We three kings of Orient are;
Bearing gifts we traverse afar,
Field and fountain, moor and mountain,
Following yonder star.
Refrain
O star of wonder, star of light,
Star with royal beauty bright,
Westward leading, still proceeding,
Guide us to thy perfect light.
Born a King on Bethlehem’s plain
Gold I bring to crown Him again,
King forever, ceasing never,
Over us all to reign.
Refrain
Frankincense to offer have I;
Incense owns a Deity nigh;
Prayer and praising, voices raising,
Worshipping God on high.
Refrain
Myrrh is mine, its bitter perfume
Breathes a life of gathering gloom;
Sorrowing, sighing, bleeding, dying,
Sealed in the stone cold tomb.
Refrain
Glorious now behold Him arise;
King and God and Sacrifice;
Alleluia, Alleluia,
Sounds through the earth and skies.
Refrain
--John H. Hopkins, Jr. (1857)
Wednesday, December 15, 2004
Monday, December 13, 2004
PLoS Biology December 2004
The new edition of PLoS Biology is out. Some articles I'll be reading:
* Algorithmic Self-Assembly of DNA Sierpinski Triangles; the synopsis to this article; and the related primer.
* The Genetics of Speciation by Reinforcement; and its synopsis and related primer.
* Modern Humans Did Not Admix with Neanderthals during Their Range Expansion into Europe.
* Phylogeography and Genetic Ancestry of Tigers (Panthera tigris).
* State-Dependent Decisions Cause Apparent Violations of Rationality in Animal Choice
* The essay on mathematics in biology.
* Algorithmic Self-Assembly of DNA Sierpinski Triangles; the synopsis to this article; and the related primer.
* The Genetics of Speciation by Reinforcement; and its synopsis and related primer.
* Modern Humans Did Not Admix with Neanderthals during Their Range Expansion into Europe.
* Phylogeography and Genetic Ancestry of Tigers (Panthera tigris).
* State-Dependent Decisions Cause Apparent Violations of Rationality in Animal Choice
* The essay on mathematics in biology.
Shepherd on Mathematical Causation
It is an interesting consequence of Shepherd's theory of causation that it implies that the same (general) sort of causal reasoning we use in discussing physical causation is also found in mathematics. Indeed, Shepherd goes so far as to say that mathematics is simply one branch of physics:
(Essay on the Perception of an External World, "On Mathematical and Physical Induction," p. 279)
The idea is this. Objects consist entirely of their features; these features are the causes of the object's being what it is. Insofar as they remain the same, they are together the cause of the object's remaining what it is; insofar as they change, they are the cause of the object's becoming different from what it was. This is true "whether in the shape of mathematical diagrams, or other aggregates in nature" (p. 279). The causal reasoning is exactly the same in both cases, and therefore imports exactly the same sort of certainty from the general causal maxims.
It is true, of course, that our inquiries into physical objects do not have the same certainty as our inquiries into mathematical objects. Shepherd attributes this difference not to the general format of the reasoning, which is the same in both cases, but to the fact that we are differently related to mathematical objects than to physical objects. In mathematics we can freely stipulate features of a system, and see what follows from those features. In physical investigations, we do not have this freedom of stipulation. In physical investigations, objects are formed independently of our stipulation, and much of the uncertainty in these investigations is due to the difficulty of pinning down precisely the formation of these objects. We could very well be missing some important feature of the objects; and in cases that seem the same it could very well be that there is some hidden feature that would, if we knew about it, require us to come to completely different conclusions about the system. This failure of certainty in the investigation, however, does not affect the certainty of the reasoning, any more than the application of mathematics to physical reality affects the certainty of mathematical reasoning. Mathematical reasoning is capable of certainty and necessity whether it is applied to physical systems or not; it is entirely possible that there is some variable in the physical system which needs to be taken into account if the mathematics is to characterize the system accurately, but this is a failure of certainty in the application of the reasoning, not in the reasoning itself. Such is the case, Shepherd holds, with all causal reasoning.
for that all the conclusions its method of induction demonstrates, depend for their truth upon the implied proposition, "That like cause must have like effect;" a proposition which being the only foundation for the turths of physical science, and which gives validity to the result of any experiment whatever, ranks mathematics as a species under the same genus; where the same proposition is the basis, there is truly but one science however subdivided afterwards.
(Essay on the Perception of an External World, "On Mathematical and Physical Induction," p. 279)
The idea is this. Objects consist entirely of their features; these features are the causes of the object's being what it is. Insofar as they remain the same, they are together the cause of the object's remaining what it is; insofar as they change, they are the cause of the object's becoming different from what it was. This is true "whether in the shape of mathematical diagrams, or other aggregates in nature" (p. 279). The causal reasoning is exactly the same in both cases, and therefore imports exactly the same sort of certainty from the general causal maxims.
It is true, of course, that our inquiries into physical objects do not have the same certainty as our inquiries into mathematical objects. Shepherd attributes this difference not to the general format of the reasoning, which is the same in both cases, but to the fact that we are differently related to mathematical objects than to physical objects. In mathematics we can freely stipulate features of a system, and see what follows from those features. In physical investigations, we do not have this freedom of stipulation. In physical investigations, objects are formed independently of our stipulation, and much of the uncertainty in these investigations is due to the difficulty of pinning down precisely the formation of these objects. We could very well be missing some important feature of the objects; and in cases that seem the same it could very well be that there is some hidden feature that would, if we knew about it, require us to come to completely different conclusions about the system. This failure of certainty in the investigation, however, does not affect the certainty of the reasoning, any more than the application of mathematics to physical reality affects the certainty of mathematical reasoning. Mathematical reasoning is capable of certainty and necessity whether it is applied to physical systems or not; it is entirely possible that there is some variable in the physical system which needs to be taken into account if the mathematics is to characterize the system accurately, but this is a failure of certainty in the application of the reasoning, not in the reasoning itself. Such is the case, Shepherd holds, with all causal reasoning.
