Answers to the Programming Quiz:

Tom got the answer to number one. The assignment

(-1 ^ (j - 1))

will always be -1 for any integer value of j, because of Visual Basic's order of operations. The carat operator is applied before the minus operator. This added about 15 minutes to my debugging time.

As for the second question, Dave was right on with his assessment:

"it seems to take a set of real numbers and multiplies them against each other, alternately adding/subtracting the products."

That is, in fact, exactly what it does, and had he known the law in question, you probably would have gotten it from here. The law (or maybe formula would be a better term) is the general form of the Addition Law for n Independent, Non-exclusive Events, and is used in the field of probability to determine the chances that at least one of n events occurs, given the probabilities of each individual event.

To explain this, let me first define independent and non-exclusive. Two events are independent if the occurrence of one does not affect the occurrence of the other. Example: a die rolling 6 and a coin landing heads.

Two events are exclusive if they cannot occur at the same time. Example: a coin landing heads, and the same coin landing tails.

So the probability of either of two independent, non-exclusive events occurring is given by the equation:

P(A+B) = P(A) + P(B) - P(A)∙P(B)

Where P(A+B) is the probability that either A or B occurs, P(A) is the probability that A occurs independently, and P(B) is the probability that B occurs independently. (I am using + notation because I can't find the stupid Union symbol in the character map.)

This can be easier to understand with a Venn diagram.

If we want to find the area covered by both ellipses (the probability that at least one of the events occurs), we start by adding the area of each ellipse (P(A)+P(B)). But then we have added the intersection of the two events twice, so we need to subtract it out once (–P(A)∙P(B)).

We can determine the probability that any of three independent, non-exclusive events occurs with the equation:

P(A+B+C) = P(A) + P(B) + P(C) - P(A)∙P(B) - P(A)∙P(C) - P(B)∙P(C) + P(A)∙P(B)∙P(C)

To understand this, let's look at another Venn diagram.

To find the area covered by all three circles, we begin by adding in the area of each circle (the independent probability of each event, P(A) + P(B) + P(C)), but then we have added some regions more than once. To compensate, we can subtract out the intersection of every two circles (–P(A)∙P(B) – P(A)∙P(C) – P(B)∙P(C)). But now we have completely subtracted out the center region, the intersection of all three circles (P(A)∙P(B)∙P(C)).

I think you see where this is going for four events, etc. It gets very complex. In fact, the general form of the Addition Law, for n independent, non-exclusive events is:

(I)

In essence, we add in the independent probability of each event, subtract the products of each combination of two events, add the products of each combination of three events, subtract the products of each combination of four, etc., until we finally add or subtract (depending on if there are an odd or even number of events) the product of every event probability. This is what my VB code was attempting.

(There is an alternate, less complex way of attempting this. Instead of a brute force method, we can instead consider the inverse probabilities. Instead of finding the area covered by the circles/ellipses, we can find the area not covered by them, and subtract that from 1. To wit:

De Morgan's theorem states: P(A+B)' = P(A'∙B') = P(A')∙P(B')

That is, the probability that neither A nor B occurs is the probability that A does not occur and B does not occur. So if we subtract that from 1, we get:

P(A+B) = 1 – P(A')∙P(B') = 1 – (1 – P(A))∙(1 – P(B))

Which, for the general form, expands to:

(II)

)

So what brought this all up?

Probability theory figures heavily in fault tree analysis. A fault tree is, essentially, a collection of events (each with an associated probability of occurrence, specifically a probability of failure) connected via logic gates, such as AND and OR gates (and sometimes VOTE gates).

What? Explanation of the logic gates? Ok, we can do that.

This is an AND gate. It denotes that the output occurs if all of the input events occur.

An OR gate denotes that the output occurs if any of the inputs occurs.

A VOTE gate denotes that the output occurs if at least n of the inputs occurs (in this case 2).

(These symbols may seem familiar to those of you who took computer architecture. The symbols are the same ones used in logic gate diagrams, but turned sideways.)

There are also other miscellaneous gates, such as a NOT gate or XOR gate, but that's a bit beyond the scope of a simple introduction.

