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03.19.2007

Newsletter: month twelve

Dear Ladybug,

Today you turned one year old. 

We celebrated the day mostly without fanfare because, although it is a monumental achievement to chronicle the duration of your existence by full solar revolutions rather than measly twelfth parts of one, you’ve celebrated it twice already this month already and, really, three times would be pushing it.  Honestly.

Your first birthday party happened a month ago, while you were still in Florida with Mommy.  While there, your Nana and Papa took your to Disneyworld and Epcot Center, thereby contributing to the time-honored cliche of Asian tourists crowding American theme parks.  To make up for it, they also threw you a big family pre-birthday bash, which included an entire cake just for you and, somewhat later, a horrible diaper just for them.

More recently, on Saturday the 17th, we celebrated your true one-year birthday with a party that included yet another entire cake for you and, somewhat later, yet a horrible diaper just for us.  (You’d figure Mom would have connected those events by then.)  For a present, we decided to get you Type 1 Diabetes.  Enjoy!

Boy, have you changed in the month between parties.  First and foremost, you have teeth!  Your front right top and bottom teeth more or less sprouted simultaneously, giving you delightfully lopsided smile and the bite power of a Rottweiler.  Your mom and I were beginning to accept that you would never have teeth, and would subsequently be forever doomed to a life of banana mush and gummy smiles.  Instead, we can now all look forward to dentally-amputated fingers for us and years of painful orthodontic work for you when you become a teenager.  (We call that karma, kiddo.)

Possibly as a consequence of feeling out your new teeth, you have developed the habit of sticking out your tongue all the time.  Initially it would pop out of the corner of your mouth as you played in a comic caricature of concentration, although  it’s recently deteriorated into a disturbingly lewd, full-on Gene-Simmons tribute.  Given your current propensity to head-bang to music, it’ll b no time until you’re flashing cornas and explaining why Master of Puppets is the best album ever.

In addition to your new dentition, you’re also now a full fledged walker.  Gone are the erratic and off-kilter klomp klomp klomps of last month, replaced instead by the never ending squeak squeak squeak of your kiddie shoes as you walk around the house.  It’s a cute bow-legged gait, much like a cowboy getting back his land legs after a long day in the saddle.  You’ll fit right in here, Ladybug.

Heck, you’ve gone beyond straightforward upright walking to experiment with other modes of bipedal conveyance, including the orangutan walk, which involves flailing your arms above your head as you walk to create a mobile personal bubble about you as you move, and the Groucho Marx walk, which involves sticking your rigid arms behind you as you walk hunched forward, which I can only assume lowers your center of gravity and makes you less like to have a rollover.  My little Volvo: boxy, but good.

Now that your hands have been freed from the task of moving you around, you’ve discovered other uses.  For one example: bling.  Your mommy bought you a collection of different “party” leis and necklaces, tacky plastic things with palm trees and fishes and beads and faux gems, and I swear all you like to do is wrap each and every one of those things around your neck one at a time, until you end up looking like a little Technicolor Mister T, or (given your predilection for lewd tongue antics and delight at running around the house topless) an extra at a Girls Gone Wild Mardi Gras party.  Of course, the necklaces have a pretty large circumference and you don’t, so over time they usually slip off one shoulder like a plastic bandolier, so that you resemble a diminutive Chewbacca, albeit a fabulously gay one.

For another (more substantial) example, you’ve discovered sign language.  Whereas last month you were signing only “more” – and that just because we continuously prompted you – this month you’ve truly grasped the sign language concept.  One day, we were playing out in the backyard when you heard a dog barking.  You looked concerned, so I told you “It’s just a dog.”  You paused for a moment, then stood straight up and started vigorously smacking your right arm against your leg.  Though you looked like a one winged bird trying to get airborne, it was crystal clear that you were signing dog.

