Political documents from the ancient and medieval world generally seem to be articulations of a certain set of political decisions and, in a broader sense, of the political order that created the document. The Declaration of Independence is the first document to imply a political order that did not yet exist. Though many of the liberties the Declaration sought to establish were existing liberties that had been abridged by the tyranny of the British crown, these liberties were asserted in the name of citizens of a state that had not yet come into being. The essence of this state was created by the Declaration itself: a true city in speech. At its foundation American political existence was rooted in rhetoric. Instead of political symbols arising from a long process of national self-identification, people identified themselves as Americans in virtue of the symbols established by the Declaration.
What makes a society created by rhetoric great is that its essential existence is ideal. The great danger of a society created by rhetoric is that people will lose touch with language, and thereby lose touch with everything that makes them who they are. The mystery of a society created by rhetoric, which can be its salvation and its destruction, is the distance that usually seems to exist between what is ideal and what is "actual."
05 July 2010
01 July 2010
Why space does not exist [1]
It is a great (and highly practical) illusion that something called space exists. This is not a mystical utterance (at least not in the typical sense of mystical); it is meant quite literally. For context, I would recommend the series of posts beginning here and continuing with the next two in December of 2009. In those posts I attempted to show that the concept of space demands to be thought as a field (sort of a cubic Cartesian plane) composed of discrete units. This point was proved more or less to my satisfaction and to the satisfaction of some others (who, I suspect, were privy to the secret we are about to discuss).
We begin by considering the manifold meanings of the word space. In common parlance we might ask someone to give us space. We might ask how much space is in a room, or how much space a certain object takes up. We speak of outer space and space travel. Things are spaced, words on the page no less than the pickets of a fence. Americans (we are told) like their space.
We can divide these meanings into the following definitions:
1) The area surrounding an object that is, in some sense, part of the object
2) The purported vacuum that composes most of the universe
3) Empty space between objects that place the objects into a certain order
4) Distance conceived in light of an abstract field composed of mathematically functional units
The fourth underlies all the other definitions, though it underlies the first the least. The existence of some sort of field (called space) in which objects exist at a certain space from each other (the 4th definition) is certainly necessary before we can begin to conceive of the universe as a series of planets with in space with space between them. Indeed, this concept seems self-evident and unquestionable.
But who among us has seen space? And do we ever actually mean space when we say space? If asked to say what we mean when we say space, we probably imagine a sort of map grid extended into all three dimensions. Is that actually how things are? For the reasons outlined in the previous post (linked to above), if such a field exists, it must be segmented in a discrete manner. This deduction was an analytic one from the very concept of space. But look around you.! The room I'm in now (messy again, unfortunately) is filled with all sorts of things all over the place. Now I imagine our cubic Cartesian plane extended around the room. Every object is located somewhere on this cubic plane. Is this actually my room? The fact that I can imagine it hardly means it is the case.
What we wish to show (and will hopefully continue to show) is that "space" is an abstraction. It is not real. There is no such thing as space anywhere. And yet science depends upon the concept of space: and this should tell us something about science...
We begin by considering the manifold meanings of the word space. In common parlance we might ask someone to give us space. We might ask how much space is in a room, or how much space a certain object takes up. We speak of outer space and space travel. Things are spaced, words on the page no less than the pickets of a fence. Americans (we are told) like their space.
We can divide these meanings into the following definitions:
1) The area surrounding an object that is, in some sense, part of the object
2) The purported vacuum that composes most of the universe
3) Empty space between objects that place the objects into a certain order
4) Distance conceived in light of an abstract field composed of mathematically functional units
The fourth underlies all the other definitions, though it underlies the first the least. The existence of some sort of field (called space) in which objects exist at a certain space from each other (the 4th definition) is certainly necessary before we can begin to conceive of the universe as a series of planets with in space with space between them. Indeed, this concept seems self-evident and unquestionable.
But who among us has seen space? And do we ever actually mean space when we say space? If asked to say what we mean when we say space, we probably imagine a sort of map grid extended into all three dimensions. Is that actually how things are? For the reasons outlined in the previous post (linked to above), if such a field exists, it must be segmented in a discrete manner. This deduction was an analytic one from the very concept of space. But look around you.! The room I'm in now (messy again, unfortunately) is filled with all sorts of things all over the place. Now I imagine our cubic Cartesian plane extended around the room. Every object is located somewhere on this cubic plane. Is this actually my room? The fact that I can imagine it hardly means it is the case.