So the basic premise of fault tree analysis is we want to know about how often (the probability) a TOP event will occur, based on the occurrence of basic events. The TOP event is usually some hazard that we would like to prevent. A basic event is a failure or occurrence which may cause the TOP event to occur.

So, to create a fault tree, we connect these basic events to the TOP event through intermediate logic gates. These logic gates represent how the failures combine to cause a TOP event occurrence. A small fault tree might look like this:

The way to read this is by looking at the logic symbol of each gate to determine which of its input events must occur to cause the gate to occur. For example, if EVENT5 and EVENT6 occur, this will cause GATE3 to occur, because it's an AND gate and requires the occurrence of all input events. If GATE3 occurs, GATE2 will also occur, because it's an OR gate and the occurrence of any of its inputs will cause its occurrence. Now, if any two of the inputs to GATE1 occurs, say EVENT1 and EVENT3, then GATE1 will occur (because it's a VOTE gate). And if both GATE1 and GATE2 occur, then TOP1 will also occur. So we could say that TOP1 will occur if EVENT1, EVENT3, EVENT5, and EVENT6 all occur at the same time. We call this occurrence of events a minimal cut set. (I might talk more about cut sets in the future, if you wish, but as it is, this post is running too long.) Another minimal cut set might be EVENT2.EVENT3.EVENT4. (Note, EVENT2.EVENT3.EVENT4.EVENT5 is also a cut set, but not minimal. Do you see the difference?)

I will skip over how to produce the full list of minimal cut sets for this tree, and just list them all. They are: 

EVENT1.EVENT2.EVENT5.EVENT6

EVENT1.EVENT2.EVENT4

EVENT1.EVENT3.EVENT5.EVENT6

EVENT1.EVENT3.EVENT4

EVENT2.EVENT3.EVENT5.EVENT6

EVENT2.EVENT3.EVENT4

By this point, you can probably see how to produce them yourself. Now each cut set can be thought of as an event, itself. So, basically, what we have here is a list of non-exclusive, independent events, the occurrence of any of which will cause the TOP event.

Sound familiar?

The obvious way to solve this, then, would be to use... the Addition Law!

And this is exactly what the software (that company I work for) writes does. You tell it the events, how they're logically connected, and some quantitative data, such as a failure rate or MTTF (mean time to failure), and it will calculate:

1) The probability of each event occurring,

2) The probability of each cut set occurring (simple: the product of the probabilities of each event in the cut set)

3) The probability of occurrence of the TOP gate (using the Addition Law).

Note how quickly the addition law gets complex. This small and simple tree produces six cut sets, which would require 6 + 15 + 20 + 15 + 6 + 1 = 63 product terms in the addition law. Just the other day I was working with a fault tree that had 152 cut sets for one intermediate-level gate. This is why our software will use approximation methods and all sorts of other tricks to be able to solve the tree. In fact, one of the approximation methods involves using de Morgan's theorem and equation II. This is called the Esary-Proschan approximation method, but you didn't really want to know that.

If you would like, I could talk a little bit more about fault tree analysis later, and give real examples, instead of odd abstractions. But this post has gone on too long.

And now you know what I do for a living!

So back to the topic at hand, why was I writing a VB program to implement the Addition Law? Basically, I needed to verify the results of a fault tree. By hand.

Programming Quiz of the Day/Week/Month.

Question 1: What is the value of x after this code executes?

dim j as integer, x as integer

j = 5

x = (-1 ^ (j - 1))

Question 2: What mathematical law does the following code implement?

'Globals

dim i as integer, j as integer

dim dValues() as double

Private Function DoEet() As Double

    i = UBound(dValues)

    For j = 1 To i + 1

        DoEet = DoEet + RecursiveHell(-1, 0, -1, 1)

    Next j

End Function

Private Function RecursiveHell(k As Integer, l As Integer, _

    m As Integer, x As Double) As Double

Dim temp As Double

    If k = -1 Then

        k = 0

        RecursiveHell = RecursiveHell + RecursiveHell(k, 1, k, 1)

    Else

        If l < j

            Do While m < i - (j - 1)

                temp = x * dValues(m)

                RecursiveHell = RecursiveHell + RecursiveHell(k, l + 1, m + 1, temp)

                m = m + 1

            Loop

        Else    'l = j

            Do While m < i

                temp  = x * dValues(m) * ((-1) ^ (j + 1))

                RecursiveHell = RecursiveHell + temp 

                m = m + 1

            Loop

        End If

    End If

End Function

(Might want to resize your browser so that this fits on one line:)

-----------------------------------------------------------------------------------

(Don't know what recursion is? Click here to find out.)

