I've recently been criticized for not using quantum computing arithmetic in my meaningless arithmetic post. I assumed that the amount of "stuff" in the universe amounted to rougly 10^80, using fundamental particles. Berkenstein and Schiffer* put a limit on quantum information in the universe at 10^122. Fine. In fact, let's say that even the various quantum computing cheerleaders are all hopelessly narrow-minded and we aren't even near the real upper limit. There is still an upper limit. The point is this: the amount of possible information about a finite universe (and therefore encodable by the universe) is also finite. It must be, if reality exists at all.
*Jacob Bekenstein and Marcelo Schiffer, "Quantum Limitations on the Storage and Transmission of Information", International Journal of Modern Physics v1, pp. 355-422, 1990.
Saturday, March 6, 2010
Sunday, February 28, 2010
Is Musical Dissonance Universal?
I've often wondered about whether there is such a thing as a universally-recognized dissonant or harmonious musical interval. For example, Westerners seem to regard diminished fifth intervals as dissonant and tension-building (famous example: the Mars movement of Holst's The Planets). And indeed, six half-steps up a heptatonic scale, the ratio is the most destructively interferent, with a frequency that's an irrational ratio of the square root of two relative to the tonal. So what? It's not clear (to me at least) why that should sound "special" universally to all humans. Do Bushmen find it equally "tense"?
This interval has a history in the West. In the Middle Ages, Europeans weren't allowed to play this interval (the dreaded tritone) for fear that it would summon the devil, and regardless of the whether this interval represents a universal, surely today we're somewhat influenced by this antecdent. Okay - where did they get it from? A colleague of mine once threw out the idea that maybe a diminished fifth sounds like an animal in pain. Okay - so why does an animal in pain make diminished fifth-sounds? Do we have examples of scared or injured animals making such sounds? Universals based on physics that we understand today as semantically-gifted primates are usually not nearly as universal as we think they are, even within our species. The conservative position is to assume until proven otherwise that our associations with culturally institutions are just that - associations, programmed by experience.
This is why the following is so interesting.
(For the musically-challenged, compare to the Mars movement.)
Taking the starting and ending tones as the tonal, the high "note" that the wolf holds is a diminished fifth (compare to Mars Assuming the description is accurate and this is a wolf separated from its pack and trying to locate them, it's worth noting that a wolf under some stress tries to get other wolves' attention by using a diminished fifth interval. Note that wolves and other canines have a studied repertoire known "words", certainly not as plastic as the way humans use language, but nonetheless specific vocalizations that are repeated in the same contexts (separated from pack, just caught small game, get out of our territory, etc.)
This interval has a history in the West. In the Middle Ages, Europeans weren't allowed to play this interval (the dreaded tritone) for fear that it would summon the devil, and regardless of the whether this interval represents a universal, surely today we're somewhat influenced by this antecdent. Okay - where did they get it from? A colleague of mine once threw out the idea that maybe a diminished fifth sounds like an animal in pain. Okay - so why does an animal in pain make diminished fifth-sounds? Do we have examples of scared or injured animals making such sounds? Universals based on physics that we understand today as semantically-gifted primates are usually not nearly as universal as we think they are, even within our species. The conservative position is to assume until proven otherwise that our associations with culturally institutions are just that - associations, programmed by experience.
This is why the following is so interesting.
(For the musically-challenged, compare to the Mars movement.)
Taking the starting and ending tones as the tonal, the high "note" that the wolf holds is a diminished fifth (compare to Mars Assuming the description is accurate and this is a wolf separated from its pack and trying to locate them, it's worth noting that a wolf under some stress tries to get other wolves' attention by using a diminished fifth interval. Note that wolves and other canines have a studied repertoire known "words", certainly not as plastic as the way humans use language, but nonetheless specific vocalizations that are repeated in the same contexts (separated from pack, just caught small game, get out of our territory, etc.)
Friday, February 26, 2010
Rationally Optimizing Pigeons
Several years ago it was shown that dogs are less prone to the sunk cost fallacy than humans (couldn't find a non-gated version; pop science article here.)
The humiliation continues: pigeons are better than humans at the Monty Hall Dilemma. The question is whether humans lack whatever circuit is allowing pigeons to inductively (one assumes) approximate the logic of the Dilemma, or whether there's something in human cognition interfering with otherwise at-least-equal optimizing ability in this task.
A reasonable way of thinking about the first option is that for this specific behavior, for whatever reason, pigeons are more optimized, though for most things they aren't very good generalists.
Next step: finding out whether hamsters one-box or two-box on Newcomb's problem.
The humiliation continues: pigeons are better than humans at the Monty Hall Dilemma. The question is whether humans lack whatever circuit is allowing pigeons to inductively (one assumes) approximate the logic of the Dilemma, or whether there's something in human cognition interfering with otherwise at-least-equal optimizing ability in this task.
