Mathematicians done for at 50?

I have been hearing and reading about mathematicians not accomplishing very much after they turn 30. It is the youth of the mathematics world, it seems, that turns out the best mathematics and comes up with the best theorems and algorithms. Perhaps part of this image comes from mathematicians who are forever young because they died young: Eisenstein and Abel, for instance, or especially Galois, who was almost a child when he was shot to death in a duel at the age of 20. There are some exceptions; for example, the people who solved Fermat's Last Theorem were around 40. So what do mathematicians like me who are over 50 do? I say that it is the childlike nature of these young mathematicians that enables them to make great discoveries. They grab for the silly and ridiculous. They imagine things out of this world, such as five-dimensional manifolds. So if you want to be able to prove theorems well into your 60s, maybe the best way is to keep forever young, and keep a childlike attitude to life, as though it were all a game. Those of us who come up with the wildest ideas are those who will be productive into our 50s and beyond. You can see some of that in my writings, where I liken hat games to aviation maintenance and contra dancing to flipping mattresses. So just keep on playing, and maybe we will be productive into our old age. No, mathematicians are not done for at 50 - they keep on going like the transfinite ordinals, which keep on coming without end.

Throbbing: Chopin's Prelude in E-flat Minor

Opus 28 Number 14 is the first of Chopin's Opus 28 preludes in a flat key. It seems simple enough. The right and left hand parts are identical, except an octave apart. I was going to say treble and bass parts, but almost all the way through the piece, both parts are bass. So this prelude grumbles. It is relatively easy to learn, since you do the same thing with your left and right hands. Some of the notes are tricky to read, especially when a D natural greets you after an F-flat major chord. Shouldn't that be an E double-flat? But the hardest thing to get is the dynamics. Follow the crescendos and diminuendos carefully. The song is a continuous rise from soft to loud to soft to loud, giving it a throbbing feel, like a pain from an injury; hence the name. The piece keeps on going with the eighth notes non-stop until thump, it ends with a concluding octave E-flat. Not a good prelude to listen to if you hurt somewhere.

Bush's chances for re-election

I know I covered this subject recently, but Bush's officially throwing his hat in the ring today brings this subject up. So how can Bush's reelection be stopped? One source says the Democrats' best chance is health costs. If so, then this is something new in Presidential politics, for it does not appear among the 13 Lichtman keys. Others say that his anti-terror stands are popular. But what is really going to happen? As I said before, Bush has lost three keys: 4 (long-term economy), 10 (foreign/military failure), and 12 (incumbent charisma). He has gained 3 (incumbency), 1 (mandate), and 7 (policy). It seems to me that the most likely scenario for defeating Bush would be an economic sputtering in 2004 together with failure to achieve our goals in Iraq (set up a democratic, peaceful government) plus something else, like a charismatic Democratic candidate or a scandal hitting the Bush administration. These things need to happen else Bush wins. But see the previous item:

The Texas Democrats

It was an absurd sight. ALL of the Democrats in the Texas legislature running off to the next state like some sort of fugitives to prevent the Republicans from ramming through a redistricting plan that could increase substantially Republican representation in the House next year. To me the foremost thing that it says is that you can't require any more for a quorum to conduct business than you require for a bill or item to pass. For if not, then a group of people greater than an anti-quorum (1 minus a quorum) but less than the bill-passing requirement can run off into the woods and kill the item. Most quorums are a majority, but the Texas legislature has 2/3, making the legend of the Texas Democrats possible.

Could this lead to Bush's defeat next year? It could happen. Texas is now shown to be the laughing stock of the nation, so much so that it affects Bush the President. The economy does not pick up and things in Iraq don't do too well. In the meantime, the US congress considers doing what the Texas legislature did, and the threat of that causes people to examine Bush and his administration more carefully, perhaps unlifting a major scandal. Or maybe the Texas Democrats would secede from the Democratic party and form a third party getting a huge share of the vote. Either of these two scenarios will defeat Bush. Not likely, but look carefully at the consequences of the Legend of the Democrats who Ran.

