Sunday, December 17, 2017

The Well of Ascension

The Well of Ascension
by Brandon Sanderson
Recommended Ages: 14+

In the first book of the Mistborn series, an elite crew of thieves and impostors with a diverse range of metal-based super-powers overthrew the Lord Ruler and his thousand-year Final Empire. Now, in Book 2, the crew struggles to hang onto the free country they have created, after crew leader Kelsier, the legendary Survivor of Hathsin (long story), sacrificed his life for the cause. A year later, they're feeling his loss deeply. With an idealistic young king named Elend Venture to lead them, their political experiment is now threatened both by a ruling assembly that doesn't share Elend's vision, and by an invading army led by Elend's father, the ruthless Straff Venture, who wants to rule Luthadel, the Lord Ruler's onetime capital city. Then a second warlord, named Ashweather Cett, arrives with his own army a few days later. Plus, a third army, this one made up of savage, blue-skinned giants known as koloss, is on its way, led by Jastes, one of Elend's former friends.

As if to ensure things still aren't too easy for Elend and company, the Deepness has returned: an evil the Lord Ruler supposedly defeated a millennium ago. The eldritch mists that have haunted the nights since the Lord Ruler's Ascension have now, since the empire's Collapse, started to invade the daytime, threatening to destroy crops and cattle, and even killing people.

Elend needs help. His lover is a Mistborn girl named Vin, revered by the working-class skaa as the Heir of the Survivor, and gifted with all the allomantic (i.e. metal-burning) powers, of which the other members of Kelsier's crew have only one each. These powers, depending on which metal one can burn - and most people, these days, can't burn any - include physical strength and agility (pewter), heightened senses and alertness (tin), being able to soothe (brass) or riot (zinc) other people's emotions, being able to pull (iron) or push (steel) on metal objects, and being able to detect (bronze) or hide (copper) the use of allomancy, plus a few more. These individual powers enable certain members of Elend's team to be excellent bodyguards, like pewter-burning "thug" Ham; influencers of people, like "soother" Breeze; scouts, like "tineye" Spook, etc. But Vin is the whole package, with additional abilities no one but a Mistborn could hope for - such as being virtually able to fly. With the addition of a vast supply of the precious metal atium rumored to be hidden in the city - a metal that enables Mistborn to anticipate their opponents' moves - and a newly discovered allomantic metal called duralumin, which concentrates any other metal being burned at the same time in one fast, super-intense flare, Vin is practically a one-woman wall of defense around Elend and his city, especially after she puts the fear of herself into Straff and Cett.

But it isn't enough. The Deepness is getting stronger, and time seems to be running out to find the Well of Ascension and re-do whatever the Lord Ruler did a thousand years ago to stop it - or, rather, to do the opposite of what he did - or something. The three armies camped outside Luthadel won't wait forever for their chance to take the city, in spite of the stalemate between them. The members of the city's assembly won't wait for Elend to learn how to be an effective king - although, with the help of a tutor from the scholarly Synod of Terris, he's making rapid strides in that direction - and is invoking a clause in the city's new charter to take his power away from him, perhaps to hand the city over to one of the warlords waiting outside. And an insane Mistborn assassin named Zane, who is secretly Elend's half-brother, has been filling Vin's head with nonsense about how he needs her more than Elend does, and how she needs him too.

If it doesn't seem events are moving rapidly in this book, it's because it's such a big book with so many events moving in it at one time. Sazed, the Terrisman who who defied his own Synod to help the revolution, using his people's metal-based arts called feruchemy - which has fascinating differences and similarities to allomancy - has come back to Luthadel, once again disobeying his Synod. He thinks he is close to understanding what must be done to stop the Deepness. Vin has been seeing a figure made of mist, and hearing a beating sound coming from the Well of Ascension. Elend risks his neck finding out how Jastes keeps the koloss under control. Both Straff and Cett send teams of allomancers to assassinate Vin and Elend, and Zane tricks a confused Vin into making a disastrous counter-strike. The hero couple's love story reaches a crisis that could either bring them together or pull them apart, forever. And after a pair of epic battles - one a one-on-one one, the other on a scale to alter the fortunes of entire nations - each charged with betrayal, carnage, and irreversible loss - the surviving heroes face a final, terrible choice whose consequences may last a thousand years or more.

