Beware the Infinite Loop!

I just lost several hours of bleary-eyed data organization/collection due to an infinite loop. Grrrrr. Fortunately I got *some* measurements first. I wrote a little script to save the newly organized files, and decided to test it on just a single file first, to make sure the script worked properly. Well, I had the following lines:

>> k = 1;
>> while k < 2,
>> ...
>> endwhile;

See the problem? I left out the line k = k + 1;

So now I get to redo all the work I had just finished. :-( But not right now... I'm bleary-eyed and tired enough that I'm just going to go home (it's just about 8pm, after all).

Thoughts about the Pentateuch

I'm going to dive right into this one without a preamble...

The Pentateuch *might* be a large chiastic structure:

Genesis
.....Exodus
..........Leviticus
.....Numbers
Deuteronomy

In a chiasm, the middle part is the central focus, the first and last parts correspond to each other, and the second and second-to-last parts correspond to each other. So we have Leviticus at the center, and the correspondences between Genesis and Deuteronomy, and between Exodus and Numbers. If this is true, the content in Deuteronomy ought to parallel the content in Genesis, and the content in Numbers ought to parallel the content in Exodus. Now, I'm not fully convinced that this really works, but I've been a little surprised to find that there actually are a number of parallels:

1) Genesis ends with Jacob blessing his sons (in the form of a poem), each one by name; and then Jacob's death is recounted. Deuteronomy ends with Moses blessing the tribes of Israel (in the form of a poem), each one by name; and then Moses' death is recounted.

2) Genesis begins with the creation of Adam and Eve in Eden, and the command to obey God, followed by their rebellion against Him (by eating the fruit of the tree of the knowledge of good and evil - making them judges), and their subsequent expulsion from Eden. Deuteronomy begins with the command to enter the Promised Land - the second Eden, which even includes the land around the Euphrates just as the first Eden did - and the command to obey Moses (as the mediator standing in the place of God toward Israel), followed by their rebellion against Moses (and God) by making their own judgment about the feasibility of occupying the Promised Land, and their subsequent expulsion from the Promised Land and the penalty of wandering in the wilderness.

3) The bulk of Genesis is all about the covenant God makes with Abraham, Isaac, and Jacob. The bulk of Deuteronomy is all about the covenant God makes with Moses and the whole people of Israel.

4) Exodus kicks off with the increase of the people of Israel, followed by God's command to "let my people go" because "Israel is my firstborn". After many plagues, the Passover occurs in which the firstborn of Egypt are slain. Following this Israel leaves Egypt and is protected by the pillar of cloud and fire. With much fanfare the cross the Red Sea and leave all of Egypt behind them. Then the people complain that they don't have food, so God sends quail and manna. After that Moses' father-in-law Jethro meets them and advises Moses to appoint elders to help him. This is the first half of Exodus. Now consider Numbers. It starts with a numbering of the people, followed by God's command that the firstborn are His. After a few chapters that don't seem to correspond to anything in Exodus, the Passover is celebrated, and then the pillar of cloud and fire protected and guided the people. After much fanfare (with two silver trumpets) Israel leaves Sinai behind. Immediately the people complain about the food (and a description of the manna they've been eating is given which is very similar to that given in Exodus), so God sends quail (with a plague this time). In between the complaining and the quail-plague, God advises Moses to appoint elders to help him.

5) The second half of Exodus is itself a chiasm. First you have the detailing of the Law and how to construct the Tabernacle and everything that goes with it. Then you have the Golden Calf incident in which Israel sins and the Levites kill a bunch of the guilty Israelites. Then you have the reiteration of the Law and the building of the Tabernacle. In Numbers there is a also a chiasm, although much more loosely defined than in Exodus. In Numbers the first part of the chiasm discusses various laws (similar to those in Exodus). Then you have the incident with Balaam and Baal worship at Beth-Peor, and Phineas (a Levite) and the chiefs of Israel kill a bunch of the guilty Israelites. Then there is a further discussion of laws and of how to set up the nation of Israel once it enters the Promised Land (parallel to setting up the Tabernacle).

