We've been living in India now for about three weeks; a mixed experience so far. Most days have started with breakfast and then a session of meditation on Lao Tsu's Tao Te Ching - reading one chapter each session we've reached number ten. It turns out that this has been an excellent discipline to help us cope with a pretty serious cultural adjustment...
Therefore having and not having arise together (Tao Te Ching 2). Indeed they do and, in India, having and not having arise right next to each other. We live in an entirely adequate flat with the luxury of a lap top and an internet connection. Since we've been here we've spent some 20 000 rupees (about £250) on "essentials" like a couple of bikes, some Indian clothes, a pair of trainers, a guitar, a couple of days out... Now that we've got what we "need" we've started to tighten our belts a little but even so we are having some difficulty keeping to our daily income of 500 rupees (about £6).
And yet 80% of Indians live on 20 Rupees (25p) a day. How they do this I have no idea. I presume it must involve being hungry every day; it must involve having to work, scrounge, hustle every day; it must involve indignity and discomfort every day. And worse, of course, for many it involves illness, disability, a hugely diminished quality of life and, ultimately, an early death (the healthy life expectancy here is more than fifteen years less than in the UK).
I knew all this long before I got here of course - in my head. But in the West we rarely encounter poverty in such a spectacular way. There is severe poverty in the West but it is ghetto-ised; we have marginalised people not just socially, economically and politically, but geographically. Middle-class Westerners are rarely forced to encounter the poor. Indeed we've separated having and not having so successfully that a lot of good middle class folk feel distinctly irritated if some poor bugger has the temerity to break the illusion and ask them for 50p...
For of course our having and their not having are intimately connected - and that's eminently obvious here. Each time I want to go to the shops here I have to cross a stinking canal (a relic of British rule) on the banks of which live a number of utterly destitute families. The same little children smile at me each time I pass; I see the same old lady sitting under her hut (several pieces of corrugated iron) but she doesn't smile as much as the children.
How am I to respond to this?
If nothing is done, then all will be well (Tao Te Ching 3). Oh really?! I wonder what that old lady would say if I were to run this by her...
A little bit of reflection has opened my eyes a little though. Two things occur to me. Firstly I need to understand how to do nothing. By which I don't mean not doing anything. Doing nothing is an active process - it won't just happen by itself! Perhaps the nearest verb that I can use to describe it is "emptying". At the end of a process of emptying one has less than when one started, but that doesn't mean you've not been doing anything...
So perhaps the sage means that to act truly I must act from a place of nothingness. In particular I'm not acting from a place cluttered by myself and my needs - I'm not achieving, I'm doing only what is to be done.
Contrary to first impressions, this is intensely practical! I have to make sure that any response to my situation here is considered and appropriate. I cannot be in the business of assuaging my Western guilt - that is not the point. I must respond in a way which affirms life for its own sake.
However I'm still not sure what form that response will take...
The wise therefore rule by emptying hearts and stuffing bellies (Tao Te Ching 3). And this is the second thing that has occurred to me. One of the beautiful things about the Tao Te Ching is that a lot of it appears to be bullshit! What is this bloke on about?
And yet herein lies the nub of its wisdom. Lao Tsu knows the danger of truth - a danger so great that he often avoids truth altogether. Rather his language is one of suggestion, implication, even plain nonsense and contradiction. The responsibility is on the reader to sort through his hints and suggestions, to make sense of his absurdities... and to jettison the bollox!
This might appear odd at first but of course it is really the responsibility that every reader has every time they open a book or a newspaper, most especially a book which has the status of a religious text. The fact that too many readers don't do this is evidenced by the fundamentalist nutters who trot about the place spouting hate. But I get the feeling that it's kind of hard to be a fundamentalist Taoist and thank God, Allah and most especially, thank Lao Tsu for saving us from that.
And of course in the light of such demonstrable wisdom from Mr Tsu, the reader of the Tao Te Ching would be well-advised to think carefully before she really does decide he's talking bollox. So the wise rule by stuffing bellies, eh? Think on that...
Tuesday 21 August 2007
Wednesday 1 August 2007
Mathematics and mushrooms
I wrote this a few years ago. I came across it again recently so thought I'd lob it on this blog...
Ever since I read Aldous Huxley's ``The Doors of Perception,'' I've been fascinated by the idea that the use of drugs could offer insight into every day life. Huxley's descriptions of the world as it appears under the influence of the hallucinogen Mescalin lead to thoughts on religion, meaning and art. Well I too am an artist - a pure mathematics student - and it struck me that the same process could be applied to that particular branch of learning, if someone were to only try...
My ambition was further strengthened after reading of Carlos Castaneda's experience with drugs, including mescalin, while under the careful guidance of a Yaqui Indian Man of Power, don Juan. In Castaneda's account of his apprenticeship to don Juan, ``The Teachings of don Juan,'' the final experience proves so terrifying that Castaneda decides to leave the apprenticeship for good and steer clear of the mind-bending drugs that are part of Yaqui culture. As it happens he changed his mind some years later and continued the process. However, this aside, it was not the terror of the experience that most impressed me (though it was genuinely fearsome,) but the truly awesome insight that Castaneda gains from his experiences - understanding which survives his return to the conscious plane and which, don Juan assures him, will eventually lead to him becoming a Man of Power.
