Saturday in Dunedin was cold foggy and drizzling, pretty depressing, so went out to the end of the Otago peninsula with 10 y/o daughter - who always drags me out there (I always end up glad she did) - and 16 y/o son (intellectually disabled, and an eating machine). We lease a crib.
Saturday in Otakou was also cold, foggy and drizzling - actually even worse as always is out there in any weather that's vaguely northerly or easterly. But as I mentioned - we were at the *end* of the Otago peninsula, so there was nowhere further to go so we stayed there.
Sunday (today) was a bit better - not much sun , but no wind at least and fog and drizzle lifted. We did some fishing (no bites) and mucked around and it sort of got me out of my rut as it always does , even though you don't think its going to before you set out - there's nothing all that flash out there that's going to explode you out of your rut, but still it somehow eases you out by next morning. So I'm always glad she drags me out.
And there's always some micro-interesting thing out there if you keep your eyes open. Like today I was thinking about how the motorbike zooming up and down the Aramoana beach - miles away over the other side of the harbour - sounded so close , as though up and down the road outside, and thinking how I'd noticed that effect the odd time before, and how what it probably is is : maybe it just happens when the harbour is quite glassy as today - smooth enough so that the sound waves are reflected coherently off the water surface - so the sound energy is only attenuating in our direction at half the rate that it normally does (though still as the second power , but with a halved constant of proportionality) - and how therefore the effect will not occur when the sea is rough as the complicated surface will just dissipate the energy incoherently.....but when the sea is rough there is also a wind so that would obscure both the effect and one's reasoning about it....I'll have to test this theory out some more.
(So tonight I asked Google to explain this to me , and there is an article about sound carrying over lakes (http://www.mnresponsiblerec.org/previoussite/resources/sound.htm ) that suggests, rather , that the main reason is the bending of sound waves by a temperature inversion. Now, it so happens that there was indeed a temperature inversion today - you could clearly sea the smoke from chimneys collecting under a layer about 300 or so feet high. Sound travels faster in the warmer air above an inversion - and this would indeed bend sound back down - as the wave fronts angle obliquely into the inversion, the top of the waves hit the warmer layer first and are sped up - so the entire wave is steered downwards a bit - like the way the outer wheel in a turn has to go faster than the inner wheel, and turns the whole system towards the slower wheel.
Of course any time the sea is smooth, then there is no wind which is rather conducive to temperature layers developing so the possible causes confound each other.
And it seems like both could be correct since they are both variations on the same theme - refraction/reflection of sound when entering a less/more dense medium - perhaps the distinctive effect today was because both were in operation - canyoning the sound out through a layer between the water surface and the inversion, so that the rate of attenuation was even less then half, since the energy was only spreading out in two dimensions rather than three - so that in fact the rate of attenuation would have been more nearly proportional to the inverse first power of distance, rather than the inverse second power of distance.
Some experimentation is needed I guess - electronic send and receive over the surface of a pond, and the same distance apart over grass, and measure it.
But then later I thought of another couple of explanations. Firstly - there are some steep cliffs behind Aramoana so there was probably some echoing of the sound back off those and out over the harbour to Otakou.
Then secondly I got to thinking about the possibility of a wake effect - though really this should only happen (I think) if the motorbike is going faster than the speed of sound ! You drop a pebble in a pond and the waves spread out and attenuate as they go , because the energy is tansferred from a 0-D point, to the 1-D concentric growing circular wave front, and so a fixed amount of energy transferred to an ever growing circle, means the energy density - i.e. the wave - must attenuate. But say now you have a boat speeding through the pond - this is like dropping "continous" pebbles in a straight line. Now the energy is being transferred from a 1-D line (the speeding boat) to the a 1-D line - the wake on each side - a wake is a straight travelling wave. These wake waves do not need to attenuate on energy density grounds , since energy is being transferred from a 1-D line - the boat (or continously dropping pebble) , to 2 other 1-D lines of the same measure - the wakes (though will attenuate due to friction effects).
(I remember flying into Sydney once , looking down while still over the sea and being intrigued by these two long straight ribboned wakes left behind by a ship (or ferry or launch , I can't remember) - that seemed to just persist, travelling on over the sea long after the boat had passed. I say "ribboned" because, although they were straight, they were made of a series of sub-wavelets like
\
\
\
\
)
(I guess you can construct a wake mathematically by superposing the continuously infinite series of growing circular wave fronts generated by the passage of the boat - I guess interference effects result in the linear wake).
So I got to thinking - is there maybe a similar wake effect when you have sound coming from something like a motorbike speeding in a straight line along a beach like that ? - the bike is not fast enough to have a trailing wake (thats I guess what a sonic boom is !) - but maybe the energy is still transferred via a linear sound wave front that does not attenuate due to energy density considerations - as would be the case for a noise source at a single point in time.
So if you're ever out at Otakou and the harbour is glassy smooth - which is quite often - and can be all day in winter but usually only in the morning in summer - see if you notice the sound carrying ! - and see if its getting quieter as the second power of distance or as the first power of distance, or some power in between ! And how it is affected by whether the noise source is either continous and moving, or a single point in time and stationary.
Reading an interesting book by Anatole Abragam , a physicist , "Time Reversal" , at the moment - an autobiography, was born in 1914 and came of age during the second world war (I think he is still alive)....so that kind of got me in the mood for thinking about things like that. He has some very wise things to say about life as well as science. On the other hand, he's a bit of a sexist (I realised on second thoughts), and it got a bit boring towards the end and a bit too much name dropping and general bragging. But heck who am I to criticise !