In my reading of his work, Brandon Sanderson has repeatedly proven himself a master at creating a dramatic structure that works on an enormous scale, building a detailed fantasy-world spanning a vast area and permeated with unique supernatural properties, and keeping it all centered on the hearts of believable characters who hold the reader's sympathy. He keeps the reader cringing in suspense for long stretches, punctuated at perfectly-judged intervals by bursts of thrilling action. He juggles the motivations of widely diverse characters in ways that often touch deep springs of emotions. For example, this book features what I will now, until further notice, describe as "the last wedding I cried at." It also features not one, but two schools of arcane arts, somewhere on the sliding scale between magic and super-powers, each relying in a different way on certain types of metal. Moreover, new facets of these arts continue to be revealed as the series grows, as witnessed by the table of allomantic and feruchemical metals and their uses, in the back of this book, which isn't complete; in fact, it mentions one metal that has never been mentioned in the first two Mistborn books, and omits two that have been mentioned, including one that sees considerable use in this book. Looking at this in the most charitable light, I suppose Sanderson didn't want to spoil too much for readers who, like me, read the glossary first, before attempting to understand the book.

Book 3 of the original Mistborn trilogy, which I plan to read soon, is The Hero of Ages. The series goes on to include The Alloy of Law, Shadows of Self, and Bands of Mourning. I am also, at the same time, enjoying Sanderson's Reckoners trilogy, including Steelheart, Firefight, and Calamity, and I'm way behind but trying to catch up in Robert Jordan's Wheel of Time cycle, of which Sanderson completed the last three novels, after Jordan's death. That's just scratching the surface of the work of this insanely creative, Utah-based writer. So I conclude, in my best vocal imitation of a superhero under strain: "No time to say more. Must get back to my reading!"

Friday, December 15, 2017

233. Christmas Prayer for the Lonely

'Tis the season for seasonal loneliness and homesickness, of which I know a great deal, having blown all my vacation hours for this year and not having time to get home to mom and/or dad for Christmas. Here is a Christmas prayer that, I hope, will spread some of the benefits of Jesus' incarnation on this malady of the heart. The tune is SOLLT ES GLEICH BISWEILEN SCHEINEN by Ahasuerus Fritsch, 1675. Merry Christmas, and God bless!
1. Jesus, in a stable born
Where no inn had room to spare,
Bless the lonely and forlorn;
Let Your presence ease our care.

2. You from ageless throne came down,
Shone upon by distant star:
Strange as may be tongue or town,
God’s right hand is where You are.

3. Far from Joseph’s shop and home,
Far from Mary’s kin and hearth,
To cold welcome have You come,
Bringing peace and joy to earth.

4. Into exile You were flung,
Marked for death by cruel king;
As a foreign flower sprung,
Life to barren wilds You bring.

5. Prophet, slighted by Your own,
To the heartsick testify:
When we stand reviled, alone,
We have fellowship thereby.

6. Birds have nests and foxes holes;
You, Lord, had no place to rest,
Till, to ransom many souls,
In grave-clothes You would be dressed.

7. Stay by us, for whom You died,
Peerless Lamb, in lonely pain.
Draw us daily to Your side,
Where fresh mercies we obtain.

8. Shelter us, Lord; make us one
By Your drowning, birthing flood;
See Your will, as promised, done
Through communion in Your blood.

9. Let us, through the bread You give,
Members of Your body be;
As one body, help us live
Till from death You set us free.

Name That Composer

Back when I lived in an area served by a classical music radio station, I became a power-player in the game of Name That Composer. To help you achieve a similar level of success, here are some of the cheats, I mean rules, I played by. These are only some of the mental shortcuts that helped me maintain a high score. For many composers, however, there is no substitute for simply listening to a lot of their music.