Cat Yodeling.

I need to try this with Bastet. She's far easier to annoy.

No, YOU'RE wrong!

[Warning: long rant on religion and politics follows]

So someone recently made the statement that a Catholic who supported the the invasion of Iraq must be just as morally confused as someone who is pro-choice.  Although I provided a clear and concise rebuttal to the originator of the statement ("your stoopid"), I thought I'd explore this statement in a little more detail.

First off, "moral confusion" is an imprecise and ambiguous phrase, so when I use it what I really mean (and what I assume the original commentator meant) is "morally incorrect."  "You're confused" as I usually see it used in this context seems to be intended as a more polite way of saying "you're wrong," except it's not more polite because everyone knows what it means, and condescending because it implies the other person isn't emotionally capable of dealing with someone telling them they're wrong.

Let's summarize why someone might be pro-choice (this has been discussed at length on this blog):

1. Unborn babies aren't human, so abortion is not an act that murders a human.

2. There's nothing inherently wrong with murdering innocent people.

3. Unborn babies are human, but it's okay to murder them because they aren't born (or crossed some arbitrary development threshold).

Note that I am assuming that we all accept that something that is inherently immoral is always morally wrong (i.e., if under some circumstances an act is not wrong, then it was not inherently so: the ends cannot justify the means).  Item #1 represents "moral confusion" by virtue of incorrect facts.  It is morally correct under the premise that unborn babies aren't human, but biology indicates otherwise.  Item #2 represents a point of view that most people do not hold, and I don't honestly think the original commentator believes that all those who support the war hold this view.  Item #3 is only morally correct with the introduction of a new moral principle that specifically excludes humans of some developmental stage or status from the prohibition against murder.  I have never seen a justification, much less a clear statement, of this new principle.  This also requires item #2, although supporters of abortion rarely admit it.  The only other possible position for someone who supports legal abortion is that it is the immoral murder of an innocent human and should not be prohibited by government.  This is an unusual view of the role of government.

In order for supporters of the war to be guilty of the same moral confusion as pro-choicers, then it must be because they believe that fighting a war is not inherently immoral, and possibly that there is some special reason that the invasion of Iraq need not be justified according to traditional just war theory.  But the Church teaches explicitly that waging war is not inherently immoral, and proponents of the war that argue it is justified within the traditional just war theory (whether you agree with their reasoning or not) do not require some new moral principle (example example example).  Therefore, proponents of the war in Iraq (including one singled out by the original commentator) clearly do not suffer the same "moral confusion" as pro-choicers in any meaningful sense.

The only other context given with the original offending comment was that the "morally confused" should have realized, after five years of tragedy, that the original decision was unjust.  This implies that the unintended, undesired, unforeseen consequences can affect whether a decision is just after it has been made, which leads to a ridiculous impossibility of making moral judgments, since all possible effects of a decision cannot be foreseen.

It is a logic error (and perhaps a lack of charity) to assume that those who seem to be wrong on a moral issue must be suffering from deficient moral reasoning.   Anyone can understand how identical logic applied to different premises can lead to different conclusions.

The only other statement by the original commentator I wish to comment on is "it is a reflection of ideology, not considered thought, to think that."  But how can one think that which is not thought?  Please be more clear.  Did you mean, "it is a reflection of belief not based on reason"?  But that is false on the face of it: as I showed above, the position (support for the war) is reasoned from facts and moral principles.  As far as I can tell, this statement means nothing.

Comments are welcome.

Trekkies Bash New Star Trek Film As 'Fun, Watchable'

Quotable quotes: "Gene Roddenberry was the hack who created the Star Trek television show, way back in the 40's or something."

Because the Murloc won't stop bugging me about it...

Photodump.

The Murloc's domestic instinct has kicked in. She cooked Easter dinner. Lamb. It was good.