Plurality of Worlds
PZ Myers has an excellent post on extraterrestrial intelligence at "Pharyngula". I don't have anything to add to it beyond a small reaffirmation of something noted briefly in the comments discussion: from all the evidence we have, we have fairly good reason to doubt that, even on the questionable assumption that there are lots and lots of intelligent species, most of them would ever reach considerable technological advancement. An immense amount of our scientific development, for instance, is tied to size of our moon. Who knows how we would have developed scientifically and technologically if we never experienced total eclipses? It's possible, of course, that we would have done just fine without it (there were, after all, other things like comets); but when we're dealing with history, it's very hard to say how any of it would have happened had we had a different solar system. That's not as helpful a consideration as some of the ones Myers brings up (in part because it's something we know so much less about); but at the very least I think it is sometimes too easily assumed that the history of human intelligence shows some special predisposition to science, in a way that is parallel to (and as problematic as, or more problematic than) the assumption that the history of life shows some special predisposition to intelligence.
I should post something sometime on the "Plurality of Worlds" dispute (the eighteenth & nineteenth century version of this issue). Most of it is actually immensely boring (being of the silly "Creation has to manifest God's glory, so there must be intelligent life all over the place" sort), but my favorite Victorian, William Whewell, wrote a book on it (On the Plurality of Worlds). I've only read it once, and that only because Whewell wrote it; but I was pleasantly surprised, since Whewell occasionally makes the subject genuinely interesting. I really shouldn't have been surprised, because Whewell (who is the father of modern history and philosophy of science) tends to introduce all sorts of historical and methodological issues into most of the things he talks about. (For a sample you can see the page I promised on Whewell's analogy between the utilitarian principle in morals and the principle of least action in physics.) But that will have to wait for quite some time, given all the other things I have to do. If anyone's interested in the subject, there's a very brief overview, with some relevant 18th century texts here. (Link via Early Modern Resources.)
I should post something sometime on the "Plurality of Worlds" dispute (the eighteenth & nineteenth century version of this issue). Most of it is actually immensely boring (being of the silly "Creation has to manifest God's glory, so there must be intelligent life all over the place" sort), but my favorite Victorian, William Whewell, wrote a book on it (On the Plurality of Worlds). I've only read it once, and that only because Whewell wrote it; but I was pleasantly surprised, since Whewell occasionally makes the subject genuinely interesting. I really shouldn't have been surprised, because Whewell (who is the father of modern history and philosophy of science) tends to introduce all sorts of historical and methodological issues into most of the things he talks about. (For a sample you can see the page I promised on Whewell's analogy between the utilitarian principle in morals and the principle of least action in physics.) But that will have to wait for quite some time, given all the other things I have to do. If anyone's interested in the subject, there's a very brief overview, with some relevant 18th century texts here. (Link via Early Modern Resources.)
Wisdom from Wollstonecraft
The fact is, that men expect from education, what education cannot give. A sagacious parent or tutor may strengthen the body and sharpen the instruments by which the child is to gather knowledge; but the honey must be the reward of the individual's own industry. It is almost as absurd to attempt to make a youth wise by the experience of another, as to expect the body to grow strong by the exercise which is only talked of, or seen.
From Mary Wollstonecraft, A Vindication of the Rights of Women, chapter 5.
From Mary Wollstonecraft, A Vindication of the Rights of Women, chapter 5.
Sunday, December 12, 2004
Another Poem Draft
Night
I walked in city-darkness underneath a stormy sky,
Dreaming of the echoes of a God condemned to die,
Dreaming of the words of a convict lifted high:
It is done; it is finished.
The darkness all around me was the blackness of my heart,
With tendrils, like living death, that entered every part;
I fell down then straightway, sharply wounded by a dart:
It is done; it is finished.
Then in a moment's clearness, I saw me as I am,
An endless sea of failings hid by denial like a dam--
Then off in thorny bushes I heard the bleating of a ram:
It is done; it is finished.
No guilt within my heart and no burden on my back,
No torment by my demons or by a conscientious rack,
Just safe and well-defended from the darkness's attack:
It is done; it is finished.
Scarce one whit am I better than the way I was before,
But this death has worked a change that no man can well ignore,
As simple and momentous as the opening of a door:
It is done; it is finished.
Though I fall, I know in truth that I never am alone,
And look to be restored in resurrected flesh and bone--
For the tomb in which I am is no longer sealed by stone:
It is done; it is finished.
I walked in city-darkness underneath a stormy sky,
Dreaming of the echoes of a God condemned to die,
Dreaming of the words of a convict lifted high:
It is done; it is finished.
The darkness all around me was the blackness of my heart,
With tendrils, like living death, that entered every part;
I fell down then straightway, sharply wounded by a dart:
It is done; it is finished.
Then in a moment's clearness, I saw me as I am,
An endless sea of failings hid by denial like a dam--
Then off in thorny bushes I heard the bleating of a ram:
It is done; it is finished.
No guilt within my heart and no burden on my back,
No torment by my demons or by a conscientious rack,
Just safe and well-defended from the darkness's attack:
It is done; it is finished.
Scarce one whit am I better than the way I was before,
But this death has worked a change that no man can well ignore,
As simple and momentous as the opening of a door:
It is done; it is finished.
Though I fall, I know in truth that I never am alone,
And look to be restored in resurrected flesh and bone--
For the tomb in which I am is no longer sealed by stone:
It is done; it is finished.
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