything that the state of Israel does.

If you’re the type of good-for-nothing coward who thinks that the correct way to
handle a political conflict is to fling insults around at some random powerless blogger,
you should at least bother to check that you’re not shooting yourself in the foot with what you’re saying.

I’m not an antisemite, you fucking jew dog. I can’t be an antisemite – I’m an arab, which means I’m a semite. I don’t hate myself. And I don’t hate jews, I hate zionists who
oppress my people.

You start off with “You fucking Jew”, but don’t worry, I believe you. You don’t really hate Jews, it’s just those zionists. Of course, you don’t know whether or not I’m a zionist. You just assume that I am because I’m a Jew. And you hate me enough to spam me with insults about being a “fucking jew dog”. But you’re don’t hate Jews, no.

And you’re not an anti-semite because you’re “arab”. Well, see, in your typical
pig-ignorance, you don’t know that “anti-semite” is a rather deceptive word. It was
created to give an intellectual gloss to jew-hatred. See, Jew-hatred just sounds
so ugly. Back in the late 19th century, a group of German intellectuals was trying
to make Jew-hatred fashionable, and they chose the word “antisemiten” in German to provide a
pseudo-intellectual term that fit with the in-vogue racial theories of the time. That’s where it comes from. It doesn’t matter that looked at in terms of etymology, it doesn’t appear to be a term related specifically to jews. It’s got a clear pedigree dating back well over a century. Antisemitism is Jew-hatred, plain and simple. That’s what the word was created to mean, and that’s what everyone, you included, mean by it.

Even if that weren’t true, it wouldn’t help you. Even if “antisemitic” really
did mean “hating people of semitic origin”, an Arab could be as antisemitic as anyone else. Being a member of a group doesn’t exist stop you from hating that group. Hell, there’s no reason that a Jew can’t be anti-semitic (in the true, Jew-hating meaning of the word): there’s no shortage of people who are Jews by family history who have a deep and intense hatred of Judaism.

People have a hard time separating Jews and Israelis. Not just people like the
assholes who triggered this post. As a child, I lived in a small town in Ohio for four long, miserable years, and constantly heard from people – including my schoolteachers – who couldn’t figure out how I could possible be a Jew and an American at the same
time – because Jews were Israelis.

It’s really not a hard thing.

Judaism is a religion; being Jewish is a matter of belief, custom, and ritual.

Israel is a country. Being Israeli is a matter of politics and citizenship in
that country.

You don’t have to be Israeli to be Jewish, and you don’t have to be Jewish to be Israeli.

Like most countries, Israel has laws describing how you can become a naturalized citizen
if you aren’t born there. It happens that under that law, it’s extremely easy for
many Jews to become naturalized Israeli citizens. That doesn’t mean that all Jews
are Israeli citizens. It means that if you’re part of the group recognized as Jews
by the Israeli government, it would be easy for you to become a naturalized Israeli
citizen if you ever moved there.

I don’t like what’s going on in Gaza right now, but I don’t pretend that the situation is
simple or clear. One one side, I don’t think that any country can afford to let someone shoot
missiles at their people on a daily basis, and not do anything about it. On the other side, I
don’t think it’s remotely acceptable to kill hundreds (or more) of innocent people in the
hopes of stopping a small group of murderous bastards. The Israeli response is complete out of proportion, and the people who are the real victims, who are paying the real price for the most part, aren’t the guilty ones.

But none of that is my choice. Because I’m Jewish, not Israeli. There’s a huge difference
there. (I know that many Israeli’s oppose this conflict; but just like I believe that I share
in the responsibility for the horrors my country has inflicted on the Iraqi people, I think
that Israelis – even the ones who oppose this conflict, share in the responsibility for what
their country has done. And the people in the Palestinian territories who voted for Hamas
share in the responsibility for what Hamas has done in their name. When you’re a citizen of o country, you become a part of it, and you own a share in both the good and the bad of what it does.)

The Z2K9 Problem

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I’ve been getting a lot of emails asking about the so-called “Z2K9” problem.

For those who haven’t heard, the software on a particular model of Microsoft’s Zune music player froze up on New Year’s eve, because of a bug. Apparently, they didn’t
handle the fact that a leap year has 366 days – so on the 366th day of 2008, they froze up for the day, and couldn’t even finish booting.

Lots of people want to know why on earth the player would freeze up over something like this. There was no problem with the date February 29th. There was nothing wrong with the date December 31st 2009. Why would they even be counting the days of the year, much less being so sensitive to them that they could crash the entire device for a full day?

The answer is: I don’t have a damned clue. For the life of me, I can’t figure out
why they would do that. It makes absolutely no sense.

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My Favorite Strange Number: Ω (classic repost)

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I’m away on vacation this week, taking my kids to Disney World. Since I’m not likely to
have time to write while I’m away, I’m taking the opportunity to re-run an old classic series
of posts on numbers, which were first posted in the summer of 2006. These posts are mildly
revised.

Ω is my own personal favorite transcendental number. Ω isn’t really a specific number, but rather a family of related numbers with bizarre properties. It’s the one real transcendental number that I know of that comes from the theory of computation, that is important, and that expresses meaningful fundamental mathematical properties. It’s also deeply non-computable; meaning that not only is it non-computable, but even computing meta-information about it is non-computable. And yet, it’s almost computable. It’s just all around awfully cool.

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