June 29, 2005

the half–truths of war

file under: thoughts about things

i didn't watch the president's speech yesterday. didn't even know it was happening. i've grown accustomed to ignoring what he says because he says so little that actually illuminates. if there is truth in the world (and i seriously doubt it), he does nothing to promote it. perhaps the job of any president is not to expose the truth, but rather to create politically expedient half–truths. but that's the cynic in me speaking.

i don't think there's a single american that would doubt that war is hard. as eulsive as truth is these days, this truth seems pretty self–evident. and yet the president reiterated it in his speech yesterday, several times. he also reiterated the need to support our troops, and to recognize the sacrifices of the brave men and women fighting (and dying) in Iraq. also self–evident.

i don't think anyone on either side of the aisle would argue these two points. so why reiterate them?

these statements have become platitudes. their obviousness almost elevates them to the level of tautologies (the color red is red, the sun rises in the east if it rises in the east). but what happens when you mix these statements with other assertions that are more tenuous, with other calls for support and faith?

maybe there's the feeling that by asserting so many things that people hold to be true, then mixing them with things that many consider suspect, you will engender positive feelings towards the latter — a truth halo effect, if you will. either that, or your speechwriters are really running out of gas and can't come up with other good things to say.

if this was the ploy, i don't think it worked. it's hard to believe this president when you just don't know what to believe in general. do you believe the democrats? the republicans? the bloggers? the sunnis? the shia? the kurds? the president? CNN? fox? rush limbaugh? truth, when it comes to the war in Iraq, seems to be caught in the shifting sands of perception, belief, and context.

in any case, the course in Iraq is one that's impossible to chart. i'm not even sure shackleton could get out of this one. i don't envy you, mr. president. you've got a hard, hard job.

Posted: 06.29.05 at 9:31 PM | Permalink | Comments (0) | TrackBack (0)

June 27, 2005

Butane or pork?

file under: thoughts about things

the local asian supermarket that elaine and i patronize has no organizational system, as far as i can tell. when it comes to blue light specials, anything goes, as the picture above demonstrates. pork fu. butane fuel. they're all just specials. who cares if there's any sense to it?

the last time i recall encountering a complete disdain for in–store classification was in hana, hawaii. there's a grocery store there called hasegawa's that has the most random assortment of items that i've ever seen. the only difference there is that they're the country grocery store that has to have everything for everyone, in one tiny establishment. 99 ranch doesn't have the same excuse.

i suspect there's something really deep to be said here about supply chains or the law of supply and demand or some other thing about marketing or sociology, but i just can't think of it. call this entry "the deep thought that wasn't".

Posted: 06.27.05 at 10:03 PM | Permalink | Comments (1) | TrackBack (0)

June 23, 2005

the case of the missing pants

file under: thoughts about things

i lost a pair of pants.

it wasn't a sudden loss, the kind where you smack your forehead with a doh! realizing that you've just left something on the train or in some mystical foreign land. instead, this was the uncertain kind of loss, the loss that creeps up on you. a sneaking suspicion starts brewing in the back of your mind that you've lost something, but you don't have the time to search to confirm or deny your fears. instead it just percolates.

and then, at some point, you reach the breaking point, the point where the brew is beyond ready; in fact, it's stinking up your brain, and you've got to do something about it.

i felt like i hadn't really seen one pair of my jeans in a few weeks. it didn't bother me too much — i figured it was in the laundry or on the drying rack or stuck in some drawer out of place. then i started to miss these particular pants, because i felt like i was paying altogether too much attention to my other levi's. one wouldn't want to convey an impression of sartorial favoritism, so i decided it was time to look for my neglected pants, not knowing whether they were in fact in the land of the lost.

the usual suspects turned up nothing (laundry hamper, drying rack, all clothes drawers, piles of clothes in the guest room waiting to be ironed, unfolded clothes on the guest room bed waiting to be folded). the next step was luggage from recent trips — no dice. hmmm. hanging somewhere on the back of a door? nope. stuck in the hall closet? no...oh oh! laundry chute! no pants (although i did find two wayward black socks and a white tshirt that had been hanging there for god–knows how long).