A reasonable way of thinking about the first option is that for this specific behavior, for whatever reason, pigeons are more optimized, though for most things they aren't very good generalists.
Next step: finding out whether hamsters one-box or two-box on Newcomb's problem.
Saturday, February 13, 2010
Altaic Pride!
I ran across this online forum for discussing issues of pan-Altaic identity, complete with a silhouette of a ravaging Mongolic horseman. Apparently they're fans of the Ural-Altaic hypothesis because there's a Magyar forum but I don't see any Suomi; don't know what they have against Finns. Lapps are apparently right out.
I think in response all us Indo-European/Aryan/Kurgans from Reykjavik to Dacca should start our own club. Hear the call, my sisters and brothers in Moscow, Rome, Athens and Oslo, Tehran and Delhi and Tirana! (And not forgetting our brave Tocharian comrades who perished in the sands of the Xinjiang.) We'll organize it into chapters of a hundred each (satem or centum depending how you swing) and instill values of horsemanship, wheel-making and triumvirate-god-worshipping. We can only speak proto-IE at meetings, or failing that, Lithuanian, and I'm sure We can find another Lithuanian besides Marija Gimbutas to lead us. Activities include driving Basques into the Pyrenees, Dravidians out of the Indus Valley, and neolithics from other continents out of existence. I think we're onto something here!
I think in response all us Indo-European/Aryan/Kurgans from Reykjavik to Dacca should start our own club. Hear the call, my sisters and brothers in Moscow, Rome, Athens and Oslo, Tehran and Delhi and Tirana! (And not forgetting our brave Tocharian comrades who perished in the sands of the Xinjiang.) We'll organize it into chapters of a hundred each (satem or centum depending how you swing) and instill values of horsemanship, wheel-making and triumvirate-god-worshipping. We can only speak proto-IE at meetings, or failing that, Lithuanian, and I'm sure We can find another Lithuanian besides Marija Gimbutas to lead us. Activities include driving Basques into the Pyrenees, Dravidians out of the Indus Valley, and neolithics from other continents out of existence. I think we're onto something here!
Thursday, February 4, 2010
Mathematical Coping Strategies for Schizophrenia
Back in September I went to a pre-exam review held in a room other than our normal classroom. At one point when the instructor filled up one markerboard with chemical pathways, and rolled back the next one only to discover this:
This third one is blurrier than the other two but I've included it for scale.
In unison the class said "What?..." but the instructor was unfazed. "That's our local homeless guy," he explained. "He often comes into these rooms and covers the board with figures." I made sure to get these shots before they were erased, wondering if we had another John Nash.
Of course it's more likely that the man is just sick and these numbers are gibberish. (For the record, there's no way to tell just from finding numbers whether the person is schizophrenic.) I actually emailed the pictures to a cosmologist friend* to see if they meant anything (they reminded me of quantum numbers) but my friend said there was no order to them that he could see. Still, it's tempting to look for patterns on the principle that, if there is indeed any method to this madness, we could get to the concepts inductively. Once at a party, as a game I decided to play what appeared to be a single-player solitaire-like game. I moved the cards around randomly but with great apparent concentration (I don't even know the rules for real solitaire) and soon enough, someone started watching. "I think I have the rules figured out," he offered after a few minutes. (Given the limited input, he may well have.)
Beyond problems of induction, there remains the question of why someone with mental health issues would develop a habit like this in the first place. My best guess is that, since he's homeless on a university campus where social status accords with intelligence (or at least proxy indicators of it), by writing opaque patterns of numbers he can maintain the delusion that he's a misunderstood genius, at least as long as he's writing his number-patterns in empty rooms where they aren't critiqued by people with real math abilities. (A similar strategy would be to write a cognitive philosophy blog with few readers.)
A more interesting possibility is that by finding a way to occupy his attention with a task requiring high concentration and that uses non-diseased parts of his brain, this person has found a way to quell the other constant disturbances to his thinking and can gain himself a moment of peace. Of course this is speculation, but if it hasn't already been asked, this might point the way to novel therapeutic approaches.
*Speaking of status, please note the casual way I refer to my cosmologist friend, which means that I'm cool.
In unison the class said "What?..." but the instructor was unfazed. "That's our local homeless guy," he explained. "He often comes into these rooms and covers the board with figures." I made sure to get these shots before they were erased, wondering if we had another John Nash.