What we wish to show (and will hopefully continue to show) is that "space" is an abstraction. It is not real. There is no such thing as space anywhere. And yet science depends upon the concept of space: and this should tell us something about science...
27 June 2010
15 June 2010
Option pricing
The Nobel prize-winning Black-Scholes option pricing formula is generally advanced by financial academics as the best possible way to value options. This may be true, but that doesn't mean it is any good.
It is further worth noting that the formula (often used for dynamic hedging) models security prices as follows:
dS = mSdt + sSdW
Where S is security price, mS is the average rate of change of the security (drift rate), t is time, sS is standard deviation of the security, and W is a geometric Brownian function.
The problem here is that stock prices generally can be modeled using geometric Brownian motion. However, there is (more or less) a hard stop to trading at market close. Despite this fact, orders can be placed after market close, to be executed immediately upon the opening of the market. For this reason, we will rarely find extreme jumps between the underlying security price at closing and opening. The possibility of what is effectively discrete motion should make us realize that using the geometric Brownian without at least including some fudge factor for the possibility of discontinuous motion (though approximating the Brownian with a discrete probability distribution such as the binomial would be preferable) will occasionally but decisively give us bad pricing information.
Against those who would suggest that the error in the formula will be relatively minor, we advance the anecdotal but highly compelling evidence that the year after Mr. Scholes won his Nobel prize, the hedge fund he was helping to run (Long Term Capital Management) imploded in a multibillion dollar disaster that left financial markets reeling.
It is further worth noting that the formula (often used for dynamic hedging) models security prices as follows:
dS = mSdt + sSdW
Where S is security price, mS is the average rate of change of the security (drift rate), t is time, sS is standard deviation of the security, and W is a geometric Brownian function.
The problem here is that stock prices generally can be modeled using geometric Brownian motion. However, there is (more or less) a hard stop to trading at market close. Despite this fact, orders can be placed after market close, to be executed immediately upon the opening of the market. For this reason, we will rarely find extreme jumps between the underlying security price at closing and opening. The possibility of what is effectively discrete motion should make us realize that using the geometric Brownian without at least including some fudge factor for the possibility of discontinuous motion (though approximating the Brownian with a discrete probability distribution such as the binomial would be preferable) will occasionally but decisively give us bad pricing information.
Against those who would suggest that the error in the formula will be relatively minor, we advance the anecdotal but highly compelling evidence that the year after Mr. Scholes won his Nobel prize, the hedge fund he was helping to run (Long Term Capital Management) imploded in a multibillion dollar disaster that left financial markets reeling.
26 May 2010
Gold
I'm in a place with a television this week and I decided to turn on the news as I was eating breakfast. I was amused/disturbed to notice that Fox News (which was, in its defense, the only "news" network not running stories about cute puppies or things of a similar nature) was running non-stop advertisements for gold investment services in between its news stories about how the sky was falling. In between wondering whether or not gold was likely to be a particularly good investment, since its convertibility into local currency presupposes some demand for the commodity (a demand that is dampened and not heightened by economic instability), I was struck by something I had written about some time ago in the context of a discussion of Beowulf. What exactly is the value of gold? And why do dragons dwell on buried gold-hoards? There is something perverse about burying refined gold-work back in the earth from which it came. Gold should be seen in the sunlight, not placed back into the earth.
As the advertisement correctly observed, gold has always held some value. This value is not "conventional" in the way that the value of our currency is conventional, nor is it derived from its practical utility in industrial applications. In the alchemical symbolism, gold is the perfection of nature subsumed by the spiritual. In Beowulf, gold is a physical manifestation of the virtue of a people personified in their hero. When the people are no more, the burial of the gold calls dragons to its glitter. This image is one the most intriguing of the poem (which is partially a reflection upon gold) and rewards careful attention and reflection. The proper meaning of gold is almost entirely erased when it is viewed as a means to stabilize one's IRA against fluctuations in equity prices; and it is highly significant that in these situations the person purchasing the gold generally does not take physical possession of the gold but controls it through shares in a mutual fund or through an ETF. Yet even in this utterly etherealized form there is still something mysterious about the manner in which gold eludes mathematization, as fluctuations of gold prices are highly difficult to model for any practical financial purpose.