There was only one thing to be done then. Apprenticeship to Men of Power is restricted to a chosen few and they don't live in England. Likewise, it might have been acceptable for a distinguished thinker like Huxley to indulge in a bit of Mescalin, but your average student Joe might not be looked on so kindly, even if it was possible to get hold of the stuff. What your average student Joe CAN do though, is go to Amsterdam. He won't find Mescalin but for a handful of Euros he can buy a packet of copelandia magic mushrooms, he can chew on them and he can see what happens. This, reader, is what I did and here are some of my thoughts...
Let's start with that archetypal hippy image of the happy day tripper staring fascinatedly at some ordinary object and exclaiming at how cool it is! For Huxley it was his trousers, for me it was the pavement - the same pavement I can look at any day which was now, not just more colourful, but much more highly patterned. Where usually I would see random chaos, now I could see symmetry and relations; an abstract structure underpinning the matrix of blue stone. One aspect is worth a particular mention - I became quite alarmed, at a certain point, about a strange covering that seemed to have been laid down on the ground and which caused my toes to curl! Looking more closely, though, I realised that this covering I was seeing was `the gaps' or the space between the objects strewn on the pavement. I was seeing what a mathematician may call a `complementary image' to my usual vision. The same information was being encoded by my eyes, but my rewired brain was decoding it in an altogether different, if equivalent, manner.
Both this search for symmetry, this perception of abstract structure beneath surface form and this reinterpereting of information to allow it to be analysed in a different way are valuable mathematical priniciples. In fact, in some sense, they completely describe the mathematician's task and method. The Game Theory, for instance which John Nash (subject of the film ``a Beautiful Mind'') dreamt up, and for which he won the Nobel Prize, is an analysis of the abstract structure underlying the interactions of a number of competing or co-operating interests pursuing dependent goals. The significance of his work was that he was able to see these situations in a new, `re-wired' way.
But it's not just in the philosophy of the working mathematician where the tripping hippy may bear a resemblance, the actual activity of doing mathematics can appear very similar: In his biography of the great Hungarian mathematician, Paul Erd\"os, ``The Man who Loved Only Numbers'', Paul Hoffman relates how one day, while trying to solve a particular problem, Erdos and a colleague were sat next to each other in a public place for an hour of cogitating silence. The silence was only brought to an end when one of them said, ``It is not naught. It is one.'' Much rejoicing followed! Who knows what strange mindscape of abstraction, Erd\"os and friend inhabited for that hour?
The case of Erd\"os brings with it, in addition, a somewhat more unusual link to the chemical world; For this most prolific of mathematicians spent his last twenty-five years working nineteen hours a day on the back of a heady cocktail of Benzedrine, Ritalin, strong espresso and caffeine tablets. This is a parallel that will not withstand generalization however!
It is at the point of paradox that the respective paths of mathematics and mushrooms most clearly diverge. Towards the end of my copelandia experience, sometime after I became aware that I was a single human entity who was neither mad nor dead (all facts of which I'd been very unsure), I found myself in a very warm, calm, beautiful state of mind in which the universe was understood and meaning accessed. This occurred through a series of `moments of clarity' in which statements of paradox were the fundamental unit. Time after time I saw truth yet knew that truth lay in its opposite also - in chaos, there was order; in mortal futility, enduring meaning. There is no place for such statements in mathematics.
In this regard, the mathematical process can be though of as the assumption of a collection of axiomatic first principles from which are deduced, using logic, a structure of `therefores': facts which must be true given our assumptions and our previous `therefores'. This process is unambiguous and is verifiable - I have heard a professor of mathematics say ``The great thing about mathematics is that you can convince people!'' Mathematicians give proofs for their arguments. This is in contrast to social scientists or even physical and life scientists who, though they use logic and argument to draw conclusions from data or suppositions, must accept that internally consistent arguments for conflicting positions may be put. No one will ever prove or disprove that drugs prohibition never works or that humans are descended from the apes, but it can and has been proved that there is no projective plane of order 6.
It may not be going too far to say that mathematics could be characterised in this way: as the study of truth that can be proven. But the implications of such truths tend to spill out beyond this boundary of proof. That the truth is beautiful, for instance, is a statement that few mathematicians would dispute but none can prove. The happy fact is that when conscious beings penetrate the abstract thought structures that underpin reality, they find crystalline structures of logic that can move the heart. In the same way that I can't explain why the colours that swirled in front of my eyes that crazy Dutch evening were so lovely yet terrifying, perhaps this much at least will always remain a mystery.
Ever since I read Aldous Huxley's ``The Doors of Perception,'' I've been fascinated by the idea that the use of drugs could offer insight into every day life. Huxley's descriptions of the world as it appears under the influence of the hallucinogen Mescalin lead to thoughts on religion, meaning and art. Well I too am an artist - a pure mathematics student - and it struck me that the same process could be applied to that particular branch of learning, if someone were to only try...