The Murloc and her friend went to the Renaissance Faire. They dressed up. They were pretty.

As usual, the Murloc got her hair done. By the same girl as usual. It was pretty.

Pictures from the latest ultrasound. In the upper-right, he's playing with his feet. It is cute.

Happy? Now STOP BUGGING ME!

Book Reviews

From the sublime to the ridiculous.

I've been on a reading kick lately, and since I'm a blogger I know you're all dying to know what I think about whatever.  So here are some (very) short reviews:

Twenty Thousand Leagues Under the Sea - Jules Verne

A fascinating story by the father of science fiction.  Part nature documentary, part high-seas adventure, it's kind of like a 19th-century underwater Star Trek.  Highly recommended.

Bartleby The Scrivener: A Story of Wall Street - Herman Melville

Funny short story about the passive-aggressive office worker that won't be pushed around, and the power of behavioral precedent.  It has a poignant touch to it, too.  Good story.

A Christmas Carol - Charles Dickens

A popular classic is both for good reasons, one of those stories where you can call it "heartwarming" without being just an over-used cliche.  Read it.

Daemon - Daniel Suarez

It's about a dying brilliant computer game programmer that takes revenge on the world by writing what is both the ultimate virus and the ultimate computer game.  What's really scary is that all of the technology in the story exists.  It's totally possible!  I do believe this will get made into a movie, and there is a sequel on the way.  Highly recommended for nerds, geeks, other techies, or paranoid conspiracy theorists.

The Zombie Survival Guide - Max Brooks

The son of Mel Brooks writes the ultimate survival guide on how to survive the coming zombie apocalypse.  Hint: be prepared, and aim for the head.  Great dry humor.

A Brief History of Time - Stephen Hawking

A summary of physics from the Greeks to string theory, this book is basically a recap of how man has tried to understand the workings of the universe.  It's well-written and easy to understand, although it's a little frustrating for someone like me who knows enough about the topics to have serious questions, which to answer would require detail well beyond the scope of this book.  Oh, and he repeats the usual nonsense about Gallileo (Church vs. Science!).  I have the original 1988 edition, so I don't know if this was corrected along with the changes made in later editions.  Still, everybody should read this book.

Orphans/Fugitives/Titans of Chaos - John C. Wright

Sort of Harry Potter meets Star Wars meets The Box of Delights, it's one of the most imaginative stories I've read, it's hard to figure out exactly which genre it's in.  Maybe fantasy, maybe sci-fi?  The characters are interesting, and it's just impossible to tell where the story is going to go.  One of the characters can move and see in four dimensions, which presented some difficulty for me since I visualize everything I read.  It also has the most ominous line I've read lately: "Prepare the thousand-dimensional object!"  Recommended.

Watchmen - Alan Moore/Dave Gibbons

Who reads the Watchmen?  I did, and it was actually pretty good.  I had read the whole debate about the book vs. the movie, and I already knew most of the plot (including the ending), but it was still very interesting.  What you get out of the story depends on your world view.  The point of view of the story is very nihilistic and cynical, although the characters are quite deep and draw you in.  I thought the ending was disappointing, in part because I don't see the universe in the way the author portrays it in this story, although as a whole I enjoyed reading the book.  Although I haven't seen the movie, from what I've heard it's much much more violent than the comic.  The worst violence in the comic is described or implied, and not depicted.  And Nixon isn't portrayed as evil (he's hardly portrayed at all).  Recommended for those who are interested.

Currently reading:

The Night Land - William Hope Hodgson

Set one million years in the future when the sun has burnt out (written in 1910, they didn't how long it would actually last back then), one of the last survivors of the human race sets out across a land of perpetual darkness to rescue his beloved.  It's very atmospheric, early sci-fi, and I'm only halfway through it, so don't tell me how it comes out.

Ender's Game - Orson Scott Card

A fellow geek chastised me for not having read Ender's Game, so I just started that one today.  I don't have anything to say about it yet.  Don't spoil it!

The Most Important Person on Earth.

"The most important person on earth is a mother. She cannot claim the honor of having built Notre Dame Cathedral. She need not. She has built something more magnificent than any cathedral—a dwelling for an immortal soul, the tiny perfection of her baby's body.