Suddenly the floodgates opened, and you began spewing forth signs.  You can sign bananas and cookies and cheese and eat and milk and baby and hot and shoes and (of course) dog.  And it’s clear you’re connecting the hand signs not just with the sounds of the words but their meaning: for example, you will sign bananas and then point to the top of the fridge where they lay hidden out of sight; when you hear a dog bark at the park (even if you can’t see it) you will sign dog.  You’ve even begun to use the sign for sun to describe bright indoor lights, which I find amazing.  Watching your raw cognitive power develop leaves me awe-struck, kiddo.  I continue to wait for a proof of the Goldbach Conjecture as my birthday present.

This month also warmed up considerably, and so we’ve spent a lot more time at the park.  While the infinitude of rocks still amuses you, you’ve moved on to bigger things.  In particular, the slide.  You can now climb the steps to the top, a feat that, given your little size, is akin to scaling the Matterhorn, but you do it with gusto.  At first you would climb to the top and wait for me to join you, so that we could slide down together.  But when you discovered that my presence was not a necessary pre-condition to sliding, you began experimenting with different ways of de-elevation.  Your initial attack was a kamikaze head-first descent, but since then you’ve adopted a more conservative feet-first slide on your belly, a technique derived not because of a concern on your part about your safety, but rather an inability to figure out how to sit at the edge of the slide and “scoot” off it.

Your play indoors has also become more active.  Our four-on-the-floor versions of “hide and seek” and “tag” have been replaced by running versions of them, as we chase each other endlessly around coffee tables and kitchen islands trying to grab each other.  You’ve just begun to climb up everything – up stairs, up chairs, up tables, and so on – but apparently you prefer to get your practice by climbing up me.  Sadly, I have gone from a daddy to fleshy set of monkey-bars.

You’re not terribly good at climbing down anything yet, and as a result, you’ve pioneered a little thing we call the “Suicidal Baby Game” in which, after you have climbed up onto our bed, you crawl at breakneck speed to one of the edges before thrusting yourself off at the floor below, with the object of the game being for whatever parent is closest to grab you by the feet before you snap your neck when you land. Prizes for winning include your continued breathing and a heart condition for daddy.

You’ve also pioneered a game that might be best described as an Un-Staring Contest: two contestants take turns rapidly and deliberately blinking at each other.  I’m not sure the criteria by which a winner is selected, but if it’s for the most pained expressions made while trying to figure out how to blink repeatedly, you’d get it:

Happy birthday, little Ladybug.  Take it easy and relax.

I love you, pumpkin.

– Ba ba

Photo album

See more pictures from your thirteenth month of existence over at flickr.

Filed under: Pictures, The Ladybug

03.14.2007

Humble pi

In honor of Pi Day, we at komplexify want to clear up a widespread pi myth.  Namely, the following “news article,” which turns up in my email inbox at least once a year every year, is completely false.

Pretty damn funny, but utterly, utterly false.

Bill seeks to change value of pi

HUNTSVILLE, Ala. NASA engineers and mathematicians in this high-tech city are stunned and infuriated after the Alabama state legistature narrowly passed a law yesterday redefining pi, a mathematical constant used in the aerospace industry. The bill to change the value of pi to exactly 3 was introduced without fanfare by Leonard Lee Lawson (R, Crossville), and rapidly gained support after a letter-writing campaign by members of the Solomon Society, a traditional values group. Governor Guy Hunt says he will sign it into law on Wednesday.

The law took the state’s engineering community by surprise. “It would have been nice if they had consulted with someone who actually uses pi,” said Marshall Bergman, a manager at the Ballistic Missile Defense Organization. According to Bergman, pi is a Greek letter that signifies the ratio of the circumference of a circle to its diameter. It is often used by engineers to calculate missile trajectories.

Prof. Kim Johanson, a mathematician from University of Alabama, said that pi is a universal constant, and cannot arbitrarily be changed by lawmakers. Johanson explained that pi is an irrational number, which means that it has an infinite number of digits after the decimal point and can never be known exactly. Nevertheless, she said, pi is precisly defined by mathematics to be “3.14159, plus as many more digits as you have time to calculate”.