(How do we know of a statement about life that it is a wise statement !? If we already knew it to be true it is unlikely to strike us as wise as we already knew it. On the other hand it must be something we believe to be true - for a statement to be wise , it must be true - or at least , we must believe it to be true.
So - on what evidence do we judge the truth or otherwise of a statement purporting to be a wise statement ? - since these generally do not come with any lengthy appendices offering empirical data as evidence.
I think a statement that strikes us as wise, is probably usually a statement that we have accumulated some evidence for ourselves , but which we have not yet formulated
any statement about - so that when we see the statement written down we are immediately able to corroborate it by referring to our own experience and memories.
This implies it is impossible to recognise wise statements about life as being such, until we have accumulated sufficient experience to be able to corroborate them as being true - until then , they will probably mean little to us as we will not have any rational basis on which to judge their truth value.
This does seem about how things go - and that it is perfectly rational for youth to ignore the wisdom of age. And also that , unfortunately, wise statements about life are often of little use - since we can only evaluate their wisdom when it is too late. Again - this does seem to be how things go)
Sunday, July 20, 2008
Saturday, July 5, 2008
Cybermen, Daleks, Terminators and other upgrades
We've had a big dumping of snow down here in the deep south - though had to drive up a few suburbs to have a go on the sled as the snow didn't quite manage to stay around on the ground around us like it sometimes has in other years. (This trip proved that alas petrol is *still* not expensive enough - we were in fear of our lives walking anywhere near the road due to boy-racers hooning up and down using their cars like motorised snow-boards ! )
My six year old is keen on Dr Who so the circle is complete - I must have been 6-ish , or perhaps a bit earlier when I was hiding behind a piece of furniture, absolutely terrified of the grey-scale (no colour TV then) Doctor and whatever he was up against - I only recall the Daleks, the Cybermen came later. I think it was the original old white-haired guy, long before the modern, post-modern and whatever-period-we-are-in-now Doctors - not to mention, long before the celebrity side-kicks (though alas Billy Piper appears to have departed into a parallel universe this week.) (I don't think it would have been a couch I was hiding behind, I don't think we had them then - and if we did it would have been called a sofa ! Like showers - didn't have those either, even in a new house that we built, I think in the late sixties, on the back of the then (alas no longer quite so) prosperous business of growing wool, lamb and mutton (we were sheep farmers) - we only had baths.....which come to think of it seems odd, given that at the end of the day we were often pretty filthy, yet often had to re-use bath water because baths use water so inefficiently and we were on rain-water supply..... - my guess is that pump, pipe, nozzle and water-heater technology and bathroom materials were not quite up to squirting warm water out over people in a pleasing fashion while yet not flooding the bathroom. (In fact I think there is still some progress to be made in this whole area - particularly that not-flooding-the-bathroom bit). This might have even been before alkathene piping - maybe getting copper pipe up and around a few bends and over our heads would have been too much of a mission ! Yikes ! Note to self - check out chemistry and history of black alkathene piping....am I really that old !?)
While my 6 year old is himself a little insecure at times with the Doctor and does sometimes disappear out of the room or come and sit on my lap when scared, he is clearly not as terrified as I was in my day, and generally far more sophisticated in his world view. He is, for example, able to observe that the Daleks can't even go up stairs, which seems odd for a race with their fearsome reputation. Its not something that ever occurred to me - and I'm not 100% sure that this is an original observation of his either - he has older siblings and also just generally lives in a much richer more sophisticated cultural environment than I did out in the back blocks of Matira. But still - its a testament to the originality of the ideas of the show and that wonderful Dr Who theme music (which 6-year old and I often sing loudly together as a duet much to the annoyance and disgust of the rest of the family- he does the high spooky weeeee-woooo bit, I do that menacing thrumming rhythmic bit in the bass) - that this little show with budget special effects is able to clear the room of 6 year olds on occasions - something that not even any of the Terminator movies was ever able to do !
There's actually an interesting contrast between the Dr Who dystopians - OK, scary dudes - and more recent ones like the terminators - which is that, the ones on Dr Who tend to be meat wrapped in metal, whereas the modern ones - like the terminators - are metal wrapped in meat. I can still remember the shock when one of the previous Doctors somehow opened up a Dalek and we got to see the pathetic little mutant that lived inside it. And when you got to see the first tantalising (and I think at that point unexpected, though I forget now) bits of robot under Arnie's skin, and realised he was metal wrapped in meat, in the first terminator movie - it was a similar kind of mild shock.
Well firstly - I guess there is something about "peeling back the layers" , that is extremely suggestive and metaphorical and all that, and that really works well as a dramatic and storytelling device. Consider for example how bland , by comparison , were the metal-wrapped-in-metal robots in something like "I Robot" ,
or even "AI" - unless there are layers hinted at, there is little dramatic potential - in any drama, not just sci-fi and cyborgs and all that, you need characters that only reveal part of themselves to start with, but hint at (and deliver) more later, as layers are peeled down to. Though the completely meat-less robots in the "Aliens" series of movies are a slight counter-example - they were pretty cool ! - but once again, still worked by appearing to be one thing -then shocking you when you discover, is something else. And I think I'd class those as metal-wrapped-in-meat anyway - even though technically I guess they were plastic-and-white-goo-wrapped-in-latex ! Dramatically and conceptually, they were metal-wrapped-in-meat - robots that appear human and organic.
Its interesting to speculate about the inside-outness of the modern cyborgs as compared with the older ones - why it is that metal-wrapped-in-meat has taken over from meat-wrapped-in-metal. Maybe material for a future blog ! It may just be that our technology - both "meat related" (genetics , cell cultures - flesh-in-a-dish...) , and "metal related" (micro-devices, quite advanced embedded smarts - though we are still miles from anything approaching AI - at least, AFAIK !) - has advanced to the point where the metal-wrapped-in-meat is more conceivable and credible.