"The angels have not been blessed with such a grace. They cannot share in God's creative miracle to bring new saints to Heaven. Only a human mother can. Mothers are close to God the Creator than any other creatures. God joins forces with mothers in performing this act of creation.

"What on God's good earth is more glorious than this: to be a mother?"

—Joseph Cardinal Mindszenty

Several fellow students (all of them women) in my writing class have left perfectly polite comments on my last two homework assignments. I have decided that I am going to go get the town crier all over them.

The comments:

At the beginning of chapter 3, Jack gives Regina the order to depart Arcas spaceport with the command "Miss Burke, take us up." Three women in the class seemed to take exception to this. One circled "Miss" and wrote "Pilot"; one wrote "Ms."; and a third circled "Miss" and left the note "Wouldn't she have a title with more dignity?"

In the next week's homework assignment, Regina referred to herself as "the new gal" aboard the ship. One of the women circled it and wrote "Women don't like this word" and gave several alternatives, such as "girl", "pilot", "crew member", "mate".

Really? Women don't like that word? You are speaking for all women? Then why do I hear my grandmother use it so often? Are you contending that she is not a woman?

Concerning the implication that "miss" is a title without dignity, this one single sentence demonstrates and proves with one single breath the heinous thing, and my biggest gripe, with political correctness: political correctness seeks not to avoid offending, but rather to find offense where none is intended or, even more likely, even present.

Does anyone argue that when Jack refers to Regina as "miss", he is doing it specifically to degrade her, or demean her? (He is quite capable of  doing this in other ways.) Would you argue that if I held a door for a young lady and said "let me get that for you, miss," that I am purposely and actively, with malice aforethought, trying to show my superiority over her, lower her dignity, take away her right to vote, and chain her to the kitchen?

Please. Be surd. (absurd : surd :: incest : cest)

The "best" argument I have heard against the titles of miss and mrs. is that these titles "chain a woman's identity to her marital status, and thus make her a slave of her husband" which is logic on par with "if a woman weighs the same as a duck, she's made of wood and thus a witch." This betrays what John Wright so expertly points out about those who follow the Religion of PC: "They think (or rather, they feel) that when they are calling one thing by another name, that the actual nature of reality changes. They put themselves in a position where they can no longer talk about real things. Words are severed from referents."

He is, of course and as always, right. Those who worship at the altar of PC, and also those in the left wing (usually the same crowd) believe in the magic of language relativity: that is, by changing the way we refer to something we can change the nature of the thing itself. This seems to me to be closely associated with moral relativism: the belief that we can change morality by wishing it away. What is wrong for you or for another is not wrong for me because I don't want it to be. We see this in other aspects of life, too: if we call a "baby" a "fetus", it is no longer human, and can be killed; if we refer to people as having "gender" instead of "sex", then by changing their gender, they can change the fundamental nature of themselves. News flash: if I name my cat "rover", refer to her as "the dog", and feed her dog biscuits, she still won't bark. Sex is a biological and supernatural reality. Changing how we refer to it won't change its nature.

The reality of miss and mrs. seems to me to be far more innocuous. In a society where men purse and women allure, one would expect simple and obvious social cues that would indicate to the pursuer if the allurer is available to be pursued. Titles are one aspect of this, as are rings (hence, a woman wearing an engagement ring; I think of a man's wedding ring more as a reminder to himself than as a signal to other women). Were we to live in a society that operated in the opposite fashion, where women sought out a mate, bought him dinner, escorted him to the opera, and took him home and kissed him goodnight on his porch, I would expect the titles to be reversed.

But the PCists, of course, are chained to their idea of language driving nature; thus if we call an unmarried woman "miss" and a married woman "mrs.", we are saying that her nature changes when she gets married. Since they feel this is offensive (and I have never heard a good explanation for how it is offensive, probably in no small part because they feel rather than think it is offensive) they think (or rather, feel) that by changing a woman's title to the generic "ms.", we have somehow altered her nature and the nature of marriage.

