Category Archives: Bad Math

More Deceptive Graphs: Scales Matter

Leave a reply

Yet More Deceptive Graphs

As you’ve probably heard, there was a horrible incident in Pittsburgh this weekend, in
which a crazed white supremacist who believed that Obama was coming to take his guns shot and
killed three policemen. Markos Moulitsas, of Daily Kos, pointed out lunatics like this shooter
are acting on conspiracy theories that are being relentlessly promoted by the likes of Glen
Beck and Michelle Bachman. It’s not an unreasonable thing to point out, given the amount of
time that Beck and Bachman have spent lately talking about the impending socialist/fascist
crackdowns that will require a revolutionary response from all right-thinking patriotic
citizens.

Now, you may think that Kos is an idiot. In fact, even though we agree on many
political issues, I think that Kos is an idiot. I (obviously from what
I wrote above) happen to agree with the basic hypothesis that if you tell
people that the government is going to come and get that and that they need to
defend themselves, that some people are going to believe that the government is
coming to get them and that they need to defend themselves. But the way
that Kos responded was disgusting; it was latching on to a tragic event in
a shallow, snide, heartless way.

But whether you think Kos is an ass ore not isn’t the point. Regardless of your opinion of
the man, there’s no arguing the fact that he’s created a website that draws a really
astonishing amount of traffic, and has become a nexus for many activists on the political
left.

And that, in turn, naturally draws hatred and mockery from the political right. Because,
you see, no one who disagrees with those fine patriotic folks could possibly be an
honest, serious person. They must be a bunch of scheming bastards, obviously.

So, when Kos came out bitching about how the rantings of various crazies really do
have a connection to the actions of people like the Pittsburgh killer, naturally it couldn’t be that he actually believed that people ranting about how the President is
creating a fascistic tyranny that’s going to come take all of your guns could actually
inspire a crazy person to believe that the President creating a fascistic tyranny that was going to come and take away his guns. No, that couldn’t be. He must be up to something – like trawling for hits!

Which, finally, brings us to our topic.

A conservative blogger named Moe Lane posted his theory about why Kos spoke out about the Pittsburgh shooter. It’s because his pageviews have declined so much. But, of course, it wouldn’t be good enough to just say that DKos pageviews are down – he’s got to show that it’s specific to those dirty liberals. So he produces two graphs – one for DKos, and one for RedState, a major conservative site. Here are his graphs; DKos first, Redstate second:

dkos-300x244.jpg
rs-300x244.jpg

A quick glance shows that both had a huge spike right around the elections, and then they
dropped off pretty dramatically. Then both had a slow upward trend. But the RedState trend
looks a lot steeper.

Continue reading →

More Stupid Graphs

Leave a reply

Remember the post I made a couple of weeks ago, flaming the wall-street idiots for
a bad graph? They were comparing the value of financial firms before and after the current
mess. But they way that they drew it was using circles, where the diameter of the
circle was proportional to the values, but the way it was drawn strongly suggested that
the area was the metric of comparison.

Well, an astute reader sent me another example of the same error – but it’s even
worse. This one is misleading in two ways. Take a look and see if you can figure out
what the two errors are. I’ll explain beneath the fold.

Bad Bailouts?

24 Replies

It’s economics time again.

I hate economics. I find it hopelessly dull. But apparently my style of explaining
it is really helpful to people, so they keep sending me questions; and as usual, I do my best to try to answer them. Even if I don’t particularly enjoy it.

So people have been asking me to explain what the proposed bank bailout plan is,
how it’s supposed to work, and why so many people are upset about it.

Continue reading →

Perverse Incentives

Leave a reply

A lot of people, reading the reporting on the current financial
disaster, have been writing me to ask what people mean when they talk
about incentives. The traders, the bankers, the fund managers, and all
of the other folks involved in this giant cluster-fuck aren’t
stupid. So naturaly, the question keeps coming up, why would they go
along with it? And the answer that we keep hearing is something along
the lines of “perverse incentives”.

The basic idea is that the way that the people in the industry got paid,
it was actually in their interest do do things that they knew would
eventually cause a disaster. How could that work?

Continue reading →

I Get Mail: Iterative Compression

Leave a reply

Like a lot of other bloggers, I often get annoying email from people. This week, I’ve been dealing with a particularly annoying jerk, who’s been bothering me for multiple reasons. First, he wants me to “lay off” the Christians (because if I don’t, God’s gonna get me). Second, he wants to convince me to become a Christian. And third, he wants to sell me on his brilliant new compression scheme.

See, aside from the religious stuff, he’s a technical visionary. He’s invented a method where he can take a source document, and repeatedly compress it, making it smaller each time.

