The number three
Feb. 21st, 2004 12:32 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
imomusToday's thought is brought to you by the number three. But because I want it to be the third thing you read, here are two other thoughts, one by Brian Eno and one by Naomi Klein.
Lessons in how to lie
The problem is not propaganda but the relentless control of the kind of things we think about, says Brian Eno.
'How exactly did it come about that, in a world of AIDS, global warming, 30-plus active wars, several famines, cloning, genetic engineering, and two billion people in poverty, practically the only thing we all talked about for a year was Iraq and Saddam Hussein? Was it really that big a problem? Or were we somehow manipulated into believing the Iraq issue was important and had to be fixed right now - even though a few months before few had mentioned it, and nothing had changed in the interim?' Read more...
Feel guilt. Then move on
Those who supported the war because of Bush and Blair's lies now cast themselves as victims. This won't help Iraq's dead and dying, says Naomi Klein.
'So long as Bush's opponents cast themselves as the primary victims of his war, the real victims will remain invisible. The focus will be on uncovering Bush and Blair's lies - a process geared towards absolving those who believed them, not on compensating those who died because of them.' Read more...
Okay, now my thought.
What's the opposite of 3?
I'm still trying to work this out in my mind, says Momus, but why is it that words often have opposites and numbers never do?
I'm still trying to work this out in my mind, but why is it that words often have opposites and numbers never do? There's no 'opposite' of the number 3. The number three has meaning in relation to all the other numbers in the decimal number system. Only in binary applications of number systems, like the one computers are based on, do numbers have opposites. The opposite of zero is one, and the opposite of one is zero. That's because numbers are being used there as words: the words 'on' and 'off' or 'yes' and 'no'. But couldn't we see numbers as essentially the same kind of self-enclosed meaning system as words? And, if that's the case, couldn't we see an exemplary pluralism in the number system? The number 3 gets its meaning because of its relationship with the whole 'community' of numbers. It acknowledges its dependence on every other number. It is not obsessed with its 'opposite number'. It doesn't have an opposite number. At worst, we could imagine the number 3 hung up on its relationships with 2 and 4, and how 4 thinks it's better than 3, and how 2 should clean up its act. Or we could imagine it feeling some kind of family affinity with 6, 9, 12 and so on, practicing nepotism or incestuous troilism with the numbers it's a multiple of. But if 3 has any brains, it ought to realize that what's important is the big picture; its place in the entire system of numbers.
Words really could learn something from numbers, it seems to me. Because, although real human power in this technocratic age works mostly with numbers, the way politicians speak to the public who elect them works with words. And words have this tendency to pair off into binaries. Us and them. Right and left. War and peace. As Brian Eno points out, politicians don't necessarily want to make us agree with them, but they really want us to accept the binaries they're proposing, and the way they're setting them up. They want to frame the questions of the day, rather than compel specific answers. As Naomi Klein points out, when we've established a binary like Iraq victor / Iraq victim, it's easy to 'spin' the definitions of who's who. Klein argues that Democrats and Republicans alike are seeking to substitute figurative American victims for literal Iraqi ones. These politicians are substituting, as victims of the Iraq war, words like 'the truth', 'our self-esteem' and 'our resources' for the 10,000 Iraqi civilians killed since the invasion. Seen from another angle, it's the substitution of a bunch of words for a number.
I was just listening to a radio programme last night about how the application of Nobel prize-winning mathematician John Nash's game theory earned the British government 23 billion pounds in the form of auctions made by the government for telecom licenses. These auctions raised this huge sum by applying the Nash Equilibrium. The Nash Equilibrium is:
'a set of strategies , one for each player, such that no player has incentive to unilaterally change her action. Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with her current strategy. For games in which players randomize ( mixed strategies ), the expected or average payoff must be at least as large as that obtainable by any other strategy.'
This picture of a harmonious and mutually-profitable game is in stark contrast to the simplest game model, the 'zero sum game', in which the winner takes all and the loser loses everything. Now, the political application of this idea of a game in which everyone wins is surely not hard to see. It would be a pluralistic liberalism with benefits to all. It would be egalitarian. It would be as far beyond war scenarios as the Nash Equilibrium is beyond the zero sum game. It would look a lot more like Clinton's America than Bush's America. And it would look more like number systems, where every number depends for its meaning on every other number, than language systems, where false and spinnable binaries are constantly coming into play, blocking our view of the interdependence of all things.
