Happy Birthday, Jen! (and We'll See Y'all in a Week)

Today is Jen's birthday.  Which brings us into the seven months of the year that she and I are the same age, at least as far as integral numbers of years are concerned.  In our family, we are fond of telling each other on our birthdays, "I'm glad you were born."  And I can say with all sincerity that, with the possible exception of my own birth-parents, I am gladder for Jen's birth than any other person on the planet.  I don't even want to contemplate what my life might have been like without her existence.

Happy Birthday, Sweetheart.  My world is a sweeter, richer place for having you in it. . .

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We're gone to Summer Camp for the coming week, so I'll be incommunicado from Blog-space.  But, just so you have something to remember me by, here's a photo of my friend Jason and me, regaling the campers with our rousing rendition of Loudon Wainright's 'Dead Skunk in the Middle of the Road'. . .

(Tie-dye napkin do-rag by Lime)

Yesterday. . .

. . . 2F and I went to Comerica Park, on a muggy and sporadically rainy evening in Detroit (we endured a light shower for 10 minutes or so just before the band took the stage, but there was lightning in the sky all around us for a good part of the evening, and a few drops fell at random points during the show itself), to see Paul McCartney in concert, along with 40,000 or so of our closest and dearest friends.

It was the fourth time I've seen Sir Paul in concert, going back to 1993, when he played the Silverdome (and my best friend's wife was my date).  I saw him with a buddy in '02, at the Palace of Auburn Hills, and Jen and I saw him at the Palace in '05, as part of our Silver Anniversary celebration.  The open-air venue this time was a cool ambience, even including the few spits of rain we had to endure.  During the 10-minute shower above, I leaned over to the guy next to me and wondered if we should break into the 'No Rain!' chant, a la Woodstock.  He smiled at me and said, "Actually, when I was at Woodstock, the rain was much worse than this."  OK, then. . .

I'm just old enough to remember when the Beatles were first on the Ed Sullivan Show in February of '64 (seriously? that was almost 50 years ago?!?), and I followed them into my teens, then Wings through my college years.  At any rate, to a large extent Paul McCartney, and the Beatles more generally, have provided the soundtrack for a large portion of my life.

2F has been a Beatles fan from early on in her life.  When she was in 6th grade, I think, she did an Academic Fair project on the Beatles, complete with a tri-fold board adorned with the Sgt. Pepper album cover (I suppose, if I were a more astute father, I'd have been quicker to recognize her desire to form a connection with her dad; but I did have a lot of fun helping her with it).  So, when Jen and I came home from the concert in '05, having been cut off in mid-'na-na' from such sharing of McCartney's greatness with our daughter as we could manage at the time (I rang her up on my cell phone for the 'Hey Jude' singalong, but an usher saw me and threatened to bounce me from the concert; no further comment in that regard), I promised 2F that, the next time Sir Paul came to town (or heck, within a manageable drive of town), I'd take her with me, so I was duty-bound to fulfill my promise (and don't you wish your duty included going to McCartney concerts?).

We went to the concert  with one of 2F's friends - a young woman who has become one of her best friends and an honorary member of our family, even apart from a shared fondness for McCartney and the Beatles - along with the young lady's mom (who, conicidentally, has actually met - and been photographed with - Hugh Jackman, as her husband is a sometime film-industry hairdresser; please don't hate her, Lime) although their seats weren't by ours.  They were originally going to be joined by another friend, a young man from Scotland, who has also become a close family friend over the course of the past year, but he took ill at the last minute, and couldn't come (he must have been really, REALLY sick); the girl and her mom offered his ticket to 4M, so I got to go to the concert with two of my kids, which was quite cool.

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The band was the same crew Paul has played with for the past 10 years or so, with Paul Wickens on keyboards, Rusty Anderson and Brian Ray on guitars and backup vocals, and Abe Laboriel on drums (and backup vocals; he also provided a bit of visual hilarity during 'Dance Tonight').  It's a tight group, and they really seem to enjoy playing together.

