Obrigado, leitor gentil

On two recent occasions someone I did not know left a complimentary comment. They were written on two different postings by two different people, but both said, in effect, that the posting was interesting and well written and that they would continue to read my blog.

I may say that I really wasn’t sure what the second one was about at first as I didn’t recognize the language in which it was written. Google Translate identified it as Portuguese. It did make me wonder why someone who reads English well enough to appreciate well-written prose is not fluent enough to write the comment in English.

Nevertheless, one appreciates appreciation in any language, and it has reminded me that last year about this time, I promised myself that I would post more writings here. While I did pretty well at first, I petered out.

Now it comes home to me that my fan base, which heretofore comprised a half dozen family members and friends, may very well be growing and that when I fail to publish I may very well be disappointing not just my loyal little coterie but complete strangers as well.

That is a heavy responsibility. I am, therefore, going to resurrect last year’s pledge to do better, to write more and publish it. After all, once you’ve been praised in Portuguese, you know you’re on your way up.

Research Paper 001 - Fibonacci

[In my post of December 31, 2013, I discussed having found a blog in which a young woman was publishing her old high school term papers, and I threatened to do the same when I didn't have anything else to write about. Well, I'm doing it. Here is a paper I wrote in March 1982 when I was a doctoral candidate in music at Michigan State University for Music 943, the History of Music Theory.]

FIBONACCI, PHI, AND GOLDEN THINGS

             Leonardo da Pisa, known as Fibonacci, dealt with mathematical problems, like all educated people of his day, by adding and subtracting Roman numerals and by using an abacus for multiplication and division because such operations are virtually impossible with Roman numbers.

            The son of an Italian merchant, Fibonacci spent much of his youth in North Africa where he became acquainted with Hindu-Arabic mathematical notation.  He found this system, with its place values and symbol for zero, far superior to the cumbersome Roman numerals still in use in Medieval Europe, and in 1202 he wrote his famous Liber Abaci (“Book of the Abacus”), which he revised in 1228.  In it, he explained and advocated the use of Hindu-Arabic numerals.  Although it had little immediate impact, Fibonacci’s treatise later became instrumental in converting Europeans to the Hindu-Arabic system.

            The man who freed the West from the drudgeries of Roman numerals is best remembered today, however, for one trivial story problem he posed in Liber Abaci, to wit:

A certain man put a pair of rabbits in a place surrounded by a wall.  How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?[1]

The answer to the problem, as shown in Figure 1, is 986 pairs of rabbits.          

Figure 1

What is more interesting is the logarithmic number series that arises in the computation of the answer:

                                    1 1 2 3 5 8 13 21 34 55 89 144 233 377 986

            Fibonacci recognized the intrinsic property of this sequence of numbers:  that each term is the sum of the two preceding terms; but otherwise he seems to have attached no special importance to it.

            Several centuries later it was shown that this sequence of numbers had another unusual property.  In each case, the term divided by the next larger term results in a ratio approaching .618.  In fact, the larger the numbers, the closer to .618 the ratio becomes, as shown in Figure 2.

Figure 2

            It was the nineteenth-century mathematician Edouard Lucas who called this number series the Fibonacci Sequence, and it has been the source of infinite fascination for the mathematically inclined ever since.  The ratio .618 is given special significance as it relates to various golden things (the Golden Rectangle, Triangle, Mean, Section, Angle, etc.) and is itself  called the Golden Ratio.  But it was not Fibonacci’s discovery or invention, and his series of numbers is best understood as a manifestation of the somewhat mysterious phi.

            Phi (φ) is the name given to this ratio by Mark Barr early in the twentieth century.[2]  It is an irrational number; that is, its decimal expansion is infinite and non-repetitive.  It is clearly exemplified by the following line:

                                                                                    |                                  

                                                A                                             B

The line is intersected in such a way that the smaller segment (B) bears the same relationship to the larger (A) as the larger segment (A) bears to the whole (A + B).  The Golden Ratio, therefore, may be expressed as:  A is to B as A+B is to A. The value of phi is 1 + \sqrt5 / 2; that is: 1 + 2.236 ÷ 2 = 1.618. If A is 1, then B is the reciprocal of phi, or .618, and A + B is 1.618.

     This relationship is implicit in the Fibonacci Sequence (with the larger numbers – see again Figure 2).  For example:  89 + 144 = 233; and 89 ÷ 144 = .618; and 144 ÷ 233 = .618; therefore, 89 is to 144 as 144 is to 233 (the sum of 89 and 144).

            Any number may be multiplied by .618 to arrive at what has come to be called the Golden Mean.[3]  In the Fibonacci Sequence, each number is the Golden Mean of the number which follows it.  It has been shown that creations of nature and of man often exhibit such golden things.  Analysts of music have discovered numerous examples of composers’ application of the Golden Mean to formal divisions of compositions.  Many of these analysts base their investigations on the Fibonacci Sequence, which is a numerical expression of phi; but it is not the origin of these phenomena – the special properties of phi were known to man millennia before Leonardo da Pisa was born.

