Wednesday, April 30, 2008

Democrats Driving Up Gas Prices

Gateway Pundit has an excellent summary of all the ways in which Democrats are manufacturing an energy crisis to please their environmentalist constituents.

A Republican presidential candidate would trumpet this news in his campaign. Too bad there isn't one.

In other news, I logged in to today and was greated by the news that my blog had been locked:

The ease of creating and updating webpages with Blogger has made it particularly prone to a form of behavior known as link spamming. Blogs engaged in this behavior are called spam blogs, and can be recognized by their irrelevant, repetitive, or nonsensical text, along with a large number of links, usually all pointing to a single site.


Somewhere, Spungen is laughing her ass off.

Saturday, April 26, 2008

Another War on Poverty?

"McCain Vows [Another] War on Poverty"

"Government has a role to play in helping people who, through no fault of their own, are having a hard time," McCain, an Arizona senator, said. He defined that role as offering choices on education, health care and job training, rather than providing handouts.

If "offering choices" means "giving people stuff" or "subsidizing stuff", how is this not a handout?

Elsewhere, the article says that McCain doesn't want another Johnsonian "Great Society" program, but all this particular article implies about where McCain departs from it is this:

Government "can't pay lost wages. It can't dig coal from the earth," McCain, 71, said. "It can't buy you a house or send all your kids to college. It can't do your work for you."

Wait a second . . . didn't McCain just say that the government should offer choices in education? Meaning what, if not paying for college?

Let's step back and assume that McCain sees healthcare, education and job training as capital investments, whereas "handouts" refer to current consumption. Let's also stipulate that it is appropriate for the federal government to undertake these expenditures on behalf of individuals. I still have a few questions:

1. Are there any actual studies supporting the notion that such unemployment as we have is structural, ie. the result of a mis-match between existing worker skills and job requirements?

2. Can we reasonably assume that the unemployed have the necessary personal, um, infrastructure to support the education and training on offer? I don't want to be unkind here, but it doesn't do much good to say, "Sorry that your sheet-rock hanging opportunities all dried up, but there's great demand over here for quantum-physicists [let's say]. All you need is some job training!" You get my point.

3. Then there's health care. I would be surprised if McCain's diagnosis of "lack of affordable healthcare" runs any deeper than that the government should help pay for it. In which case, how is the government going to find the money to do this in a sustainable way?

But the fact is, I'm giving McCain way too much credit here. It is obvious from these remarks that McCain has no damn clue what he is talking about. He no doubt thinks that his gestures at the Great Society as something we DON'T want to do sufficiently distinguishes him from the Democrats, but the rest of what he says only concedes rhetorical ground to his opponents.

How much better would it be if he forsook the micro-initiatives and developed a coherent set of policies addressing the macro-conditions that make America a good place to create jobs in the first place. Stuff like: fiscal policy, monetary policy, regulatory policy, trade policy, and, oh yeah, immigration.

Here is an example of the kind of thing I have in mind:

Apartment hunting site cannot shield itself from an housing discrimination lawsuit by claiming it is just an internet forum, because the site requires users to answer questions about their gender, marital status and sexual orientation, the 9th U.S. Circuit Court of Appeals ruled Thursday.

It should be glaringly obvious, even to those of you who think that it is any of the government's business who I rent or sell my house to, that individuals advertising for roommates are not what the Fair Housing Act had in mind by regulating "housing providers". But somehow this obviousness excaped the Ninth Circuit, which exists to take the most expansive view possible of the Civil Rights Laws.

So let's assume that a couple of guys who put up a website can take the time to wade through thousands of pages of federal code, and thousands of pages case law. They can STILL get screwed by a bunch of lawyers who come up with a NEW way to interpret the law!

Multiply this by about one million, and you begin to have some idea of the regulatory environment facing business in America. It's not just that the regulations are onerous, although they are. It's that it is extremely difficult to quantify the risk analysis of a business model. No wonder, then, that nobody wants to create jobs here.

It's pretty obvious to me that these have been badly managed for the last 8 - 20 years. The only thing that can be said on McCain's behalf is that his recommendations probably won't make the macro-conditions appreciably worse. This contrasts favorably with the Democrat plan to actively drive the economy into the ditch.

