Suppose we observe an event e — how much information do we acquire?
We'd like a function I such that for any e, I(e) tells us how much information is contained in the occurrence of e.
Intuitively, if the probability of e occurring is very large, then I(e) should be very high. We learn a lot when something unlikely occurs. If your math teacher stands on one leg, barks like a dog, turns around three times, then leaps through the window, you learn a lot about him.
If the probability of e occurring is very high, though, I(e) should be very small. In the limit, as the probability of e approaches 1, i.e. certainty, I(e) should approach zero — we don't learn very much when we see the sun rise in the morning (at least, not if we've been paying attention!).
In the limit in the other direction, as the probability of e approaches zero, the information we gain from observing e approaches infinity.
Finally, if two unconnected (i.e. independent) events occur together then the information we receive about them is just the sum of the information we would have received had each of them occurred separately. (Remember that two events are independent if the probability of both of them occurring equals the probability of one times the probability of the other.) If my math teacher puts a banana on his head, and your english teacher, in a different state, smothers himself in jello, then we learn everything I would have learned separately about my math teacher, plus everything you would have learned separately about your english teacher.
So, we now have several constraints on the function I:
1. P(e1) < P(e2) implies I(e1) > I(e2)
2. P(e) = 1 implies I(e) = 0
3. P(e) = 0 implies I(e) = ∞
4. P(e1 ∧ e2) = P(e1) × P(e2) implies I(e1 ∧ e2) = I(e1) + I(e2)
One convenient analysis of information which satisfies these four constraints is
I(e) = − log P(e)
Thursday, July 23, 2009
Friday, July 17, 2009
Wednesday, July 15, 2009
Monday, June 29, 2009
Thursday, June 25, 2009
Thursday, June 18, 2009
what is post-post-modern?
Modernism invited artists to play with technique, to utilize the medium as medium in their storytelling.
Post-modernism encouraged the use of technique for its own sake: story and character, depiction and meaning became subordinate to self-awareness, self-reference, and alinear linguistic puzzles. If there was a surface narrative in the post-modern work, it was always subordinate to the numerous subnarrative strands which served to subvert it, seeping in through the interstices, reversing the author / reader power structure, etc.
But what of the post-post-modern narrative arts? Once the door to self-awareness and self-reference has been opened, it can never be closed. Nevertheless, the luster of for its own sake self-referentialism has worn thin.
Let's look at three strategies for bridging this gap, for moving beyond the self-indulgence of post-modernism while retaining its techniques; and reclaiming (if at all possible) the traditional narrative ideas of story and character and meaning.
David Foster Wallace, for example, explicitly speaks of finding a "compromise" between a fractional nonlinearity and a seductive and compelling story in this interview with Charlie Rose, discussing Infinite Jest from 19 or so min. and post-modernism ("after modernism") from 21 or so min.
What's of interest about Infinite Jest (in this context) is that the meaning of the novel has nothing to do with its techniques (or language, relativism, power-structures, etc.). The novel is a deep investigation of the contemporary American cultural of addiction, and unabashedly so. But it is not language which is convicted, but something subtler. And at all times, the individual is held to task and examined, rather than subordinated to the political and cultural commentary.
The centrality of the individual and his struggle to construct meaning in his life is also at the heart of Lars von Trier's The Five Obstructions, a film about filmmaking in which one director forces another to repeatedly remake his most famous short, each time following a different set of bizarre rules. Despite the blatant self-referentialism and absorbtion in the medium of film itself, The Five Obstructions culminates in a touching a deeply humanistic affirmation of the human spirit, one which feels all the less trite for transcending its deconstructionist trappings.
As a final example, consider the Southpark 2-part episode, "The Cartoon Wars." A cartoon about cartoons and censorship, which itself is censored. The creators' commentary on the second episde is here:
Not only is the storyline self-referential and self-aware in the extreme, it overtly comments on the need for story and character development rather then mere fractured joke telling. Although the ultimate message is political, the emphasis is again on the responsibility of the individual rather than the culpability of society, language, or power structures.
Post-modernism encouraged the use of technique for its own sake: story and character, depiction and meaning became subordinate to self-awareness, self-reference, and alinear linguistic puzzles. If there was a surface narrative in the post-modern work, it was always subordinate to the numerous subnarrative strands which served to subvert it, seeping in through the interstices, reversing the author / reader power structure, etc.
But what of the post-post-modern narrative arts? Once the door to self-awareness and self-reference has been opened, it can never be closed. Nevertheless, the luster of for its own sake self-referentialism has worn thin.
Let's look at three strategies for bridging this gap, for moving beyond the self-indulgence of post-modernism while retaining its techniques; and reclaiming (if at all possible) the traditional narrative ideas of story and character and meaning.
David Foster Wallace, for example, explicitly speaks of finding a "compromise" between a fractional nonlinearity and a seductive and compelling story in this interview with Charlie Rose, discussing Infinite Jest from 19 or so min. and post-modernism ("after modernism") from 21 or so min.
What's of interest about Infinite Jest (in this context) is that the meaning of the novel has nothing to do with its techniques (or language, relativism, power-structures, etc.). The novel is a deep investigation of the contemporary American cultural of addiction, and unabashedly so. But it is not language which is convicted, but something subtler. And at all times, the individual is held to task and examined, rather than subordinated to the political and cultural commentary.
The centrality of the individual and his struggle to construct meaning in his life is also at the heart of Lars von Trier's The Five Obstructions, a film about filmmaking in which one director forces another to repeatedly remake his most famous short, each time following a different set of bizarre rules. Despite the blatant self-referentialism and absorbtion in the medium of film itself, The Five Obstructions culminates in a touching a deeply humanistic affirmation of the human spirit, one which feels all the less trite for transcending its deconstructionist trappings.
As a final example, consider the Southpark 2-part episode, "The Cartoon Wars." A cartoon about cartoons and censorship, which itself is censored. The creators' commentary on the second episde is here:
Not only is the storyline self-referential and self-aware in the extreme, it overtly comments on the need for story and character development rather then mere fractured joke telling. Although the ultimate message is political, the emphasis is again on the responsibility of the individual rather than the culpability of society, language, or power structures.
Sunday, May 24, 2009
the philosopher's oath
If you are a practicing philosopher, please consider taking this oath:
I, [insert name here], do hereby vow to never use, in speech or in print, the locution "X taught us that Y", where X is a famous philosopher and Y is a claim which they have defended. Furthermore, whenever I read or hear claims of the form "X taught us that Y" made by some other philosopher, I vow to remind myself that mentioning a claim in conjunction with its most famous defender does not constitute an argument for that claim, and that it is a defining feature of philosophy that it should have no dogmas, that all claims are open to question. Finally, I recognize that it is this feature of philosophy which distinguishes it from science, but also which prevents it from degenerating into hollow and dogmatic scholasticism, and I vow to maintain an open mind and protect philosophy from the descent into scholasticism until my dying day, or forfeit my right to practice philosophy.
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