            The Great Pyramid of Giza, constructed in 4700 B.C.E., was said to have been built according to some “sacred ratio.”  The ratio of the distance from ground center to base edge to slant edge has been shown by modern investigators to be .618.  The ancient Babylonians were also aware of this ratio, as were the Greeks, who gave us the name Golden Section.

            In the sixth century B.C.E., followers of Pythagoras adopted the pentagram – the familiar five-pointed star – as a symbol of their brotherhood.  The star is derived from diagonals interconnecting the angles of the regular pentagon, as shown in Figure 3.

  

Figure 3

Each line of the star intersects two other lines at the Golden Mean – .618.

            Golden proportions are found in Greek Architecture, including the Parthenon, seen in Figure 4.

Figure 4

This figure shows that A is to B as B is to C and as C is to D and as D is to E, etc.

            The abbey church at Cluny, built about 1180, also displays proportions resultant of phi.  Mark Barr chose phi to designate the Golden Ratio because it is the first letter of the name of the great Greek sculptor Phidias whose work shows multiple manifestations of the ratio.  The Golden Ratio was known to Euclid as “extreme and mean ratio,” and in the Renaissance it was referred to as a “divine ratio.”

            The Golden Rectangle, whose height is the Golden Section of its width, has long been considered by artists as most aesthetically pleasing.  From this rectangle is derived yet another golden thing:  if a square is made within the rectangle, the remaining figure is also a Golden Rectangle (see Figure 5).

Figure 5

If the process is continued, smaller and smaller Golden Rectangles are produced; and if points of the division of the Golden Section are connected by a logarithmic spiral, the result is the only spiral that does not change its shape as it grows larger.  The shells of mollusks and the arrangement of seeds on the heads of certain sunflowers are the same logarithmic spirals, as are the spiral arrangements of leaves or branches around the stalks of some plants. Other manifestations of phi are found in abundance in nature.  The Fibonacci Sequence is found in patterns of daisy petals and in patterns of scales on pine cones and pineapples. Golden proportions are also to be found in the ancestry of male bees, in the relationship of the length of a bird’s bill to its leg, and in the refraction of light through panes of glass.

            Adolf Zeising (Der goldene Schnitt, 1884) contended that the Golden Ratio governs human anatomy, and a study by Frank A. Lonc in the 1950’s concluded that the happiest and healthiest people are those whose height is 1.618 times the distance from the soles of their feet to their navels.

            The current craze of golden investigations has also turned up Fibonacci- or phi-related patterns in the mosaic tiles on ancient floors, the meter of Virgil’s poems, and stock market quotations.

            In the first two decades of the twentieth century, Jay Hambridge of Yale expounded at length on what he called “dynamic symmetry” – growth symmetry as compared to static – and on the application of this phi-related geometry to design in architecture, the arts, and myriad inanimate objects.  Although not taken very seriously now, it is assumed that a number of creative artists deliberately included golden proportions in their works, as Hambridge had admonished them to do.  Salvador Dali’s The Sacrament of the Last Supper is awash in a sea of Golden Rectangles and a wide variety of other plane and solid figures based on phi.  Erno Lendvai has shown that Bela Bartok made extensive use of the Golden Section in his music, and analyses have revealed similar applications in the works of other composers, including Franck and Xenakis.

            The Fibonacci fad that began late in the last century and that has come to full flower in this century may have been of sufficient interest to some composers to compel them to incorporate certain golden proportions into their works.  That does not explain, however, why this special ratio turns up in the compositions of Dufay, Obrecht, J. S. Bach, Beethoven, and, no doubt, countless others.  It may well be that there is something subconsciously appealing about the Golden Mean (or Section, or Ratio) and that proportions based on phi creep into musical compositions without the composers’ awareness.

    In the case of Dufay, the preponderance of Fibonacci-like number relationships in his music must be deliberate.  Music is, after all, ideally suited to such proportions since its basic materials – intervals, rhythm and such – are  themselves proportional.  Because the peculiarities of the Fibonacci Sequence were not recognized until the eighteenth century, it must be concluded that late Medieval and Renaissance composers were not directly influenced by Fibonacci’s treatise; but it cannot be assumed that they were totally ignorant of the concept of phi in principle.  Fibonacci and phi were known to them as one of the ten Greek proportions.