As mentioned before, one of the primary aspects of political correctness is how it assumes offense where none exists. To refer to a married woman by a different title as an unmarried woman seems reasonable to the normal, rational person. In fact, these are the terms that were used for decades, if not centuries, and no offense was meant or taken. But then one day (and that is probably quite literal) some follower of the dogma of PC decided that words that had no offense attached to them before suddenly were offensive and that they had to be changed. Granted, language changes, but suddenly deciding that words have new meaning never before intended is not the sort of gradual change as "chuse" changing to "choose". Other examples of this include suddenly deciding that using the pronoun "he" to refer to groups of mixed sex is offensive, where it never was before, and that the term "secretary" to refer to those with a secretarial job, is offensive. (I once asked a PCist why it was that "secretary" was demeaning to women. She explained that it was because it harkened to a time when women were only allowed three careers: secretary, teacher, and nurse. She did not explain why "teacher" and "nurse" were still allowable. (This is one reason I'm Catholic and not PC; the rules are far more intuitive and easier to understand.))

Another aspect of Political Correctness is that it only seeks to find offense directed a certain groups that are mascots of the left. Surely, the PCists object to "offenses" against blacks, American Indians, women, homosexuals, and other "protected" groups. I have never heard one so much as flinch at offenses directed at Irishmen, men, Catholics, or evangelical Christians. Somehow, Muslims have weasled themselves onto the "protected" list, which means those outside the Church of PC get to watch, with wonderful bemusement, how those in the PC Church "protect" from offense those who are probably the least PC, and indeed viciously hate some of the other protected groups. (For instance, my writing instructor mentioned, perhaps in a doubt of the faith, that she was having a hard time accepting the PC dogma that fundamentalist Islamic societies had a "right" to horribly abuse their women. I remain blissfully outside of PCism, so I can answer as any sane man should: no such right exists and we can kill the bastards for doing such.)

If you want evidence of how imbalanced the double-standard for offensive speech is, look no further than the NCAA. Remember a few years ago when, out of sensitivity to "Native Americans" they tried to outlaw all schools with American Indian mascots? (They apparantly had a very selective use of "Native American"; I am a native to America too, but they didn't outlaw any team called "the Josephs". However, since no team with that name exists, perhaps they thought it a non-issue. I will give them the benifit of the doubt, and assume that they would have.) This, of course, was a monumental search for offense, such that they must have been using NASA's Spitzer space telescope to find it, as they clearly ignored the fact that many colleges with American Indian mascots do so with the approval and blessing of the tribe! One thing I found particularly interesting was that the University of Illinois Fighting Illini were to be banned, because "Fighting Illini" is offensive. However, there never was any mention of banning the University of Notre Dame Fighting Irish. How, exactly, is "Fighting Illini" racially insensitive and "Fighting Irish" is not? Are you going to argue that the Irish have not been oppressed? Are you going to argue that it is politically correct to portray Irishmen as drunken, brawling, leprechauns, but incorrect to portray American Indians as tomahawk-wielding warriors with feathered headdresses? Now we must play a game of measuring relativism, and explain why one offense is more offensive than the other.

So it is because of political correctness that society jumps at imagined shadows of offense, but only those shadows cast from a certain angle and from certain objects, that you have to turn your head sideways and squint to see, but then it just looks like a bunny. It is because of political correctness that I can't say "miss", but no politically correct person would bat an eyelash over the term "hocus pocus", with all its associated anti-Catholic bigotry. (For those not in the know, "hocus pocus", originally, was a mockery of the Latin words of consecration: "Hoc est enim corpus meum" or "This is my body", the climax of the Mass, and that sacred moment when a host of unleavened bread is turned into the Body, Blood, Soul, and Divinity of Christ. I, personally, do not take offense to "hocus pocus", because I know that no one today uses it to offend Catholics, and probably no one who is not Catholic even knows where the term comes from. I would not stoop to correct someone who uses such a term in ignorance.)  It is because of political correctness that I can't refer to a secretary as a secretary, but the followers of PC can—and do—take Our Lord's name in vain, without so much as a worry or care to whether or not they offend me (and I do take great offense to that). I am not in a protected group; I am not worthy of avoiding offense towards. (In fact, someone once argued on this very blog that it is allowable to insult and offend white Christians because they have it coming.) But if those followers of PC don't care if they offend me, on what grounds do they argue that I should not offend them?