This is a stupid idea that I’ve seen entirely too many times. But instead of just making fun of it, I thought it would be interesting to explain in detail why it doesn’t work. It touches on a bunch of basic facts about how data compression works, and provides a nice excuse for me to write a bit about compression.

basic-compression.png

The basic idea of data compression is that you’re eliminating redundancies in the original text. You can’t discard information. Mathematically, a compression function is an invertible function C from an array of characters to an array of characters (or you could use bits if you prefer), such that if y=C(x), then on the average input, the length of y is smaller than the length of x.

An ideal compression system is one where for all possible values of x, C(x) is shorter than x. C is your compressor; and since C is reversible, it has a unique inverse function C-1 such that C-1(C(x)) = x. An illustration of this basic compression system is in the diagram to the side.

Continue reading →

Tax Thresholds: Why the horror stories about the Obama tax plan are lies

Leave a reply

Watching news reports about President Obama’s proposed tax changes,
I’ve seen a number of variations on a very annoying theme, which involves
a very stupid math error.

A typical example is this story on ABC news, which contains a non-correction
correction:

President Barack Obama’s tax proposal — which promises to increase taxes for those families with incomes of $250,000 or more — has some Americans brainstorming ways to decrease their pay in an attempt to avoid paying higher taxes on every dollar they earn over the quarter million dollar mark.

A 63-year-old attorney based in Lafayette, La., who asked not to be named, told ABCNews.com that she plans to cut back on her business to get her annual income under the quarter million mark should the Obama tax plan be passed by Congress and become law.

“We are going to try to figure out how to make our income $249,999.00,”
she said.

“We have to find a way out where we can make just what we need to just under the line so we can benefit from Obama’s tax plan,” she added. “Why kill yourself working if you’re going to give it all away to people who aren’t working as hard?”

The original version of this article continued to follow this basic theme. The
updated article pretends to correct it, while still basically mantaining the
same focus.

The idea behind this, and similar stories, is that raising the income tax
rate on people earning over $250,000 per year creates a threshold, where earning
more than that threshold will result in your taking home less
after-taxes pay than if you earned less.

Continue reading →

Financial Morons, and Quadratics vs. Linears

50 Replies

I wasn’t going to write about this, because I really don’t have much to add. But people keep mailing it to me, so in order to shut you all up, I’ll chip in.

As everyone knows by now, we’re in the midst of a really horrible
financial disaster. I’ve argued in the past on this blog that the root cause of the entire disaster is pure, simple stupidity on the part of people in the financial business. People gave out mortgages that any
sane rational person would have considered ridiculous. And then they built huge, elaborate financial structures on top of those mortgages, pretending that by somehow piling layer upon layer, loan upon loan, that
they were somehow creating something that could be considered real wealth.

bankcap6-1024x747.jpg

They gave themselves bonuses that boggled the mind. Even after the whole ridiculous system came tumbling down, they continue to give themselves ridiculous bonuses. Insane bonuses. They’ve been writing themselves checks for millions of dollars to continue to operate their
businesses – even after taking billions of dollars in loans from the government to prevent them from going out of business. I consider
this to be downright criminal. But even if it’s not criminal, it’s
incredibly stupid. The very people who ran those firms right to the edge of bankruptcy, who nearly took down our entire financial system
are being rewarded. Not only are they being allowed to continue
to rut the businesses that they pretty much destroyed, but they’ve
been paying themselves an astonishing amount of money to do it. And now they’re complaining bitterly about the fact that the government
wants to limit them to a paltry half-million dollars of salary per year.

They argue that they must be allowed to earn more than that. Because after all, the people who run those businesses are special. They’re “the best and the brightest”. They’re
extra-smart. No one else could possibly run those businesses. We can’t rely on anyone who’d accept a puny half-mil – they won’t be smart enough. They don’t have the special knowledge of the business that these people do.

There’s one minor problem with that argument: it doesn’t work. A couple of weeks ago, some idiot at JP Morgan circulated a chart that was supposed to summarize just how bad the financial disaster has been. The chart circulated for a couple of weeks – bounced from mailbox to mailbox, sent from one financial genius to another.

Only the chart was blatantly, obviously, trivially wrong, and anyone who had the slightest damned clue of the assets those businesses managed – i.e., the kind of thing that the idiot who drew the chart was supposed to know – should have been able to tell at a glance how wrong it was. But they didn’t. In fact, the damned thing didn’t stop circulating until (of all people) Bob Cringely
flamed it. Go look at the chart – it’s up at the top of this post.

