Sex Crimes and Illegal Immigrants: Misuse of Statistics for Politics

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Yet another reader sent me a great bad math link. (Keep ’em coming guys!) This one is an astonishingly nasty slight of hand, and a great example of how people misuse statistics to support a political agenda. It’s by someone
named “Dr. Deborah Schurman-Kauflin”, and it’s an attempt to paint illegal
immigrants as a bunch of filthy criminal lowlifes. It’s titled “The Dark Side of Illegal Immigration: Nearly One Million Sex Crimes Committed by Illegal Immigrants in the United States.”

With a title like that, you’d think that she has actual data showing that nearly one million sex crimes were committed by illegal immigrants, wouldn’t you? Well, you’d be wrong.

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Meta: Typekey Re-Enable for Comments

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I’ve gotten complaints from a bunch of commenters about problems with comments getting thrown into the moderation queue by the spam filter. Things with too many links, or with certain text properties, were getting caught even though they are clearly not spam.

In order to get around this, I’ve re-enable typekey authentication. You don’t have to login via typekey to post comments – it’s entirely voluntary. But you’re welcome to if you want, and if you do, your posts will be almost guaranteed to get posted without being pushed into the mod queue. (If you write a post containing links to viagra-selling websites, you’ll still get trapped by the spamfilter. But anything less egregious than that should go right through.

Basics: Standard Deviation

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When we look at a the data for a population+ often the first thing we do
is look at the mean. But even if we know that the distribution
is perfectly normal, the mean isn’t enough to tell us what we know to understand what the mean is telling us about the population. We also need
to know something about how the data is spread out around the mean – that is, how wide the bell curve is around the mean.

There’s a basic measure that tells us that: it’s called the standard deviation. The standard deviation describes the spread of the data,
and is the basis for how we compute things like the degree of certainty,
the margin of error, etc.

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The Invisible Link Between Bad Math and Bad Theology

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Another piece of junk that I received: “The Invisible Link
Between Mathematics and Theology”, by a guy named “Ladislav Kvasz”,
published in a rag called “Perspectives on Science and Christian Faith”. (I’m
not going to quote much from this, because the way that the PDF is formatted,
it requires a huge amount of manually editing.) This is a virtual masterwork of
goofy clueless Christian arrogance – everything truly good must be Christian, so
the author had to find some way of saying that mathematics is intrinsically tied to Christianity.

This article actually reminds me rather a lot of George
Shollenberger. His arguments are similar to George’s: that there’s some
intrinsic connection between the concept of infinity and the Christian god.
But Kvasz goes further: it’s the nature of monotheism in general, and
Christianity in particular, which gave us the idea of using
quantifiers in predicate logic. Because, you see, the idea of
quantifiers comes from the idea that existence is not a predicate, and the
idea that existence is not a predicate comes from a debate over an invalid
proof for the existence of god.

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Math: Progressive or Reactionary?

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A reader sent me a link to this, thinking that it would be of interest to me, and he was absolutely right. I actually needed to let it sit overnight before writing anything because it made me so angry.

I’ve come to realize that probably one reason I struggled with algebra,
geometry et.al., was that it seemed to me that these were basically
reactionary academic disciplines, useful for designing weaponry or
potentially repressive computer technology, but not with any obvious
humanistic or social positive uses.

If I’m wrong about this, I’d appreciate it if people could show me how this
discipline can have progressive uses.

I also feel this could be useful in developing better ways of teaching
higher mathematics if such uses could be found.

Leaving aside the incredible irony of an alleged “progressive” participating in a discussion with a community of people he would never
have been able to reach without the products of that “reactionary” discipline, I have one basic response to this kind of babble.

Math is.

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Haskell: the Basics of Type Classes

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One thing that we’ve seen already in Haskell programs is type
classes. Today, we’re going to try to take our first look real look
at them in detail – both how to use them, and how to define them. This still isn’t the entire picture around type-classes; we’ll come back for another look at them later. But this is a beginning – enough to
really understand how to use them in basic Haskell programs, and enough to give us the background we’ll need to attack Monads, which are the next big topic.

Type classes are Haskell’s mechanism for managing parametric polymorphism. Parametric polymorphism
is a big fancy term for code that works with type parameters. The idea of type classes is to provide a
mechanism for building constrained polymorphic functions: that is, functions whose type involves a type parameter, but which needs some constraint to limit the types that can be used to instantiate it, to specify what properties its type parameter must have. In essence, it’s doing very much the same thing that parameter type declarations let us do for the code. Type declarations let us say “the value of this parameter can’t be just any value – it must be a value which is a member of this particular type”; type-class declarations let us say “the type parameter for instantiating this function can’t be just any type – it must be a type which is a member of this type-class.”

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Quantum Computation Complexity: BQP

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What started me on this whole complexity theory series was a question in
the comments about the difference between quantum computers and classical
computers. Taking the broadest possible view, in theory, a quantum computer
is a kind of non-deterministic machine – so in the best possible case,
a quantum machine can solve NP-complete problems in polynomial time. The set
of things computable on a quantum machine is not different from the set of
things computable on a classical machine – but the things that are tractable (solvable in a reasonable amount of time) on a quantum
computer may be different.

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Basics: Normal Distributions

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In general, when we gather data, we expect to see a particular pattern to
the data, called a normal distribution. A normal distribution is one
where the data is evenly distributed around the mean in a very regular way,
which when plotted as a
histogram will result in a bell curve. There are a lot of ways of
defining “normal distribution” formally, but the simple intuitive idea of it
is that in a normal distribution, things tend towards the mean – the closer a
value is to the mean, the more you’ll see it; and the number of values on
either side of the mean at any particular distance are equal.

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Basics: Mean, Median, and Mode

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Statistics is something that surrounds us every day – we’re constantly
bombarded with statistics, in the form of polls, tests, ratings, etc. Understanding those statistics can be an important thing, but unfortunately, most people have never been taught just what statistics really mean, how they’re computed, or how to distinguish the different between
statistics used properly, and statistics misused to deceive.

The most basic concept in statistics in the idea of an average. An average is a single number which represents the idea of a typical value. There are three different numbers which can represent the idea of an average value, and it’s important to know which one is being used, and whether or not that is appropriate. The three values are the mean, the median, and the mode.

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Back to the Basics?

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Here at ScienceBlogs, we’ve got our own back-channel forums for the bloggers to chat with each other. An idea that came up, which a bunch of us are interested in, is doing some posts about basic definitions and basic concepts.
There are many people who read various blogs around here who’ve had problems with definitions of some basic ideas. For example, there’s the word vector – there are at least two very different uses of the word vector around here at SB: there’s the form that people like me use (the mathematical vector), and there’s the form that epidemiologists/biologists use.
For another example, there are things like the logic and proofs – a lot of people just aren’t familiar with the concept of a proof, or how to tell whether an argument is a proper mathematical proof, or whether a conclusion follows logically from an argument.
So the question: what kinds of basic ideas or terms would you like to see a very basic-level introductory post about?