Nash actually went mad thinking about how to apply his ideas to politics. He says in the autobiography he prepared for the Nobel committee:
'Gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation. This began, most recognizably, with the rejection of politically-oriented thinking as essentially a hopeless waste of intellectual effort.'
But if attempts to politicize science drive scientists crazy, attempts to make politics scientific drives politicians crazier. Some academics have said that governments and big companies are now under huge pressure to think through every possible outcome of their actions before they make them, and that this 'forensics of the future' is not only impossible, it forces governments to go through all sorts of deceptions, to keep changing their explanations for the things they've done, to keep spinning the framing binaries so that the opposite of Iraq invasion is one minute destruction of Britain in 45 minutes, the next tolerance of a 'madman', and the next failure to act against 'a prominent supporter of the 9/11 terrorists'.
This is a slippery slope for governments. It takes them into a realm in which only bright children, brilliant liars, imaginative artists and amazing storytellers survive. That realm might be seen as 'the land of lies', but in fact it's a remarkably realistic place, because it's where we acknowledge that there is a third term to every binary, and beyond the third a fourth and fifth, and that they are all equally valid. It's the realm of pluralism and equilibrium. In this world, things work not because they're true or false, but because they're interesting. Or because they're there. De facto, sociological, present, alive. Nobody wins and nobody loses. We just all live together. Like numbers, everybody counts. Relativism, pluralism.
It's ironic that Tony Blair's big idea used to be the third way, a step beyond the stale old binaries of past politics. The number three is indeed the symbol of a way beyond binaries, a signpost to pluralism. The number three says 'Don't stop at me, all the other numbers in the number system lie just beyond, and they're all just as true as three.'
Lessons in how to lie
The problem is not propaganda but the relentless control of the kind of things we think about, says Brian Eno.
'How exactly did it come about that, in a world of AIDS, global warming, 30-plus active wars, several famines, cloning, genetic engineering, and two billion people in poverty, practically the only thing we all talked about for a year was Iraq and Saddam Hussein? Was it really that big a problem? Or were we somehow manipulated into believing the Iraq issue was important and had to be fixed right now - even though a few months before few had mentioned it, and nothing had changed in the interim?' Read more...
Feel guilt. Then move on
Those who supported the war because of Bush and Blair's lies now cast themselves as victims. This won't help Iraq's dead and dying, says Naomi Klein.
'So long as Bush's opponents cast themselves as the primary victims of his war, the real victims will remain invisible. The focus will be on uncovering Bush and Blair's lies - a process geared towards absolving those who believed them, not on compensating those who died because of them.' Read more...
Okay, now my thought.
What's the opposite of 3?
I'm still trying to work this out in my mind, says Momus, but why is it that words often have opposites and numbers never do?
I'm still trying to work this out in my mind, but why is it that words often have opposites and numbers never do? There's no 'opposite' of the number 3. The number three has meaning in relation to all the other numbers in the decimal number system. Only in binary applications of number systems, like the one computers are based on, do numbers have opposites. The opposite of zero is one, and the opposite of one is zero. That's because numbers are being used there as words: the words 'on' and 'off' or 'yes' and 'no'. But couldn't we see numbers as essentially the same kind of self-enclosed meaning system as words? And, if that's the case, couldn't we see an exemplary pluralism in the number system? The number 3 gets its meaning because of its relationship with the whole 'community' of numbers. It acknowledges its dependence on every other number. It is not obsessed with its 'opposite number'. It doesn't have an opposite number. At worst, we could imagine the number 3 hung up on its relationships with 2 and 4, and how 4 thinks it's better than 3, and how 2 should clean up its act. Or we could imagine it feeling some kind of family affinity with 6, 9, 12 and so on, practicing nepotism or incestuous troilism with the numbers it's a multiple of. But if 3 has any brains, it ought to realize that what's important is the big picture; its place in the entire system of numbers.