The other meat-in-metal cyborgs on Dr Who I am familiar with are the "cybermen" - though it is only in this latest series that I saw their genesis and process of manufacture - which is , that you take a stock-standard human and, in a lurid blood-spattering process called "upgrading" , extract his or her brain and stick inside a metal suit ! (I am sure that the pun on software "upgrades" , and the similar level of unpleasantness and buggering of one's brain when you do one of these as compared with being upgraded to being a cyberman , is deliberate !).
One last thing though is.....we are in fact being cyber-ishly upgraded even as we speak, but in a more subtle way. The English language is being "upgraded" at a rather frighteningly fast rate , by cell-phone technology. Consider this extract of written English from a young 20-something :
"Sup? im laxin chch for a bit b4 a little travel n amped for the snow. Listenin 2 da top40"
Which translates roughly as ....
"Hows it going - what are you up to ? I am relaxing for awhile before doing some travelling - keen to do some skiing when the snow arrives. Listening to the top 40 music show at the moment"
....and you get the feeling when you see the way groups of people are half in conversation with those present and half with other people via text - that there is maybe a change to a somewhat different, more collective consciousness going on , different to the isolated awareness we have known.....its possibly not too far from the truth to describe a gaggle of 14 y/o teenagers + cell phones as a single cybernetic organism !
....and of course the incredible access to knowledge that we now have - this futuristic network we take for granted that seems like it arrived out of nowhere, that we can address plain language queries to on almost any subject and get answers - this also is part of the "upgrade" each of us is receiving.
(....though the extent to which we were ever isolated awareness's, as opposed to brains always talking to other brains across time and space in a very complex and intrinsically social way, has I think been grossly over-stated - we got led astray by the French school (Descartes, JP Sartre) , not to mention a number of Germans, Dutch....actually it may be more of a historical time period, a fad we went through - though does seem to be a particularly continental Europe development. It was a possibly a very big, perhaps fatal mistake....more thought needed !)
My six year old is keen on Dr Who so the circle is complete - I must have been 6-ish , or perhaps a bit earlier when I was hiding behind a piece of furniture, absolutely terrified of the grey-scale (no colour TV then) Doctor and whatever he was up against - I only recall the Daleks, the Cybermen came later. I think it was the original old white-haired guy, long before the modern, post-modern and whatever-period-we-are-in-now Doctors - not to mention, long before the celebrity side-kicks (though alas Billy Piper appears to have departed into a parallel universe this week.) (I don't think it would have been a couch I was hiding behind, I don't think we had them then - and if we did it would have been called a sofa ! Like showers - didn't have those either, even in a new house that we built, I think in the late sixties, on the back of the then (alas no longer quite so) prosperous business of growing wool, lamb and mutton (we were sheep farmers) - we only had baths.....which come to think of it seems odd, given that at the end of the day we were often pretty filthy, yet often had to re-use bath water because baths use water so inefficiently and we were on rain-water supply..... - my guess is that pump, pipe, nozzle and water-heater technology and bathroom materials were not quite up to squirting warm water out over people in a pleasing fashion while yet not flooding the bathroom. (In fact I think there is still some progress to be made in this whole area - particularly that not-flooding-the-bathroom bit). This might have even been before alkathene piping - maybe getting copper pipe up and around a few bends and over our heads would have been too much of a mission ! Yikes ! Note to self - check out chemistry and history of black alkathene piping....am I really that old !?)
While my 6 year old is himself a little insecure at times with the Doctor and does sometimes disappear out of the room or come and sit on my lap when scared, he is clearly not as terrified as I was in my day, and generally far more sophisticated in his world view. He is, for example, able to observe that the Daleks can't even go up stairs, which seems odd for a race with their fearsome reputation. Its not something that ever occurred to me - and I'm not 100% sure that this is an original observation of his either - he has older siblings and also just generally lives in a much richer more sophisticated cultural environment than I did out in the back blocks of Matira. But still - its a testament to the originality of the ideas of the show and that wonderful Dr Who theme music (which 6-year old and I often sing loudly together as a duet much to the annoyance and disgust of the rest of the family- he does the high spooky weeeee-woooo bit, I do that menacing thrumming rhythmic bit in the bass) - that this little show with budget special effects is able to clear the room of 6 year olds on occasions - something that not even any of the Terminator movies was ever able to do !
There's actually an interesting contrast between the Dr Who dystopians - OK, scary dudes - and more recent ones like the terminators - which is that, the ones on Dr Who tend to be meat wrapped in metal, whereas the modern ones - like the terminators - are metal wrapped in meat. I can still remember the shock when one of the previous Doctors somehow opened up a Dalek and we got to see the pathetic little mutant that lived inside it. And when you got to see the first tantalising (and I think at that point unexpected, though I forget now) bits of robot under Arnie's skin, and realised he was metal wrapped in meat, in the first terminator movie - it was a similar kind of mild shock.
Well firstly - I guess there is something about "peeling back the layers" , that is extremely suggestive and metaphorical and all that, and that really works well as a dramatic and storytelling device. Consider for example how bland , by comparison , were the metal-wrapped-in-metal robots in something like "I Robot" ,
or even "AI" - unless there are layers hinted at, there is little dramatic potential - in any drama, not just sci-fi and cyborgs and all that, you need characters that only reveal part of themselves to start with, but hint at (and deliver) more later, as layers are peeled down to. Though the completely meat-less robots in the "Aliens" series of movies are a slight counter-example - they were pretty cool ! - but once again, still worked by appearing to be one thing -then shocking you when you discover, is something else. And I think I'd class those as metal-wrapped-in-meat anyway - even though technically I guess they were plastic-and-white-goo-wrapped-in-latex ! Dramatically and conceptually, they were metal-wrapped-in-meat - robots that appear human and organic.