“I think that it is the mathematicians that are being irrational, and it is time for them to admit it,” said Lawson. “The Bible very clearly says in I Kings 7:23 that the alter font of Solomon’s Temple was ten cubits across and thirty cubits in diameter, and that it was round in compass.”

Lawson called into question the usefulness of any number that cannot be calculated exactly, and suggested that never knowing the exact answer could harm students’ self-esteem. “We need to return to some absolutes in our society,” he said, “the Bible does not say that the font was thirty-something cubits. Plain reading says thirty cubits. Period.”

Science supports Lawson, explains Russell Humbleys, a propulsion technician at the Marshall Spaceflight Center who testified in support of the bill before the legislature in Mongtomery on Monday. “pi is merely an artifact of Euclidean geometry.” Humbleys is working on a theory which he says will prove that pi is determined by the geometry of three-dimensional space, which is assumed by physicists to be “isotropic”, or the same in all directions.

“There are other geometries, and pi is different in every one of them,” says Humbleys. Scientists have arbitrarily assumed that space is Euclidean, he says. He points out that a circle drawn on a spherical surface has a different value for the ratio of circumfence to diameter. “Anyone with a compass, flexible ruler, and globe can see for themselves,” suggests Humbleys, “it’s not exactly rocket science.”

Roger Learned, a Solomon Society member who was in Montgomery to support the bill, agrees. He said that pi is nothing more than an assumption by the mathematicians and engineers who were there to argue against the bill. “These nabobs waltzed into the capital with an arrogance that was breathtaking,” Learned said. “Their prefatorial deficit resulted in a polemical stance at absolute contraposition to the legislature’s puissance.”

Some education experts believe that the legislation will affect the way math is taught to Alabama’s children. One member of the state school board, Lily Ponja, is anxious to get the new value of pi into the state’s math textbooks, but thinks that the old value should be retained as an alternative. She said, “As far as I am concerned, the value of pi is only a theory, and we should be open to all interpretations.” She looks forward to students having the freedom to decide for themselves what value pi should have.

Robert S. Dietz, a professor at Arizona State University who has followed the controversy, wrote that this is not the first time a state legislature has attempted to redifine the value of pi. A legislator in the state of Indiana unsuccessfully attempted to have that state set the value of pi to 3. According to Dietz, the lawmaker was exasperated by the calculations of a mathematician who carried pi to four hundred decimal places and still could not achieve a rational number. Many experts are warning that this is just the beginning of a national battle over pi between traditional values supporters and the technical elite. Solomon Society member Lawson agrees. “We just want to return pi to its traditional value,” he said, “which, according to the Bible, is three.”

In fact, this was an April Fool’s Day piece of humor posted to the newsgroup talk.origins on April 1, 1998.  It was also sent to list of New Mexican scientists and citizens interested in evolution and printed in the April issue of the New Mexicans for Science and Reason newsletter NMSR Reports.  The authors confessed that it was a gag the following day, but by then, due to the unforseen power of Teh IntraWeb, it spread to inboxes eveywhere and acquired an air of authenticity (mostly because the first line of the article, which mentions an April holiday by the Associmated Press, conveniently disappeared).  A full debunking is over at Snopes.

That being said, there are two aspects of this prank that are true, which is interesting in and of itself, and make for fine discussion on this most transcendental of holidays.

The first aspect is the reference to 1 Kings 7:23 is, in fact, true.  It reads:

And he [Hiram on behalf of King Solomon] made a molten sea, ten cubits from the one brim to the other: it was circular in compass, and its height was five cubits: and a line of thirty cubits did compass it round about. 

This verse is famous for its implicit approximation of pi, namely, pi = 3, and infamous for the nutjob defenders and decriers it inspires.  Atheists and anti-Christians love to point out that God can’t even get pi correct, which kinda disproves His whole infallibity thing.  (”‘Oh dear,’ says God, ‘I hadn’t thought of that,’ and vanishes in a puff of logic.”)  

