The Image Fulgurator

Many of you will have probably seen this (e.g. on Wired), but just in case you haven't, Rod at Reasonable Deviations has a discussion of Julius von Bismarck's device, which looks a bit like a camera with a speedgun mounted in the back of it. Camera flashes when other people take pictures set off its own flash unit, which fires through the image on film in the camera, projecting it onto whatever the camera is focused on... like a kind of instantaneous graffiti - it's too brief to be seen by eye, but it shows up in the shot.

I'm not sure what to think of it (aside from, "Damn, that's clever"), but I can see the potential for a lot of shenannigans of various kinds.

Examples of the genre

In my previous post I said:

Unfortunately, based only on the information that the third central moment was zero, many people would in fact describe it as symmetric.

I've seen many examples over the years, so I figured it shouldn't be hard to find one or two. A quick google search reveals some examples:

• This page on using a TI83 calculator has:
  • "Skewness measures the departure from symmetry" (it defines skewness as the third moment measure I mentioned, so it is saying that 0 third moment implies symmetry)
  • it goes on to suggest a test statistic for symmetry based on this, and concludes that discussion with "If that fraction is between −2 and 2, you can’t say whether the population is symmetric (skewness = 0) or skewed."
• This paper on brain evolution has:
  • "SK, subclade skewness (- negative skew; 0, symmetric distribution; + positive skew)"
  • "the system is probably passive if average subclade skew is neutral (symmetric distribution) or negative"
    
• This set of notes for a university* subject called "Introduction to Statistics" has the following complete howlers:
  
  • "If the skewness is approximately zero, the histogram (distribution) for the data is symmetric and usually normal"
  • "'varB' has a skewness close to zero so that its distribution should be normal and mean and median should be similar."
    

*I won't name the institution here. Let's just say you've heard of it.
That last site approaches farce, and it's trying to teach statistics!. This is often what happens when people whose own area is not statistics get put in charge of teaching it. (For some reason mathematicians are among the worst offenders.)

There were more examples. The above ones are pretty standard.

Not fooling ourselves (I) - the unmeasuring of asymmetry

In order to impose some kind of structure on our understanding of complex phenomena, we tend to use simple terms to describe what may be surprisingly nonsimple.

In order to make progress, we often attempt to quantify those descriptives. This is not just useful, it's often unavoidable, but the act carries with it a special danger, because we then (almost universally) invest the nonunique quantification of the concept with a "reality" that it doesn't merit - and that can lead to nonsense.

[It may be this is another version of the common phenomenon of believing mathematical models when at the beginning we knew them to be at best a rough approximation. Models tend to take on a life of their own, and their conclusions are often treated with a respect we did not accord the original model when it was first tentatively adopted. We need to step back and remember the model was never exactly the thing it was used to describe.]

I think this may be the flip side of what Blake Stacey was talking about when he was discussing the confusions that come in when an inherently mathematical concept is translated into a nonmathematical description.

Let me take a concrete example with which I am familiar. It relates to descriptions of probability distributions.

We begin with something that is inherently mathematical - symmetry. Symmetry is an extraordinarily useful, almost universal concept in mathematics. For what I'll be talking about you can just use the more common senses of reflection symmetry and rotational symmetry.

In the case of symmetry of distributions, there are several ways to define it (if you have a continuous or a discrete random variable, you can define it in the usual "mirror symmetry" sense), but the more general definition would have something like "m is the centre of symmetry if Prob(X≤ m-a) = Prob(X≥ m+a) for all a" (which effectively corresponds to rotational symmetry of the distribution function about the points (m, 1/2), if you tidy up details the right way).

Anyway, "symmetry" is both easily understood and fairly easy to pin down. Of course, almost all distributions are not symmetric (but symmetry arises in a natural way in particular circumstances, so it's far from a useless concept).

Aside from "unimodal" (one "hump"), or the overused and badly abused "bell-shaped", one of the most common descriptions of a distributional shape that is applied would probably be "skewed". An elementary book might have a diagram like the top one below (see for example, the diagram at Wikipedia's entry on skewness). The corresponding distribution function is underneath.

Diagram of a right (positive) skewed density and distribution function.

If you flipped the above density left-to-right (or rotated the distribution about the median), it would have left (negative) skewness.

Notice that "right skewed" means the long tail is to the right (this is often the opposite of a beginner's intuition about what the term should mean).

The problem comes when this seemingly clear but actually vague notion is quantified. There are numerous quantities that have been called "skewness". By far the most popular is the standardized third moment (or, equivalently, the standardized third cumulant) - so much so that it is frequently called "the" skewness. Equivalent sample statistics are used for samples.

Now for a distribution like the one above, this quantity is positive (when it exists). If you flip that density shape left to right, the skewness measure is negative. Importantly, when the density is symmetric and the first three moments exist, the skewness is 0. So far so good - left and right skewness and symmetry in pictures generally correspond to negative, positive and zero quantities on the measurement.