Its interesting to speculate about the inside-outness of the modern cyborgs as compared with the older ones - why it is that metal-wrapped-in-meat has taken over from meat-wrapped-in-metal. Maybe material for a future blog ! It may just be that our technology - both "meat related" (genetics , cell cultures - flesh-in-a-dish...) , and "metal related" (micro-devices, quite advanced embedded smarts - though we are still miles from anything approaching AI - at least, AFAIK !) - has advanced to the point where the metal-wrapped-in-meat is more conceivable and credible.
The other meat-in-metal cyborgs on Dr Who I am familiar with are the "cybermen" - though it is only in this latest series that I saw their genesis and process of manufacture - which is , that you take a stock-standard human and, in a lurid blood-spattering process called "upgrading" , extract his or her brain and stick inside a metal suit ! (I am sure that the pun on software "upgrades" , and the similar level of unpleasantness and buggering of one's brain when you do one of these as compared with being upgraded to being a cyberman , is deliberate !).
One last thing though is.....we are in fact being cyber-ishly upgraded even as we speak, but in a more subtle way. The English language is being "upgraded" at a rather frighteningly fast rate , by cell-phone technology. Consider this extract of written English from a young 20-something :
"Sup? im laxin chch for a bit b4 a little travel n amped for the snow. Listenin 2 da top40"
Which translates roughly as ....
"Hows it going - what are you up to ? I am relaxing for awhile before doing some travelling - keen to do some skiing when the snow arrives. Listening to the top 40 music show at the moment"
....and you get the feeling when you see the way groups of people are half in conversation with those present and half with other people via text - that there is maybe a change to a somewhat different, more collective consciousness going on , different to the isolated awareness we have known.....its possibly not too far from the truth to describe a gaggle of 14 y/o teenagers + cell phones as a single cybernetic organism !
....and of course the incredible access to knowledge that we now have - this futuristic network we take for granted that seems like it arrived out of nowhere, that we can address plain language queries to on almost any subject and get answers - this also is part of the "upgrade" each of us is receiving.
(....though the extent to which we were ever isolated awareness's, as opposed to brains always talking to other brains across time and space in a very complex and intrinsically social way, has I think been grossly over-stated - we got led astray by the French school (Descartes, JP Sartre) , not to mention a number of Germans, Dutch....actually it may be more of a historical time period, a fad we went through - though does seem to be a particularly continental Europe development. It was a possibly a very big, perhaps fatal mistake....more thought needed !)
Saturday, June 28, 2008
Pythagoreans, Orbifolds and Catherine the Great
I've just decided - in future when asked to state my religion I'll enter "Pythagorean".
(reference - "The Music of Pythagoras" by Kitty Ferguson, my current reading - I'm currently a perfect fifth (1/3rd - pythagorean joke ! ) the way through it).
Not that I think Pythagoras would have admitted me as one of his disciples - I a bit too shallow and stupid and not a good enough listener. And its not as though I am confident that anybody really knows much about the pythagoreans at all - Ferguson is very up-front about how little solid historical evidence there is , and how unreliable many of the re-tellings down the ages are likely to be. Seems like Pythagoras almost made it into the classical limelight but not quite - he lived about 570-500BC - and by the second half of the fifth century BC , 450 to 400BC , we have Aeschylus, Aristophanes, Hippocrates and his oath, and the parthenon. A pythagorist Philolaus was in the limelight period and almost a direct link with Pythagoras himself - he was born only 25 years or so after the death of Pythagoras, and was educated by pythagorists, the older of whom must have known Pythagoras. Evidently Philolaus did write a detailed account of the teachings of the pythagorists - but unfortunately only fragments survive, and it is not clear which parts of those are Pythagoras and which are Philolaus. So the real Pythagoras and his teachings remain outside the limelight - in the twilight zone of history.
So why a pythagorist ? Its certainly not that I believe in numerology or have any sort of mysticism about numbers. Nor do I, as apparently did the pythagorists, believe that beans contain souls. (Their chain of reasoning was : (1) beans cause flatulence (2) flatulence is air (3) it was widely believed that souls were air (4) => beans contain souls. The belief is reputed to have led to Pythagoras's death - he was fleeing some hostile locals, whipped up by a disgruntled pillock of the community who had been refused admission to the pythagorean school : when confronted by a field of beans blocking his way, Pythagoras because of his beliefs had to run around it (can't trample all those souls !) while those in pursuit just ran across, so catching and killing him). Nor do I believe in other pythagorean (non-bean !) staples such as reincarnation or the uncomplicated purely number-based rationality of the universe . Nor do I think they sound a very attractive bunch really - rather humourless and puritanical.
Its just that, like the pythagoreans, I have this need to see - dimly, probably deludedly, and in a rather half-baked and I suppose somewhat embarrassing, dilettantish way - mathematical concepts in domains where they are not generally (currently) admitted. And I suppose, a kind of literary or ramblingly discursive or in some other sense oblique, rather than directly technical and computational, relationship with mathematics (of necessity since I do not possess any significant mathematical talent). Maybe could put it as, mathematics as a source of inspiration and metaphors, but slightly more than that - metaphors that can almost , but not quite , be used for computation and prediction in the target domain of their allusion, as well as in the source domain.