Rule 1. When you tune in and you find what sounds like a symphony in progress, if it sounds like Haydn...
  • 1a. ...but its slow movement drags, it's by Mozart.
  • 1b. ...but it takes unexpectedly daring harmonic risks that totally pay off, it's early Beethoven.
  • 1c. ...but it takes unexpectedly daring harmonic risks that don't entirely pay off, it's early Schubert.
  • 1d. ...but it's scored entirely for strings, it's early Mendelssohn.
  • 1e. ...but nothing, it's Haydn.
Rule 2. If it sounds like Schumann, it's Schumann. Nobody else wrote music that sounded like Schumann's.
Exception: Max Bruch.

Rule 3. If it sounds like Berlioz, it's Berlioz. Nobody else wrote music that sounded like Berlioz's.

Rule 4. If it sounds like Bruckner, it's Bruckner. Nobody else wrote music that sounded like Bruckner's.

Rule 5. If it sounds like Sibelius, it's Sibelius. Nobody else wrote music that sounded like Sibelius.
Exceptions: Early Lars-Erik Larsson and Luís de Freitas Branco.

Rule 6. If it drips with Central Asian exoticism, it is probably by one of a handful of Russian romantic composers. But no matter who is credited with writing it, Rimsky-Korsakov most likely meddled with it.

Rule 7. If it turns out to be an early symphony or orchestral suite by Bizet, Gounod, Massenet, or Holst, your classical radio station sucks. Someone should tell its programming director to play significant music.

Rule 8. If it fills you with an urge to dance,
  • 8a. ...with satyrs and unicorns, it's Beethoven's Sixth (Pastoral) Symphony.
  • 8b. ...with hobnailed boots on, it's Beethoven's Seventh Symphony.
  • 8c. ...while wearing lederhosen, it's the scherzo of Schubert's Great C Major Symphony.
  • 8d. ...with tutu-clad hippos, elephants, crocodiles, and ostriches, it's a ballet by Ponchielli.
  • 8e. ...with anthropomorphic flowers, sugarplum fairies, nutcrackers, or fairy-tale characters, it's a ballet by Tchaikovsky.
  • 8f. ...with a fur coat on, because at the same time the music chills you like a wind off the Siberian steppe, it's a ballet by Stravinsky.
  • 8g. ...because the moment you stop dancing, a Red Army firing squad will open fire on you, it's either Prokofiev (if you feel like you learned your steps at the dacha of your wealthy, upper-class family) or Shostakovich (if you feel like your vodka-merchant father sent you to a dancing school).
Rule 9. If it bores the daylights out of you,
  • 9a. ...in a stuffy, British way, it's Elgar.
  • 9b. ...in a blue-collar, British way, it's Vaughan Williams.
  • 9c. ...in an bourgeois, German way, it's Richard Straus.
  • 9d. ...in a proletarian, German way, it's Hindemith.
  • 9e. ...in a lush, French way, it's Saint-Saëns.
  • 9f. ...in an austere, French way, it's Milhaud or possibly Honegger.
  • 9g. ...in a next-to-banal, French way, it's Poulenc.
  • 9h. ...in the manner of a prosperous Russian émigré, it's Rachmaninoff.
  • 9i. ...in the manner of a starving Russian nobleman, it's Medtner.*
  • 9j. ...in the manner of an obedient member of the Soviet Composers' Union, it's Kabalevsky.
Rule 10. If it sounds like the aural equivalent of an impressionist painting,
  • 10a. ...but with a touch of English folk melody, it's Delius.
  • 10b. ...but with a certain Slavic twinge, it's Scriabin.
  • 10c. ...but with a French or Spanish warmth, it's Debussy.
  • 10d. ...but with French or Spanish coldness, it's Ravel.
I might add more rules in a later post, to deal with genres other than "what sounds like a symphony."

*...although, I suppose, he didn't write much that sounds like a symphony - unless you count Piano Concertos.