Friday, April 25, 2008

As a slumlord, I would probably qualify as "overexposed" in the housing market. But I am morally certain that taxpayer-funded bailouts of greedy and foolish investors, lenders, and home-buyers (including me) are both bad economics and grossly unfair to the millions of people who recognized the housing bubble for what it was, and would very much like to purchase a house at proper market pricing. But the end result of the bailout they are being asked to pay for is to prop up the inflated prices--doubly screwed.

So it is with enthusiasm that I recommend the website The website will give you an opportunity to sign a petition to Congress asking it to let the free market fix the housing "crisis" on its own, and specifically to refrain from any bailouts.

WHEREAS: Most Americans rent or own their home outright, and the vast majority of homes (98%) are not in foreclosure.

WHEREAS: Both banks and borrowers should be reponsible for their actions, and the government should not reward reckless behavior.

WHEREAS: It is wrong to force all taxpayers-- including renters who are already subsidizing home owners through the tax code-- to pay for additional bailouts for big banks and home flippers.

BE IT RESOLVED: That Congress should not pass any bailout programs that reward risky borrowing and lending. Let the free market sort it out!

Tuesday, April 22, 2008

A Derivation of the Variance for the Poisson Probability Distribution

Last week, I searched that Font of All Wisdom, the internet for a derivation of the variance of the Poisson probability distribution. The Poisson probability distribution is a useful model for predicting the probability that a specific number of events that occur, in the long run, at rate λ, will in fact occur during the time period given in λ.

For instance, let’s say that you are waiting at a bus stop for a bus that is known to come at an average rate of λ equals once per hour. But there is no schedule, and you are not guaranteed that the bus will come by exactly once in the next hour. It might come by two or more times, or it might not come by at all. So what is the probability that it comes by k times in the next hour? The probability is given by: where “e” is an irrational number that equals approximately 2.718, and the exclamation point is the factorial function, where k! = k(k-1)(k-2)…(2)(1), all multiplied together. (Note: 0! = 1, for some strange reason.) Wikipedia has an acceptable derivation of this formula, so I will not reproduce it here. Applying this formula to our example, the chance that a bus whose average arrival rate is λ = 1 visit/hour will not come by in the next hour is P[#visits = 0] = 10e-1/0! = e-1 = 0.368 = 36.8%. The chance that it will come by exactly once in the next hour would be P[#visits = 1] = 11e-1/1! = 36.8% as well. The chance that the bus will come by exactly twice is P[#visits = 2] = 12e-1/2! = 18.3%. These probabilities continue to diminish for increasing numbers of busses predicted to come by in the next hour. As you might expect, the sum of these probabilities = 100%; you are guaranteed that zero or more busses will visit your bus stop in the next hour!

A more useful probability would be, what is the probability that one or more busses will come by in the next hour? Because the probabilities sum to 100%, the math can be done thusly: P[#visits ≥ 1] = 100% - P[#visits = 0] = 100% - 36.8% = 63.2%.

But what if you don’t want to wait an hour? What if you want to catch a bus in the next 15 minutes? This can be easily done by subdividing the rate λ. A bus whose average visit rate is once per hour also has a average visit rate of ¼ visits per 15 minutes. Again to our formula: P[#visits ≥ 1|λ = ¼] = 100% - P[#visits = 0|λ = ¼] = 0.250e-0.25/0! = e-0.25 = 100% - 77.9% = 22.1%. Considerably lower probability for a visit in the next 15 minutes.

What if we want to know the average number of busses that will come by in the next hour. Answer: duh! We already told you that the busses come by at rate λ = 1 bus per hour! But let’s derive this from first principles.

To start, we must remember the Taylor Series expansion for e: Because the factorial function is undefined for arguments less than zero, the summation is independent of indices less than zero. Thus: etc.

We also need the definition of the mean, or expected value μ = E(N) of a quantity N whose distribution is defined by P(n). This definition is: μ = E(N) = ∑nP(n) for all n. We can apply this formula to calculate the mean of the Poisson distribution: As expected.