(The link between music and mathematics that was first made by Pythagoras is now a commonplace - yet still has legs for future discovery - e.g. see the recent "The Geometry of Musical Chords
Dmitri Tymoczko (7 July 2006)Science 313 (5783), 72". This uses a fascinating mathematical object known as an orbifold. Now my understanding of orbifolds is pythagoristic rather than technical - I had a concept of something like an orbifold before I came across the term - and have been assuming for awhile that what is denoted by this term corresponds to my concept.... could be wrong. I wanted - just for my own interest - something to describe the manifold represented by the combined state of a set of cyclical functions. Lets say for example - the space occupied by the expression levels of a set of genes. The expression of each gene varies continuously in some no doubt cyclical fashion (unless it is some odd one-shot developmental gene that only ever turns on once), and the high-dimensional space that the expression of N genes lives in is clearly a continuous N-dimensional manifold (my understanding of which is mostly technically OK I *think*, but also a little pythagorist in the above sense ) - yet because of the cyclical nature of each of the N expression levels, it seems to be a slightly different type of manifold, because of these orbits in each of the dimensions. Another example would be - the combined state represented by the position of the tip of every leaf of a tree blowing in the wind. Again - each leaf gyrates in its own orbit and the combined high dimensional set of leaf-tip positions clearly lives in a continuous N-dimensional manifold (N = the number of leaves) - yet it has this structure in which each dimension lives in an orbit. (I think this is what is meant by the technical orbifold definition (e.g. see Wikipaedia ) that "Like a manifold, an orbifold is specified by local conditions; however, instead of being locally modelled on open subsets of Rn, an orbifold is locally modelled on quotients of open subsets of Rn by finite group actions..." - the finite group actions here being the rotations of the leaf tips of the tree, or the rotations/oscillations of the expression levels of the genes...(user beware - do not requote any of this as it may be misinformation !)....more on orbifolds in a future blog !)
(....or are the manifolds I described N-dimensional torii ? For example a cross product of two circular one-dimensional manifolds is a torus - so maybe the cross-product of N orbits of the type I describe is an N-dimensional torus. Question : is there an isomorphism of some sort between orbifolds and N-dimensional torii ?)
(Hypothesis : pythagorists (in the above sense) could play a role in bringing far-fetched mathematical objects like orbifolds down from the mount and finding them useful employment in the fields. Mathematicians themselves won't do that - they are slaving at the top of the mountain. Non mathematician specialists won't, they are too busy slaving on other mountains. Then again the non-specialist pythagorist dilettante has little credibility on either mountain so its unlikely after all but possibly worth trying, though I suspect he/she is likely to anger some technical specialist mob or other and get chased around the bean fields a bit doing this sort of thing !)
(I note in passing that Kitty Ferguson is as well as being an author on various mathematical and physics subjects also a "Juilliard trained professional musician". I can't believe the number of young people I have met in the last few years , multi-talented in this way - science / maths careers and also accomplished musicians - composers, performers, conductors.... I don't remember it being like that when I was younger and at 'varsity - there were some smart people alright (I was not one of them ) - and I know one that went on to be a well known poet and others that rose to academic success but.....we were....kind of ordinary in comparison, and really just tended to mooch around.....or at least it seems that way in retrospect. (In my case there wasn't even a "we" - I just mostly mooched my way solitarily through various crushes). Maybe there is an interaction effect, between talent and the technology and educational opportunities and expectations now that enables talented people to burn brighter sooner nowadays.....something like the famous Flynn effect maybe - an interaction specifically between natural talent and the modern world)
For something completely different - and for a much raunchier read (in between the lines ) - read the excellent "The Memoirs of Catherine the Great" , a new translation by Mark Cruse and Hilde Hoogenboom. I love a quote (from a section that was left out of a 1907 Russian edition)..."No one holds his heart in his hand and restrains or releases it by closing his hand at will." (page 200! - its hot ! ). Her diary reminds me a bit of the Pepys one, in its surprising accessibility and the way it draws you in to a story of day to day life which on the face of it would appear likely a dull read yet somehow becomes the opposite. They were both writing also at about the time of the Enlightenment when change and progress was scented on the wind - perhaps it is the background optimism shining through (and despite the various disasters and discomforts they endured - the great fire, plague, political and career problems) that make these diaries so good to read. And in Catherine's one - court life is surprisingly like office life - with courtly notes playing the role of email, and a similar caste of personalities and rivalries and manipulative behaviours.
(reference - "The Music of Pythagoras" by Kitty Ferguson, my current reading - I'm currently a perfect fifth (1/3rd - pythagorean joke ! ) the way through it).
Not that I think Pythagoras would have admitted me as one of his disciples - I a bit too shallow and stupid and not a good enough listener. And its not as though I am confident that anybody really knows much about the pythagoreans at all - Ferguson is very up-front about how little solid historical evidence there is , and how unreliable many of the re-tellings down the ages are likely to be. Seems like Pythagoras almost made it into the classical limelight but not quite - he lived about 570-500BC - and by the second half of the fifth century BC , 450 to 400BC , we have Aeschylus, Aristophanes, Hippocrates and his oath, and the parthenon. A pythagorist Philolaus was in the limelight period and almost a direct link with Pythagoras himself - he was born only 25 years or so after the death of Pythagoras, and was educated by pythagorists, the older of whom must have known Pythagoras. Evidently Philolaus did write a detailed account of the teachings of the pythagorists - but unfortunately only fragments survive, and it is not clear which parts of those are Pythagoras and which are Philolaus. So the real Pythagoras and his teachings remain outside the limelight - in the twilight zone of history.
