dem doggone bloggin’ blues …

one more hole in the water …

1982 Catalina 27 sailing classroom

I love my wife. Dearly, as I am constantly reminded. After 40 years of marriage, one might think I have her figured out. Not so! Debbie is getting promoted to 6th grade science and math teacher, and has apparently conspired with a working acquaintance to buy his boat. Yes, all in the name of science! She says here in an email, not so cryptically, ‘What better science laboratory than a sailboat? And you can teach my students to sail when we return from Europe each Summer!’ Uh .. doesn’t that presuppose that I actually know how to sail, which is a dubious claim at best? And didn’t we marry each other in 1982? It’s kismet I tell you!

So, what do we have here? A 1982 Catalina 27, in what looks to be perfect condition other than the sad original Universal 14hp diesel engine. Yes, it is claimed to start easily and run great, but for how long before I must perform a disembowelment or cast our fate to the winds and pray each time we venture out thru Cattle Pass and across the Strait enroute to Port Townsend?

Tea for the Tillerman ... and French toast?

You know, I could actually get excited about this new venture. After all, I love children, and love to teach math and science. Indeed, I could get really excited about nurturing a love for science in 6th graders, not to mention promoting a love for sailing. It looked bodaciously good on paper, until reality bit. And it bit hard! The boat comes with a 50′ slip. I emailed the marina and there is a 5-year (minimum) waiting list for 30′ slips, which could spoil the deal. We would have a 50′ slip .. for a 27′ sailboat. And then the crusher .. $528.21 per month for moorage. That buys a lot of fine wine and French escargot in Paris, and well … certainly leads one to reconsideration.

It’s my first boat with an actual honest-to-god tiller. I’ve been tillerman, via email, since my early years (1986) of engineering on the web from my fondness for Cat Stevens (Tea for the Tillerman), and always felt a bit guilty sailing our beautiful Hallberg-Rassy 42 sailboat, sans tiller, resorting to a large wheel at the helm. Ah … perhaps now I can be a true tillerman and find a brighter star to steer by.

And to think of all the new, and state-of-the-art, electronics she might require!

tillerman

Musée du Louvre …

Leonardo da Vinci's Mona Lisa

In my pursuits of studying Art History, I applied for and received an l’artiste pass for the Musée du Louvre in Paris. It’s one of my favourite places in the world, and one I find myself visiting several times each week. There are times when the museum appears empty. That is, until you walk down the hall and around the corner and see this sight. Hundreds of tourists with flashing point-and-shoot cameras, jockeying for position, to take one more poor photo of da Vinci’s Mona Lisa. It’s quite comical to watch them rush past some of the most exquisite paintings known, take the emblematic photo of a smallish and faded painting residing behind bullet-proof glass, and then make a beeline to the Carrousel du Louvre below, for a Café Américain at Starbucks.

Fermat’s Last Theorem …

from the archives …

looking at this equation, it might pique your analytical interests enough to wonder if there are positive integers (counting numbers) other than 0 and 1, where the equation has a solution. the Greeks knew that for n = 2 there most certainly are solutions (as shown), and in fact, they had their own Pythagorean Theorem to prove it. and it is true, that we can build triangles with all sides including the hypotenuse as integers. now I’m not much of a gambler, but I would bet against anyone finding a solution to the equation with n = 3 or greater. Pierre de Fermat took it to heart, and in 1621, took hold of this conjecture and made it his very own theorem (which it wasn’t). Fermat’s Last Theorem to be exact. Pierre said no .. for integers where n is greater than 2, there are no solutions. he went on to write in the margins of one of his math texts “To divide a cube into two other cubes, a fourth power, or in general, any power whatever into two powers of the same denomination above the second, is impossible.”

but here’s the kicker …

“I have found an admirable proof of this, but the margin is too narrow to contain it.”

and with that .. Fermat’s Theorem became the most celebrated unsolved problem in mathematics for almost four-hundred years.