However, the problem comes when interpreting a standardized third moment back in terms of the density.

A positive number will lead people to call the distribution "right skew" without looking at it. A number near zero will cause people to call the distribution "symmetric". In the first case, the distribution will be asymmetric but it may not appear to be skewed with a tail to the right. And the value can be exactly zero without the distribution being symmetric. While symmetry implies zero third moment (if it exists), the implication does not go back the other way.

Consider a fair six-sided die with the following labels on its faces: 0, 0, 5, 5, 5, 9. The distribution of outcomes is not symmetric, yet its "skewness" measure is zero. Unfortunately, based only on the information that the third central moment was zero, many people would in fact describe it as symmetric.[Added later: here's one that most people would say on inspection was "right skew" - an ordinary die labelled 0, 0, 5, 5, 7, 10. But the third central moment is zero.]

Other examples, both continuous and discrete, abound. Continuous asymmetric distributions exist for which all odd central moments are zero.

Other measures of skewness (and there have been many) also have their problems, though some are very useful.
The sort of problem described here is essentially unavoidable - there are so many ways a distribution may be asymmetric that a single measure of asymmetry cannot possibly suffice, except perhaps within the framework of a particular family of distributions.

This cautionary tale is not an argument against using measures like the third central moment to attempt to capture something of deviations from symmetry - it's an argument against investing them with more than the limited meaning than they posses.

Tyson

Saw Neil deGrasse Tyson on Colbert last night.

He was very quick with his response to Colbert's bit about "Goddiddit" ("You can say that, but then you can't find out anything," if memory is working okay).

Then again, I guess he's been on enough to know it was coming.

Is the man hot, or is it just me?

(Link now goes to correct segment, not just the right show, so you don't have to find it in the list.)

Ecstathy in Wordle

click for larger version

Am I A Positive Atheist?

I wrote a longer version of this post, but it has been eaten by a grue. This one is different.

I was about to start writing the first version of this when I noticed that Dana asks "What kind of atheist are you?". An interesting coincidence, because in some way this post is related.

I must admit a certain amount of confusion with the term "positive atheism". I don't see atheism as inherently positive or negative. (I see the step of throwing off irrational faith in favour of reality as a positive one, but that's a benefit of becoming an atheist, not of being one in the sense that it's not an active process.)

Being an atheist, living as an atheist, is neither positive nor negative. You can live a positive life, or a negative one, or anything in between, and be an atheist. Atheism is orthogonal to positivity.

This might seem incongruous, given I just had a post in the 21st Humanist Symposium. Humanism is the sort of philosphy people tend to associate with "positive atheism" and the Humanist Symposium's brief is definitely about living positively, but humanism and atheism are quite different - many atheists are humanists, and many others are not. Many humanists are also not atheists. But, nevertheless, many atheists are attracted to humanism. I agree with many of its tenets, but I don't see humanism as connected to atheism, so to me it's not really "positive atheism", it's just humanism, and neither is necessary to the other. Similarly, my post was about using probability to figure out that some apparently worrisome things may be nothing to worry about, and that an understanding of probability could help lift burdens of worry from our lives. But again, it's not atheism that's doing that. Atheism's job came earlier, in removing the attempt to explain such events as the acts of an incomrehensible and all-powerful god (the positive step of becoming an atheist). With that non-answer out of the way, there is room for the rational explanations of probability to make their positive contribution. So it is with humanism and other positive worldviews that many atheists have.

I'm generally a very positive and content person. I happen to be positive, and I happen to be an atheist.

But the phrase "positive atheism" (and for that matter, all the negative epithets theists throw at atheism) just doesn't have any more resonance for me than "yellow music" does.

The fate of the planet may depend on it!

Scott Aaronson of Shtetl Optimized explains why safety considerations demand that we must turn on the LHC right away!

The tale of "The square root of a rectangle"

Wow. Just wow.

I was just flicking through channels and caught a little of "Engineering an Empire" on the History Channel. The episode was on the Maya.

The narrator said something about the Maya knowing how to "compute the square root of a rectangle".

I was so boggled, I concluded I must have misheard - but no, it was repeated a minute or so later. It was emphasized; apparently we were expected to find this an impressive feat.

The Maya, apparently, knew how to compute the square root of a rectangle. That's pretty clever of them, because that, as far as I can see, is utter nonsense.

As Inigo Montoya might have put it: I do not think it means what you think it means.

I wondered if they meant "compute the hypotenuse of a right angled triangle" (which is equivalent to the diagonal of a rectangle). I also wondered if perhaps they meant "the geometric mean of two numbers" (since that would be the square root of the area of a rectangle). I also wondered if they possibly intended something else.