Since I can't think of a witty or snappy end to this article, I will let the inestimable John Wright do it for me, even though I think I am over my allocated "John Wright quote or link" quota by quite a lot this month:

Quoted for Truth:

The rudest society imaginable is one where everyone is hyper-sensitive, thin-skinned, and willing to see insults where none are intended, and, most of all, a society were everyone demands, as a matter of right, as a matter of entitlement, that no one cross or offend his ultra-fine nerves, which have been sandpapered to the most exquisite pitch of sensitivity. The professional crybabies have been given a trump card that wins every hand and always collects the kitty. So, we get more crybabies. Dignity, adieu: rudeness, hail! Hail, horrors!

In non-breast-related news....

My second-favorite blogger, Shamus Young, finally released the "PixelCity" he has been working on as a screen saver. He did a series of posts about the development that I found quite fascinating. PixelCity is a procedural city generator that creates a picturesque night-time city scene. You can find the start of the series here. He also made a procedural terrain project a few years back which was also interesting.

So now all we have to do is create the procedural galaxy generator, extend the terrain generator to create an entire planet, integrate it with the city generator, and Bob's your uncle, SPM3DOF!

We really ought to get on that.

Happy Monday. How was your weekend? You do anything fabulous? Good, good. I spent mine looking at breasts.

You think I am joking?

Maybe you think that I'm creating a play-on-words, and I cooked chicken breasts, or some such; or perhaps you think that I went to the beach and there were lots of shirtless men showing their chests; or maybe you are thinking that I'm making some real stretch of a joke about shopping for a suit (y'know, a double-breasted suit). I assure you none of those are the case. I am talking about exactly what you think I am talking about when I talk about breasts. Human female breasts. Uncovered.

So, as part of this whole "child birth" thing, the Murloc had a class on breastfeeding at the hospital at which she is to give birth. I was informed that my attendance was required, if not by the hospital, by the Murloc herself. (Attendance at the breastfeeding class, not the birth; well I gather that my attendance at the birth is also required, although that has not explicitly been stated. It's just been sorta, y'know, gathered.) That is my excuse for being there: I daren't disobey the direct commands of a pregnant Murloc.

And in fact, I was not the only man there. Discounting the nurse giving the class, the male/female ratio was 1:1. Most were young-ish couples, undoubtedly having their first child. (And further, most of them had rings on the appropriate fingers, indicating that the destruction of marriage and decline and fall of civilization may not be as imminent as prior reports indicated.)

So what did the class involve you ask? Breastfeeding how-tos and such. This is a field that, up until Saturday, I was blissfully unaware of the complexities and intricacies of, and had no urgent desire to study in-depth. But, like a terror master at Gitmo, I was forcibly plunged headlong into the cold and choking waters of knowledge, but with perhaps a bit less kicking and screaming. 

Apparently, there is a lot more to breastfeeding than "take baby; attach to nipple". I always figured it was something that, y'know, came rather naturally. Survival of the fittest would seem to crop out the babies that couldn't figure it out. I mean, what has evolution been up to for the last 150,000 years if not culling the human race to be natural breast-feeders? But no, there is all sorts of specialized knowledge and techniques and dos and don'ts that one has to keep in mind. And of course, the hospital would be remiss in their duties if they just gave all these eager and expecting young parents a quick-and-dirty explanation. No, they must, to properly inform us and make sure that we are adequately prepared, show us exactly what is entailed in proper breastfeeding technique.

To this end, there were—and Dave Barry swears I Am Not Making This Up™—a PowerPoint presentation and several instructional videos—complete with animated 3D graphics—showcasing exactly what goes on during breastfeeding. All the points, major and minor, were covered. At least I hope it was all the points, because I would be somewhat shocked to learn that there is much more to this field than what we have already been shown, in all it's engorged and supple detail.