In case anyone is interested, here's the setlist they played last night:

Hello, Goodbye
Junior's Farm
All My Loving
Jet
Drive My Car
Sing the Changes (from his album Electronic Arguments under the pseudonym The Fireman)
Hitchhike (a Marvin Gaye number added just for his Motown friends)
The Night Before
Let Me Roll It (ending with a jam on 'Foxy Lady')
Paperback Writer
The Long and Winding Road
Nineteen Hundred and Eighty-Five
Let 'Em In
Maybe I'm Amazed
I've Just Seen a Face
I Will
Blackbird
Here Today
Dance Tonight (from his '07 album, Memory Almost Full)
Mrs. Vanderbilt
Eleanor Rigby
Something
Band On the Run
Ob-La-Di, Ob-La-Da (you don't think he reads my blog, do you?)
Back In the USSR
I've Got a Feeling
A Day In the Life (ending with 'Give Peace a Chance')
Let It Be
Live and Let Die
Hey Jude

(1st encore)
Lady Madonna
Day Tripper
Get Back

(2nd encore)
Yesterday
Helter Skelter
Abbey Road Medley (Golden Slumbers/Carry That Weight/The End)

36 songs in all (which has been pretty standard for him in his recent shows) - 23 Beatles songs, 10 Wings songs, 9 that he's never done live before (at least in front of an American audience), spanning three amazing hours.  I've long thought that his '90 concert (the one chronicled on the CD Tripping the Live Fantastic) was the best of his recent live shows, and I've regretted ever since that I missed it.  But this show was right up there, on a par with the one 21 years ago.  And I can only hope to have anything close to Paul's energy level when I'm 69.

McCartney is a consummate performer and showman.  His concerts have always left me happily satisfied, and yet wanting more at the same time.  Having seen him on multiple occasions over the course of nearly 20 years, it has seemed to me that, as the years pass, he is coming to a greater and greater appreciation of the warm affection in which he is held by his audience; he added a couple singalong numbers (beyond 'Hey Jude') to his setlist this time, but it almost didn't matter - all through the show, we were hearing the band in one ear, and in the other, 40,000 people singing along.  It was a magical evening.

I don't know how many more of these concerts I'll end up attending (heck, I don't know how many more of 'em Paul is gonna play), but every time I start to think that it's becoming 'old hat', I'm just blown away by the one I'm seeing today.  It was an amazing evening; an amazing show by one of the great performers of all time. . .

Two Girls and a Boy

Our first two children were girls. I wasn't really all fixated on the idea of having a son, but there was that part of me that hoped for one - someone to carry the family name forward from me, and all that. In the mid-80s, though, just as I was passing into my 30s and gearing up my genealogy hobby, it was a matter of some small concern to me to consider the generation of my cousins, the descendants of my paternal grandfather. My grandfather had three sons (ie, bearers of the family name); my Uncle Neville (as I'll call him here) had three daughters, so the name wouldn't be passing on through his kids; Uncle Levi had six kids, four of whom were sons, but none of them had gotten married, much less had kids, as they were passing into their own 30s; and my Dad had seven kids, five sons, of whom I was the only one married, and up to that point, I only had girls. So the survival of our family name was somewhat of an open question at that point.

Of course, I needn't have worried. Within a couple years, I had the first of what would eventually grow to a group of five sons (none of whom is married as I write this, but there's still plenty of time). Three of Uncle Levi's sons married, and each of them had at least one son, and three of my four brothers married, producing one more son between the three of them. So the family name seems reasonably safe for another generation or two (and I wouldn't even be all that concerned about it, but our name is not a common one, and we're kinda proud of it).

Anyway, I hasten to be clear that, 'passing on the name' aside, I love my daughters (and nieces), and cherish their place in my life just as much as I love and cherish my sons. And even where The Name is concerned, what was I gonna do about it, anyway? God gives us the children He gives us, and we bring them all into our family with gratitude and love. Just, you know, for the sake of saying so. . .

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My first three children gave me small opportunities to observe certain, shall we say, tendencies, demarcating differences between girls and boys. Which is an interesting idea, all by itself, because neither Jen nor I are very 'stereotypical' in terms of 'gender roles'. She was a pretty tomboy-ish girl who liked playing in the mud, and working with tools, and all that, and I was a pretty bookish, nerdy boy (tea parties and doll-houses never much interested me, though). Even now, I tend to be more emotional than she does; we often joke between ourselves that she's a pretty 'guy-ish' woman, and I'm a more 'chick-ish' guy, at least as far as many of the common stereotypes go.