Dream: Chopin's Prelude in F-sharp Major

Opus 28 Number 13 is a dream. It is a relaxed 3/4 piece with sustained chords suggesting a contented state. The middle section goes into some dreamy harmonies: first into C-sharp major, then into B major, then finally ending on an elusive D-sharp minor/F-sharp major ambiguous chord that does not resolve itself until the final chord. This piece is the last of the sharp key preludes in Opus 28. The next one would be in D-sharp minor, but here Chopin flip-flops into flats into E-flat minor, presumably because the leading tone there would be a natural instead of a double-sharp. The piece reminds me strongly of Chopin's Posthumous Etude Number 2, which is marked by a duple-time bass with bass notes that come up and down in an sine-wave pattern with a 3/4 treble. I call that one "Mercury" because to me it symbolizes the 3/2 pattern of Mercury's rotation and revolution around the Sun. This 3/2 juxtaposition appears also in Opus 28 Number 13, as does the sine-wave bass, in the middle dreamy section. This piece also has some interesting harmonies, such as E natural over E sharp in the middle section, and apparently Chopin at the end wanted to play some chords that are unplayable because they stretch more than a tenth. A good prelude to play just before going to bed. Tomorrow starts the flat preludes.

What's all this about Matrix?

In 1999 I was in a group of two men and two women who wanted to decide what movie to watch one night. The two movies that were offered were Sleepless in Seattle and Matrix. The women were interested in Sleepless in Seattle and it seemed intriguing to me. Matrix, though, was based on an intriguing idea. Look at the world you see. Hear it. Feel it. This is not the real world. It is enough like the real world so you can maneuver in it, get meals, find friends, read and understand integral calculus and so forth. But it is not the real world, but rather, what your brain perceives of as the world. If something could go in there and change the references of your brain cells, might not your brain think it is in an office building in a dot com in 1999 whereas the real world is a burnt-out hulk in 2199? That is the theme of Matrix and that is exactly how it starts out. However, after seeing the movie, I began to feel the women were right. This movie, although it was based on an excellent idea, was far, far too violent. Every time you turn out someone is threatening someone, or pointing a gun at someone, or shooting someone, and one scene shows someone shooting a gun and shows zillions of gun shells falling to the ground. I therefore rated it a bomb.

Now here comes Matrix Unloaded. Unloaded? That's gun talk. It seems to me as though this new movie is just as violent as the predecessor. And I hear lots of excitement about it. But I hear most of it coming from the movie industry and the media. They are really hyping this movie up good. No matter where you turn to, you get matrix. You turn on the news, you get matrix. You turn on Larry King, you get matrix. You turn on Phil, you get matrix. Even if you turn on sports, you get matrix. Matrix, matrix, matrix. And people are lapping it up good, as can be told by the box office figures and the predicted lines to get in the theater. So this movie is going to attract crowds far beyond what one would expect from a movie of this type. Already, the local newspaper rates the story plot a dud. I can predict by how the previous movie turned out and by the hype necessary to carry this movie to the movie fans, that almost certainly this movie is just as much a bomb as Number 1 was. I feel that on a scale of 0-10, it rates 0.8; i.e., a shade less than 1. If I see it, it will be while I have time to kill and it will be from a video tape, not in a movie theater. Matrix indeed. I'd like to invert this matrix and extract its eigenvector.

Agitated: Chopin's Prelude in G-sharp Minor

Here, in Opus 28, Number 12, is a fast and agitated waltz. First there is the rising strain of notes from a G-sharp minor chord, reminding me of a climactic buildup, misplaced at the beginning of a number, not the end. The buildup resolves itself, only to rebuild again. The waltz goes like this for a while, shifting keys a bit and building up to a big climax with its D-sharp minor chords. It then continues on and on, until it reduces to just two notes jumping back and forth. The waltz then resumes and ebbs away, only to have two sprightly octaves pop up at the end. It is not too hard to learn to play, although some of the chords are a bit of a stretch. There is also the problem of moving one finger of the right hand while keeping the thumb on the same note. I suppose one could dance the waltz to this, but it would be a bit more forceful than the usual waltz, because every one of the three beats is accented, not just the first one. As a waltz, this piece has somewhat of a Slavic feel, but that may just be because of the minor key. In any case, it seems to be the direct opposite of the previous prelude in B Major.

Contentment: Chopin's Prelude in B Major

This prelude, Opus 28, Number 11, suggests contentment to me, hence the name. It is a happy and resolved piece. Down under the contented exterior, there are some unexpected turns. These come out if you play the prelude. You stumble all over the place to begin with because the notes are not where you expect them. An arpeggio goes zigzag up and down then it unexpectedly goes up after an up. The pieces of the prelude do fit together into an organized whole. So this can be thought of as a Yin-Yang piece: there is a disturbance in the contentment. It terminates with a one-note solo (as do the preludes in D flat, A minor, and some others) followed by parallel fifths (Fx-Cx -> G#-D#), something the classical musical theorists say should not be done. So Chopin is breaking ground with this pleasant-sounding piece.