6) In a broader sense, Exodus is about the travels from Egypt to Sinai and the giving of the Law and setting up the Tabernacle. Numbers is about the travels from Sinai to Canaan and the giving of the Law and setting up the nation of Israel.

7) In the same broad sense, Genesis is about Eden, how it was ours, how it was lost, and how it will be restored (in the future). Deuteronomy is about the Promised Land, how it should have been Israel's, how it was "lost" (they failed to occupy it), and how it will be restored (in the future, in Joshua). Oh, and another interesting point is that just as in Joshua (which means "God saves") the promises are fulfilled, the Promises are fulfilled in Jesus (which means "God saves"). ("Joshua" and "Jesus" are really the same name, but one is the Hebrew form and the other is the Greek form - just like "John" and "Johann" are the same except that one is English and the other is German). After the Promised Land has been occupied, we have (all too human) Judges. After Jesus redeems and renews the heavens and the earth, He will set up judges (in the sense that Paul says "we will judge angels", and in the sense that David says "you have put all things under [man's] feet", and in the sense that God gave dominion to Adam, then to Noah). Unlike the history of imperfect Israel which clamored for a king from among themselves and to replace God as their King, God will continue to be our King in the new heavens and the new earth. (This, by the way, is the ordering in the Jewish Bible - Ruth does not come between Judges and Samuel.) The rest is history - because Jesus has not yet come and because the new heavens and earth have not yet been established, Israel cannot permanently succeed. The results are 1) the history that proves the point in Kings/Chronicles, 2) the prophetic warnings, 3) the unraveling of the entire thing in the Assyrian and Babylonian captivities, and finally 4) the partial redemption of God's people and the rebuilding of the temple. What happens next? 5) Israel, kingless, waits for her King. But "the Lord, whom ye seek, shall suddenly come to his temple" - this is the promise in the last book of the Old Testament, in Malachi, the last prophet.

Ok, enough for now. But I would like to suggest that perhaps we should call Deuteronomy ("the second law") Deuterogeny ("the second beginning"). And we could change Numbers to Eisodus to mirrow Exodus and the fact that Numbers is about Israel being about to enter the Promised Land. I don't have any clever suggestions for renaming Leviticus, but just wait! ;-) Maybe we could call it "Holiness"? And on one last note, I think it's interesting that Adam and Eve thought God didn't want them to be like Him although they wanted it for themselves, so they ate the forbidden fruit. But in Leviticus God says that we're supposed to be holy just like Him - our problem is that God wanted/wants us to be like Him but we end up being unlike Him, so the effect of the first sin by the first Adam has to be undone by the final atonement by the final Adam (Jesus).

Two Observations Thanks to C. S. Lewis

I know, I know, I still haven't written about my trip to Europe...

I'm reading C. S. Lewis' book The Discarded Image, which is an introduction to Medieval and Renaissance literature. Mostly the book is going about describing the Medieval sense of the organization of the universe and the relations between its parts. Lewis does this because when an author like Chaucer writes

Every kindly thing that is
Hath a kindly stede ther he
May best in hit conserved be;
Unto which place every thing
Through his kindly enclyning
Moveth for to come to.

It cannot be understood apart from the physics of Chaucer's day - that different elements have their proper places in the universe and will tend to move toward those places if ever they find themselves elsewhere - hence, objects made of dirt or wood or stone fall to the earth, air escapes upward, water flows between earth and air, and fire rises highest of all. So when Chaucer says that every natural (kindly) thing has its natural (kindly) place, unto which everything moves by its own natural (kindly) inclination, he is simply putting the physical understanding of his day into poetry. (Thanks to Lewis' other book, Studies in Words, which points out that "kindly" in this time means "natural" rather than "nice"). Chaucer is being very precise, not vaguely metaphorical or allegorical - Chaucer's readers would have understood him to be speaking directly about how things are, whereas we now look for a deeper half-concealed meaning. Lewis' prime concern is to read a text as its intended audience would have read it. Hence the need to understand the context in which that audience lived. Another example that I particularly like is Donne's poem Riding Westward, which I have posted here before, but I will post it again!