Words really could learn something from numbers, it seems to me. Because, although real human power in this technocratic age works mostly with numbers, the way politicians speak to the public who elect them works with words. And words have this tendency to pair off into binaries. Us and them. Right and left. War and peace. As Brian Eno points out, politicians don't necessarily want to make us agree with them, but they really want us to accept the binaries they're proposing, and the way they're setting them up. They want to frame the questions of the day, rather than compel specific answers. As Naomi Klein points out, when we've established a binary like Iraq victor / Iraq victim, it's easy to 'spin' the definitions of who's who. Klein argues that Democrats and Republicans alike are seeking to substitute figurative American victims for literal Iraqi ones. These politicians are substituting, as victims of the Iraq war, words like 'the truth', 'our self-esteem' and 'our resources' for the 10,000 Iraqi civilians killed since the invasion. Seen from another angle, it's the substitution of a bunch of words for a number.
I was just listening to a radio programme last night about how the application of Nobel prize-winning mathematician John Nash's game theory earned the British government 23 billion pounds in the form of auctions made by the government for telecom licenses. These auctions raised this huge sum by applying the Nash Equilibrium. The Nash Equilibrium is:
'a set of strategies , one for each player, such that no player has incentive to unilaterally change her action. Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with her current strategy. For games in which players randomize ( mixed strategies ), the expected or average payoff must be at least as large as that obtainable by any other strategy.'
This picture of a harmonious and mutually-profitable game is in stark contrast to the simplest game model, the 'zero sum game', in which the winner takes all and the loser loses everything. Now, the political application of this idea of a game in which everyone wins is surely not hard to see. It would be a pluralistic liberalism with benefits to all. It would be egalitarian. It would be as far beyond war scenarios as the Nash Equilibrium is beyond the zero sum game. It would look a lot more like Clinton's America than Bush's America. And it would look more like number systems, where every number depends for its meaning on every other number, than language systems, where false and spinnable binaries are constantly coming into play, blocking our view of the interdependence of all things.
Nash actually went mad thinking about how to apply his ideas to politics. He says in the autobiography he prepared for the Nobel committee:
'Gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation. This began, most recognizably, with the rejection of politically-oriented thinking as essentially a hopeless waste of intellectual effort.'
But if attempts to politicize science drive scientists crazy, attempts to make politics scientific drives politicians crazier. Some academics have said that governments and big companies are now under huge pressure to think through every possible outcome of their actions before they make them, and that this 'forensics of the future' is not only impossible, it forces governments to go through all sorts of deceptions, to keep changing their explanations for the things they've done, to keep spinning the framing binaries so that the opposite of Iraq invasion is one minute destruction of Britain in 45 minutes, the next tolerance of a 'madman', and the next failure to act against 'a prominent supporter of the 9/11 terrorists'.
This is a slippery slope for governments. It takes them into a realm in which only bright children, brilliant liars, imaginative artists and amazing storytellers survive. That realm might be seen as 'the land of lies', but in fact it's a remarkably realistic place, because it's where we acknowledge that there is a third term to every binary, and beyond the third a fourth and fifth, and that they are all equally valid. It's the realm of pluralism and equilibrium. In this world, things work not because they're true or false, but because they're interesting. Or because they're there. De facto, sociological, present, alive. Nobody wins and nobody loses. We just all live together. Like numbers, everybody counts. Relativism, pluralism.
It's ironic that Tony Blair's big idea used to be the third way, a step beyond the stale old binaries of past politics. The number three is indeed the symbol of a way beyond binaries, a signpost to pluralism. The number three says 'Don't stop at me, all the other numbers in the number system lie just beyond, and they're all just as true as three.'
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Where 3 is bad
Date: 2004-02-21 04:48 am (UTC)http://www.salon.com/news/feature/2004/02/21/nader/
Because in this case all 3 can do is chop the 2 vote in half and leave us with 1 for another 4.
(no subject)
Date: 2004-02-21 04:55 am (UTC)History Lesson
Date: 2004-02-21 05:28 am (UTC)When you're a hunter-gatherer, you breast feed your children until they are at least 2, maybe 3, (see, Pygmies) and as a natural reaction, your body becomes less fertile. Something about hormones as a self-defense mechanism (see, science).
Settling down, growing crops, living in one place for your whole life, etc. was a product of fear. Early humans were affraid the food supply had dried up, and came up with the "innovation" of farming. Why venture off into the unknown when you can make your own food. Why not just completely subvert the system and fuck over the whole planet in the process? We started multiplying like rabbits.