I concluded they probably meant the first thing (since that's a very valuable thing for a civilization to be able to do, crucial to surveying land - and then they had a shot of a Mayan guy squinting across the top of a stick as if he was indeed surveying). So that would kind of make sense.

But what the heck is someone who isn't comfortable with mathematics supposed to make of it?

The show was no cheap-and-nasty affair. They made some pretty fancy graphics. They had actors dress up in costumes, and they had some pretty fancy sets and location shots. This was a pretty involved documentary. Why the hell couldn't they have had the script looked over by anyone with even a modest bit of mathematics? Say, a mathematics undergrad? (Heck, I could have told them that was obvious nonsense before I was 16.)

That bit of (repeated, emphasized) mathematical nonsense is enough to make the entire program suspect - because if they were that lax with the mathematics, who knows what care was taken with the rest of it?

A misplaced sense of self-importance (II - you ain't so special)

(Part I is here.)

If deflating misplaced self-importance in hypocrites is a good thing, we should be prepared to deflate our own as well.

Fortunately this is easy. The universe is happy to disabuse us of any sense of importance, if we're prepared to listen to it. Here's a few examples from the last few days:

Other apes can plan for their future needs just as we humans can – by using self-control and imagining future events.

At the same time, our human sense of empathy is nothing special either. Chimps calm each other after an attack with hugs and kisses, in the same way that humans do.

Our memory of what happens to us is not as good as we think

And we may (just possibly) be in for a biggie - since there's ice on Mars, the chances improve substantially that one day we'll find evidence of life there in the past. There will be good reason to think that the universe is filled with life. We would know, then, that life just tends to pop up whenever the conditions are suitable.

Which I find is kind of a cosy feeling.

A misplaced sense of self-importance (I: "elitism"-ism)

A month ago, I made the point that accusations of elitism tend to come from people who are in fact from an elite group themselves.

Whether it's to deflect attention from their own situation, or an attempt to "get in" with a group to which they do not belong, or simply an attempt to shut up a message they don't like, or for some other reason, it's a common occurence.

This was recently brought home by the ironic situation of David Brooks of the New York Times claiming "Obama had a problem" because he wouldn't be comfortable with the people at an Applebee's. Except Brooks fucked up, showing he's completely ignorant of what can be found at an Applebee's himself.

This is not an occasional happenstance - the "charge" of elitism always seems to come from a member of some elite. It's hypocrisy writ large - writ large because the stakes are usually big.

They're making another person or group scapegoats for a "crime" that they themselves are guilty of, in order to incite support among a group of people to which they simply do not belong.

[And really, it's not such a surprise that this is almost always the case. An ordinary Joe doesn't use a word like elite. It's insufficiently exoteric (as are words like "insufficiently" and "exoteric" - the irony isn't lost on me, but at least I've linked to a definition - I may be an elitist bastard, but anyone's welcome to join me!)]

I'm almost tempted to call this a law:
(1) If a person calls another an elitist, they are almost guaranteed to be a member of a social, economic or political elite themselves.

If that law is true, it carries with it something like Godwin's law as a corollary -

(2) the first person to level a charge of "elitism" is a loser

The appropriate response is to simply indicate that we know the speaker is hypocrite - a loser of the worst kind. Let them know you're onto them. You know you want to.

I think this hypocrisy comes from a misplaced sense of self-importance - that the rules they play by don't apply to them. Helping deflate that sense of self-importance is a public service.



(Image from Demotivate Us)

(Part II is here.)

Cectic's take on the atheist billboard

Regular readers will have seen my take on the atheist billboard hullaballoo:

(click image to embiggen)


Cectic has a terrific comic on the same issue.

(Displayed here with permission.)

Be careful what you wish for

One thing the Republicans have done over the past couple of decades is increasingly polarize the electorate, and really put effort into the politics of hate. That's a popular strategy with totalitarian governments, because it gets people looking the direction you want them to (anywhere but at what you're actually doing).

It worked, as it usually does. Among other things, they pandered to what they call "values voters". The thing is, people on both "sides" of politics (an oversimplification if ever there was one) vote their values. The Republican fear-mongering grabbed a bit of the middle as well, and so it worked well - a die-hard core plus a good chunk of the ordinary everyday person, at the expense of the people who are less likely to vote for you will get you power - for a time.

But the problem is that the people they have upset the most are growing, while the people that they're relying on are both shrinking and abandoning(1) them(2) in revulsion(3). Young voters, in particular, are increasingly secular, and that's a problem for Republicans, because they have attacked the secular and their values at every turn.

The Republicans are beginning to reap what they have sown.

Blogger Nate at FiveThirtyEight talks about the problem McCain has with nonreligious voters.