Goodfriday, 1613. Riding Westward

LET mans Soule be a Spheare, and then, in this,
The intelligence that moves, devotion is,
And as the other Spheares, by being growne
Subject to forraigne motions, lose their owne,
And being by others hurried every day,
Scarce in a yeare their naturall forme obey:
Pleasure or business, so, our Soules admit
For their first mover, and are whirld by it.
Hence is't, that I am carryed towards the West
This day, when my Soules forme bends toward the East.
There I should see a Sunne, by rising set,
And by that setting endlesse day beget;
But that Christ on this Crosse, did rise and fall,
Sinne had eternally benighted all.
Yet dare I'almost be glad, I do not see
That spectacle of too much weight for mee.
Who sees Gods face, that is selfe life, must dye;
What a death were it then to see God dye?
It made his owne Lieutenant Nature shrinke,
It made his footstoole crack, and the Sunne winke.
Could I behold those hands which span the Poles,
And turne all spheares at once, peirc'd with those holes?
Could I behold that endlesse height which is
Zenith to us, and our Antipodes,
Humbled below us? or that blood which is
The seat of all our Soules, if not of his,
Made durt of dust, or that flesh which was worne
By God, for his apparell, rag'd, and torne?
If on these things I durst not looke, durst I
Upon his miserable mother cast mine eye,
Who was Gods partner here, and furnish'd thus
Halfe of that Sacrifice, which ransom'd us?
Though these things, as I ride, be from mine eye,
They'are present yet unto my memory,
For that looks towards them; and thou look'st towards mee,
O Saviour, as thou hang'st upon the tree;
I turne my backe to thee, but to receive
Corrections, till thy mercies bid thee leave.
O thinke mee worth thine anger, punish mee,
Burne off my rusts, and my deformity,
Restore thine Image, so much, by thy grace,
That thou may'st know mee, and I'll turne my face.

Why would Donne begin by imagining that man's soul is a sphere? Today one might as well suppose that he is simply simplifying the issue so as to be able to deal with it, like the engineering joke that begins "Suppose a horse is a perfect sphere..." But Donne isn't calling the soul a round ball - he is suggesting that its properties are those of "the spheres", the different levels of the heavens, where you have the successive spheres of the moon, of Mercury, Venus, the Sun, Mars, Jupiter, Saturn, the fixed stars, and the Primum Mobile. The universe is a vast cathedral with several levels of crystal ceilings. At the top is the Zenith, Donne's "endless height", and on the other side of the world, "humbled below us" from our perspective, are the Antipodes, the anti-pedestrians (who walk upside down). Each sphere moves in a love-harmony with its Creator (it is Jesus who turns "all Spheares at once"), and this movement is accomplished by the action of a separate "intelligence" for each sphere. So lines one and two, "Let mans Soule be a Spheare, and then, in this, the intelligence that moves, devotion is". Donne is saying that, just as each sphere has its natural motion which is carried out by its own "intelligence" (not in the sense of "smarts"), the human soul also has a natural motion (toward God) which is driven by devotion. But there is a problem. Just as the motions of the other spheres are not completely uniform because they are driven away from their natural places by "forraigne motions", so our souls admit "pleasure or business" "for their first mover, and are whirld by it". For this reason, Donne is "carryed towards the West" "when my Soules forme bends toward the East", toward "a Sunne, by rising set", which is his metaphor for Christ's crucifixion, as he makes clear two of lines later. And one last little comment: "the Sunne winke[s]" because the sun was considered to be the eye of the universe, enlightening all of the universe at all times (except for the parts where the earth's shadow is cast - this is what causes night to be dark). (On the other hand, it is interesting that in another very different poem - The Sun Rising - Donne claims that he could eclipse the sun's beams with a wink of his own!)

But this entry has so far been one long digression! I have two observations to make!

First, at church today we sang the hymn All Creatures of Our God and King, written by Francis of Assisi in the 13th century. 13th century - that's the Middle Ages. So the understanding of the universe that informs Chaucer's poetry (and Donne's, although Donne has many later influences as well, living post-Newton and post-Columbus as he did) also informs Francis' poetry. So:

All creatures of our God and King,
Lift up your voice and with us sing
Alleluia, Alleluia!
Thou burning sun with golden beam,
Thou silver moon with softer gleam:
O praise Him,
O praise Him!
Alleluia, Alleluia!
Alleluia!