So why a pythagorist ? Its certainly not that I believe in numerology or have any sort of mysticism about numbers. Nor do I, as apparently did the pythagorists, believe that beans contain souls. (Their chain of reasoning was : (1) beans cause flatulence (2) flatulence is air (3) it was widely believed that souls were air (4) => beans contain souls. The belief is reputed to have led to Pythagoras's death - he was fleeing some hostile locals, whipped up by a disgruntled pillock of the community who had been refused admission to the pythagorean school : when confronted by a field of beans blocking his way, Pythagoras because of his beliefs had to run around it (can't trample all those souls !) while those in pursuit just ran across, so catching and killing him). Nor do I believe in other pythagorean (non-bean !) staples such as reincarnation or the uncomplicated purely number-based rationality of the universe . Nor do I think they sound a very attractive bunch really - rather humourless and puritanical.
Its just that, like the pythagoreans, I have this need to see - dimly, probably deludedly, and in a rather half-baked and I suppose somewhat embarrassing, dilettantish way - mathematical concepts in domains where they are not generally (currently) admitted. And I suppose, a kind of literary or ramblingly discursive or in some other sense oblique, rather than directly technical and computational, relationship with mathematics (of necessity since I do not possess any significant mathematical talent). Maybe could put it as, mathematics as a source of inspiration and metaphors, but slightly more than that - metaphors that can almost , but not quite , be used for computation and prediction in the target domain of their allusion, as well as in the source domain.
(The link between music and mathematics that was first made by Pythagoras is now a commonplace - yet still has legs for future discovery - e.g. see the recent "The Geometry of Musical Chords
Dmitri Tymoczko (7 July 2006)Science 313 (5783), 72". This uses a fascinating mathematical object known as an orbifold. Now my understanding of orbifolds is pythagoristic rather than technical - I had a concept of something like an orbifold before I came across the term - and have been assuming for awhile that what is denoted by this term corresponds to my concept.... could be wrong. I wanted - just for my own interest - something to describe the manifold represented by the combined state of a set of cyclical functions. Lets say for example - the space occupied by the expression levels of a set of genes. The expression of each gene varies continuously in some no doubt cyclical fashion (unless it is some odd one-shot developmental gene that only ever turns on once), and the high-dimensional space that the expression of N genes lives in is clearly a continuous N-dimensional manifold (my understanding of which is mostly technically OK I *think*, but also a little pythagorist in the above sense ) - yet because of the cyclical nature of each of the N expression levels, it seems to be a slightly different type of manifold, because of these orbits in each of the dimensions. Another example would be - the combined state represented by the position of the tip of every leaf of a tree blowing in the wind. Again - each leaf gyrates in its own orbit and the combined high dimensional set of leaf-tip positions clearly lives in a continuous N-dimensional manifold (N = the number of leaves) - yet it has this structure in which each dimension lives in an orbit. (I think this is what is meant by the technical orbifold definition (e.g. see Wikipaedia ) that "Like a manifold, an orbifold is specified by local conditions; however, instead of being locally modelled on open subsets of Rn, an orbifold is locally modelled on quotients of open subsets of Rn by finite group actions..." - the finite group actions here being the rotations of the leaf tips of the tree, or the rotations/oscillations of the expression levels of the genes...(user beware - do not requote any of this as it may be misinformation !)....more on orbifolds in a future blog !)
(....or are the manifolds I described N-dimensional torii ? For example a cross product of two circular one-dimensional manifolds is a torus - so maybe the cross-product of N orbits of the type I describe is an N-dimensional torus. Question : is there an isomorphism of some sort between orbifolds and N-dimensional torii ?)
(Hypothesis : pythagorists (in the above sense) could play a role in bringing far-fetched mathematical objects like orbifolds down from the mount and finding them useful employment in the fields. Mathematicians themselves won't do that - they are slaving at the top of the mountain. Non mathematician specialists won't, they are too busy slaving on other mountains. Then again the non-specialist pythagorist dilettante has little credibility on either mountain so its unlikely after all but possibly worth trying, though I suspect he/she is likely to anger some technical specialist mob or other and get chased around the bean fields a bit doing this sort of thing !)
(I note in passing that Kitty Ferguson is as well as being an author on various mathematical and physics subjects also a "Juilliard trained professional musician". I can't believe the number of young people I have met in the last few years , multi-talented in this way - science / maths careers and also accomplished musicians - composers, performers, conductors.... I don't remember it being like that when I was younger and at 'varsity - there were some smart people alright (I was not one of them ) - and I know one that went on to be a well known poet and others that rose to academic success but.....we were....kind of ordinary in comparison, and really just tended to mooch around.....or at least it seems that way in retrospect. (In my case there wasn't even a "we" - I just mostly mooched my way solitarily through various crushes). Maybe there is an interaction effect, between talent and the technology and educational opportunities and expectations now that enables talented people to burn brighter sooner nowadays.....something like the famous Flynn effect maybe - an interaction specifically between natural talent and the modern world)
For something completely different - and for a much raunchier read (in between the lines ) - read the excellent "The Memoirs of Catherine the Great" , a new translation by Mark Cruse and Hilde Hoogenboom. I love a quote (from a section that was left out of a 1907 Russian edition)..."No one holds his heart in his hand and restrains or releases it by closing his hand at will." (page 200! - its hot ! ). Her diary reminds me a bit of the Pepys one, in its surprising accessibility and the way it draws you in to a story of day to day life which on the face of it would appear likely a dull read yet somehow becomes the opposite. They were both writing also at about the time of the Enlightenment when change and progress was scented on the wind - perhaps it is the background optimism shining through (and despite the various disasters and discomforts they endured - the great fire, plague, political and career problems) that make these diaries so good to read. And in Catherine's one - court life is surprisingly like office life - with courtly notes playing the role of email, and a similar caste of personalities and rivalries and manipulative behaviours.