The religious only slightly favour McCain over Obama. The nonreligious overwhelmingly favour Obama. As time goes on, unless the Republicans move toward the centre, they're going to increasingly lose the now-secularizing middle, and their history of vile attacks on them won't be quickly forgotten. If they do move toward the centre, they'll lose what remains of the right-wing evangelicals. Things are not looking good for the Republicans in the next 3 or 4 elections, unless they can completely reinvent themselves. I don't think they'll be able to do it.

They could stew for a generation in the cesspit they've dug for themselves - and they'll still stink less than they do now.

Weekend news

A couple of items from the local news over the weekend:

Obama has the confidence of people in Europe, Asia, Africa and Australia and is strongly preferred as president over McCain

"In Australia, 80 per cent of participants said they had confidence in Senator Obama, against 40 per cent for Senator McCain. Similar results were reported from Britain, France, Germany, Spain, Japan and Tanzania."


The secretive religious group at the heart of US politics

"The Family organises Washington politicians into intimate "prayer cells", influences foreign policy, inspired the creation of the president's annual prayer breakfast in 1953 and sponsored George Bush's faith-based 2001 policy of transferring social welfare responsibilities to religious groups."

Read about them, and be scared. Or angry. Or both. But know they they're there, and they may well be behind a lot of what you really hate about what goes on in US politics. They're the elitists we should be fighting against.

Technorati blog claim

Taking vjack's advice and trying to add my blog to Technorati - here I'm claiming my blog there ... so here goes. There's my Technorati Profile.

Edit: Currently not showing my blog under blog tags nor my posts under post tags. A lot of effort for zip so far. Now seems to work thanks to admin assistance

A possible place to look for an explanation for religious belief?

Dana has a review of Julie Sweeney's movie Letting Go of God.

Now, on a completely unrelated note, there are various potential explanations that have been suggested for the fact that religious belief is very common - generally either taking the form that it in some sense carries a social benefit, or that it is a side effect of something else (or an interaction of several somethings) that carry a benefit. Some of these explanations have some evidence for them, though I don't think there's really conclusive evidence that any of them forms a complete explanation.

Anyway, something Dana said brought up a thought:

She doesn't ever state this directly, but the end of the movie talks about her daughter reaching for magical explanations when Julia's trying to explain things like death in rational, material terms. And that struck me: religion is never growing up. What her daughter invented to make herself feel better about things she didn't understand sounded exactly like the answers most human religions invent.

We as a species have never seemed to mature past the age of four.

And then I thought... if you add in the "invisible friends" bit, you've got a couple of indicators of development typical of maybe a three year old.

That reminded me of neoteny - the retention of juvenile characteristics into adulthood. This is a common evolutionary trick - rather than change an underlying gene, alter the timing of its development - it's generally going to be a much smaller change (this sort of idea should be standard fare for the evo-devo crowd, but I first encountered the concept in one of Dawkins' books, many years ago), but the effects can be dramatic.

Humans are "masters" of neoteny. We retain dozens of juvenile-ape characterstics. It's why our faces tend to be almost hairless. It's why we play games and retain curiosity into adulthood. It is one of the major drivers of our success; it is, not to put too fine a point on it, a prime cause of why we are who we are: I gather chimp brain development continues until about 1 year of age. In humans it lasts until we're about 23!

Is it so surprising then, that certain mental development characteristics of toddlers might hang on? If our evolution has caused us to so dramatically retain certain juvenile aspects of brain development, might associated mental milestones tend to come along with them?

Is religious belief a side effect of neoteny?


If speculation is not to your taste, have some (tangentially related) science - on genes in humans that have shown a much higher rate of evolution since our last common ancestor with chimps - what potentially makes us what we are.

Any day now...

(click comic for a larger version)

Adding percentiles means there's probably more oil than we thought

Isabel Lugo has an interesting post up that points out that because "proven reserves" figures for individual oil fields are given as the tenth percentile (that is, the amount of oil in a field is estimated to have a 90% chance of being larger than the stated amount), you can't just add up the individual "proven reserve" figures and have a figure that means the same thing. But apparently that's exactly what many bodies do with the figures!

(She refers to this New Scientist story.)


Isabel gives an example where adding two tenth percentiles gives much lower than the tenth percentile of the estimate of the total oil for both (with the implication that if you add enough of these things together, the true amount of oil is probably far, far larger).

[I pointed out in comments that the conservatism in the sum is not necessarily the case (but for readers here - it very likely is the case; the counterexample to conservatism that I give is not a likely situation).]

Changing patterns of belief

A very interesting article on falling rates of belief (in percentage of population terms).

I'm not sure the evidence is completely clear for a few things they say, but overall gist looks pretty solid.

Sign of the tomes

(click image to embiggen)

Scary atheists

Ebonmuse has an interesting post up at Daylight Atheism, about what's going on with the sense of distrust believers feel for atheists.

I disagree with some of it, but it's a great post, and brings up some great points.