Bible-thumpers, on the other hand, give elaborate physical constructs for the “molten sea” and magically convenient units for “cubits” and “handwidths” that give extraordinarily accurate approximations of pi, the justification for their choices based solely on axiom of the Infallibility of God.  Interested readers might take a look at Russell Grigg’s nicely justified argument that the 10 cubits described in the Bible do not correspond to the diameter of the circle, thereby allowing God to save face.

The second, and more surprising, aspect is the reference to Indiana attempting to legislate the value of pi.  The article claims that the Indiana legislature once considered legislation to set the value of pi to be 3.  That is completely false — no body of legislators has ever been dumb enough to try that.  That’s just stupid.

No, Indiana tried to legislate that pi was 3.2.  Apples and oranges, buddy.

Here’s the story.  In 1897, the House passed Engrossed House Bill No. 246, a piece of legislation authored by amateur mathematician and bona fide crank William Goodwin that, among other things, legislates that the diameter of a circle is to the circumference as five-fourths is to four.  Said differently, House Bill 246 establishes 3.2 as the exact value of pi.  (Section 2 of the Bill goes on in great detail about this, asserting that a square inscribed in a circle of diameter 10 implies the following relationships among the circumference of the circle and perimeter of the square:

Astute eyes will note that, in addition to giving pi a value of 32/10, this figure also implies that the square root of 2 is equal to both 10/7 and 7/5 at the same time.  Neat!)

Apparently, Goodwin was convinced he’d discovered that the Archimedian formula for the area of a circle — you know, the pi r-squared” one — was incorrect.  In fact, Goodwin claimed (without proof) that the area of a circle was the same as the area of a square with the same perimeter, and then copyrighted his formula along with a corresponding “solution” the the Greek “quadrature of the circle” construction.   His idea was to offer these new and improved facts for free to schools in Indiana, but to charge a royalty for their use outside the state.  He was apparently pretty persuasive too, because he convinced the House of Representatives to pass it by a vote of 67-0 on February 5, 1897.

The bill appeared to be fast-tracked for approval by the Senate as well, but luckily for the future reputation of Indian, a mathematics professor from Purdue named Clarence Waldo (who was lobbying the state for University funding at the time) caught wind of the bill and hurriedly “coached” a number of state Senators on the bill.  That is, he gave them a ”basic geometry for dummies” refresher course.  Apparently it took, since the Senate voted on February 12 to “postpone indefinitely” the so-called Indiana Pi Bill, thereby preseving the March 14 statuse of Pi Day for perpetuity.  Or until the next whackjob squares the circle.

Anyways, here is Engrossed House Bill No. 246, in its entirety.

Engrossed House Bill No. 246

A Bill for an act introducing a new mathematical truth and offered as a contribution to education to be used only by the State of Indiana free of cost by paying any royalties whatever on the same, provided it is accepted and adopted by the official action of the Legislature of 1897.

Section 1

Be it enacted by the General Assembly of the State of Indiana: It has been found that a circular area is to the square on a line equal to the quadrant of the circumference, as the area of an equilateral rectangle is to the square on one side. The diameter employed as the linear unit according to the present rule in computing the circle’s area is entirely wrong, as it represents the circle’s area one and one-fifth times the area of a square whose perimeter is equal to the circumference of the circle. This is because one fifth of the diameter fails to be represented four times in the circle’s circumference. For example: if we multiply the perimeter of a square by one-fourth of any line one-fifth greater than one side, we can in like manner make the square’s area to appear one-fifth greater than the fact, as is done by taking the diameter for the linear unit instead of the quadrant of the circle’s circumference.

Section 2

It is impossible to compute the area of a circle on the diameter as the linear unit without trespassing upon the area outside of the circle to the extent of including one-fifth more area than is contained within the circle’s circumference, because the square on the diameter produces the side of a square which equals nine when the arc of ninety degrees equals eight. By taking the quadrant of the circle’s circumference for the linear unit, we fulfill the requirements of both quadrature and rectification of the circle’s circumference. Furthermore, it has revealed the ratio of the chord and arc of ninety degrees, which is as seven to eight, and also the ratio of the diagonal and one side of a square which is as ten to seven, disclosing the fourth important fact, that the ratio of the diameter and circumference is as five-fourths to four; and because of these facts and the further fact that the rule in present use fails to work both ways mathematically, it should be discarded as wholly wanting and misleading in its practical applications.