By the way, I am going to put all of these reviews of Chopin's Opus 28 on a separate web page and will tell you when it is ready.

Tricks: Chopin's Prelude in C-sharp Minor

This is one of those pieces that float around, not doing much of anything. It sounds like improvising, which has taken the greatest strides in jazz, producing what I call "deedle-deedle" jazz. Chopin's Prelude in C-sharp Minor, Opus 28, Number 10, is not so much deedle-deedle as it is a bunch of conjurer tricks. Imagine a magician appealing to the sky, causing a magic effect to drop down and achieve some paradoxical result. This is what this piece reminds me of. So I call this prelude "Tricks". It happens four times, and then suddenly it's gone, like the Cheshire Cat in Alice in Wonderland. It is not too hard to play; the fingerings in the downward "tricks" are what have to be learned. Altogether, a little frill of magic.

Incidentally, the key of C-sharp minor seems to be a favorite with classical composers, so much so that I call this the "classical key". Beethoven's Moonlight Sonata and Chopin's Waltz in C-sharp Minor are other pieces written in this key. It is said to be Chopin's favorite key, and it is interesting to note that the longest C-sharp minor passage in Opus 28 is not in this prelude but in Number 15 in D-flat (C-sharp's alter ego), the Storm, which I will review in a few days.

Sunrise: Chopin's Prelude in E Major

Chopin's Opus 28, Number 9, rumbles in the bass like an enormous church organ. It sets off a theme, then reaches a peak before settling down to a big climax at the end. Indeed it reminds me of a hymn, but its deep tones and its climaxing reminds me of something else - the Sun rising in the east. To me the notes suggest the lightening that gradually takes place in the sky before Sunrise before the Sun makes its grand appearance. It is fairly easy to play; the main difficulty would be to deal with repeated notes in the chords. This is a good one to play if you want something dramatic to play on the piano somewhere to catch someone's attention. It would be a good part of any church service, especially the prelude in the service.

Frantic: Chopin's Prelude in F-sharp Minor

Opus 28 Number 8 reminds me of some of the angry-mood pieces of Beethoven such as the Appassionata Sonata and the third movement of the Moonlight Sonata. This one has a driving melody in the treble with a descending triplet bass. It also has an obbligato in the treble written with small notes. When I hear the piece I wonder how one can move one's hand so fast on the keys, but I tried it once and found that the notes were selected to fit into the hand, so it is not that hard to catch its rhythm. Nevertheless, this is a difficult piece to play and I have not attempted to play it much. Instead, I put it into Cakewalk. When I do that I find that I have to double the melody notes, else they can't be heard over the din of the frantic obbligato. I feel that this piece sounds frantic, hence my name for it. Its discordant chromatic scales contribute to the agitation in the piece. It reaches a peak near the end and descends into a soft ending, finally concluding, like several of the other preludes, with three or four slow chords. To me this is the most Beethoven-like of Chopin's Opus 28 preludes.

Short and Sweet: Chopin's Prelude in A Major

This is the shortest of the preludes in Chopin's Opus 28. Number 7 is a brief waltz, that takes a theme and repeats it four times, following fairly standard harmonies, and ends in an A major chord. It comes, and then it is gone; too bad, because it is a really sweet number. Hence I call this one "Short and Sweet". At times I thought of continuing it but it is hard to do; it is like finding compounds of noble gases such as argon because the piece is complete as it is. This is the first Opus 28 prelude I have ever heard; I was only about 7 or 8 when I heard it the first time on a 45-rpm record that my parents had bought; it came with the Prelude in D Minor (Epic, number 24, which I will cover on 2003 May 27) on the same side, and that one seemed so complicated that I thought that it was forever out of my reach. I will discuss that later, but indeed I also learned how to play the A Major prelude. It is easy to play, but it needs to be played with feeling. One huge chord in the treble at the end of the third theme looks unplayable; the way to play the chord is to hit the A-sharp and the C-Sharp simultaneously with the thumb astraddle the two black keys. This means that the piece can't be transposed into another key without risking the playability of this chord. But no matter; the piece was made to be played in A Major and it stands as a completed work as it is.