things were getting desperate. i wracked my brain trying to remember when i might have worn them, but this is precisely the kind of thing i always forget. i started wandering aimlessly through the house and garage at this point, suspecting that my pants weren't the only thing i'd lost.

and then it came to me. i had recently done a pants transfer operation — i moved old pants out of my jeans drawer into the Goodwill stack, so that there would be room for my new pants. had i inadvertently cast aside my new jeans as if there were some ill–fitting throwaways?

i had. i pulled down my stack of Goodwill pants, and right at the bottom were the almost–lost jeans.

there's some sort of deep lesson in here that i wanted to convey, but i'm afraid i lost my train of thought.

Posted: 06.23.05 at 8:51 PM | Permalink | Comments (0) | TrackBack (0)

June 21, 2005

incompleteness

file under: books

i haven't been documenting any of the books i've been reading. this is my first attempt at rectifying that oversight. the chronology will likely get a bit jumbled as i dig back through books i've read over the last few months, but that probably doesn't matter too much from your perspective. :-)

during my trip to palm springs, i read rebecca goldstein's biographical analysis of gödel and his proofs: incompleteness: the proof and paradox of kurt gödel. it was a fascinating and rewarding book, one that i would heartily recommend to anyone with even a passing interest in the philosophy of science or mathematics.

what follows is synopsis and review focused not on mathematics, but on some aspects of philosophy and gödel's life. my friend Chookyfuzzbang has already done an admirable job of reviewing the mathematics of gödel's proof (and other aspects of the book as well). the interested reader is referred there for a complementary review and analysis.

and so...here we go.

...

on gödel

kurt gödel is one of the most important mathematicians (and people) of the 20th century (and i suspect few would argue that he is the most influential logician since aristotle). it's also entirely likely that you've never heard of him (not that most people have heard of any mathematicians). his two most famous theorems transformed not only the world of mathematics, but probably the philosophy of science and of the human mind itself. his contribution to our world cannot be underestimated.

and yet his life and work are wrapped in two tremendous ironies: (1) one of the best logicians in the history of mankind died by his own hand as a result of paranoia and irrationality, and (2) his preeminently logical results were misinterpreted to support philosophical causes that he would have rejected. goldstein pens her book using these two points as central theses: the apparent contradiction between gödel's results and behavior, and the way his work was perverted to suit ends other than what he intended.

gödel's incompleteness theorems

in 1900, david hilbert enumerated ten challenges to the greatest mathematical minds of the world, the problems that needed to be solved. he did this with a great sense of conviction that a mathematician can solve any problem; he believed there was no ignoramibus (claim about which we remain ignorant).

gödel contributed enormously to two of the ten problems (cantor's continuum hypothesis and the consistency of arithmetic) and supposedly to a third (stated by Goldstein, although i can't locate a reference to gödel's other contribution). one very critical problem was to prove the consistency of the axioms of arithmetic (hilbert had already proven the consistency of geometry assuming the consistency of arithmetic, known as a proof of relative consistency).

gödel's incompleteness theorems effectively demolished the consistency problem (thus enraging hilbert and a lot of other people) — he proved that it is not possible to prove the consistency of arithmetic. he also did something quite astonishing: using the rules of mathematical logic, he managed to prove something larger than mathematics, which is why his proofs are often referred to as being metamathematical — they say something beyond math while still abiding by its most rigorous tenets. the seeming impossibility of this has caused many great thinkers to ponder and argue over gödel's results for the past 75 years.

the incompleteness theorems state the following (very roughly — i'm no mathematician):

1. in any finite axiomatic system strong enough to create rules for the natural numbers, there exist undecidable propositions (i.e., propositions that cannot be proven to be either true or false within the system).
2. a finite axiomatic system cannot be proven to be complete (i.e., logically consistent) within the rules of the system itself; one must appeal to a higher system to prove consistency.