Saturday, December 9, 2017

The Shadow Throne

The Shadow Throne
by Jennifer Nielsen
Recommended Ages: 12+

In this concluding installment of the Ascendance trilogy, Jaron, the boy king of Carthya, has scarcely recovered from securing the additional job of pirate king when he finds his country at war with three surrounding enemies. The main foe is King Vargan of Avenia, who is tired of Jaron standing in the way of his plots to make Carthya the first conquest of his hoped-for empire. Vargan proves he will stop at nothing, including taking hostage the girl Jaron loves, capturing and torturing his most trusted adviser, and treating the young king himself - once he falls into Vargan's trap - like the common thief he once pretended to be. But each time Jaron and his kingdom seem past saving, the young scamp pulls off another amazing trick.

Can he keep it up, though, when hundreds, even thousands of his citizens are falling in battle against an enemy that knows no mercy? Can he keep fighting when each wall he is backed against looms higher, and a leg injury has taken away his ability to climb? Can he defend the people he loves when Vargan seems to have a genius for using that love against him? Read and see - and weep, and laugh, and be amazed.

In contrast to what I did, I recommend reading this book in swift succession with the rest of the trilogy, to make it easier to keep track of past developments that prove significant in the finale. They are memorable enough stories, however, that I think a little prompting will bring back Jaron's earlier feats, such as turning enemies into devoted followers, surviving assassination attempts, convincing a traitorous nobleman to set him up as a pretender to the throne that is actually his, etc. Jaron's exploits have the gosh-wow appeal of tall tales featuring a ne'er-do-well-who-makes-good type of hero, along with a touching survey of the heart of a really noble young man. His character is complicated in just the right way, and to just the right degree, to engage young readers who may need nothing more than a fun hero to root for. Whatever "ascendance" means, here's a young man who goes through hell, and puts us through suspense that seems close to the same, without losing hope, or goodness, or the sense of adventure. It is a great relief for me, to know such heroes are still being written into being.

The first two books of the Ascendance trilogy were The False Prince and The Runaway King. Other titles by Jennifer Nielsen include the Underworld Chronicles (Elliot and the Goblin War and two more), the Mark of the Thief trilogy, A Night Divided, and The Scourge.

Steelheart

Steelheart
by Brandon Sanderson
Recommended Ages: 13+

In the first book of The Reckoners, a young man named David seizes a risky opportunity to join a group of terrorists known as, like, the Reckoners, so he can help them kill superheroes. Maybe I should have phrased that differently. The Epics, who started taking over the world 10 years ago, aren't exactly superheroes. They're just people with superhero-ish powers who seem to think they're gods, and spend a lot of time squishing ordinary people like bugs. Ten years ago, when he was 8, David witnessed his father being squished by an Epic named Steelheart, who is rumored to be invincible. But just before Steelheart killed David's dad, who foolishly believed the Epics had come to save mankind, David saw Steelheart bleed. Against all odds, the boy survived the Epic's attempt to destroy all memory of the incident that left a scar on his cheek - including murdering the rescue workers who arrived at the scene after the deed was done.

Since that day, the only thing that has kept David going is the knowledge that Steelheart has a weakness, though he doesn't know exactly what it is, and a thirst for revenge. Now he uses that knowledge to persuade the Reckoners to stay put in Newcago - known as Chicago, before Steelheart turned it into a maze of steel catacombs cloaked in everlasting night. He convinces their leader, a brooding scientist named Prof, to draw Steelheart out into what he believes is a duel against a nonexistent Epic named Limelight, meanwhile disrupting his stranglehold on Newcago. He basically hijacks a whole unit of anti-Epic insurgents to use them for his personal revenge, even if it means creating a power vacuum that will, at least in the short term, cause more human suffering.

Prof thinks taking Steelheart down will convince more ordinary folks to rise up against Epic rule. His teammates have different views. There's a French-Canadian guy named Abraham, who like David's father, has faith that Epics will eventually turn toward good and save mankind, though for now he's happy to blow stuff up. There's Tia, an operations expert who relishes the challenge of analyzing David's memory of the day Steelheart took over Chicago, trying to spot his crucial weakness. There's Cody, a sniper with a Tennessee accent who likes to pretend he's Scottish. And lastly, there's Megan, a beautiful but unapproachable girl David would like to figure out. Although his knowledge of what makes Epics tick rivals anybody's, something about Megan eludes him.