in June, 1993, Andrew Wiles of Princeton University published a 200-page proof that Pierre de Fermat’s conjecture was indeed, now a theorem.

da gamba’d …

It’s raining … again. Cold and wet. It seemed reasonable to sit by the fire and play Bach Cello Suites on the cello. That is, if I still had my cello, which I do not. After storing it in the V-berth of our sailboat for several years, I (Debbie) made the decision to find it a new home. A niece I have never met now owns it and hopefully they are making beautiful music together. I still have a cello bow – a Christopher English baroque bow, with nothing to play on. No worries … I am having another cello built. A little different this time around. A viola da gamba. Since I had such difficulty in playing the cello with four (4) strings, it’s only natural to now play one with seven (7) strings!

My main issue is that the tunings of the two instruments are not the same! The cello is tuned in fifths, and much like the guitar, the viola da gamba is tuned in fourths. Not a problem if one doesn’t strive to play the Cello Suites by J.S. Bach, written for the cello tuning. I attacked the problem by attempting to play the Prelude in G-major on the guitar in what is called DADGAD tuning. This would have been perfect, since I tend to play guitar in this tuning (Bruce Cockburn, Patty Larkin, Richard Thompson), but it simply presented too many problems. I tuned the guitar in fifths and can play as I would on the cello, but the genesis of this project was to learn the viola da gamba and play the cello suites in its native tuning.

Da Gamba’ists .. any suggestions?

daniel

Bernoulli’s brachistrone …

from the archives …

the brachistrone

admittedly, there is little that is intuitive here. it would seem that a straight-line dash to the finish would be the fastest. indeed, that is the shortest distance but we constrain our velocity induced from gravity in doing so.

this problem has always fascinated me. it’s associated with the problem of the rim on the flange of a railroad train wheel, that travels below the top of the train track. does it actually move backwards? a speeding train .. and yet there are parts of it that move backwards even as it speeds along? get out! well .. enter the cycloid. the prolate cycloid.

the question is – if we were to roll a ball down a path of our own design, to get the ball to a point not directly beneath our starting point in the shortest interval … what would this curve look like? you might guess that it is a straight line. that is, the shortest distance between two points. it’s really not a trivial problem at all, and one that stumped many a mathematician. of course, Issac Newton solved the problem in a day .. but then, we aren’t Issac Newtons or the Bernoullis! I have also been told that the Peregrine Falcon uses this exact curve to catch its prey. a smart bird! I’m just wondering how it figured out those difficult differential equations in such a short lifetime?

daniel

Pilsners and pretzels in Prague …

iPhone'd along the Charles Bridge on the Vltava River

returning from the Institute of Mathematics in Prague … seeking out a cold Pilsner and pretzels.

causal determinism …

“We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.”

 -Pierre Simon Laplace, A Philosophical Essay on Probabilities

causality – the relation of cause and effect. Life has such a wonderful way of providing opportunities from the slightest of motivations. My studies of partial differential equations (system causality and time-invariance), led to Pierre Simon Laplace, that led to a visit of his grave in Paris, that led to living in Paris, that led to learning the French language to read the original French scientific texts of Laplace, Fourier, and Lagrange.

I’ve explored many avenues, and admittedly, I am not a student of languages. I struggle. I found Coffee Break French and Walk, Talk, and Learn French, both from the Radio Lingua Network, to be just my cup of tea coffee. Video and audio podcasts lead the beginner (that would be me) gently through the maze of conjugation and the foundations of conversational French. The true benefit, for me, is that it is accessible via iPad and iPhone. That is to say … everywhere I go.

If you find yourself wanting to learn French, or Spanish, I encourage you to peruse www.radiolingua.com for more details. A great way to justify that new iPad 3 we’re all waiting for!

daniel

game theory and Monsieur Black …

from the archives …

game theory is a fascinating pursuit in mathematics to describe the structures of how we humans play games. chess, poker, and even economics. there are no shortages of interesting mind-benders and puzzles, and this is one of my favourites. enjoy!

truel – similar to a duel but with three participants rather than two.