            The tenth Greek proportion, in fact, is the “extreme and mean ratio,” and is described by Nicomachus in his Introduction to Arithmetic (second century B.C.E):

The tenth [proportion]…is seen when among three terms, as the mean is to the lesser, so the difference of the extremes is to the difference of the greater terms, as 3, 5, 8, for it is the superbipartient ratio in each pair.[4]

            The Greek proportions, as reported by Nicomachus, probably came down to Medieval musicians through Boethius.  In De institutione musica, he gives only the first three proportions (arithmetic, geometric, and harmonic) but he refers his readers to his De institutione arithmetica, a free translation of Nicomachus, for the other seven.

         It is clear, then, that the tenth Greek proportion is yet another example of phi at work and that, through Nicomachus and Boethius, composers from the Middle Ages on were aware of it and its special properties.

            Whether or not there is anything truly mystic in phi and the Fibonacci Sequence, it seems to intrude into a great many places.  The first movement of Beethoven’s Piano Sonata No. 17 in d minor (“Tempest”), for example, has 228 measures.  The Golden Mean, therefore, would occur at about measure 141 (228 x .618).  It is at measure 143 that the recapitulation begins.  We will never know if Beethoven planned it or whether the close coincidence of the beginning of the recapitulation and the Golden Mean was, in fact, coincidence.

            Fibonacci devotees will continue to seek new and wondrous ways in which phi pervades our world and the things in it, including, no doubt, our artistic creations.  Nature provides us with ample evidence of the phenomenon, and art, as Bartok pointed out, follows nature – consciously or unconsciously.  Perhaps the skeptics would do well to consider the prosaic fact that in any given octave on a keyboard instrument there will be found five black keys and eight white keys, for a total of thirteen.

BIBLIOGRAPHY

Basin, S. L. “The Fibonacci Sequence as it Appears in Nature,” Fibonacci Quarterly 1:1 (February 1963), pp. 53-56.

Bicknell, Marjorie and Verner E. Hoggatt, Jr.  “Golden Triangles, Rectangles, and Cuboids,” Fibonacci Quarterly 7:1 (February 1969), pp. 73-91.

Gardiner, Martin.  “Mathematical Games:  The Multiple Fascinations of the Fibonacci Sequence,” Scientific American CCXX/3 (March 1969), pp. 116-120.

            .  The Second Scientific American Book of Mathematical Puzzles and Diversions.  New York: Simon & Schuster, 1961.

Gies, Joseph and Frances.  Leonard of Pisa and the New Mathematics of the Middle Ages.  New York:  Thomas Y. Crowell Company, 1969.

Lendvai, Erno.  Bela Bartok:  An Analysis of his Music.  London:  Kahn and Avarill, 1971.

Nicomachus.  Introduction to Arithmetic, translated by Martin Luther D’Ooge.  New York:  The MacMillan Company, 1926.

Powell, Newman W., “Fibonacci and the Golden Mean:  Rabbits, Rumbas, and Rondeaux,” Journal of Music Theory 23:2 (Fall 1979), pp. 227-273.

Sandresky, Margaret Vardell.  “The Golden Section in Three Byzantine Motets of Dufay,” Journal of Music Theory 25:2 (Fall 1981), pp. 291-306.

---

[1] Joseph and Frances Gies, Leonardo of Pisa and the New Mathematics of the Middle Ages (New York: Thomas Y. Crowell Company, 1969), p. 77.

[2] Also sometimes called tau.

[3] A mean is a quantity somewhere between two other quantities; e.g., the arithmetic mean of two numbers is their average.

[4] Nicomachus, Introduction to Arithmetic, trans. Martin Luther D’Ooge (New York:  The MacMillan Company, 1926), p. 284.

A-tisket, a-tasket

This afternoon I've been sitting at my desk folding paper and listening to an album called “The Intimate Ella” on which Ella Fitzgerald abandons the snappy jazz and scat that made her famous and renders some old standards low and slow in the purest dulcet tones. She is just way too good.

I couldn’t stop myself from singing along here and there, but then in the middle of “September Song” I stopped suddenly, wondering if maybe it's disrespectful, or pretentious, or blasphemous to sing with Ella Fitzgerald. But I bet she wouldn’t have minded.

It was about  twenty years ago now (June 15, 1996, actually) that a co-worker stopped me one morning as I came into the office. "What's the matter?" she asked. "You look sad.”

I replied, “I am. I just heard on the radio that Ella Fitzgerald died.”

“Who’s that?” asked she.

Only slightly exasperated, I answered, “Probably the greatest jazz singer of all time.”

She squinted her eyes slightly, and I could see a light bulb had flipped on somewhere. "Oh," she said, "is she the old black woman with the eyeglasses?”

Uh-huh.

Last week's mini-vacation

About a year ago, the Little Traverse Bay Band of Odawa Indians opened a new casino in Mackinaw City, Michigan, under the same name – Odawa – as their casino/resort in Petoskey. I wanted to maintain our record of having been to and gambled in every casino in Michigan.

For her birthday, which was last week, my wife wanted to spend a couple days at her favorite Michigan casino, the Little River in Manistee.