But what about the variance? The variance is a measure of how far a typical result will depart from the average result. In our example, for instance, we know that, on average, we can expect one bus to visit the bus stop each hour. But that number could be zero busses, or it could be multiple busses. So how much variation can we expect? The standard deviation σ is the average that we can expect a particular number of busses to vary from the average number of busses. The variance is the square of the standard deviation, or σ2. It is defined thus: σ2 = E[(N – μ)2 = ∑(n – μ)2P(n) for all n. Applying this formula to the Poisson distribution: So, the variance of a Poisson distribution with average rate λ is . . . λ.


BLEG: I created the post above on my Dell laptop. I composed the equations in MS Word 2003's MathType, and saved the document as an HTML file. This created the .gif files containing the equations that you see above. But when I tried follow the same process using my desktop computer, When I tried to create the webpage using the exact same methodology, except on my desktop, the equations came out looking like this: Relatively ugly. Clearly, there is some setting that is set correctly on my laptop that is set incorrectly on my desktop, but I don't know what it is. Please help.

Sunday, April 20, 2008

Razib on FLDS

Outstanding piece by the great Razib on the Texas mess. An excerpt:

The emblematic violation of those norms was of course plural marriage, polygyny. I don't think that plural marriage is wrong like murder is wrong, but the social dynamics which emerge from its ubiquitous practice among the FLDS are well known, and I am skeptical that the practice is conducive to the perpetuation of a bourgeois republic. Even within the Muslim world modernizers are very critical of polygyny because of the familial destabilization it portends. In a world where time is finite one can make quick back of the envelope inferences about the effect upon parental inputs in a situation where one man fathers dozens of children with multiple wives.

Saturday, April 12, 2008

What does this say about Φ?

Which of the young women shown above is prettier?

Here we have the faces of two women, the differences between whom are so subtle that I cannot articulate them. And yet, there is no question that the girl on the right is the prettier of the two.

According to this Reuters story, the two pictures are composites created from a population of women separated into two groups based on a single survey question: would you consider a one-night-stand?

The composites then became part of a survey of men, who were asked to guess which of the two would answer "yes" to being agreeable to a one-night-stand. And guess what? Seventy-two percent of the male respondents correctly identified the image on the right as belonging to women who were open to a one-night-stand.

At a conscious level, I would have no idea what features identify women with loose morals. But I wonder: what does the fact that Φ is more attracted to such women say about him?

And if this bias is widely held, as it appears, what does it say about our standards of beauty? And how much does this explain why the ranks of movie stars, selected for their beauty, also wind up behaving with such . . . immorality?

Thursday, April 10, 2008

Does Culture Matter?

A few weeks ago in Sunday School, we watched a video* of a lecture by Voddie Baucham, who addresses the question of why we believe thusly:

"I choose to believe the Bible because it is a reliable collection of historical documents, written by eyewitnesses during the lifetime of other eyewitnesses. They report supernatural events that took place in fulfillment of specific prophecies, and they claim to be divine rather than human in origin."

Mr. Baucham, a very dynamic speaker, here makes reference to the vastly more abundant and authentic accounts contained in the Bible, compared to the much thinner support for other historical texts that we take at face value:

AuthorDate WrittenEarliest CopyTime SpanCopies (extent)
Secular Manuscripts:
Herodotus (History)480 - 425 BC900 AD1,300 years8
Thucydides (History)460 - 400 BC900 AD1,300 years?
Aristotle (Philosopher)384 - 322 BC1,100 AD1,400 years5
Caesar (History)100 - 44 BC900 AD1,000 years10
Pliny (History)61 - 113 AD850 AD750 years7
Suetonius (Roman History)70 - 140 AD950 AD800 years?
Tacitus (Greek History)100 AD1,100 AD1,000 years20
Biblical Manuscripts: (note: these are individual manuscripts)
Magdalene Ms (Matthew 26)1st century50-60 ADco-existant (?)
John Rylands (John)90 AD130 AD40 years
Bodmer Papyrus II (John)90 AD150-200 AD60-110 years
Chester Beatty Papyri (N.T.)1st century200 AD150 years
Diatessaron by Tatian (Gospels)1st century200 AD150 years
Codex Vaticanus (Bible)1st century325-350 AD275-300 years
Codex Sinaiticus (Bible)1st century350 AD300 years
Codex Alexandrinus (Bible)1st century400 AD350 years

(Total New Testament manuscripts = 5,300 Greek MSS, 10,000 Latin Vulgates, 9,300 others = 24,000 copies)

(Total MSS compiled prior to 600 AD = 230)

(Note: I observe that the last two columns don't fit on the blog. Click the link for the rest.)