with these two relatively terse statements (which he proved within the confines of mathematical logic), gödel managed to destroy an entire philosophy of mathematics, one that held that math was the ultimate ivory tower, a place immune to contradiction, paradox and inconsistency. while some people still debate this point (Wittgenstein certainly would, if he were still alive), the general consensus seems to be aligned with this notion of a paradigm shift.

for a longer overview and proof of the two incompleteness theorems, the interested reader is referred to Chookyfuzzbang's review of the proofs (using the language and symbolism of Goldstein's book). for more information, the ultra–interested reader is referred to the Wikipedia entry for gödel's theorems as a starting point for a broader analysis. (fwiw, i can neither confirm nor deny the validity of the opinion's expressed in the Wikipedia articles). two other books that are good references are gödel, escher, bach and infinity and the mind. goldstein also references several books she considers to be good, although i haven't had time to look at those.

platonism vs. positivism

gödel was an avowed mathematical platonist, one who believed in the existence of a higher objective truth beyond what we can necessarily experience or understand. einstein believed the same; this connection was probably a large part of the bond between them. as a wonderful side note, and one that testifies to gödel's brilliance, einstein was one of gödel's closest friends at the institute for advanced study. indeed, in his later years, einstein said that the main reason he went to his office at the institute was so that he could have the privilege of walking and speaking with gödel on the way to and from work. it's hard to imagine higher praise.

einstein stated his platonist beliefs as follows:

it is quite clear to me that the religious paradise of youth, which was thus lost, was a first attempt to free myself from the chains of the "merely personal," from an existence which is domainted by wishes, hopes, and primitive feelings. out yonder there was this huge world, which exists independently of us human beings and which stands before us like a great, eternal riddle, at least partially accessible to our inspection and thinking.

— A. Einstein

gödel stated his beliefs in somewhat less poetic terms when discussing the implications of transfinite set theory (a fascinating field in and of itself, and closely related in spirit to the paradoxes that gödel explored):

the objects of transfinite set theory...clearly do not belong to the physical world and even their direct connection with physical experience is very loose....

but despite their remoteness, we do have something like a perception also of the objects of set theory, as is seen from the fact that axioms force themselves upon us as being true. i don't see any reason why we should have less confidence in this kind of perception, i.e., in mathematical intuition, than in sense perception, which induces us to build up physical theories and to expect that future sense perceptions will agree with them, and moreover, to believe that a question not decidable now has meaning and may be decided in the future. the set–theoretical paradoxes are hardly any more troublesome for mathematics than deceptions of the sense are for physics.

— k. gödel

gödel and einstein both believed that there was an objective truth out there, whether or not we could fully understand it. this is the essence of platonism, and the reason why einstein always had issues with quantum mechanics. indeed, people often threw gödel, einstein, and heisenberg into the same camp (incompleteness, relativity, and uncertainty, respectively — a holy trinity of ambiguity), but heisenberg was philosophically opposed to the other two men. gödel and einstein are probably still churning in their graves when people think there is a logical connection between heisenberg's work (seminal in the field of quantum mechanics) and their own.

heisenberg would fall into the camp of logical positivism. the logical positivists asserted, basically, that man is the measure of all things; empirical experience is the metric for verifying truth. anything beyond the realm of experience is essentially meaningless. the one exception is the class of mathematical tautologies that are true by definition. a concise statement of logical positivism would sounds something like this:

we shall maintain that no statement which refers to a "reality" transcending the limits of all possible sense experience can possibly have literal signficance; from which it must follow that the labours of those who have striven to describe such reality have all been devoted to the production of nonsense.