Continue reading →

Metric Abuse – aka Lying with Statistics

Leave a reply

I’m behind the curve a bit here, but I’ve seen and heard a bunch of
people making really sleazy arguments about the current financial stimulus
package working its way through congress, and those arguments are a perfect
example of one of the classic ways of abusing statistics. I keep mentioning metric errors – this is another kind of metric error. The difference between this and some of the other examples that I’ve shown is that this is deliberately dishonest – that is, instead of accidentally using the wrong metric to get a wrong answer, in this case, we’ve got someone deliberately taking one metric, and pretending that it’s an entirely different metric in order to produce a desired result.

As I said, this case involves the current financial stimulus package that’s working its way through congress. I want to put politics aside here: when it comes to things like this financial stimulus, there’s plenty of room for disagreement.
Economic crises like the one we’re dealing with right now are really uncharted territory – they’re very rare, and the ones that we have records of have each had enough unique properties that we don’t have a very good collection of evidence
to use to draw solid conclusions about recoveries from them work. This isn’t like
physics, where we tend to have tons and tons of data from repeatable experiments; we’re looking at a realm where there are a lot of reasonable theories, and there isn’t enough evidence to say, conclusively, which (if any) of them is correct. There are multiple good-faith arguments that propose vastly different ways of trying
to dig us out of this disastrous hole that we’re currently stuck in.

Of course, it’s also possible to argue in bad faith, by
creating phony arguments. And that’s the subject of this post: a bad-faith
argument that presents real statistics in misleading ways.

Continue reading →

Sloppy Arguments about Mutation Rates

Leave a reply

My friend Razib, who is one of my
fellow ScienceBloggers sent me a
link to an interest attempt by creationist at arguing why evolution can’t
possibly work.

I say interesting, because it’s at least a little bit unusual in
its approach. It’s not just the same old regurgitation of the same talking
points. It’s still not a great argument, but it’s at least not as boring as
staring at the same stupid arguments over and over again. Alas, it’s not entirely
new, either. It’s an argument that the mutation rates required for humans to have evolved from a primate ancestor would have to be impossibly high.

Continue reading →

The Continuum Hypothesis Solved: All Infinities are the Same? Nope.

Leave a reply

Of all of the work in the history of mathematics, nothing seems to attract so much controversy, or even outright hatred as Cantor’s diagonalization. The idea of comparing the sizes of different infinities – and worse, of actually concluding that there are different infinities, where some infinities are larger than others – drives some people absolutely crazy. As a result, countless people bothered by this have tried to come up with all sorts of arguments about why Cantor was wrong, and there’s only one infinity.

Today’s post is another example of that. This one is sort of special. Unless I’m very much mistaken, the author of this sent me his argument by email last year, and I actually exchanged several messages with him, before he concluded, roughly “We’ll just have to agree to disagree.” (I didn’t keep the email, so I’m not certain, but it’s exactly the same argument, and the authors name is vaguely familiar. If I’m wrong, I apologize.)

Anyway, this author actually went ahead and wrote the argument up as a full technical paper, and submitted it to arXiv, where you can download it in all it’s glory. I’ll be honest, and admit that I’m a little bit impressed by this. The proof is still completely wrong, and the arguments that surround it range from wrong to, well, not even wrong. But at least the author has the Chutzpah to treat his work seriously, and submit it to a place where it can actually be reviewed, instead of ranting about conspiracies.

For those who aren’t familiar with the work of Cantor, you can read my article on it here. A short summary is that Cantor invented set theory, and then used it to study the construction of finite and infinite sets, and their relationships with numbers. One of the very surprising conclusions was that you can compare the size of infinite sets: two sets have the same size if there’s a way to create a one-to-one mapping between their members. An infinite set A is larger than another infinite set B if every possible mapping from members of B to members of A will exclude at least one member of A. Using that idea, Cantor showed that if you try to create a mapping from the integers to the real numbers, for any possible mapping, you can generate a real number that isn’t included in that mapping – and therefore, the set of reals is larger than the set of integers, even though both are infinite.

This really bothers people, including our intrepid author. In his introduction, he gives his motivation:

Cantor’s theory mentioned in fact that there were several dimensions for infinity. This, however, is questionable. Infinity can be thought as an absolute concept and there should not exist several dimensions for the infinite.

Philosophically, the idea of multiple infinities is uncomfortable. Our intuitive notion of infinity is of an absolute, transcendent concept, and the idea of being able to differentiate – or worse, to be able to compare the sizes of different infinities seems wrong.

Of course, what seems wrong isn’t necessarily wrong. It seems wrong that the mass of something can change depending on how fast it’s moving. It seems even more wrong that looked at from different viewpoints, the same object can have different masses. But that doesn’t change the fact that it’s true. Reality – and even worse, abstract mathematics – isn’t constrained by what makes us comfortable.

Back to the paper. In the very next sentence, he goes completely off the rails.

Continue reading →