Now all this strikes me as pretty compelling in its way. But I have to ask myself: if I didn't know all this, would I still believe? I would; indeed, I did: upon hearing the gospel, I simply believed, and without asking for proof or evidence beyond the power of the message itself. And furthermore, if you assented to the bare facts cited above, this wouldn't make you a Christian.

In fact, I can't account for my faith in human terms at all, nor would I try. Evolutionists hear my testimony, and reply that this is strictly a neurological phenomenon, the evolved response of our brains to (1) natural selection favoring a hypertrophied social intelligence at the individual level, and to (2) social selection favoring collective mythologies that discourage free-loading and establish ingroup solidarity at the social level. Like I always say, that's probably part of the story. But it's not the entire story; according to theShorter Catechism:

Q. 31. What is effectual calling?

A. Effectual calling is the work of God’s Spirit, whereby, convincing us of our sin and misery, enlightening our minds in the knowledge of Christ, and renewing our wills, he doth persuade and enable us to embrace Jesus Christ, freely offered to us in the gospel.

Or the Bible itself:

And you were dead in the trespasses and sins in which you once walked, following the course of this world, following the prince of the power of the air, the spirit that is now at work in the sons of disobedience—among whom we all once lived in the passions of our flesh, carrying out the desires of the body and the mind, and were by nature children of wrath, like the rest of mankind.

But God, being rich in mercy, because of the great love with which he loved us, even when we were dead in our trespasses, made us alive together with Christ—by grace you have been saved—and raised us up with him and seated us with him in the heavenly places in Christ Jesus, 7so that in the coming ages he might show the immeasurable riches of his grace in kindness toward us in Christ Jesus.

"Dead in the trespasses . . ." With respect to Mr. Baucham, dead things don't choose to believe. Dead things don't choose anything. Dead things just lie there, rotting and stinky. God is the one that calls us to and enables our faith.

I was put in mind of all this upon reading Bobvis' account of his adherence to Hinduism:

As a man of science, I believe that there are mystical experiences that are:

  1. marked by pure joy
  2. marked by blinding clarity
  3. marked by a calming sense of connectedness with the world
  4. repeatable
  5. accessible

He quotes the great Razib Khan, who writes:

Reading the Bhagavad Gita, I am struck (as usual) by commonalities between mystical philosophies rooted in a method of psychological introspection and meditation . . . . The heightened consciousness of mysticism and the sense of the One is probably reflecting underlying neurological realities.

Now, both Bobvis and Razib are smart guys. Bobvis has an above-average understanding of the fundamentals of Christianity, and Razib, truth be told, probably knows the Bible better than I do. Having said this . . . I read at the Bhagavad Gita**, and the nicest thing I can say about it is that it is not culturally accessible to me, nor did it induce any mystical experience, repeatable or otherwise. But then, I'm not really in the market for a calming sense of connectedness with the world, or even its analogue within the Christian tradition. One could fairly say, "but you haven't tried it!" Alas, I can no more summon a felt need for mystical experience than a Hindu can summon a felt need for substitutionary atonement. And since the stakes in Hinduism are otherwise fairly low (Bobvis: straighten me out on this), it will have to be an opportunity I let pass by.

I felt the same way about the Koran***: as John Derbyshire once noted, it has no narrative thread, and such profundities as it may contain were not accessible to me. So, Islam spreads by (1) demographics and (2) the sword. Like Hinduism, it's appeal outside of its native cultural mileu is, shall we say, highly limited.

Christianity arguably enjoys the broadest cross-cultural penetration, which proves . . . nothing, or a whole lot, depending on your perspective.

*Footnote: We don't usually do videos in church, which I would find very . . . Baptist.

**Footnote: I was mainly curious to find the passage allegedly quoted by J. Robert Oppenheimer at the culmination of the Manhattan project. I decided that I didn't know what "I am become death" means exactly, but I was pretty sure it doesn't mean, in context, what Oppenheimer thinks it means.