This presented the perfect opportunity for a mash-up road trip.

The new casino really is tiny, about 5,000 square feet accommodating 120 slot machines but no table games, no hotel, no restaurants, no gift shop. What they do have, which is very cool, is a machine into which you insert your driver’s license, and out pops a player’s card.

Before making our way to the Little River, we spent the first night at the Kewadin Casino in St. Ignace, and the next night in Brimley at Bay Mills Casino. Then we took off for Manistee.

We needed directions, so we called OnStar. We use this service frequently when we travel, sometimes even close to home if we get lost trying to find something. The OnStar people we talk to can be friendly or hostile and anything in between (frequently bored) but they are generally all business and relatively efficient.

This time our "Advisor" was very pleasant and sounded young. We told her where we wanted to go, and in just a moment she said, “I have the Little River Casino and Resort in Manistee, Michigan. I’m downloading the directions to your vehicle now. Thank you for using OnStar.”

Then she added, “Know when to hold ‘em, know when to fold ‘em,” and terminated the call.

The Prowler

One time when I lived in Kalamazoo a few decades ago, I was reclining on my couch reading when I heard a slight commotion outside my apartment door. I was sure I had turned the deadbolt, but I got up to check anyway. There was also a chain lock which I put in place making as much noise as I could doing it. I had heard it discourages a housebreaker to know there's somebody inside.

Then I stood on my tip-toes to look out the peep-hole, but I didn't see anybody or anything except for the door to the apartment directly across the outside entryway. As I backed away from the door, I looked down and saw that the doorknob was turning very slowly.  I looked out the peep-hole again and still saw nothing, which meant that whoever was out there was either crouching or standing off to the side so as not to be seen.

I didn’t exactly panic, but it frightened me. I went directly to the telephone and called 911. The dispatcher took my address and told me she was sending a patrol car, and she made me stay on the line with her until it got there.

When the officers arrived, one scouted around outside while the other came to my door to let me know they were there, and then he too went off to see what he could find. Other apartment doors began to open and neighbors stuck their heads out, curious about the arrival of the police. I made a very brief explanation, and the man from the apartment across from mine waited with me until the officers came back.

The two policemen came back to my apartment having found nothing suspicious. They checked my windows and the locks on the door, and they recommended charlie-bars for the windows, but otherwise said my apartment was pretty secure. After they left, I locked the door behind them and tried to calm down.

About four days later, the man across the way came out to talk to me as I was coming home one evening. He said he had seen who was trying to get into my apartment and had chased him off. I asked if he got a good look at the guy and could describe him to the police. “Sure, I can,” he said. "It was a great big black cat."

What!?!

It seems this big cat was standing on his hind legs, stretching up to rub one front paw across the top of the doorknob, which is what made it turn. Maybe the cat had lived in that apartment at one time, or perhaps the people who lived there had fed him.

I was relieved, of course, but also somewhat chagrined that I had called police to come save me from a killer-rapist pussy cat.

Play away, please.

I caught a couple minutes of some major professional golf tournament last week and saw some major professional golfer not bother, after teeing off, to pick up his tee. He simply walked off down the fairway.

There has never been a suggestion that bending down to pick up one’s tee after a drive is beneath the dignity of any golfer, even a famous champion. I suppose it's possible he has back trouble and left it to his caddie, which I would not have seen as the camera followed him; or he might just be a real slob who does not pick up after himself.

Anyway, it reminded me of Betsy Pickens who played on the company golf league. Betsy was unfortunately burdened with an inflated sense of self-importance which manifested itself in various ludicrous pretensions, not the least of which involved the golf tees she used.

Betsy used wooden tees that had her name imprinted upon them. After teeing off, she left the tee right where it was – stuck in the ground, driven into the ground, four feet away, whole or broken -- no matter. Wherever and in whatever state, she left it.

Not because she was lazy, nor because she considered it undignified, nor because she had a caddie to pick it up for her. No, as she was perfectly willing to explain if questioned, she left her tees on the teeing ground so that golfers who came after her would find them, see that Betsy Pickens used golf tees with her name on them, and be impressed.

Will I ever own it?

I learned a new word yesterday:  demonym. It appeared in one of the word games I play every morning, and I admit, I had to look it up.

I figured it had something to do with words or names, from the suffix -onym, as in homonym. Once I read the definition, the prefix demo- made sense too – something to do with people or populations, as in demographic.

A demonym, then, is the name given to the people of a place. French is the demonym for people in France, and, as if often the case, is also the name of their language.

The people of Greece are Greek and speak Greek. People in Germany are German and speak German. People in the United States are American and speak English.

Well, it works most of the time.

In grade school they told us, “Use a new word ten times, and it’s yours.”  I am wondering what my chances are of slipping “demonym” into even one conversation, but you never know.