— Alfred Jules Ayer (member of the Vienna Circle)

the amazing thing is that gödel spent some of his most productive years in the company of vocal, unapologetic logical positivists, people whose basic philosophy was quite opposed to his own. and yet he said nothing to disagree with their point of view.

the vienna circle, wittgenstein, and our buddy kurt

gödel spent a bit of time with a bunch of folks who called themselves the vienna circle, a loose collective of thinkers from vienna who went on to influence a large number of other prominent intellectuals in europe and elsewhere. as i said before, the core of their thinking centered on logical positivism.

gödel apparently attended many of their weekly meetings, but despite the fact that his beliefs were basically in opposition with theirs, he rarely dissented openly. and so some later assumed that his theorems were aligned with the notions of logical positivism; goldstein's basic argument is that they were not, and her case is pretty strong. one of the strongest points of this case is the relationship between the vienna circle's philosophy, wittgenstein, and gödel.

for me, wittgenstein was one of those philosophers i always wanted to read, but somehow never did. he seemed like a philosophy rockstar, and i had a lot of respect for him before reading goldstein's book (assuming that his stature in the world of philosophy was unimpeachable, for some bizarre reason). of course, i knew little about him or his philosophy, but he always seemed one of those thinkers that people put up on a pedestal and genuflected before, repeatedly muttering "i'm not worthy" a la wayne's world. now, i'm not so sure. in fact, he seems like an arrogant jerk based on the several anecdotes goldstein puts forth.

[aside: shortly after reading incompleteness, i read an essay titled on bullshit, in which a quote from wittgenstein is related that was also used in goldstein's book. i thought it was a really odd coincidence to come across this quote twice in the space of a week.]

the logical positivists put wittgenstein on that pedestal i mentioned, but he only rarely chose to attend their meetings. many times, when he did, he would stand facing the wall quoting inflammatory indian poetry while people tried to talk with him. they thought he was god, and in a bit of literal irony, it seems he thought they were bugs.

wittgenstein seems to have espoused a lot of the traits of logical positivism, although he firmly denied he was a positivist. it was the last statement of his Tractatus Logico–Philosophicus that Wittgenstein felt set him apart from them:

7. Of what we cannot speak we must remain silent.

— L. Wittgenstein, Tractatus Logico–Philosophicus

apparently, the vienna circle mistook this to mean Wittgenstein's requisite silence hides nothing at all, whereas he probably meant that this requisite silence hides the most important things.

the primary reason i bring this up is that Wittgenstein had a profound dislike for both the positivists and gödel's theorems. he felt that gödel's theorems should be described as logische Kunstücken (logical conjuring tricks):

my task is not to talk about gödel's proof, for example. But to by–pass it.

— L. Wittgenstein

and yet he did not bypass it. he talked about it repeatedly in his own works, because he felt he needed to dismantle it, to show "that its meaning is at odds with its intent." (Goldstein, p. 190) the irony is that, viewed in a certain light, wittgenstein's proposition 7 regarding the unsayability of certain things, was in its own way a form of linguistic incompleteness: we cannot speak the unspeakable truths, but they exist.

gödel, for his part, seems to have had little or no interest or patience for wittgenstein. he wrote a letter to abraham robinson, a young mathematical logician, in which he remarked that wittgenstein's comments on gödel's proofs consitututed a "completely trivial and uninteresting misinterpretation" of his results. as an interesting addendum, it appears that turing had the same disdain for wittgenstein, ultimately, and wound up proving things that had great affinity with gödel's work.

misunderstandings of gödel have meaning

gödel did very little himself to disabuse people of notions about his theorems incompatible with his own beliefs. wittgenstein is only one example. goldstein cites a number of others, both past and present, who interpret gödel's results inappropriately. it seems he was reticent to openly disagree with people unless he could prove his point of view with some degree of rigor and certitude.

the fact that some of the greatest minds of the last century seemed to argue endlessly over the precise meaning (or meaninglessness) of gödel's results implies to me their importance. indeed, if you take wittgenstein's proposition 7 in conjunction with gödel's theorems, maybe we can't even discuss their real meaning or importance within the confines of the linguistic system in which we try to express ourselves.

the logic of illogic

gödel starved himself to death. he died on january 14, 1978 and was buried on january 19, 1978 (my 9th birthday, oddly enough).