"there laid within it his lordly heirlooms
and heaped hoard of heavy gold."
Beowulf XXXII
As the advertisement correctly observed, gold has always held some value. This value is not "conventional" in the way that the value of our currency is conventional, nor is it derived from its practical utility in industrial applications. In the alchemical symbolism, gold is the perfection of nature subsumed by the spiritual. In Beowulf, gold is a physical manifestation of the virtue of a people personified in their hero. When the people are no more, the burial of the gold calls dragons to its glitter. This image is one the most intriguing of the poem (which is partially a reflection upon gold) and rewards careful attention and reflection. The proper meaning of gold is almost entirely erased when it is viewed as a means to stabilize one's IRA against fluctuations in equity prices; and it is highly significant that in these situations the person purchasing the gold generally does not take physical possession of the gold but controls it through shares in a mutual fund or through an ETF. Yet even in this utterly etherealized form there is still something mysterious about the manner in which gold eludes mathematization, as fluctuations of gold prices are highly difficult to model for any practical financial purpose.
"there laid within it his lordly heirlooms
and heaped hoard of heavy gold."
Beowulf XXXII
15 May 2010
Discourse
Political society of any kind requires that discourse be engaged in with pure intentions. The moment that the choice of words becomes subjugated to a preordained ideological outcome, political speech is no longer discourse. The purpose of political speech is to establish a course of action in harmony with the principles of society and the needs of the given circumstance. None of us can engage in political speech without preconceptions of some kind (preconceptions are what make us all "individuals"), but we can attempt to conform our speech to the truth of the matter under discussion and not conform speech to some extrinsic standard or conclusion provided in advance. Such action denigrates speech and makes real discourse impossible; it removes political speech even further from truth itself and pushes it deeper into the realm of opinion, feeling, and unreality.
These reflections are prompted by an article I saw today on an American news service that referred to persons illegally present in the US as "undocumented immigrants" instead of "illegal immigrants." I hadn't seen that phrase before so I attempted to ascertain its origin. As it turns out, certain persons had decided that the phrase "illegal immigrant" was too negatively charged and needed to be changed. Let us leave aside (for a moment) our views on the topic of illegal immigration, a topic of incredible complexity admits of no easy answers, and ask ourselves whether it is appropriate to try and modify discourse in this manner. The phrase "illegal immigrant" has a specific political meaning. Insofar as the people under question exist (politically) as immigrants, and insofar as the have not legally immigrated to this country, their being qua immigrant is qualified by its illegality. Contrary to the slew of bumper stickers that proclaim that "no person is illegal," the phrase "illegal immigrant" does not attempt to subject the fundamental personhood of anyone to a declaration of illegality. Rather, it simply states the (mutable) fact that the person's political existence as immigrant is illegal. This could be changed by amending immigration laws to allow such persons to legally immigrate, but as things stand now, the phrase "illegal immigrant" is objectively correct.
The phrase "undocumented immigrant" seems to suggest that the people in question merely are missing documentation. As such, it is a less precise description of what the political existence of these people actually are. While it is entirely true that they are undocumented, it is incomplete merely to say this. As a general rule we ought refer to things by their most important attribute to the matter at hand. The fact that these immigrants lack documentation is entirely predicated on the fact that they are not in the country legally. We aren't referring to people who came to the country legally and whose immigration papers were lost (a more accurate use of the phrase "undocumented immigrant").
Therefore, it seems clear to me that the appropriate phrase that ought to be used is "illegal immigrant" (again, note that we are making no judgments as to whether such immigration ought to be legal or illegal). To attempt to subordinate discourse towards a preconceived goal through altering the words that we use is horribly dangerous, even if employed towards good ends. It lowers the quality of our discourse and makes most of us less likely to think about what is actually being said. The corruption of discourse is the poison can undo any democracy, and I feel we are dangerously on the brink of this happening. The right calls politicians on the left variously "communists" and "nazis" (terms that are generally inaccurate) while the left calls politicians on the right "bigots" and "racists" (also terms that are generally inaccurate). The more that people believe these insults the less likely they are to listen to each other. And once no one is listening to anyone, democracy is no longer possible.