But, as has been noted on occasion (although it's not such a popular idea just now), stereotypes don't just appear out of thin air; they usually arise out of some basis in 'general' fact, even if it isn't terribly helpful in specific cases.

We have often gotten a chuckle from the disparate responses of our kids to things like weird bugs that they found on the sidewalk. Toddler 1F would spy the strange-looking critter, and run away from it, maybe even crying. Little 2F would most likely squat down for a closer look, maybe even pick it up in the palm of her hand and pet it. But 3M's response was more, um, 'elemental' - he'd stomp on it, usually with a triumphal shout.

So, you know, the contrast was pretty clear. . .

Testosterone - it's a wonderful thing. . .

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And estrogen!  Estrogen is wonderful, too!  If, you know, you happen to rock that way. . .

;)

Potty Talk

OK, my friend Suldog has done it again.  A while back, he posted about HIS WIFE'S accidental misadventure (at least, he presented it as accidental, and I have no reason to doubt him) with a public restroom.  Which, as Suldog's posts often seem to do, called forth a couple of stories from my own young life, which I left in his comment-space, but later decided that they would work just fine for taking up some space in my own humble blog.  You all can tell me whether or not I assessed their quality accurately. . .

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Many years ago, Jen and I were at the annual Mackinac Bridge Walk, held every Labor Day, in which a couple lanes of the majestic bridge joining Michigan's peninsulas are given over for a few hours, so that Michiganders (or, really, anybody who shows up) can walk the 5-mile span. Something like 50,000 people do the bridge walk every year, proceeding from north (St. Ignace) to south (Mackinaw City).  Bridge-walkers can park their cars at either end of the bridge, but south-to-north bus transport will be required, either to take you from your car on the south end to the beginning of the walk, or from the end of the walk to your car on the north end.  Michiganders have learned, from 50+ years' experience, that, if you are in the UP on Labor Day, and want to drive south, you either cross the bridge before the sun rises, or you wait until later in the day.

So we walked the bridge, and we had a great time.  There is something fairly awesome about walking across a five-mile expanse of open water, with its views of Michigan's two peninsulas, and Mackinac Island (which is probably my favorite place in all the earth).  And it is not unusual for a freighter to pass under the bridge, and thus, beneath the walkers' feet, in the course of the hour-plus it takes to complete the walk.  At the highest point of the bridge, the walker is more than 200 feet above the water (and the center lanes of the suspension portion of the bridge are decked with an open steel grid, for aerodynamic reasons; if a walker suffers from vertigo or acrophobia, he is well-advised to keep to the solidly-paved outer lane)

Anyway, with so many walkers, the, uh, need for toilet facilities is particularly acute, given that the normal population of Mackinaw City is a bit under1000 souls (altho, during the summer tourist season, the town is considerably more crowded than that). One of the years I went, I got to the end of the walk and really had to go.  There were something like 50 porta-johns lined up in an open field near where the buses were lined up to take us back to the north end of the bridge, where our cars were parked. Half of 'em were labeled 'MEN' and the other half 'WOMEN'. For some odd reason, there were long lines at all the 'MEN's' porta-johns, but none at all at the 'WOMEN's' (which, I think, is the absolute only time I've ever seen that, but that's how it was).

I was somewhere around 20th in line, crossing my legs and urging the lines to move faster, when the thought slowly crept from the deep recesses of my brain to the level of outward conscious thought - 'Waaaaiiiiit a miniiiiitttt. . . only one person at a time can use a porta-john. . .  They don't need to mark 'em for MEN and WOMEN at all. . ."  Evidently, the exact same thought percolated to the front of several other men's minds virtually simultaneously, because several of us together wandered over to the WOMEN's porta-johns and quickly availed ourselves of their amenities.  By the time I emerged a minute or two later, having finished my business, and being considerably more relieved than when I'd gone in, the 'MEN' and 'WOMEN' signs had all been taken down, and all the porta-johns had lines, half as long as the previous ones, and, uh, urinary throughput was doubled. . .