***Footnote: I was checking on all those passages about killing Jews. I am inclined toward humility about my exegetical skills on others' sacred texts, but that is the subject of another post.

What is it for?

Bobvis retails a WSJ report on the hookup culture in universities, when Trumwill throws a grenade in the comments:

I would be hesitant to dedicate myself to a young lady that had chosen to save herself for marriage. Not because I don't think that is an honorable thing to do (in fact I would greatly admire the discipline), but because I would I would be concerned that she had some sexual/religious hangups about sex in general (even after marriage) and that the not-married rationale was a cover or stalling tactic.

Naturally I asked:

Do you have stats?

He didn't, but then neither do I. After googling around for an hour, I came up with three studies that might address this, but they are tucked inside pay-per-view journals whose prices exceed my motivation. So, lacking data, I will here attempt to engage the model at an intuitive level.

The substantive question before the house is: Does a woman's desire to remain chaste indicate "frigidity," defined here as a lack of interest in or a distaste for sex. This question would lead to a testable hypothesis: does the extent of a woman's premarital sexual history (number of partners, frequency of sex per partner, etc.) correlate positively or negatively with the frequency of sex in her eventual marriage.

I will begin with the following concessions:

1. The general expectation in favor of chasity has largely perished from the broader culture. The specific religious worldview(s) from which the injunction to chasity flows is not universally held. And few people (certainly not I) believe that chasity is "natural" (as opposed to a civilizational artifact). In this context, a woman without any apparent religious affiliation who wants to wait for marriage "just 'cuz" is plausibly indicating a low sex drive. (She is also plausibly indicating a lack of physical attraction for a particular class of suitors, a separate issue.)

2. A shared religious and moral worldview is important in a relationship. An expressed preference for chasity could well indicate a larger incompatibility with a man who doesn't share that preference.

But on the other hand.

1. There are larger considerations. The elephant in the living room is the amply documented connection between pre-marital sex/cohabitation and post-marital adultery/divorce. From a proper religious understanding of sex, it is not hard to understand why. Sex has been given to us to bond us to another person: "the two shall become one flesh." Much as sticky-tape, once applied and ripped away, loses its stickiness, so too will the sex act, repeatedly applied and then ripped away, eventually lose its ability to perform the bonding function.

2. There are other background variables. Fact: with few exceptions, men have higher sex drives than women. Thus, few men will find a woman whose interest in having sex matches their own. Plus, we get old. We get busy and stressed with the business of managing a communal life, especially when children enter the picture. We get tired. Eventually, we get rather ugly. None of these things is conducive to a woman's sex drive. In light of all this, I would much rather choose a woman with a proper understanding of her covenant duties* with regard to sex than attempt to tease out the predictive value of a woman's sexual past on how often she'll be as ready as I am to take a roll in the hay ten years into the marriage.

3. Trumwill, specifically, wants to draw the following distinction:

My personal preference is for sex to be reserved for stable, monogamous relationships. I've not advocated anything else. To the extent that I differ from Phi (and apparently you), it's that I don't believe that marriage is necessarily a precondition for it.

Trumwill subsequently defines stable as "a year or two". I'm not impressed. As Bobvis points out in the subsequent post, this deal really bites from a woman's perspective. On the one hand, she is to save sex for stable, committed relationships. But she must embark on a one- to two-year trial wherein she must prove her sexual athleticism. In the mean time, she can be overturned at any time for any reason. So . . . "stable" and "committed" in this context really mean temporary and contingent, undermining the stated conditions under which she is expected to have sex in the first place. Trumwill is undoubtedly arguing in good faith here, but ultimately, this circle cannot be squared.

Update: In the comments, Trumwill takes issue with my interpretation of his words. The discussion continues . . . .

*Footnote: Inevitably, the usual people will try to spin this as saying that a man has a right to demand sex from, or force sex on, his wife. I will pre-emptively point out that this is not what I wrote, nor what I believe.

Sunday, April 06, 2008

Brief Thoughts on Season 4

As all bitheads already know, the first episode, "He That Believeth in Me," of the final season of Battlestar Galactica played Friday night.