Fishing, with emesis

The summer before my fourth birthday, my parents and grandparents and brother and I embarked on a fishing vacation that involved a cabin on Lake Kabetogama, about 10 miles from International Falls and about as far north as you can go in Minnesota and still be in the United States of America.

Dad's big Oldsmobile was loaded with suitcases, fishing gear, cabin needs, and everything else a family of six would need for such an excursion, and off we went at some ungodly hour of the morning for a one-day trip of 630 miles on two-lane roads. The men were in the front – my dad driving, my brother on the hump, and Grandpa by the passenger window; in the back it was Mother, me in the middle, and Grandma.

I was car sick.

Everyone quickly tired of stopping every couple miles for me to climb out of the car to vomit, so my father got a minnow bucket out of the trunk for me to puke into. Every 50 or 75 miles he'd stop near a stream or some other source of water so the bucket could be rinsed out.

After 250 miles of this, we interrupted the trip with a stop in Black River Falls, Wisconsin. There was a clinic open where some young doctor very cleverly diagnosed motion sickness and gave us a supply of pills which were small and yellow and very, very bitter and which put me soundly to sleep.

The rest of the story is family legend because of the complete and utter despondency my neat-freak mother experienced trying to keep house in a place where there were bugs and critters and fish and sand and live bait and all manner of other unsavory things. She never went on another trip to a lake, never rented another cabin, never again went fishing, and never had any more children who were car sick because she made me take those damn pills before every car ride of 50 or more miles until, at about age 13, I was finally able to convince her I had outgrown it.

Good Advice

I woman I used to know, a professional photographer, told me about a time she had to deliver some photos to a client whose office was in downtown Chicago. She drove into the Loop and found the building, but she couldn’t find a parking place anywhere near it.

She did not want to resort to one of those public garages that charged $27 for the first half hour, so she drove around the block six or eight times hoping somebody would leave and a spot would open up on the street. None did.

Finally, she pulled into the alley behind the building and ascertained that there was a back entrance. She was sitting there trying to decide if she and her car would be safe when she saw a dirty and disheveled man shuffling toward her.  He was obviously a street person, a genuine bum complete with a bottle in a brown paper bag.

At some level, she recognized the absurdity of seeking reassurance from such as he; nevertheless, as he approached, she rolled down her window and called out, “Hey – do you think I could leave my car here for five minutes while I run into that building?”

The guy came up to her side of the car and leaned down to look directly at her through the open window. After studying her face for a moment, he said, “Lady – take a chance.”

That was over 40 years ago, yet at any time in my life that a bold decision is needed, I always recall the sage advice of the wino in the alley and say to myself, "Lady, take a chance."

Mine Ears Have Heard the Glory

One of my mother’s favorite songs was “The Battle Hymn of the Republic,” words by Julia Ward Howe, sung to the tune of a camp-meeting song called “John Brown’s Body.” It arose and became quite popular during the American Civil War.

I mentioned in a previous post (“Quite an undertaking,” October 26, 2011) that my mother had pre-arranged her funeral, which actually consisted of a single night of what they now call “visitation” or (worse) “viewing,” but which we used to call a wake.  On the instruction sheet for the arrangements, she had marked that organ music was acceptable but added a note in the margin that said, "Do not play 'In the Garden,' or I will get up and walk out.”

She included, among the few hymns and songs she wanted to be played, "The Battle Hymn of the Republic,” but when the time came, I asked the organist to omit it.  I was afraid that thereafter I would always associate that song with my mother's death.

“The Battle Hymn of the Republic” came up as a correct response on “Jeopardy!” recently, and it immediately reminded me that my mother wanted that song played at her funeral service.

I might as well have let the organist play it.

Book Covers

I've mentioned before the British company I worked for back in the 70's that made very large and very expensive things like electron microscopes and mass spectrometers. It was headquartered in Manchester, England, and the main American location was in New York. I worked in the Chicago sales office.

One of my favorite people in New York was a guy named John Tinnon who was in charge of shipping and receiving. He was intelligent and witty and fun to talk to, and completely reliable. If he said the equipment would be shipped on Tuesday, it shipped on Tuesday. He never let me down, and I thought the world of him.

An important customer needed a replacement part urgently, and I called John to see what could be done. He said he had the part in stock and promised he would get it to our office the next day. Now, this was before FedEx and over-night shipping had been  invented, so I asked him how he proposed to do that. He said, "If I have to, I'll hire a courier and put him on an airplane with it."

Sure enough, about 10:30 the next morning, a dude came into our office carrying a box with the company logo on it. I was a little alarmed because of his appearance -- long, stringy hair and a very long, stringy beard, tie-died tee-shirt and love beads around his neck. I was thinking, "Oh, John -- couldn't you find somebody besides this long-haired hippy freak?"