As their plan to challenge Steelheart races forward with reckless speed, David encounters dangers to body, soul, heart, and mind, each of which keep the reader engaged at a gut level, even while mindblowing concepts scream past and incredible surprises pop up at every turn. It's another astonishing feat of world-building, engineered to thrill, by the author of Elantris, The Rithmatist, the Mistborn series, and the conclusion of the late Robert Jordan's Wheel of Time cycle. A discerning reader might pick up some common threads between the quests of these books' heroes, but the differences between the worlds they inhabit make each one an exciting realm to explore. This time, Sanderson blows the door off Superman's quick-change phone booth with the question, "What if super powers turned people into monsters?" My synopsis, above, does not begin to do justice to how deeply or how rewardingly this book delves into that question. Set in a world that, until 10 years ago, apparently looked just like ours, it makes that question count for us as though it affected us personally - and, with only a minor tweak in one's definition of "power," it actually might. I definitely plan to read the next book in this series, Firefight. There is also a third novel, Calamity, as well as a short story titled Mitosis.

Tuesday, December 5, 2017

Musical Analogy to Math?

For some reason, I woke up this morning wondering whether music could provide an analogy to help people understand higher-dimensional math.

I'm not very advanced in my mathematical studies. I enjoy watching the "Numberphile" channel Youtube, but I often find the concepts don't stick. One of the concepts that doesn't even seem to make contact is the idea of imagining the topology of objects in space that has more than three dimensions.

But now - bear with my ignorance - I'm thinking I might have the corner of something between my very confused fingertips. And it's basically an analogy from music to spatial dimensions.

Click to enlarge the illustration, if you like. I'm putting all the figures into one image, to save myself time and effort, but I'm going to talk about each image separately.

Consider Fig. 1. Suppose that this note, the D just one step above Middle C, represents a dimensionless dot on a one-dimensional line extending forever in both directions.

To keep it company, add the notes F-sharp and A (Figs. 1a and 1b), but only as separate dots on the same conceptual line - the line, say, of musical pitches extending upward and downward from the origin (say, Middle C), clear out of the range of human hearing. You could say the integer units on that line represent the tones of the equally-tempered 12-tone scale, repeating through a succession of octaves, like a Base-12 grid that has a heavier line at every 12th unit.

Moving on to a two-dimensional plane, suppose you plotted points D, F-sharp, and A on a graph with any arbitrary origin point (Middle C would do). In this instance, the points needn't be integer units or lie on a single line. When you transpose those notes up a half-step, as in Figures 2, 2a, and 2b, the new notes E-flat, G, and B-flat are interrelated in a way similar to the relationship between D, F-sharp, and A. The process of transposing the three notes, as a group, would be analogous to using three-dimensional math (with complex numbers, involving the "imaginary unit") to rotate a group of three points on a plane while preserving the angles between them.

But there is more you can do on a two-dimensional plane than plot a bunch of dimensionless dots and rotate them. I'm not yet up to delving into all the possibilities, but a blatantly obvious one is to draw line segments of various lengths, connecting pairs of dots on the plane. Likewise, when two notes sound together, consecutively or simultaneously, they form an interval. For example, D and F-sharp (Fig. 3) form the interval of a major third; D and A (Fig. 3a) form a perfect fifth; and F-sharp and A (Fig. 3b) form a minor third.

As with the single points, complex-number math can rotate line segments, individually or as a group, on the plane while preserving their lengths and the angles between them. Likewise, a set of musical intervals can be transposed, or as it were rotated, into similar intervals in a different key, like transposing the D/F-sharp/A intervals in Figs. 3, 3a, and 3b to the E-flat/G/B-flat intervals in Figs. 4, 4a, and 4b.