Of course it's more likely that the man is just sick and these numbers are gibberish. (For the record, there's no way to tell just from finding numbers whether the person is schizophrenic.) I actually emailed the pictures to a cosmologist friend* to see if they meant anything (they reminded me of quantum numbers) but my friend said there was no order to them that he could see. Still, it's tempting to look for patterns on the principle that, if there is indeed any method to this madness, we could get to the concepts inductively. Once at a party, as a game I decided to play what appeared to be a single-player solitaire-like game. I moved the cards around randomly but with great apparent concentration (I don't even know the rules for real solitaire) and soon enough, someone started watching. "I think I have the rules figured out," he offered after a few minutes. (Given the limited input, he may well have.)
Beyond problems of induction, there remains the question of why someone with mental health issues would develop a habit like this in the first place. My best guess is that, since he's homeless on a university campus where social status accords with intelligence (or at least proxy indicators of it), by writing opaque patterns of numbers he can maintain the delusion that he's a misunderstood genius, at least as long as he's writing his number-patterns in empty rooms where they aren't critiqued by people with real math abilities. (A similar strategy would be to write a cognitive philosophy blog with few readers.)
A more interesting possibility is that by finding a way to occupy his attention with a task requiring high concentration and that uses non-diseased parts of his brain, this person has found a way to quell the other constant disturbances to his thinking and can gain himself a moment of peace. Of course this is speculation, but if it hasn't already been asked, this might point the way to novel therapeutic approaches.
*Speaking of status, please note the casual way I refer to my cosmologist friend, which means that I'm cool.
Monday, December 21, 2009
Existence and Consciousness
To ask why there is something rather than nothing seems to assume on some level that it's less natural for the universe to exist than to not exist. It also assumes that some kind of existential inertia means that there will continue to be something rather than nothing.
This second assumption at least is not universal to humans, and is covered by Robert Nozick in the most effective treatment of this question yet. The Inuit believe that if hunting ceases, even for an instant, the universe will end. Several religious traditions hold that if at any given moment, at least one person somewhere is not copying their holy text, reality will sink back into chaos. These examples are interesting but are probably better explained as cultural technologies to keep people motivated in performing important activities, than as insightful cosmogonies.
Another question is whether it is clearly meaningful to ask counterfactuals about the fact of existence itself - whether existence had to exist - versus finite entities within existence. It is clearer that the pine tree outside my window, or you, might not have existed. In this way existence as a whole, the capacity for things to exist, is qualitatively different than a pine tree.
Changing gears to the ever-popular deep mystery, is it meaningful to talk about a universe that has no consciousness? Is self-awareness, a part of the universe experientially looping back on itself, necessary for existence? There is an intuition (which I share) that questions about necessity of existence and of subjective experience are getting at the same things.
This second assumption at least is not universal to humans, and is covered by Robert Nozick in the most effective treatment of this question yet. The Inuit believe that if hunting ceases, even for an instant, the universe will end. Several religious traditions hold that if at any given moment, at least one person somewhere is not copying their holy text, reality will sink back into chaos. These examples are interesting but are probably better explained as cultural technologies to keep people motivated in performing important activities, than as insightful cosmogonies.
Another question is whether it is clearly meaningful to ask counterfactuals about the fact of existence itself - whether existence had to exist - versus finite entities within existence. It is clearer that the pine tree outside my window, or you, might not have existed. In this way existence as a whole, the capacity for things to exist, is qualitatively different than a pine tree.
Changing gears to the ever-popular deep mystery, is it meaningful to talk about a universe that has no consciousness? Is self-awareness, a part of the universe experientially looping back on itself, necessary for existence? There is an intuition (which I share) that questions about necessity of existence and of subjective experience are getting at the same things.
Sunday, December 20, 2009
James Cameron and the Problem of Reference
Artificial languages are interesting, though I always find myself longing for some index of strangeness relative to the creator's language (pick a Native American language at random; is the conlang ever going to be more different than the creator's native language than the natural language is? I doubt it.) That said, James Cameron did it right for the Na'vi language in Avatar, reportedly claiming to have out-Klingon'ed Klingon. The linguist Cameron chose to create Na'vi summarizes its structure and during the preamble of the article, his interviewer states this gem:
"...since there is already tremendous interest in the [Na'vi] language, and some less-than-accurate information about it is currently floating around online, I asked Paul [the creator] if he could write up a formal description of Na’vi as a Language Log guest post."
The problem of reference is really a set of problems in different situations. The answer to this one is I think implicit and relatively obvious. Maybe we don't know if the current king of France is bald, but we do know whether Romeo is gay or Na'vi is agglutinating.
"...since there is already tremendous interest in the [Na'vi] language, and some less-than-accurate information about it is currently floating around online, I asked Paul [the creator] if he could write up a formal description of Na’vi as a Language Log guest post."
The problem of reference is really a set of problems in different situations. The answer to this one is I think implicit and relatively obvious. Maybe we don't know if the current king of France is bald, but we do know whether Romeo is gay or Na'vi is agglutinating.
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