The guy set the package down on my desk and said, "Hi. I'm John Tinnon."

In for a penny ...

The Coinage Act of 1792 established our monetary system and also called for the building, equipping, and staffing of a mint to be located in our nation's capital, which at the time was Philadelphia. When it was the only mint, there was no point in putting mint marks on the coins produced there. Later when branch mints were opened, they used a letter (or two) to indicate where the coins were minted, except for those coins from Philadelphia. They continued to have no mint mark.

After a couple hundred years, that policy was changed.  Starting in 1980, all U.S. coins had a mint mark, even P for Philadelphia, with one exception: the penny. Philadelphia-minted one-cent coins still have no mint mark.

Here are two coins from last year. The one on the right is from Denver, indicated by the small D under the date. You know the one on the left is from Philadelphia by the absence of a mint mark.

Here are two pennies from this year:

Notice anything? Like a small P under the date on the first one?

Instead of issuing a special coin or series of coins in gold or other precious metal to commemorate its 225th anniversary, the folks at the Mint decided to do one very small but very special thing: they put the P mint mark on the pennies from Philadelphia.

The fun part is -- they didn't tell anybody they were going to do it. They just issued the coins and then sat back to see how long it would take people to notice.

The U.S. Mint has a playful side.  Who knew?

Why do we do the things we do?

Well, you probably know the story about the woman who always cut a slab off one end of a pot roast before putting it in the roaster. When asked why, she said that’s how her mother always did it. Intrigued, she called her mother and asked her why she always cut some of the meat off the roast. “That’s the way my mother always did it,” she replied.

They called Grandma and asked, “Why do you always cut a chunk off a roast before baking it?” to which Granny replied, “Because I never had a pan big enough.”

One thing my mother always did was break spaghetti in half before putting it into the boiling water, but I know why she did that – she didn’t have a pot big enough. She always used a Mirro four-quart aluminum pot for pasta, and she always broke the long strands in half so they would fit better.

I’m still using that same pot, which is at least as old as I am (i.e., 70), and I have been breaking the long pasta in half my whole cooking life.

Until now. Mueller’s has started packaging “Pot-Sized” spaghetti, linguini, and angel hair (my personal favorite) already broken into what you might call half sizes.

There must be more people out there than I ever realized who are using four-quart pots for boiling s'getti.

Are we there yet?

I saw an advertising video on Facebook this afternoon for something called the Dash Toaster. Instead of two or four slots abreast, this one has one long opening, long enough to insert  two pieces of bread end to end. It also has a see-through glass front so you can watch your toast toast.

What was really more fascinating was the demonstration, not of toasting a piece of bread in the Dash but what they did to it afterwards.

First, butter is spread over the toast. Okay. Then some jam. That's fine.

Oh, wait -- now a few blackberries. Nice touch.

Well, hold on -- a couple strawberries are added now. That'll be great.

No, there's more.  Whipped cream on top, a very generous squirt thereof from the Reddi-Wip can. All right, that oughta do it.

Well, wait -- not done yet.  A sprinkling of slivered almonds.  Nice touch.

Oh -- and here comes a shower of powdered sugar. Done, thanks.

Oops, not so fast -- finally a drizzle of honey.

Seriously?

Strike 'em out, throw 'em out, blow 'em out

The Chicago Cubs were being blown out by the Yankees in last night’s game at Wrigley Field.  Because of heavy use in recent games, the Cubs’ bull pen was pretty much worn out, so Manager Joe Maddon, a bit of a quirky guy anyway, decided to save their arms and sent catcher Miguel Montero to the mound in the top of the ninth inning.

Montero walked two batters but threw a scoreless inning. The Cubs lost 11 to 6.

It reminded me of a game played on the Fourth of July 1977 in which the Cubs were being creamed by the Montreal Expos.

A Cubs outfielder named Larry Biittner, who had pitched a couple times in the minors, had been lobbying Manager Herman Franks for a chance to pitch. With the score 11 to 2, Franks gave Biittner his opportunity in the eighth inning.

I watched that game on television, and I will always remember it, but not for Biittner's performance as a pitcher. What I remember particularly about it is that while Biittner was on the mound, some imaginative member of the WGN-TV crew put a graphic up on the screen that said:

BIITTNER PIITTCHING

That’s the only reason I remember that game. I generally like to forget games the Cubs lose 19 to 3.

Aw, go float yourself.

As I unwrapped a bar of Ivory soap, I heard the advertisements of my childhood clearly in my head:  "It floats!" and especially, "99 and 44/100 percent pure!"

And I said to myself, “Pure what?” I never really gave it a thought.

Some casual research revealed the answer: it is pure soap. Huh?

That required a little further research as I know diddly about soap making. It seems that soap is made from an alkali (basically lye or potash) and a fat (animal or vegetable). Manufacturers often add substances or chemicals that affect the smell, color, consistency, or generality of it.