One morning Mr. Black, Mr. Grey, and Mr. White decide to resolve a conflict by truelling with pistols until only one of them survives. Mr. Black is the worst shot, hitting his target on average only one time in three. Mr. Grey is a better shot hitting his target two times out of three. Mr. White is the best shot hitting his target every time. To make the truel fairer Mr. Black is allowed to shoot first, followed by Mr. Grey (if he is still alive), followed by Mr. White (if he is still alive), and round again until only one of them is alive. The question is this: where should Mr. Black aim his first shot?

Let us examine Mr. Black’s options. first, Mr. Black could aim at Mr. Grey. If he is successful then the next shot will be taken by Mr. White. Mr. White has only one opponent left, Mr. Black, and as Mr. White is a perfect shot then Mr. Black is a dead man.

A better option is for Mr. Black to aim at Mr. White. if he is successful then the next shot will be taken by Mr. Grey. Mr. Grey hits his target only two times out of three and so there is a chance that Mr. Black will survive to fire back at Mr. Grey and possibly win the truel.

it appears that the second option is the strategy which Mr. Black should adopt. however, there is a third and even better option. Mr. Black could aim into the air. Mr. Grey has the next shot and he will aim at Mr. White, because he is the more dangerous opponent. if Mr. White survives then he will aim at Mr. Grey because he is the more dangerous opponent. by aiming into the air, Mr. Black is allowing Mr. Grey to eliminate Mr. White or vice versa.

this is Mr. Black’s best strategy. eventually Mr. Grey or Mr. White will die and then Mr. Black will aim at whoever survives. Mr Black has manipulated the situation so that, instead of having the first shot in a truel, he has first shot in a duel.

daniel

lunch with Pierre-Auguste Renoir …

Le déjeuner des canotiers

The painting depicts a group of Renoir’s friends relaxing on a balcony at the Maison Fournaise along the Seine river in Chatou, France.

We’re taking the train to Chatou to lunch at the Maison Fournaise restaurant, and then off to Giverny to see Monet’s waterlilies.

watercolouring …

Nothing in my life has been as difficult – not my flying, sailing, or engineering, as compared to my attempts at drawing a line with a pen or brush that accurately reflects my intent!

Montmartre, Paris …

Amedeo Modigiiani

Our new home is located in the 18th arrondissement of Paris called Montmartre. Famous for the filming of Amelie, and the La Boheme district of so many artists from Modigliani and Picasso, to Renoir and Cézanne.

And the Sacre Couer and Moulin Rouge of course …

our block in Montmartre, Paris

a house in Paris …

Air France Airbus A380 to Paris

and I thought homes on San Juan Island were overpriced!

in the belly of Paris …

+1 UTC

suspended belief …

The Louvre, Paris - Napolean III meets I.M. Pei

Serendipity is one of life’s great gifts. A Walt Disney Sunday television show about a boy who learns to fly gliders, ‘The Boy who flew with Condors’ sparked over forty years of flying for me. An extemporaneous road-trip to Port Townsend for our anniversary led us to unbelievable adventures that included buying a sailboat and living aboard for seven years. And now – a latent interest in architecture and my passion for mathematics has paved the way toward extended travels and my studies of our world’s greatest architects and their designs.

just landed - Heathrow Airport, London

floating the Thames, London

The Gherkin, London

St. Paul's Cathedral

enroute Amsterdam via Holland overnight ferry

Prime Meridian - abreast two timezones

definitely not Sir Isaac Newton

sloshing towards Mozart in Haarlam

Basilica di Santa Maria del Fiore - Firenze, Italy

…

playing with blocks …

from the archives …

not drawn to scale

playing with diverging infinite series would be more accurate I suppose, though slightly less tantalizing. within my efforts to teach mathematics and hopefully instill that MATH IS FUN and not abject terror into the minds of our youth, let me try this attempt to show the beauty of math.