The presentation started out with the expected scare-mongering and lies/damned-lies/statistics one would expect. You know, explanations about how breastfed babies are less likely to be eaten by wild dogs and the sort. The culmination of this was when it was explained to us that studies have shown (so it must be true!) that babies who are not breastfed have lower IQs than those who are. Oh no! If you don't breastfeed your baby, he won't be able to get into Harvard Law! (Of course, there may be some truth to the correlation of breastfeeding/IQ, but has causation been proven? What, exactly, is the difference? Half a point? Is there a standard deviation on that? Margin of error?)

Note to the nurse giving the class: we are sitting in a class on how to breastfeed. Chances are we are already planning such. Save the sales pitch.

From there, the nurse talked about the mechanics of breastfeeding: the glands; how they produce milk; the glands around the nipple that keep the skin oiled; the 7-9 tubules inside the nipple through which the milk comes out; the technical term for the milk that is produced right after birth (colostrum); let-down; and various healthy practices and urban legends. For instance, it is not necessary, and in fact a bad idea, to "toughen" the nipples prior to birth by rubbing them with a washcloth or—and I'm sure all my female readers will be pleased about this—fine sandpaper. (Dave Barry also swears that the nurse was not making up that one attendant of one class had been told by her sister to do just that.)

Some of this was accompanied by pictures and videos. For instance, when explaining proper latch-on, a close-up image of a baby latched on to the breast was shown. The nurse explained that the angle of the baby's mouth created when on the nipple was about 120°, tracing the angle on the image. This is a bad thing to tell a math major. Now, whenever the Murloc is breastfeeding, a protractor will be involved. If a protractor is not available, I think I still remember the geometric construction for a 120° angle using a compass and straight edge.

Also, when explaining proper milking-procedure and about let-down, there was a demonstration video showing how squeezing the nipple in different ways would or would not produce a stream of milk. This video showed a close-up of a nipple (a real one, just in case that wasn't excruciatingly clear) while a doctor explained that squeezing the very tip (he demonstrates this in the video) would not produce much milk, but if the nipple is squeezed farther back (again, he demonstrates), a stream will squirt out at the camera. I have one thought and one question during this video. Thought: I am amazed that this women is comfortable having her nipples squeezed by a male doctor, on camera. Question: how do I get that doctor's job?

Once the video was over, the lactation nurse (NB: not lactating nurse) instructing the class explains that, if you look closely, during the first squeezing, even though no streams were shooting out of the nipple, there was a little bit of milk, visible as a faint glistening on the skin. She then repeats the video, telling us all to look closer to see what she is talking about. I think that is probably the first time in my life I've been shown a woman's breast with explicit instructions to look more closely at it, instead of the opposite.

There was also another instructional video that showed several different women, still in the hospital after giving birth, learning to breastfeed. We, the viewing audience, are provided with extreme close-ups, as the cameraman leans in for a better view, of the baby latching on, first incorrectly, then correctly. Afterwards, I asked the Murloc, rhetorically, how she would feel about allowing a camera in her hospital room to film her first attempts to breastfeed. She asked how much they would pay. Clearly, there are some untapped business opportunities pertaining to my wife, about which I was previously unaware.

Throughout this, my "custody of the eyes" reflex kept manifesting itself. A pair of breasts would flash up on the wall. Without thinking, I would turn away before realizing I'm supposed to be looking at these breasts. It's educational. I guess it's good that the reflex is so strong, and it tends to be even stronger when I'm in public, as I don't want to be that one weird pervert in a crowd who can't peel his eyes off some tawdry image. A quick look at the other males in the room revealed that there was never any real danger of people thinking that about me in particular.

The end of the class consisted of the nurse talking about different ways to position oneself and one's baby while breastfeeding, as well as different ways a woman could grasp her breast, such as "C" or "U" holds. She demonstrated this with an analogue baby and breast. She informed each couple that they could obtain a baby of their own from a closet in the back of the room, with which the mother could practice the different holds. I was moderately relieved to confirm that they were not real babies. I mean, you never know. But even then, my relief was short lived, as the plastic babies seemed to have an uncanny resemblance to Kuato.

After the class, the Murloc and I were discussing the events of the day, and I remarked to her much of what I have recounted to you, expressing my surprise about the explicit nature—shall I call it lactation porn?—of the class. I asked her for her thoughts, and she mostly agreed with me.

"Besides," she said, "none of those women's breasts looked as good as mine."