It would be hard for the writers to under-do season three, which could have been titled, "As the Galaxy Turns" or "Space of our Lives", what with the endless soap opera between Sam/Kara/Lee/Anastasia, or Helo's moral self-indulgence, or any of the other displays of the character's inner mawkishness.

And yet, I'm afraid this season's weakness will be that the show starts to buy too heavily into its own eschatology. Don't get me wrong: the religious content of the show was always, for me, a primary source of its appeal. In contrast to the Gene Roddenberry universe, which condescends to the religions it bothers to notice, religion is a vital part of BSG life, both to the individual characters and, more interestingly, as a social phenomenom.

Wisely, in my view, the show has heretofore muted its efforts to resolve the rival truth-claims of the various religious systems vying for loyalty. Wisely, not because religion can't be metaphysically true -- unsuprisingly, I believe it can -- but because the actual content of show's religions is made up by its creators. Usefully, the show demonstrates how religion can work in everyday life. It would be somewhat less useful for it to attempt to resolve whether the Colonists' made-up Greek Pantheon or the Cylons' made-up monotheism is more faithful to BSG's made-up reality. At the end of the hour, it's just a T.V. show.

And yet, this is exactly what the final season is setting itself up to do. The resurrection of Kara Thrace presents the audience with a bona-fide supernatural event that begs to be resolved. Unless the re-appeared Kara is either a Cylon-cloned copy of her original self, or one of the Final Five, then some other "higher power" in the BSG-verse must make itself known, and render a verdict on his/her/its own apprehension by the other characters. And so what? It's all made up!

Someone might object that for the show to present its own version of metaphysical religious truth would be nothing that, say, LOTR or Star Wars didn't do as well. However, the supernatural (or, perhaps, subnatural, in the case of Star Wars) reality was never a point of contention in these movies. Good and Evil battled for power within an acknowledged spiritual framework. The facts were not in dispute. Not so with BSG.

Here is Half Sigma's take.

Saturday, April 05, 2008

The Wisdom of Robert Frost

From "The Black Cottage":

Do you know but for her there was a time

When to please younger members of the church,

Or rather say non-members in the church,

Whom we all have to think of nowadays,

I would have changed the Creed a very little?

Not that she ever had to ask me not to;

It never got so far as that; but the bare thought

Of her old tremulous bonnet in the pew,

And of her half asleep was too much for me.

Why, I might wake her up and startle her.

It was the words ‘descended into Hades’

That seemed too pagan to our liberal youth.

You know they suffered from a general onslaught.

And well, if they weren’t true why keep right on

Saying them like the heathen? We could drop them.

Only—there was the bonnet in the pew.

Such a phrase couldn’t have meant much to her.

But suppose she had missed it from the Creed

As a child misses the unsaid Good-night,

And falls asleep with heartache—how should I feel?

I’m just as glad she made me keep hands off,

For, dear me, why abandon a belief

Merely because it ceases to be true.

Cling to it long enough, and not a doubt

It will turn true again, for so it goes.

Most of the change we think we see in life

Is due to truths being in and out of favour.

As I sit here, and oftentimes, I wish

I could be monarch of a desert land

I could devote and dedicate forever

To the truths we keep coming back and back to.

Thursday, April 03, 2008

What are the Assumptions?

How important are underlying assumptions?

Let's suppose that you are asked to guess the age of a person based on nothing but his height. You are told that the age of the person is either six years old or twenty-six. You further know that the mean height of the six-year-olds is 48 inches and the mean height of the twenty-six-year-olds is 68 inches.

What you would reasonably do is calculate the midpoint between the two heights, 58 inches, and classify anyone with a height above 58 inches as an adult, and anyone with a height below 58 inches as a child.

Of course, you know perfectly well that not all adults are taller that 58 inches, nor are all children shorter than 58 inches. So your decision rule carries with it some probablility of error.

This error is calculable, generically, from the graph on the right. Shown are two normal distributions: p0(x) is the distribution of children's heights, with mean μ0 = 48 inches, p1(x) is the distribution of adult's heights, with mean μ1 = 68 inches. Those with training in statistics will recognize these graphs as probability density functions; those without it can think of them as plots of the relative number of people in each population (on the vertical axis) as a function of a particular height (on the horizontal axis). Thus, most children's heights are clustered around their average height, μ0, where the curve p0(x) is at its maximum value. Yet some children are taller, and a diminishingly small percentage of children are much taller. The inverse would be true for the adult population.