the idea is simple. we have an infinite supply of blocks, each 2 units long, and we would like to stack them such that we build an arch where the top block’s length will extend out entirely from the left-edge of the bottom block to start. and yes, our arch must remain standing by supporting itself. can we do so without our best construction efforts plummeting earthward?

the basic idea here, using the first six blocks for example, is to stack them such that the center of mass lies directly on the left-edge of the block adjacent to it. you’ve seen this in architecture of course, but we’re going to attempt it without support or mortar. a hint – it can’t (realistically) be done by starting with the bottom block and working upward. it can be accomplished by starting at the top and working downward.

it is obvious what is happening. with each successive block, the distance changes between the two left-edges of adjacent blocks. it works for our six blocks, but can we continue on forever? can we span a ten-foot arch as an easier goal than infinity? remember, each block is 2 units long. let’s call a unit measure as 1-foot.

upon reflection, it is obvious that with each block, the center-of-mass moved to the right, 1/(n+1) the distance it moved previously. that is, if we add up all the distances of how the last left-edge moves, it would start with 1 unit for the top block, 1 + 1/2 for the next, 1 + 1/2 + 1/3 + … for the next block, and on and on. this looks suspiciously like the harmonic-series we all studied in high-school Algebra. and it is!

poking around a bit, it appears that the more blocks we use, the farther out we go along our arch. it does slow down for sure, and we will be using quite a few blocks to span … let’s say 25 feet. how many?

let’s look at a few numbers and graph the first 1000 blocks to see how the center-of-mass behaves as we add more and more blocks.

look familiar? this shape is called the natural logarithm curve.

our objective is to span a 25 foot distance or 25-units (12.5 block lengths). based on the properties of the harmonic series, a few calculations yield that Log[N] = 23 and N = 9.7448×10⁹ blocks. that’s a lot of blocks. in fact, if each block has a 1.5″ thickness, the height of our arch will be approximately 1.46172×10¹⁰ inches or just about the distance to the MOON!

the answer is, yes, we can build our arch. because our infinite series is divergent (continues to increase forever), we can do it but it will take more resources than our planet can reasonably provide!

daniel

a move to Paris …

Paris, 2011

one foot on San Juan Island, the other in France.

more to follow …

oh dear …

I just received word that American Airlines has filed for bankruptcy protection.

Normally this wouldn’t be much of a concern, but for the fact that I have a flight on American Airlines out of Paris to get back home.

I personally like to have happy and content employees (pilots, mechanics, handlers) cheerfully doing their best to get me home safely!

vortexual …

Hotel Erzherzog Rainer in Vienna, Austria

Debbie makes a beeline for her morning Viennese coffee.

iPhone’d not far behind!

light and shadow …

deck chairs

I can’t say much for Winter. It generally leaves me in a funk, counting the days till the vernal equinox. It seems I am always cold and less than thrilled to freeze nose and fingers looking for something to photograph. At least the iPhone facilitates wearing gloves.

According to Wolfram Alpha, I have only 171919 minutes to go.

Guernica …

Picasso's Guernica

I finally ordered train tickets from Paris to Nice, Barcelona, Madrid, and Lisbon. My evenings find me plowing through John Richardson’s 3-volume biography of Picasso and making plans to see much of the art. Even though the Musee Picasso in Paris is still closed for renovation, I am anxious to travel to and visit the Picasso museums at Antibes, Barcelona, and Madrid.

bon appétit …

Midnight in Paris …

searching for Bordeaux

Napolean’s garden …

iPhone'd in Paris

oculusious …

a fly does math …

from the archives …

students -

two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 mph. at the same time, a fly that travels at a steady 15 mph starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels.

question: what total distance did the fly cover?