Proctor and Gamble did not do that, and to prove it (to whom, nobody seems to know), sometime in the 1890's somebody from P&G sent samples of their white soap to independent laboratories for analysis. One scientist’s report noted that the total sum of the impurities in the soap was 0.56%. Some enterprising P&G executive who could subtract got the bright idea to advertise its purity with the famous appellation, “99 and 44/100% pure.”

As for the floating, that's the result of whipping it full of air. Whether the air is hot or not, it is extremely appropriate for advertising purposes.

Brain Fuzz

Everybody knows that the mind tends to get a little fuzzy as we grow older. I can still be surprised, however, by the extent of the effects of my own fuzzy brain.

As for instance last evening, when I decided my aperitif would be one of my newer favorites, a Tom Collins.

I put light rum, lime juice and simple syrup in a tall glass, used my tiny battery-powered frother to mix it thoroughly, added ice cubes, then filled the glass with club soda, stirring with a wooden chop stick (more on that some other time).

It was terrible. Well, okay, maybe not terrible, but not good. It basically tasted like carbonated lime. Adding a little more sugar syrup helped, but it was still a disappointment.

I mentally reviewed every step I had taken, and found no fault. In case I had gotten the proportions wrong, I looked up the recipe I always use. It then became perfectly clear that I had used the correct manner and method for a Tom Collins with the ingredients for a Daiquiri.

Maybe old people with fuzzy brains should drink fuzzy navels.

Neighboring States

When the U.S. Mint started their State Quarters series in 1999, I started saving them. When the program was over ten years later, I had six complete sets, and I decided that was enough.

Any time one comes my way, I still do save the Illinois quarter, however, it being my favorite. Yes, I live in Michigan, but I’m from Illinois. (See my post on this topic from October 3, 2010.)

A few years ago I happened to be in a coin store and decided I would buy a silver proof Illinois quarter. Proof coins are intended for collectors and are struck with highly polished dies on highly polished blanks and are – well, highly polished, and very shiny and pretty. Some coins, the State Quarters among them, also come in a silver proof variety. Instead of the regular copper and tin alloy of common quarters, these are 90 percent silver, just like our quarters (and dimes and half dollars and dollars) used to be back in the day.

When I got home, I was admiring the coin, but I suddenly realized it was not silver. There was a distinct coppery tinge to the edge of it. I took it back to the store, complained to the guy who sold it to me, and was given a genuine silver Illinois quarter in exchange.

Last week I was in that same coin shop, and I thought it would be fun to get another silver Illinois quarter. The man waiting on me went off to see if he had one.  At one point he called out, “What year is the Illinois?”  I told him it was 2003, and in a minute he came back with a bright, shiny coin.  I studied it very closely, making sure there was no tell-tale copper color on the edge. Finally convinced it was silver, I paid the man and went away happy.

When I got home, I was admiring my new coin -- there was George Washington on one side, and on the other side where Abe Lincoln should be, there was the Gateway Arch.

Yep, it’s genuine silver, all right. But it’s Missouri.

Un is Un, no?

I am bombarded with enough unwanted emails that I have grown quite adept at scrolling to the bottom of the page and finding the link labelled unsubscribe.

I click on it, and it takes me to an Internet screen that asks me what I want to do. Well, since I clicked on unsubscribe I probably want to unsubscribe, don't I? I, therefore, click on "unsubscribe from all emails" or equivalent, and then a screen comes up and asks me why I don't want to receive these emails anymore.

Sometimes I am to fill in with a word or phrase, and sometimes I am given several choices. My favorite one is, "The content is inappropriate." Almost makes it sound like they're sending me porn, doesn't it?

So, I click on whatever answer I like best at the time, whereupon some sort of message pops up -- sometimes telling me they're sorry to see me go, often telling me how to subscribe again if I should ever change my mind, but usually just assuring me that my effort to unsubscribe was a success.

And within ten minutes they send me an email telling me I won't be getting any more emails from them.

Sheesh.

Well, here we go

Toward the end of December, I promised myself that in the new year I would post more often on this here blog thing, aiming at something like three or four times a week at minimum. So far this year, I've published four (count 'em) blog postings, all in January. And here we are halfway through March.

Part of the problem is not having much to say. Occasionally a good topic will occur to me, and five minutes later I've forgotten what it was. I guess I need to carry paper and pencil with me wherever I go.

Another really big problem is the inordinate amount of time I spend folding paper. I love to fold paper. I love it so much, in fact, that I have started a second blog, called Fugitive Origami. (Click here to go there. It will have more content soon.)

I decided a few months ago that anybody with serious origami ambitions needs to be able to fold a decent crane, so I practice making cranes almost every day. My wife liked them so much she told me I could "leave those all over the house" if I wanted to. So far she has not admitted she regrets saying that. I haven't reached 1000 cranes yet, but I plan to get there.