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Another time, I was at a conference at a small liberal-arts college in Michigan. During a break between sessions, I made use of the restroom facilities. The urinals (ladies, if you really don't know what 'urinals' are. . . uh, ask your brother, or something) were of an odd type that I hadn't seen before - sort of a 'pedestal' design, away from the wall, that required the, uh, user to sorta split his legs on either side of the, uh, receptacle, in order to 'do his business'. Afterward, I was commenting on the uniquely-configured urinals to one of the other (male) conferees, when an employee of the college, standing nearby, overheard us.

"Oh, that is quite intentional," he informed us. "They're unisex urinals." I invested a few seconds' thought toward how that might work if I were, you know, an actual woman (and it seemed to me that, in actual usage, it might not work quite as, um, cleanly as what the designer originally thought it would) (I should also mention here that I never wandered into the women's restroom to see if they had also been installed there).  Then I quickly shook my head to clear the image from my brain.

Only, you know, at a college (probably the same folks who dream up stuff like this). . .

The Patent and the Formula

A while back, Uncle Skip gave me a bloggity award, the acceptance of which entailed me telling you all a few things about myself. And so I did, without actually telling you much at all about myself. Except for one thing - I mentioned that I have a patent to my name, and possibly a mathematical formula. Which struck a few of my commenters (I'm lookin' at you, Bijoux, Sailor and Lime) as interesting, and they asked me to give more details. So I left my own responsive comment, giving the short version of the two stories. And, in the ensuing months, I've come to think that those stories might be worth a full-blown post, giving a fuller account. You know, for posterity, and all that. (See, I'm just vain enough to think that somebody, somewhere, centuries in the future might stumble across this blog, and say, "Wow, this dude had a patent and a formula! I wonder who the hell he was?")

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The Patent

When I was still working at my first job, I did some work on a project that was a bit unusual, for a customer that usually worked closely with one of our competitors. They had an idea for a non-pneumatic spare tire/wheel, to save space and cost (as against the typical pneumatic mini-spare, or even moreso, an actual full-size spare). They had gone first to our competitor, with whom they had a long-standing working relationship, and asked them to develop the design for them. But the competitor was unable to come up with an actual working design, so they came to us.

When we got the design, we could see immediately that, as given to us, it wouldn't work. But our company had had, for many years, contracts with the US Defense Department, to make wheels for tanks and other tracked vehicles, which were also non-pneumatic, and there were a couple of design 'tricks' that made such a wheel actually work.

So when I was given the project, I did my usual analysis and immediately saw that the stresses were way too high. But, I told my bosses, this was really a pretty similar thing, conceptually, to a tank wheel, and what if we applied tank-wheel design principles to it? So I did a re-design according to tank-wheel design principles, and when I analyzed it, lo and behold, we got a working design! So we made a few prototypes and tested them, and they seemed to work just fine. And I, having done my job, was happy, and moved on to my next project.

At that point, our top management got a little nervous (and not without reason), that our customer could just take all our great design/development work and hand it back to our competitor, with whom they had a nice comfortable business relationship. So they decided (unbeknownst to me) to seek a patent, in order to protect our 'intellectual property' rights.

Thus it was that, a year or so after I'd worked on the project, and had all but forgotten about it, I was called into a series of meetings to describe to a bunch of lawyers what I'd done, and blah, blah, blah. And the upshot was, that when the patent was granted, my name (among others) was on it. It had been an interesting project, and I was a little proud of having made the 'conceptual leap' to incorporate tank-wheel design principles, but as far as I was concerned, I was just doing my job. Getting the patent was never my idea (although I was certainly not opposed to it); someone else sought the patent, and in the end, because I'd worked on it, my name was one of the ones that got slapped on it.  So they paid me a dollar for rights to the patent, and I was invited to the annual Patent Luncheon for as long as I worked for the company (which turned out to be just a couple more years).

So now, I've got a patent to my name, which is nice. (Honestly, though - my dad has something on the order of 20 patents, in half-a-dozen countries, so I don't make a bigger deal of it than it merits. . .)