My ambition was further strengthened after reading of Carlos Castaneda's experience with drugs, including mescalin, while under the careful guidance of a Yaqui Indian Man of Power, don Juan. In Castaneda's account of his apprenticeship to don Juan, ``The Teachings of don Juan,'' the final experience proves so terrifying that Castaneda decides to leave the apprenticeship for good and steer clear of the mind-bending drugs that are part of Yaqui culture. As it happens he changed his mind some years later and continued the process. However, this aside, it was not the terror of the experience that most impressed me (though it was genuinely fearsome,) but the truly awesome insight that Castaneda gains from his experiences - understanding which survives his return to the conscious plane and which, don Juan assures him, will eventually lead to him becoming a Man of Power.
There was only one thing to be done then. Apprenticeship to Men of Power is restricted to a chosen few and they don't live in England. Likewise, it might have been acceptable for a distinguished thinker like Huxley to indulge in a bit of Mescalin, but your average student Joe might not be looked on so kindly, even if it was possible to get hold of the stuff. What your average student Joe CAN do though, is go to Amsterdam. He won't find Mescalin but for a handful of Euros he can buy a packet of copelandia magic mushrooms, he can chew on them and he can see what happens. This, reader, is what I did and here are some of my thoughts...
Let's start with that archetypal hippy image of the happy day tripper staring fascinatedly at some ordinary object and exclaiming at how cool it is! For Huxley it was his trousers, for me it was the pavement - the same pavement I can look at any day which was now, not just more colourful, but much more highly patterned. Where usually I would see random chaos, now I could see symmetry and relations; an abstract structure underpinning the matrix of blue stone. One aspect is worth a particular mention - I became quite alarmed, at a certain point, about a strange covering that seemed to have been laid down on the ground and which caused my toes to curl! Looking more closely, though, I realised that this covering I was seeing was `the gaps' or the space between the objects strewn on the pavement. I was seeing what a mathematician may call a `complementary image' to my usual vision. The same information was being encoded by my eyes, but my rewired brain was decoding it in an altogether different, if equivalent, manner.
Both this search for symmetry, this perception of abstract structure beneath surface form and this reinterpereting of information to allow it to be analysed in a different way are valuable mathematical priniciples. In fact, in some sense, they completely describe the mathematician's task and method. The Game Theory, for instance which John Nash (subject of the film ``a Beautiful Mind'') dreamt up, and for which he won the Nobel Prize, is an analysis of the abstract structure underlying the interactions of a number of competing or co-operating interests pursuing dependent goals. The significance of his work was that he was able to see these situations in a new, `re-wired' way.
But it's not just in the philosophy of the working mathematician where the tripping hippy may bear a resemblance, the actual activity of doing mathematics can appear very similar: In his biography of the great Hungarian mathematician, Paul Erd\"os, ``The Man who Loved Only Numbers'', Paul Hoffman relates how one day, while trying to solve a particular problem, Erdos and a colleague were sat next to each other in a public place for an hour of cogitating silence. The silence was only brought to an end when one of them said, ``It is not naught. It is one.'' Much rejoicing followed! Who knows what strange mindscape of abstraction, Erd\"os and friend inhabited for that hour?
The case of Erd\"os brings with it, in addition, a somewhat more unusual link to the chemical world; For this most prolific of mathematicians spent his last twenty-five years working nineteen hours a day on the back of a heady cocktail of Benzedrine, Ritalin, strong espresso and caffeine tablets. This is a parallel that will not withstand generalization however!
It is at the point of paradox that the respective paths of mathematics and mushrooms most clearly diverge. Towards the end of my copelandia experience, sometime after I became aware that I was a single human entity who was neither mad nor dead (all facts of which I'd been very unsure), I found myself in a very warm, calm, beautiful state of mind in which the universe was understood and meaning accessed. This occurred through a series of `moments of clarity' in which statements of paradox were the fundamental unit. Time after time I saw truth yet knew that truth lay in its opposite also - in chaos, there was order; in mortal futility, enduring meaning. There is no place for such statements in mathematics.
In this regard, the mathematical process can be though of as the assumption of a collection of axiomatic first principles from which are deduced, using logic, a structure of `therefores': facts which must be true given our assumptions and our previous `therefores'. This process is unambiguous and is verifiable - I have heard a professor of mathematics say ``The great thing about mathematics is that you can convince people!'' Mathematicians give proofs for their arguments. This is in contrast to social scientists or even physical and life scientists who, though they use logic and argument to draw conclusions from data or suppositions, must accept that internally consistent arguments for conflicting positions may be put. No one will ever prove or disprove that drugs prohibition never works or that humans are descended from the apes, but it can and has been proved that there is no projective plane of order 6.
It may not be going too far to say that mathematics could be characterised in this way: as the study of truth that can be proven. But the implications of such truths tend to spill out beyond this boundary of proof. That the truth is beautiful, for instance, is a statement that few mathematicians would dispute but none can prove. The happy fact is that when conscious beings penetrate the abstract thought structures that underpin reality, they find crystalline structures of logic that can move the heart. In the same way that I can't explain why the colours that swirled in front of my eyes that crazy Dutch evening were so lovely yet terrifying, perhaps this much at least will always remain a mystery.
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