Another operation those Numberphile videos taught me you can do with a two-dimensional figure on a plane is to draw a plane inversion of the figure - and inversion, like rotation, can be done in higher-dimensional spaces too. I'm really straying into dangerous waters here, way over my head, but as I understand it, one can discover the reciprocal of a number (like turning a fraction upside down) by plotting a point and/or a circle around it in relation to the origin and radius of an arbitrary reference circle, then graphing an inversion of that point and/or circle's position and/or size, via a bunch of conditions that don't seem too far-fetched when someone who knows what he's talking about explains them.

After that no doubt compelling description, I am sure you'll agree this procedure bears some analogy to the process of transforming the musical intervals in Figs. 3, 3a, and 3b to their inversions in Fig. 5, 5a, and 5b. In the latter series of intervals, we find the D on top of the F-sharp instead of under it, changing a major third into a minor sixth; the D above rather than below the A, changing a perfect fifth into a perfect fourth; and the F-sharp above rather than below the A, changing the minor third into a major sixth. It is as if, in my imaginary universe governed by very shaky analogies, the reciprocal forms of the previous intervals were plotted in reference to an invisible, or rather inaudible, circle of musical inversion. Gads, that's terrible. Or maybe, if you catch what I'm throwing, it's brilliant.

Nah, it's probably just terrible.

But wait, I'm not done yet! There's still Fig. 6 to consider. When I first started cooking up this series of analogies, I was thinking of relating three-dimensional figures to the musical triad - a three-tone chord that, by a little note-shuffling, sort of like reducing fractions to their simplest form, can be distilled down to an interval of a third (like D to F-sharp) on top of another third (F-sharp to A), or a third (F-sharp) and a fifth (A) above the root tone (D). But now, it occurs to me the triad could also, and perhaps more aptly, illustrate the idea of a closed shape in the two-dimensional plane. Then again, when I moved from one dimension to two, I re-positioned the three notes as points on a plane, not on a straight line. So, perhaps I can be excused for using the same musical example two different ways.

So, yeah, in the 2-D plane, you can do the same operations with a closed figure as you could do with one or more line segments. I didn't bother to illustrate the rotation principle by transposing the D-major triad (Fig. 6) into an E-flat-major triad, but based on what I did with Figs. 3 and 4, I trust your imagination can get you there. You could do the same thing with Figs. 6a and 6b, the first and second inversions of the D-major triad - and inversion really is the musical term that applies here; I'm not just letting the planar-inversion analogy get away from me here. Each of these triad inversions could also be "rotated" into E-flat-major, or whatever key you want, sort of like using quaternion numbers (like complex numbers, only more so) to rotate a 3-D figure in space. 6a and 6b are still D major, even though a different tone in the original triad has been stuck at the bottom of the pile; but they have been transformed enough to give them a distinct sound.

Nevertheless, I think the triad could also be useful in an analogy to 3-D space, with a three-dimensional figure (sphere or otherwise) being transformed in some way, perhaps quite a dramatic way, when subjected to spherical inversion. But where I really wanted to go with this comes in Fig. 7, where I attempt to extend the analogy into a higher-dimensional space (in this case, 4-D space). If you accept a triad as comparable to a 3-D figure, where do you go from there? To start with the simplest possible answer, you could go to Fig. 7, which combines sequentially or, Fig. 7a, simultaneously, three similar triads - in this case, three major triads, D major, F-sharp major, and A major. It's as if you took the D-major triad from Fig. 6, rotated it to reveal a similar major triad rooted on each tone of the D-major chord, then brought all three major triads together into one figure - analogous to a tesseract or a 4-D supersphere.

Attempts to visualize 4-D figures using geometric imagery can never be quite precise, somewhat like the limitations of a 2-D picture representing a 3-D figure. But with music, it is possible to hear three different triads, each rooted on a different tone of the first triad, all at once. If you play them all together, but in such a way that you can hear each triad as a distinct identity within the superchord - say, by playing each triad in a separate register - you can actually hear it as a chord of chords. You can, to drive the analogy home, make the 4-D figure pop out of 3-D space - just as certain optical illusions can make a 3-D figure seem to pop out of a 2-D illustration.