Every innovation since them has been basically the same thing: just another way to squeeze the last bit of resources from this vastly over-populated planet. And at some point, we'd already extracted the last bit of value from the Earth, so the only place left to turn was each other (see, feudalism, merchantilism, capitalism).
So basically, it's always been a zero-sum game. There has only been a certain amount of resources on this planet, and to extract them, you must sacrifice energy in some form or another. At a certain point, the energy needed is only available as people (see, Holocaust)
Re: History Lesson
Date: 2004-02-21 05:57 am (UTC)Read it and weep, plebe...
Date: 2004-02-21 06:58 am (UTC)(no subject)
Date: 2004-02-21 08:24 am (UTC)Re:
Date: 2004-02-21 09:14 am (UTC)'two numbers are OPPOSITES if they are the same distance from 0 on a number line(have same absolute values), but on opposite side of 0 (with different signs).
3 and -3 are opposites since |3|=|-3|
4 and -4 are opposites since |4|=|-4|
* the sum of two opposite numbers is 0:
5+ (-5)= 0, 6+(-6)=0'
I suppose I think of negative numbers as 'not real' or 'cheating', because I've never seen minus three sheep. Certainly they work differently from semantic 'opposites' in language, which don't cancel each other out but help define each other, and are rather more than mirror images of each other. Minus three doesn't really tell us any more about three, but the fact that it's the opposite of 'quickly' does tell us something about 'slowly'.
What really interests me, in today's thought or this one (http://www.livejournal.com/users/imomus/10660.html) is the way that context, power, or imagination can change what the perceived opposite of a word is, and how narrative, which is made retrospectively from the future to the past, can reveal shady new 'repressed' or marginalised terms, opposites unsuspected or even unthinkable at the time. An example would be how Abstract Expressionism gained its identity for itself by opposing its values to those it saw as its opposites: figurative realism, European academicism, and so on. But for later generations -- for 'the future' -- AbEx's opposites, its suppressed marginal values, were quite different ones. To people like Warhol the AbEx movement was 'repressing' values like commerciality, contemporariness, superficiality, triviality, relevance. Once you stopped looking at Paris (or once Paris was beaten by New York) the whole context shifted and AbEx began to look both flabby and oppressive.
And the reason I'm so interested in this -- in the hidden, almost invisible, repressed opposites created by things -- is that I'm interested in the way huge semantic weights can shift so suddenly when they seem to have an unassailable centrality. Just by beginning to think about something differently from the way the victor thinks about it, by defining the victor's opposites differently from the way he does, we can begin the victor's displacement, like one sumo wrestler throwing another out of the ring. It's just a question of seeing the hidden opposites that history might see, instead of the ones which seem so 'obvious' right now. I'm looking around for something to call this way of looking, and maybe a nice term would be 'red shift'. (http://www.arachnoid.com/sky/redshift.html) Red shift is the changed colour things have when viewed from the future, and I'm convinced there's a way to see the present with some kind of 'red shift goggles' and get to the future a little quicker as a result.
(no subject)
Date: 2004-02-21 09:26 am (UTC)Here's what a galaxy looks like when it's advancing towards us.
Here's what a galaxy looks like when it's receding away.
Then again, red shift may be a bad metaphor, too complex. Perhaps all we need to say is: 'Seen from here, that house (or AbEx, or whatever) has these buildings as its backdrop, its defining context. But seen from here it has quite different ones.'
Re:
Date: 2004-02-21 09:50 am (UTC)Re:
Date: 2004-02-21 07:46 pm (UTC)indeed, it's not that simple about the opposite numbers
Date: 2004-02-23 02:47 am (UTC)actually, the first step in this way was the notion of zero (the indians "invented" it first). the negative numbers are often illustrated like the debt - if you owed somebody three sheep... But then still you won't see them.