over the course of his life, he experienced a number of nervous collapses and episodes of depression. during the final years of his life, especially after the death of his closest friend einstein, he descended into complete paranoia. he became convinced that people were trying to poison him, which ultimately led to his avoidance of food. he manufactured elaborate (and logical) persecution fantasies, taking logic to its illogical extreme (which is apparently not uncommon for paranoid delusional behavior).

it is a profoundly sad and ironic end to a profoundly important life. goldstein's work sheds interesting light on the puzzle, inside a box, hidden in a maze that was kurt gödel's life and philosophy. i also believe she shows quite well how ideas, even those couched in the rigor of mathematics, can be misinterpreted to suit many ends.

Posted: 06.21.05 at 11:01 PM | Permalink | Comments (1) | TrackBack (0)

wired for sleep (or not)

file under: my life

sleep is a precious gift, a blissful punctuation mark between day and night (or some other circadian rhythm that suits you (cf. Eastern Standard Tribe)). it keeps us calm, it keeps us happy; it keeps us from wanting to stick our fingers into light sockets or scream at people unnecessarily. it makes the never–ending stream of days into rewards, instead of punishments. (i'm speaking in terms of ideals here, people — work with me.)

in short, we could not live without it. and yet, many people don't sleep well, and they suffer for it. indeed, some of them die because of it.

a few nights ago, i took a first step into exploring my own world of sleep. i went to a sleep disorder clinic to undergo testing for sleep apnea.

...

sleep apnea is a not–so–silent destroyer, a wraith that descends in the night and rips the breath from your body. more accurately, it's a common sleep disorder; it's estimated that at least 12 million americans suffer from it (although people guess that many more cases go undiagnosed).

apnea literally translates as "without breath"; people who suffer (obstructive) sleep apnea stop breathing during their sleep, usually due to blockage of their air passages. snoring is a related issue; it's really just one step away from apnea, because the physiological causes of apnea are similar. for more information about apnea (and the menagerie of sleep disorders from which one can suffer), check out the national sleep foundation (NSF) (not to be confused with the other NSF, i.e., the National Science Foundation).

my journey to the sleep clinic began a month or so back when i went in for a pre–consultation. they screen people before sending them to the clinic; it's not for every tom, joe and josephine who feels like getting wired up for a night of fun. after a lengthy discussion of my sleeping patterns, my tendency to snore on my back, and a brief physical exam, i made it to the next level (woo hoo! oh...maybe not). i scheduled an appointment for the clinic (one month later – lots of people not sleeping very well, it seems).

if i had had no time to think about it, i probably would have gone in and things would have been ok. as it was, i had a month or more to ponder what it would be like to sleep wired up with more electrodes than a high–school science experiment. sometimes my mind gets the better of me in this regard, which means that by the time i actually went to the clinic, i had already biased myself into thinking that it was going to be next–to–impossible to go to sleep.

it was.

the clinic itself is on the top floor of UCSF Mount Zion medical center in San Francisco. there are several separate rooms, each with its own bathroom, TV, bed, armchair, and Monet painting against a suitably mauve background. when i arrived at the clinic at 8:30pm, the sleep tech David told me to make myself comfortable, asked me what time i usually went to sleep, asked me to fill out some standard disclaimer forms, then went away. more time to think about it.

he came back around 10:30pm, and told me that it would take about 30 minutes to get me wired up. forget unobtrusive cranial meshes or other high–tech devices engineered for a relaxing experience. we're talking cables. we're talking colloidal head cement. we're talking harnesses and straps.

i couldn't get an exact count. i'm fairly certain i had at least four electrodes on my face, five or six on the rest of my head, two on my throat, two on my upper chest, and four on my legs. as if that weren't enough, i also had two circumferential straps wrapped around my upper and lower chest, and a clip monitor on the end of my right index finger. the cherry on top of this nightmare was the breath sensor that was wrapped around my head, over both ears and stuck up my nose.

et voila. beauty sleep, frankenstein style.