Thou rushing wind that art so strong,
Ye clouds that sail in heav'n along,
O praise Him!
Alleluia!
Thou rising morn, in praise rejoice,
Ye lights of evening, find a voice:
O praise Him,
O praise Him!
Alleluia, Alleluia!
Alleluia!

And so on. There are two things I want to point out about this hymn, which I noticed this morning as we sang it in church. First: For Francis, the sun is golden and the moon is silver. Ok, that seems natural enough to us as well. But Francis is doing more than just telling us what color they are - he is bringing into his poem an entire worldview that assigns characteristics and personalities and influences to the heavenly bodies. Gold and silver are metals just as much as they are colors, and it is the metals as well as the color, I think, that Francis is referring to - in Medieval thought the sun was associated with gold, so that Spenser writes about Mammon bring his out out to "sun" it, to turn it into gold by the application of the sun's beams (cf. Lewis, p. 106). And the moon was associated with silver. Second: The medievals thought that the whole universe was full of music. The notion that space is a vast emptiness where little matter is and no sound is transmitted is a very modern one. We think it is self-evident, and the ancients who thought otherwise were merely superstitious or something. But think of it from their perspective: all the heavens move in circular motions within their proper spheres. Circular motion is mathematically very closely related to sinusoidal motion. In fact even today we talk about "the unit circle" in much of our mathematics and engineering where they relate to sinusoids. And sinusoids are the building blocks of music. Again, even today we call any period motion (which may be circular) "harmonic". So if the spheres are moving, of course they are moving harmonically, and of course they will produce music! Hence a couplet by Henryson (cf. Lewis, p. 112) to the effect that "every planet in his proper sphere/In moving makand harmony and sound." So for Francis to call on the golden sun and the silver moon to praise God - to call on the wind, the clouds, the rising morn, the lights of evening to "find a voice" - he is being poetical, yes, but he is also being quite straightforward. Why does he call on the stars to sing to God? Because he believes that they *do* sing to God!

And now my second observation. Coleridge's poem Kubla Khan gets more interesting all the time. If anyone tries to tell you that Coleridge was simply describing an opium dream, don't believe them! Yes, that's what Coleridge himself said, but don't believe him either! :-P The entire poem is about Paradise and how, in Coleridge's view, God is not to be praised for His Creation since under the surface there was a built-in sinisterness - "It was a miracle of rare device,/A sunny pleasure-dome with caves of ice!". In the last part of the poem Coleridge speaks of "an Abyssinian maid [...] Singing of Mount Abora." I never really knew what to make of this, except that Milton also puts Abyssinia and Mount Amara in Paradise Lost, from which Coleridge draws extensively for his poem. But apparently (thanks to Lewis for pointing this out), it was commonly thought that the earthly Paradise, where Adam and Eve first lived, was in the mountains of Amara in Abyssinia! (Just as he makes up a new spelling/pronunciation of "Xanadu", Coleridge changes "Amara" to "Abora".) So I thought that was a neat connection to make. :-)

Wondefully and Fearfully Made

I know I'm trying some patiences out there by still not writing about my trip to Europe (I'll get to it sooner rather than later, don't worry), but...

I have been playing with the lower airway model that I made (in MATLAB) as part of my thesis, looking at how the resonances change in frequency as the lengths of the bronchii and trachea are scaled up and down, and how these frequency changes are affected by the scaling of the radii. As it turns out......... There is a relatively narrow range of length scaling factors for which the radius scaling almost doesn't matter. This range of length scaling factors is *exactly* what we find in adults! What this means is that the radii of the airways can vary as much as they like (within physiological bounds) without affecting the frequencies of the resonances. Since the frequencies of the resonances are therefore quite stable across such physiological conditions, they are able to play a reliable and consistent role in defining distinctive features!!!! Or put another way (and phrased too strongly), the fact that adults tend to be between 5 and 6.5 feet tall is precisely what allows speech to be possible!

And with that exciting bit of news, I shall go to bed. :-)