Tuesday, June 10, 2008
theory of action 2
In part 1 of this theory of action it was claimed that while the valuations derived from one's theory of ones self and ones actions was a fragile thing, the value of the actions themselves can be secure - actions are substantive and incompressible, real things in time and space. If true this seems (albeit probably in a sense that would be fairly cryptic to many people !) very liberating...it is legitimate, good, essential even, to be and act and do, even when one's confidence in the whole enterprise of ones' self and ones actions is lacking - when one lacks an adequate theory of action and self.
Or the argument can be put more simply like this : it is common to infer the fitness and goodness of our actions, from our estimation of the fitness and goodness of ourselves : we are good so the things we do are good ; yet even if the inference can't be made, we are not to be deterred - we can still act and our actions can still be good.
Which raises the question - how can we know our actions are fit and good when we do not currently have a theory that asserts our own goodness and fitness ? Clearly this requires some external arbiter of the moral value of our actions - we need to be able to know a priori that it is good to help an old lady across the street, for the injunctions of theory of action 1 to hold.
Yet if we do have such an external arbiter, surely this would induce a very simple theory of ourselves and our actions - which is that, we ourselves are fit and good, if our actions are fit and good.
But if this robust theory is available, why then did we get into trouble in the first place - what sort of theory did we originally have that failed, and why did it fail ?
There are two possible answers. The first is that our theory was , indeed, that we ourselves are fit and good, simply if our actions are fit and good ; but that our actions have not recently been fit and good, so that our theory has failed. In this case to continue to act we need a special act of will and steadfastness - and / or perhaps some forgiveness from the external arbiter. (Many religious theories of self and action are of this type - we are valued as the sum of our actions, and there is some process of forgiveness or other remedy available when the theory fails). I will deal with this special act of will and steadfastness, in a future part of the theory of action, since it has a very interesting structure.
The other possible answer is that our original theory was not one that judged us as the sum of our actions. Perhaps , for example , it was a theory derived from our pedigree - that we were fit and good because of high birth.....and perhaps it failed because we have just found out our birth (or that of one of our ancestors) was illegitimate ! Or perhaps it was a theory based on some other intrinsic measure - say, exceptional ability in some specific domain, such as mathematics, music, art, athletics, intelligence tests, and we have come to doubt the measure in some way.
My guess is that the theories of self and action that fail and leave us stranded and stalled are often of this second sort - based on some intrinsic metric of self.
These types of theories are not robust for several reasons. Firstly, the intrinsic metric itself is likely to be error prone - it will be difficult to be certain about the nobility of our birth, the degree of our talent in our chosen domain. Secondly the metric is relative - there is no absolute level of nobility of birth or talent in some domain : there are only relative measures - we are more or less noble or talented than somebody else. This means that the intrinsic metric can change abruptly - for example when we meet for the first time people who are vastly more nobly born or talented than we are. Thirdly, even if we could achieve some robust intrinsic metric of our own worth, the inference that if we are fit and good we will do fit and good things, is not certain.
It is tempting to speculate that theories of self and action that are based on intrinsic metrics, rather than being extensionally based - "we are what we do" - are a feature of modern times and the modern psyche and likely to become more so - for example, the progressive educational strategy of attempting to inculcate intrinsic self-esteem is a possible example ; intrinsic genetic merit will be a possible metric in the future. On the other hand, the English and other class systems are a historical counter example, which show that these theories are nothing new.
(I should confess that I have recently read Richard Reeves very enjoyable biography of John Stuart Mill so am maybe "under the influence". Not that I started these theories of action consciously thinking about Mill, but I seemed to have ended up in his vicinity. Reeves describes Mill's life-long intense hostility to "intuitionist" philosophy. I am not sure I completely understand the meaning of "intuitionist" - but I suspect that those theories of self and action that are based on intrinsic metrics, rather than extrinsic canons of deeds done, are in some sense "intuitionist" theories. And a distinctive thing about Mill was his activism - as a journalist, politician, champion of womens' suffrage and many other causes - so that I am describing a theory of action and self which might be something like the one Mill himself lived by)
Or the argument can be put more simply like this : it is common to infer the fitness and goodness of our actions, from our estimation of the fitness and goodness of ourselves : we are good so the things we do are good ; yet even if the inference can't be made, we are not to be deterred - we can still act and our actions can still be good.
Which raises the question - how can we know our actions are fit and good when we do not currently have a theory that asserts our own goodness and fitness ? Clearly this requires some external arbiter of the moral value of our actions - we need to be able to know a priori that it is good to help an old lady across the street, for the injunctions of theory of action 1 to hold.
Yet if we do have such an external arbiter, surely this would induce a very simple theory of ourselves and our actions - which is that, we ourselves are fit and good, if our actions are fit and good.
But if this robust theory is available, why then did we get into trouble in the first place - what sort of theory did we originally have that failed, and why did it fail ?
There are two possible answers. The first is that our theory was , indeed, that we ourselves are fit and good, simply if our actions are fit and good ; but that our actions have not recently been fit and good, so that our theory has failed. In this case to continue to act we need a special act of will and steadfastness - and / or perhaps some forgiveness from the external arbiter. (Many religious theories of self and action are of this type - we are valued as the sum of our actions, and there is some process of forgiveness or other remedy available when the theory fails). I will deal with this special act of will and steadfastness, in a future part of the theory of action, since it has a very interesting structure.