We should always insist on clarity and precision in our discourse, even when such clarity and precision work against the goal we wish to achieve.
These reflections are prompted by an article I saw today on an American news service that referred to persons illegally present in the US as "undocumented immigrants" instead of "illegal immigrants." I hadn't seen that phrase before so I attempted to ascertain its origin. As it turns out, certain persons had decided that the phrase "illegal immigrant" was too negatively charged and needed to be changed. Let us leave aside (for a moment) our views on the topic of illegal immigration, a topic of incredible complexity admits of no easy answers, and ask ourselves whether it is appropriate to try and modify discourse in this manner. The phrase "illegal immigrant" has a specific political meaning. Insofar as the people under question exist (politically) as immigrants, and insofar as the have not legally immigrated to this country, their being qua immigrant is qualified by its illegality. Contrary to the slew of bumper stickers that proclaim that "no person is illegal," the phrase "illegal immigrant" does not attempt to subject the fundamental personhood of anyone to a declaration of illegality. Rather, it simply states the (mutable) fact that the person's political existence as immigrant is illegal. This could be changed by amending immigration laws to allow such persons to legally immigrate, but as things stand now, the phrase "illegal immigrant" is objectively correct.
The phrase "undocumented immigrant" seems to suggest that the people in question merely are missing documentation. As such, it is a less precise description of what the political existence of these people actually are. While it is entirely true that they are undocumented, it is incomplete merely to say this. As a general rule we ought refer to things by their most important attribute to the matter at hand. The fact that these immigrants lack documentation is entirely predicated on the fact that they are not in the country legally. We aren't referring to people who came to the country legally and whose immigration papers were lost (a more accurate use of the phrase "undocumented immigrant").
Therefore, it seems clear to me that the appropriate phrase that ought to be used is "illegal immigrant" (again, note that we are making no judgments as to whether such immigration ought to be legal or illegal). To attempt to subordinate discourse towards a preconceived goal through altering the words that we use is horribly dangerous, even if employed towards good ends. It lowers the quality of our discourse and makes most of us less likely to think about what is actually being said. The corruption of discourse is the poison can undo any democracy, and I feel we are dangerously on the brink of this happening. The right calls politicians on the left variously "communists" and "nazis" (terms that are generally inaccurate) while the left calls politicians on the right "bigots" and "racists" (also terms that are generally inaccurate). The more that people believe these insults the less likely they are to listen to each other. And once no one is listening to anyone, democracy is no longer possible.
We should always insist on clarity and precision in our discourse, even when such clarity and precision work against the goal we wish to achieve.
05 May 2010
Beautiful changes
I've been thinking about the last lines from Richard Wilbur's marvelous poem "The Beautiful Changes" a lot recently. They are quoted below (I have probably misplaced the line breaks, for which I apologize):
"the beautiful changes
In such kind ways,
Wishing ever to sunder
Things and things' selves for a second finding,
to lose
For a moment all that it touches back to
wonder."
There is the appearance of a Hegelian quality to the lines "wishing ever to sunder... for a second finding," but this image is dispelled by the suggestion that the sundering is not itself illusory but actually quite real, since it results in loss. We don't normally think of sundering and loss as "kind," but the poem suggests that the result (wonder) is worth the price, even though it is just "for a moment." Against the radical despair (indeed, despair beyond despair!) inherent in Hegelianism, we should find great comfort in the conclusion of the poem's second stanza:
"Any greenness is deeper than anyone knows."
Fewer phrases more hopeful than this have been placed into poetry.
"the beautiful changes
In such kind ways,
Wishing ever to sunder
Things and things' selves for a second finding,
to lose
For a moment all that it touches back to
wonder."
There is the appearance of a Hegelian quality to the lines "wishing ever to sunder... for a second finding," but this image is dispelled by the suggestion that the sundering is not itself illusory but actually quite real, since it results in loss. We don't normally think of sundering and loss as "kind," but the poem suggests that the result (wonder) is worth the price, even though it is just "for a moment." Against the radical despair (indeed, despair beyond despair!) inherent in Hegelianism, we should find great comfort in the conclusion of the poem's second stanza:
"Any greenness is deeper than anyone knows."
Fewer phrases more hopeful than this have been placed into poetry.
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