Indeed, psychologically only boolean (0/1 - FALSE/TRUE) logic has such a binary structure. and unfortunately a lot of people think this way (although attributing strange meanings to the "opposites" - like the opposite of "you're with us" is "you're against")
though there's also such thing as fuzzy logic,
Fuzzy logic is a superset of conventional (Boolean) logic that has been extended to handle the concept of partial truth -- truth values between "completely true" and "completely false". It was introduced by Dr. Lotfi Zadeh of UC/Berkeley in the 1960's as a means to model the uncertainty of natural language. (http://www-2.cs.cmu.edu/Groups/AI/html/faqs/ai/fuzzy/part1/faq-doc-2.html)
(one can also remember the indian logic like "it's true, but we will never know it", "it's true but nobody will ever know it", "it's true, Shiva knows it" etc :-))
(no subject)
Date: 2004-02-21 01:38 pm (UTC)Re:
Date: 2004-02-22 09:06 am (UTC)isn't that the job of marketing people?
Last year I was hanging out with a very smart publicity student and he taught me many tricks to do exactly that-it's all about language in a way, about talking fast and pinpointing the binaries with up-to-date words, it takes a lot of practise because you have to be able to analyze everything at hyperspeed...I can't really do it when this friend of mine is not around and I can't explain it better, sorry.
mario
(no subject)
Date: 2004-02-23 05:47 am (UTC)Sorry to lower the tone massively here, but yanatonage's comment above reminded me of two amazing TV comedy moments.
In Blackadder, When Blackadder accidentally burns Dr Johnson's Dictionary and then attempts to rewrite it, Baldrick's suggested definition of 'dog' is "Not a cat". Baldrick using Saussurian logic a good century before it was defined ;-)
Also, there's a Paul Merton sketch where he's sitting in his living room reading a book and the lights go out. He goes over to a meter on the wall marked "Electricity" and puts a coin in. The lights come back on. He resumes reading until, a few seconds later, his book disappears. He goes over to another meter on the wall, marked "Book" and puts a coin in. His book re-appears. Then, a few seconds later, a zebra appears in the room in front of him. He gets up and goes over to a meter in the wall marked "No Zebra" and puts a coin in.
(no subject)
Date: 2004-02-22 06:15 pm (UTC)A scientific model of the old "balance of power" political model of the 18th Century. Works well enough for foreign policy, I suppose, (although there is pressure from within that causes the strategy to change, if you accept the within/without binary) but I'd hate to apply this model of stasis to the artistic realm. I'd be interested in your thoughts on the intersection of the two (and of course, life/art is another uncomfortable, idealized binary, in which art inevitably seems superior and thus feeds the artist's ego). One could call the genocide conducted by Hitler an aesthetic project, and in more subtle ways our leaders are creative makers...
(no subject)
Date: 2004-02-22 08:36 pm (UTC)I've worked for the US gov't for about a year, and it's been amazing to see how what on the outside looks like a fairly restricted set of binaries on the inside looks more like a vast quantity of pieces of (broken?) glass refracting each others' light. I am really impressed by those very successful beaureaucrats whose ability to navigate a sea of forceful opinions enables them to actually exact something of their will on the governing apparatus while at the same time projecting the proper image for the press. Somebody like Donald Rumsfield, who tends to project the Us/Them dynamic that so many Americans understand and even require, could only, in my opinion, be as successfully manipulative as he appears to be through an almost superhuman comprehension of difference.
On the subject of numbers. The unopposableness of 3 is, I think shared by the elements of most ordered systems. For example, what is the opposite of Hydrogen? However, there are some who maintain that all of these orderings rely on some deconstructable binary. In the case of math, at least the kind that's based in classical logic, that binary is generally called 'true' and 'false'. If I'm not mistaken, a result known as Godel's Theorem from the 30's shows that in mathematical systems in which we can derive the natural numbers, we can also show that there is some statement that is 'undecidable'. That is, a statement which can neither be shown to be only true or only false. A slightly more formal way of saying this is "mathematics is either inconsistent or incomplete".
If math is inconsistent, that means the whole enterprise is shot, so the reasonable thing to do if you're into order is to go with "incomplete" and just avoid making undecidable statements.
That leaves a whole lot of undecidable statements laying around, cluttering up the culture. Some people knew they were there, but no-one wanted to deal with them - not over here anyway, what with the depression and then a war. Luckily, in France, there were wierd French people who somehow seemed to get off on undecidability, making it an object in its own right, fetishizing it and forcing it out of every metaphysical system they could get their hands on. Built on a metaphysics of 0 and 1 (or, more properly, high wavelength and low), computers, which are theoretically very strong mathematical systems, encountered a 'halting problem' when faced with a task which required them to determine an undecidable value. Mathematicians continued to study undecidability if only to understand and ultimately avoid it.