My real passion is folding boxes. I love folding boxes so much that I don't know what to do with all of them. Sometimes I fold a box just because I want to fold a box, and then I throw it away. Right now I am struggling with some of the modular box designs by my idol, Tomoko Fuse, but I have finally mastered a relatively tricky one-piece triangular box of hers. Makes me proud.

So, that's all the excuses I've got for now.

And speaking of ambition, I read a quote this morning that I liked so much I want to share it here. Asked what she wanted to be, a young child wrote, "When I grow up I want to get a hat and put it on."

'Tis the gift to be simple.

Set 'em up, Barkeep!

I was in my early twenties when my mother was very ill and was hospitalized a number of times. One time I stopped at the hospital on my way home from work and my dad was already there, feeling worried and sad and helpless, as we do when a loved one is ill and there’s nothing we can do about it.

When visiting hours ended and we were on our way out to the parking lot,  I suggested that we meet somewhere for a drink before going home. I thought we could both use one. Dad agreed, and we went to a local restaurant that had a nice cocktail lounge.

We sat at the bar, and Dad ordered scotch for me and beer for him. I don’t recall what we talked about, but between the booze and the comfortable companionship, not to mention my father’s irrepressible sense of humor, we were able to relax and simply enjoy each other’s company.

The first drink was so good, we ordered another round. “This one’s on me,” I said, getting out my wallet and putting some bills on the bar.

“Oh, no,” the bartender said, slightly alarmed. He leaned over the bar toward me and said in a hoarse whisper, “You let him pay!”

He was serious, and my dad was delighted. For long afterward, he would smile to himself whenever he remembered the bartender thinking he was capable of picking up a young girl.

It made me smile too. Still does.

Inauguration Day

I sometimes have trouble falling asleep, especially now that I am retired and keep weird hours because I have no place to get up and go to in the morning.

At various times in my life I have lain awake because I was worried about something -- how to pay my rent, could I find a job, will I pass the test, am I sick or getting sicker, is it requited love, what did I eat to give me such heartburn, and, especially, wondering why I can’t fall asleep.

In all my 70 years of life, however, I have never once gone to bed worrying about the direction in which my country is headed, nor have I ever worried about losing those things I innocently took for granted – my country and its leaders keeping me safe from enemies foreign and domestic; striving for, if not achieving, equality for all; establishing just laws and tasking responsible, intelligent people to carry them out.

Until last night. It was the only time in my life I have ever gone to bed afraid for the future of my country.

Sad goodbyes, indeed

At the beginning of her cooking show on the Food Network, Ree Drummond introduces herself as “a writer, blogger, photographer, mother, and accidental country girl.” She lives on a ranch in Oklahoma with a husband, four children, and a bunch of dogs.

Last week, she published a blog posting entitled "A Sad Goodbye" that began, “I don’t want to write this post, but I have to write this post.” She goes on to describe the passing of her most famous and beloved Basset Hound, Charlie. It is a moving piece, dwelling not on his illness and death but celebrating his life and his place in hers.

I know how Ree felt, not wanting to write that post. My beloved Chihuahua, Soji, died in the fall of 2015, and I did not want to write that post either. Unlike Ree, however, I did not make myself do it.

I’m sure Ree felt obligated to share the news with her legions of fans, whereas Soji’s importance was limited to relatively few of us.  Nevertheless, even fifteen months later, I still don’t feel like I am capable of writing about my remembrances of Soji and the joy she brought into my life.

I have mentioned Soji in any number of postings over the years, and those glimpses into our life together and our love for each other are probably more telling than any tribute I could write about her now.

My condolences to Ree and her family, and my thanks for inspiring me to write even this much in memory of my tiny dog.

Was he worth his salt?

My Aunt Blanche has a vast collection of salt and pepper shakers. Most of them are souvenirs she picked up on her extensive travels in North America. They number in the hundreds.

Up until about 40 years ago, she kept them in a huge cabinet with glass doors that her father built for her. Nowadays they are packed in cardboard boxes, wrapped in old newspaper.

It has been decades since I’ve seen any of them, but there is one set I remember particularly because it was so silly that it made me laugh out loud.  They were shaped like tombstones, and the salt shaker bore an inscription I've never forgotten:

Here lies
Salty McQuaid,
Slow on the draw,
And now he’s daid.

There was a matching pepper shaker, but I don’t remember what it said. I don't know where she obtained them, but I'd have to guess it was out West somewhere.


STOP THE PRESSES!

Through the miracle of the Internet, I have found a photograph of those salt and pepper shakers. The other guy, it seems, was Pepper Wyatt ("talked too much but now he's quiet").

I swear, you can find anything out there on the Internet.