The decision point, δ = 58 inches, is the point where the curves cross, and the total probability of error is:

For those without a calculus background, all this is saying is that we are adding up all the children with heights above 58 inches and all the adults with heights below 58 inches, and say in advance that these will be mis-classified by our decision rule δ. But we can also see that δ is still at its optimum value; moving it to the right, for instance, will slightly diminish the number of children mis-classified as adults, but dramatically increase the number of adults mis-classified as children.

However, we make three critical assumptions to choose 58 inches as our decision point.

Assumption 1: the distributions are the same shape.

Since the effect of this first assumption is fairly easy to illustrate, let's redraw the distributions given the mean values listed above. Fellow bitheads will recognize the work of Matlab, vice the MS Word drawing tool used before. Now let's make the distribution for the adults twice as wide as for the children: Notice the effect on the crossover point. If the distribution of heights is greater for adults than for children (as it almost certain is), the cross-over point moves from 58 inches to approximately 56 inches. This would be the new point at which we would minimize the error (although our optimum error increases with the wider distribution). Yes, I realize that I have exaggerated the width of the distributions for effect.

Assumption 2: the number of children equals the number of adults in my population.

We can illustrate this by increasing the number of adults relative to the number of children.(Fellow bitheads: I did this by multiplying the adult pdf by 2. Obviously, it's no longer a valid pdf, but I think it's a valid way of calculating the appropriate decision point. Let me know.)

Once again, we see that the effect of doubling the number of adults relative to the number of children is to move the optimum decision point to the left, ie. around 56 inches instead of 58. One can even imagine a sufficiently large imbalance between adults and children at which the adult distribution completely absorbs the child distribution, and there is no non-zero decision height at which we could minimize our error. We would then decide that the entire population was adult.

Assumption 3: That the cost of my mistakes are equal.

Similar in effect to creating a population imbalance is to create an imbalance between the cost of mistaking a child for an adult vs the cost of mistaking an adult for a child. This is hard to illustrate with my made-up example, so let's look at a real-life example: testing for contagious diseases. Obviously, we want such tests to be as accurate as possible, but consider: if an AIDS test (routine screening, say) tells me I am sick when I am not actually sick, then I will begin unnecessary testing and treatment, but I will probably receive the correct diagnosis eventually, and will be out a lot of bother. However, if the test tells me that I am healthy when I am not, I will proceed to go home and infect my wife and, potentially, my family. In this illustration, the cost of making the second mistake greatly exceeds the cost of making the first. We would therefore want such errors as there are in AIDS testing to be "false positives" rather than "false negatives."

The point

This essay has a broad range of application to the use of statistics, but it's not really why I'm writing it. I was thinking about the assumption that many people will insist is fundamental to the use of statistics at all: the fundamental randomness of nature. Since the age of Newton, most people, and up until this century, most scientists, think of nature as fundamentally deterministic: a set of conditions and treatment {X} will always produce effect Y, or the relationship doesn't really exist. Scientists now understand that a valid relationship means that X will usually produce Y, but the randomness of nature implies that there are no metaphysically certain guarantees that this effect will always happen.

I'm using statistics a lot in my graduate work, yet I do not accept the premise that nature is fundamentally random. I will accept that it appears random, and therefore can be analyzed as such, because it is impossible to fully account for the full range of conditions under which we perform our experiments. But at a philosophical level, were it possible to so fully account for every input, then it would be possible to determine every output. And at a theological level, God hath foreordained whatsoever comes to pass.

This is not dissimilar to my take on evolution. Unsurprisingly, I reject the materialistic premise that many athiest tub-thumpers will insist is both a vital premise and an inexhorable conclusion of Darwinism. But somewhere along the line I decided I was comfortable applying the evolutionary paradigm anyway. It is highly probable, in my view, that the evolutionary process began by operating on the divinely created order, and produced the full extent of the variation we now see.

Note: I probably will not be blogging much this semester. My academic load has gone up, and my muse is underperforming.