Section 3

In further proof of the value of the author’s proposed contribution to education and offered as a gift to the State of Indiana, is the fact of his solutions of the trisection of the angle, duplication of the cube and quadrature of the circle having been already accepted as contributions to science by the American Mathematical Monthly, the leading exponent of mathematical thought in this country. And be it remembered that these noted problems had been long since given up by scientific bodies as insolvable mysteries and above man’s ability to comprehend.

As a final postscript to this story, after the Senate debate, a Representative offered to introduce Professor Waldo to the bill’s author Mr. Goodwin.  Waldo declined, remarking “I am already acquainted with as many crazy people as I care to know.”  Snap!

Happy Pi Day, everybody!

Filed under: Math musings

03.7.2007

Reintarnation

The Queen B, the Ladybug, and I were shopping at Target the other day when out of the blue a woman walked straight up to me and asked, “Are you a math professor at Tech?”

This sort of thing isn’t entirely uncommon in the smallish city where we live, and there’s hardly a day that goes by that I don’t run into a current or former student busily employed in the retail and/or food service industry.  It’s terrific at hardware emporiums and electronics stores, since I can always find relatively qualified help, although it can be a bit harrowing when it comes to eating out.  (Did I fail my waiter last semester, and if so, can I expect the salsa-ptooey-especial on my burrito?)

This, however, was a complete stranger.  I was taken slightly aback, and quickly checked to see if I was wearing a tee-shirt reading “Hi, I’m a math dork, please interact with me.” I wasn’t, and so, slightly flightly flummoxed, I nodded yes to the woman.

“Oh, I knew it!” she bubbled.  “My daughter is in your calculus class, and she just thinks you’re a great teacher.  I knew it was you, because she said that you look juuuust like her cousin Jebediah, except that you have spiky hair and wear Converse tennis shoes.  Anyway, I just wanted to say hi!”

And with that, she was gone.

The Queen B and I stood dumb for a moment, before finally articulating our thoughts on the encounter.

The Queen B’s first thought focused on its positive aspects. ”That’s so cool!” she said. “Your students must say great things about you if complete strangers come up to you to congratulate you on your teaching.”

My first thought was more troubling.  “I look like a Jebediah?”

Filed under: Anecdotes

03.5.2007

Prime example of speechlessness

The end of a conversation I had today at the Social Security office, where I went to get the Ladybug a social security number.

Clerk: And I just need you to sign and date… here.

Me: Um, what’s today’s date?

Clerk: March 5th, 2007.

Me: (scribbling down the date) Three… Five… Seven…

[ Pause ]

Me: Hey!  Did you know that today is the last time in the next one thousand years that the date wil consist of three consecutive odd prime numbers?

[ Pause ]

[ Pause ]

[ Pause ]

Clerk: Next!

Filed under: Anecdotes

03.3.2007

The symbol of null and void

A famous bit of dialogue from the train scene in North by Northwest, which was on TCM tonight.

Eve Kendall: Roger O. Thornbill…  What does the “O” stand for?

Roger Thornhill: Nothing.

I think your reaction to this line is a good indicator of your mindset.

If your first thought was that this was a deep but succinct meditation on the nature of self-identity or the lack thereof, you’re a film buff.

If instead your first thought was that this was a snappy pun on the typographical similarity between the letter “O” and the number “0,” with the humor derived from the dichotomy between the very different concepts of “nothingness” connoted by those, you’re a mathematician.

And if you actually spent time on the web researching examples of humor using as its basis the aforementioned dichotomy between the concept of the empty set and the (non-empty) set of symbols whose sole purpose is to identify it, you’re beyond professional help.

Filed under: Math musings, Observations