i read for awhile (my usual routine) then turned out the light. the cables pulled. the electrodes on the back of my head felt like little pebbles on my pillow. i rolled over on my side and rotated my legs for a more comfortable position. two cables came loose (not enough electrode glue in my hair, i suppose). i also ripped the cables off my lower leg. sigh.

the tech came in and made adjustments. i tried to settle in for a calm night's sleep, not rolling or turning or making excessive movements. no, really, just relax.

did i mention you can't get up to go to the bathroom, since you're attached to the wall by about 15 cables?

you can see where this went. i couldn't get to sleep. i tried and tried and tried. i tried breathing techniques. i tried thinking of nothing. i tried thinking of calm places. nothing worked.

and there's something else.

before we started the experiment, i had to do a series of tests to verify that all the connections were appropriately located and attached. the room was wired for both sound and infrared video, so everything i did was under scrutiny. david told me to stare straight ahead, eyes open. now with eyes closed. (hmm...he can tell if my eyes are open or closed from the other room). look left. look right. look up. look down. breathe in. breathe out. lift your left leg. lift your right leg. ok, everything looks good...sleep well!!

what do you mean, everything looks good? i feel like a lab rat. *i* don't look good. what happens if i fart in my sleep or inadvertently grab my genitals? all recorded for medical posterity? and what about the side of me that likes to pass tests? how am i supposed to pass this one?

the whole experience reminded me of an old thought experiment: tell someone to NOT think of a pink elephant in the corner of the room. the first thing they think of is said pink elephant. in similar fashion, in a circumstance where i'm effectively being told, "whatever you do, don't stay awake", what's the first thing i do?

i think i slept for two hours. i woke up over and over and over. the cables kept coming loose. the tech kept coming in. restful is not an adjective that comes to mind. at 6am, david came in and said, "well, i saw that you were awake, so i figured i'd come in and just wrap things up." i appreciated it...he was very nice, although he seemed a little inured to people's potential difficulty with the whole process.

***

our dream lives are our own, and sleepers always walk with imaginary friends. if an observer is present, they are at a distance, and their gaze usually doesn't fall on us for long. our partners in sleep may occasionally watch us fidget or snore or sigh, but only because they lie beside us, becuase we've chosen to let them near our world of sleep. they certainly couldn't tell from the living room if our eyes were open, or if our heart rate was elevated, or if we were clenching our teeth.

when undergoing the test, the sense of being watched (on more than one level) made me feel like a central part of my human experience was stripped away. the attachments to my body were a bridge between a sacred, selfish world and the one outside. my thoughts were still my own, but their usually silent echoes were now audible to someone other than myself. for those few hours of restlessness, someone looked through the best window into the soul that modern medicine can provide.

ultimately, if the whole experience helps me to overcome my issues with sleep, it will have been worth it. but if the experiment fails, if they didn't get enough data to make an assessment, will i go back again?

perhaps the somnogram could tell me...

Posted: 06.21.05 at 8:27 PM | Permalink | Comments (0) | TrackBack (0)

moblogging doesn't count

file under: about this blog

i have been told by my good friend Chooky that "moblogging doesn't count for squat", which apparently means that to get back in the good graces of my blog readership (such as it is), i will have to start writing thought–provoking, insightful entries.

i will do my best. all i can really promise is words.

Posted: 06.21.05 at 8:16 PM | Permalink | Comments (0) | TrackBack (0)

June 14, 2005

book reading results

file under: my life

for the record, during my trip to palm springs, i read 'incompleteness' and one or two old articles from the new york times that i brought with me. based on my previous entry regarding reading for this trip, it's left to the reader to spot the irony.

Posted: 06.14.05 at 10:08 PM | Permalink | Comments (3) | TrackBack (0)

June 9, 2005

Cesar

file under: my life

Posted: 06.09.05 at 10:38 PM | Permalink | Comments (0) | TrackBack (0)

June 1, 2005

one hundred years

file under: my life

Posted: 06.01.05 at 10:49 PM | Permalink | Comments (2) | TrackBack (0)