But these French - they bathed in it like a bubble bath.
At any rate, working for the government, one can hardly utter a statement that isn't both true and false at the same time, given all the different ontologies floating around. No one wants to be inconsistent or wrong, so the skill lies in saying something that's true for everyone, but not too true. A converging point in a network of difference becomes the basis for a powerful binary that concentrates action. Everyone will remember it differently.
Clay
Re:
Date: 2004-02-23 03:40 am (UTC)'In one sense the number 3 does have an opposite, which is -3. But if you view an opposition, with Deleuze, as a 'maximum of difference', it isn't so obvious, because -4 is further from 3 than -3. The trouble with oppositions is that they are always like this - they pretend to be maximal differences when they are
not. Hence the use of the word Other - not so much opposite as the
difference against which identity is contrasted.
I'm sure I'm preaching to the converted here, but so useless is the
opposition numerically that computers cannot do anything on a binary
system. You will know all about fuzzy logic. It is a mathematical and
philosophical rebellion against the value of opposition in favour of
numerical gradation, so that the identity of something is never
understood as 'not its opposite' but is expressed as a percentage.
Badiou thinks that numbers are more ontological than words. They are
abstract, in the sense that they have had all particularlity subtracted
from them. 3 whats? The beings have been subtracted, so that numbers
deal with being, not beings. They are pure multiplicities.'
indeed
Date: 2004-02-23 05:30 am (UTC)But there's another angle to all this logic/fuzzy sets etc. story - one may also consider all this to a certain extent random.
I'm a probabilist/statistician, we tend to think about everything as being random... So everything around is deformed, with noise etc..
Re: indeed
Date: 2004-02-23 02:00 pm (UTC)Using the first method over a set of me, you are 1.0 cute as hell. Using the second method one would need, of course, (wait for it) a body of reference data for emperical study.
Clay
Re: indeed
Date: 2004-02-23 02:03 pm (UTC)Re: indeed
Date: 2004-02-23 02:23 pm (UTC)clay
Re: indeed
Date: 2004-02-24 10:42 am (UTC)but what you are talking about is actually much closer to what interests me in my own field at the moment (at least the popular/psychological side of it) - apart from the "conventional" way to define probability of an event (like the proportion of success in many replications. if we flip a coin many time we'll get tails in about half cases),
there's another one, more intutive - we're just estimate our confidence in something - like if we believe that the coin is symmetrical, then it's 1/2 probability to get tails. (in my view this is actually what's happening all the time - we're just estimating something from our expectation and information we have. if we don't have any information - then we tend to think of all the outcomes being equally likely). the same way we can define "fair bet" for example - wen two things are equal for is, minding the probability of getting one of them. (and the "fair game" with the 0 sum) (like 1 ot of 5 chances of winning 5$ against 4 out of 5 of loosing 1$. though it might be different for different people - if I just get very upset about loosing any money, then it might seem "fair" for me to have 1 out of 5 chances of winning 100 against loosing 1 in other cases. in a book i was reading there was a chapter called "the value of money" (and it is indeed in this sense not that obvious - for a normal person the numbers $$ 10 000 000 and $$ 100 000 000 are almost equal, but 10 and 100 are much more different :-)), the auther by the way is supposed to be the best paid statistician (in academy) in the US :-) )
anyway, i'm quite fascinated by these things... and it will i'm afraid turn me into bayesian one day :-)
Re: indeed
Date: 2004-02-25 12:59 pm (UTC)(no subject)
Date: 2004-02-23 05:57 pm (UTC)(no subject)
Date: 2004-02-24 12:51 pm (UTC)Ah, Charles, you cunning devil, that's a trick question, isn't it? We all know that herds contain zero sheep, because a group of sheep is a flock. Three sheep added to a herd would probably get stampeded to death, turning into three ex-sheep. Whether ex-sheep are the same as negative sheep is a theological question, not a mathematical one.
(no subject)
Date: 2004-02-24 05:38 pm (UTC)