The other possible answer is that our original theory was not one that judged us as the sum of our actions. Perhaps , for example , it was a theory derived from our pedigree - that we were fit and good because of high birth.....and perhaps it failed because we have just found out our birth (or that of one of our ancestors) was illegitimate ! Or perhaps it was a theory based on some other intrinsic measure - say, exceptional ability in some specific domain, such as mathematics, music, art, athletics, intelligence tests, and we have come to doubt the measure in some way.
My guess is that the theories of self and action that fail and leave us stranded and stalled are often of this second sort - based on some intrinsic metric of self.
These types of theories are not robust for several reasons. Firstly, the intrinsic metric itself is likely to be error prone - it will be difficult to be certain about the nobility of our birth, the degree of our talent in our chosen domain. Secondly the metric is relative - there is no absolute level of nobility of birth or talent in some domain : there are only relative measures - we are more or less noble or talented than somebody else. This means that the intrinsic metric can change abruptly - for example when we meet for the first time people who are vastly more nobly born or talented than we are. Thirdly, even if we could achieve some robust intrinsic metric of our own worth, the inference that if we are fit and good we will do fit and good things, is not certain.
It is tempting to speculate that theories of self and action that are based on intrinsic metrics, rather than being extensionally based - "we are what we do" - are a feature of modern times and the modern psyche and likely to become more so - for example, the progressive educational strategy of attempting to inculcate intrinsic self-esteem is a possible example ; intrinsic genetic merit will be a possible metric in the future. On the other hand, the English and other class systems are a historical counter example, which show that these theories are nothing new.
(I should confess that I have recently read Richard Reeves very enjoyable biography of John Stuart Mill so am maybe "under the influence". Not that I started these theories of action consciously thinking about Mill, but I seemed to have ended up in his vicinity. Reeves describes Mill's life-long intense hostility to "intuitionist" philosophy. I am not sure I completely understand the meaning of "intuitionist" - but I suspect that those theories of self and action that are based on intrinsic metrics, rather than extrinsic canons of deeds done, are in some sense "intuitionist" theories. And a distinctive thing about Mill was his activism - as a journalist, politician, champion of womens' suffrage and many other causes - so that I am describing a theory of action and self which might be something like the one Mill himself lived by)
Saturday, June 7, 2008
theory of action 1
When you are fit and confident and strong, you have available a theory of action. The theory is maybe just something like - that you are fit and confident and strong, loved and loving, intelligent and kind etc, and the theory is a theory of all the actions available to such a person - and the theory allows you to act and do and be, without faltering.
When as happens from time to time you are somewhat more dented and ding-ed and knocked about a bit - perhaps really quite completely crumpled by that general flux of minor or major or sometimes completely illusory rejections ,disappointments and complete failures (...that flux that appears to increase in intensity with age, though perhaps this is just a failure of recollection), you often find yourself struggling to act because you make the mistake of thinking you need that good old red-blooded theory of action before you can act.......so you stall and freeze, furiously trying to panel-beat your theory of yourself and of action back into shape so that you can set off once more.....or in other words , trying to lift yourself by your bootstraps....
But the thing to remember is that - while your theory of yourself and of action is so easily compressible down to nothing by the flux- it is made of very insubstantial stuff - your actions are substantive and incompressible. Sure - if you help an old lady across the street while you are all depressed and theoryless, it feels wrong - or at least , profoundly unfulfilling - as though there is a zombie in charge. You have no theory of your action so you can't even be sure of your motives.....but the action is real and out there in time and space, it is good and cannot be compressed away by the flux.
The thing then is to force yourself to act , even when theoryless, even if it feels profoundly unfulfilling , as though there is nobody at home, just a zombie walking.
This is probably natural to many people. But to others (well , at least one other) it is surprisingly difficult - forcing yourself to act and do and be without your theories of yourself and of action intact, can feel like walking down a path with your eyes shut, or maybe more like, landing too fast and out of control down the runway, with the machine far ahead of the pilot in command.
But this is a way of feeling that you need to get used to
When as happens from time to time you are somewhat more dented and ding-ed and knocked about a bit - perhaps really quite completely crumpled by that general flux of minor or major or sometimes completely illusory rejections ,disappointments and complete failures (...that flux that appears to increase in intensity with age, though perhaps this is just a failure of recollection), you often find yourself struggling to act because you make the mistake of thinking you need that good old red-blooded theory of action before you can act.......so you stall and freeze, furiously trying to panel-beat your theory of yourself and of action back into shape so that you can set off once more.....or in other words , trying to lift yourself by your bootstraps....
But the thing to remember is that - while your theory of yourself and of action is so easily compressible down to nothing by the flux- it is made of very insubstantial stuff - your actions are substantive and incompressible. Sure - if you help an old lady across the street while you are all depressed and theoryless, it feels wrong - or at least , profoundly unfulfilling - as though there is a zombie in charge. You have no theory of your action so you can't even be sure of your motives.....but the action is real and out there in time and space, it is good and cannot be compressed away by the flux.
The thing then is to force yourself to act , even when theoryless, even if it feels profoundly unfulfilling , as though there is nobody at home, just a zombie walking.
This is probably natural to many people. But to others (well , at least one other) it is surprisingly difficult - forcing yourself to act and do and be without your theories of yourself and of action intact, can feel like walking down a path with your eyes shut, or maybe more like, landing too fast and out of control down the runway, with the machine far ahead of the pilot in command.
But this is a way of feeling that you need to get used to
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