Fig. 7b suggests one further level of sophistication. By musical analogy, we have already generated an optical illusion of a tesseract or supersphere, as it were, a very basic 3-D figure that seems to pop out into 4-D. But why stop at a supersphere? Why not go for another order of strangeness, and have each rotated sphere that pops out of the surface of the original sphere, be not only a rotation but also an inversion? Why not, indeed, include two different inversions - ah, but here the analogy is stretched past the breaking point, since I don't think math allows for more than one reciprocal of a given number. Music does, which is why I guess music beats math. It actually makes it possible, just conceivable, to "visualize" (in your mind's ear) a superfigure that has 3-D figures rotated three different ways, each a distinct inversion of the other two, and that pop out of each other.

In higher dimensions still, I guess you could be building musical tesseracts on each of the tones of all three chords in Figure 7b, rotated into the additional triads rooted on A-sharp (B-flat) and E, not to mention the other notes in those triads. And since your chord has more than three tones in it, you can also invert it in more distinct ways - sort of like how a four-note chord (like a dominant seventh chord, D/F-sharp/A/C) has three inversions, including the one with the 7th at the bottom; and a 9th chord has four inversions; etc. You could get super-crazy in your exploration of higher dimensions in harmony, though to our 3-D ears the resulting tone clusters may soon stop sound as if anything new had been added.

But in case I haven't sufficiently beaten up on math at the expense of music, I should point out that I've only touched on one aspect of musical complexity in the above analogies. Nowhere have I mentioned rhythm, melodic shape, tonal design, formal/dramatic structure, contrapuntal texture, number and type of movements, tone color, dynamics, lyrics, etc, etc. Counterpoint itself forks into such layers of complexity as number of voices, free imitation vs. canon vs. fugue, inversion and retrograde, augmentation and diminution, etc. One of those Numberphile videos shows evidence that origami (the traditional Japanese art of paper folding) is capable of doing harder math than Euclidean geometry (that stuff with a compass and a straight-edge). Perhaps it shouldn't be amazing that a soft subject like music rivals higher-dimensional topology for sheer complexity. Maybe this makes it good news that the Voyager Golden Record, now traveling through interstellar space, includes music by Beethoven, Bach, Mozart, and Stravinsky, among others in addition to greetings in 55 languages and a bunch of mathematical and scientific diagrams. If mankind's bright future ever depends on one thing on the Voyager spacecraft making an impression on E.T., my money is on the Brandenburg Concerto.

At least, saying so helps me feel good about being way better at music than at math. Fish out.

Monday, December 4, 2017

232. Prayer About Late-Stage Dementia

I couldn't go to sleep last night without completing this hymn, written in love for a couple that belongs to the church I attend. The husband showed up solo at Bible class yesterday morning, and when asked how he was doing, he said, "I think this is the worst I've ever been hurt." He went on to announce that his wife, who is in late stage dementia, has been put in hospice care. He expressed feelings that were almost too painful to live with, about looking in the eyes of the woman he has loved his entire life and seeing the life in them end, even while the body went on living. I wish I could say words that would bring comfort in his situation. Whether or not it will come true, I don't know, but that wish now takes the form of the following hymn. The original tune, titled LORETTA, has already been harmonized (I really couldn't sleep until it was finished!).
1. When those we love forget our name,
Remember us, Lord Jesus.
When serving them exhausts our frame,
Remember us, Lord Jesus.
Their agitation, mental strain,
Confusion, helplessness, and pain
Surpass our power to explain;
But You will make them whole again.
Remember us, Lord Jesus!

2. When no one gazes through their eyes,
Remember us, Lord Jesus.
When body lives, but spirit flies,
Remember us, Lord Jesus.
You, who descended into hell,
Forsake us not, who sink as well.
To hearts in bondage, tidings tell
Of peace that will all sorrow quell.
Remember us, Lord Jesus!

3. When all our taxing care is past,
Remember us, Lord Jesus.
When we have time to grieve at last,
Remember us, Lord Jesus.
Assure us that, restored by grace,
Our loved one has a dwelling place
Where, after we have run our race,
We’ll recognize each other’s face.
Remember us, Lord Jesus!