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The Formula

(OK this is math; if your eyes start to glaze over, feel free to stop at any time)

This one comes from my first job, as well. In the course of doing Quality Assurance on our parts, we would scan them in a machine that essentially took a series of points (typically a number in the hundreds, or at least the tens) from the surface of the part. Then we had to take those hundreds of points and generate the key dimensions we were trying to measure from them - a radius, an angle, or what-have-you, in order to determine whether they were within the specified limits, or not. Getting an angle from the point data was pretty straightforward - there are lots of well-understood methods and formulas for computing a line (and thus, an angle) from a set of points (I should note that the key thing here is that we had so many points - if we only had two points, then it's straightforward to calculate the line between them; any middle-school student could do it. But when you have more than two points, to say nothing of hundreds, it gets more complicated to compute the line that 'best fits' the large set of points.)

For a circle, though, there weren't any readily-accessible methods or formulas available, as far as I could tell. From high-school Algebra, I knew that I could calculate a circle from three points, but I had no idea how to do it for five, or fifty, or five hundred points. I played with calculating a circle from every possible set of three points taken from the larger point set, and that gave me a 'bracketed' answer - the limits between which the 'real answer' had to lie - but that wasn't a very satisfying answer. I even went to the Math Library at the University, to see if there were any obscure formulas published anywhere, but they couldn't easily point me to one, either.

So, over the course of six months or so, I played around with the problem, trying to figure out a way to attack the problem. From time to time, I'd have an idea that seemed like it might be fruitful, and I'd make some progress on it, but it was slow. And I still had to work on my regular job, so I didn't just have unlimited time to work on the 'best-fit-circle' problem.

Then one day, I had a flash of insight (it involved choosing a workable error-measure, if any of you are math-y enough to know what that means), and cranked the formula through (it involved a LOT of cranking). Then I wrote it into a computer program, and ran a few point sets through it, and what do you know? It worked! It calculated a circle that by-golly corresponded to the set of points. So, I put the computer program into a more-usable form, and we went on our merry way, using the formula in the day-to-day work of checking radius dimensions on the parts we manufactured.

Now, I didn't for a minute suppose that I had actually derived an original formula. I thought all along that someone, somewhere, had derived this formula years before, and I just wasn't clever enough to track it down. No big deal - many times, in Math classes I'd had over the years, we'd derived the classical formulas that were in our textbooks, just for the instructional purpose of seeing where they came from. And I was sure that this was one of those - I could have looked it up, but failing that, I just derived it myself.

Fast forward 15 years - A guy I know runs a 'Math' column in a little engineering journal, and I'd written a few articles for his column over the years. He was running low on columns 'in the can', and he asked me if I could write another article for him. I showed him my notes for the 'best-fit-circle', and he thought that would make a great article, so I wrote it up, and a year or so later, he published it.

Now, whenever I've written one of those 'Math columns', I always get a few emails in the aftermath of it being published - it's a lot of fun to hash over the column with other interested folks. Once, I wrote an article on how the sun's position in the sky varies over the course of a year, and I got all sorts of interesting emails, from guys wanting to talk about how to design their house to get more sun in winter, and less in summer, or a professor sending me a little 'solar calculator' he'd invented.

When the 'Best-Fit Circle' article ran, I got emails from a couple of pretty high-powered academic-type guys, thanking me for the article, saying that it was obviously really useful, and asking me where I'd gotten the formula from. When I said, sheepishly, that I hadn't found it anywhere, that I'd worked it out myself, and by the way, could they tell me where it might be published, they wrote back, congratulating me for deriving a really useful formula. One guy was on the development team for one of the major commercial computer-graphics codes, and he said he'd searched all through the literature for all the various different methods for computing a circle, and he'd never seen it before. Which kinda stunned me, actually.

Then one day, one of my kids did one of those things that kids will do - he googled his dad's name - and found, among various letters to editors I'd written, and whatnot, at least two instances of college professor-types assigning homework to their classes, involving the formula I'd published in my friend's little journal (properly attributed, and everything). Then, when 4M had a calculus class at the junior college, he mentioned to his instructor that his dad had written a math article, and the instructor asked if I'd send her a copy. She really liked it, and started assigning it to her own classes. I spoke to her once, and she mentioned it to me, and I told her that I couldn't really believe that it was original with me. But she said she'd never seen it anywhere else, and as far as she was concerned, it should properly be called [Craig]'s Method, and I'd be within my rights to call it that.

So there you have it - nothing is officially 'written in stone', or anything like that, but if anybody wants to make reference to the Best-Fit Circle formula by that name, I welcome you to do so. . . ;)