... especially concerning the future, as Niels Bohr is meant to have said.
I have been thinking about what could have been predicted in the past. If you had asked Isaac Newton in 1710 to predict life in 2010, what could he have got right and what would he have missed?
I don't believe, by the way, there was much of a concept of future extrapolation back in the seventeenth and eighteenth centuries. The idea that the future will be different to (better than?) the past depends on the idea of relentless technological innovation, a uniqely capitalist phenomenon. It was only in the nineteenth century that the concept of permanent capitalist progress became clear, both to K. Marx and to H. G. Wells.
Still, based on what Newton knew I think he wouldn't be too surprised by cars, modern apartments and even radio and TV. Atomic energy meanwhile is based on principles unknown to Newton but today it's an embedded technology and in its utilisation behaves like a super form of exothermic chemical reaction. (That's probably an indictment of our lack of imagination).
On the other hand, I think ubiquitous computers would be a genuine paradigm-level mystery. What kind of thing are they and what are they for? I think David Deutsch almost uniquely got it right when he asserted that a computer is a way of constructing virtual realities: of animating rules of behaviour which need bear no connection to the laws of this physical universe. Getting an unbounded virtual reality machine to work using parts firmly grounded in this reality requires some really sophisticated engineering as you will fail to fully comprehend if you open your laptop (unless you have electron microscope eyes).
So predicting the computer is, I think, the one area of modern life which would have been a paradigm beyond Newton. Also of Leibnitz, despite his dreams of mechanical calculators (a mundane extrapolation).
As we look into the future on this last day of 2010, what could we realistically predict?
The first issue is that every possible extrapolation of currently-understood reality has already been worked on by SF writers.
* We have scenarios which encompass the entire history of the universe factoring in extra dimensions and various species of multiverse.
* No aspect of artificial intelligence or virtual reality has been overlooked.
* In fiction we have colonised not one but billions of galaxies, terraformed worlds and transformed utterly our physical and psychic selves.
Never in the history of humankind have we been more active in anticipating the broad forms of every conceivable future. So in a sense, it's impossible to be surprised (at a sufficiently coarse granularity) by any conceivable scientific breakthrough.
* A future unified field theory in physics? So we get to manipulate gravity.
* Brain uploading and stardrive? We get to colonise the galaxy.
* The aliens show up? We beat them, they beat us or we nod along uneasily.
I can refer you to titles discussing these and half a dozen other big ideas.
If you're still interested in surprises, the place to look is where the greatest gap exists between the phenomena, the science and the engineering. I would cautiously flag two areas.
1. Materials (or condensed matter physics). There is so much work going on at the moment in areas like high-temperature superconductors, metamaterials and the applications of new kinds of nanoscale-structure stuff that our physical environment seems set to alter in fascinating and unimagined ways.
2. Artificial Life. Today, we and our pets are smart and our environment (roads, houses, cars, myriads of artifacts) are almost entirely cognitively-inert: that is going to change. In the future, the best metaphor for our artificial environment, our created infrastructure will be that we are surrounded by artificial creatures. Some will be more adept at urban living than ourselves. Wow, that's going to be interesting.
Now, I wonder what I've missed because I just don't have the concepts?
Friday, December 31, 2010
Things not to say ...
... to your wife as you groggily wake up.
"Oh, there's a woman in my bed.
"Do you come courtesy of the hotel?"
--
[Too much film noir over the break]
"Oh, there's a woman in my bed.
"Do you come courtesy of the hotel?"
--
[Too much film noir over the break]
Wednesday, December 29, 2010
The Kindness of Very Strangers
I have never believed in the kindness of aliens. In any case, the question is the province of evolutionary exobiology rather than the extrapolation of problematic values of human decency. Stand aside, heart-on-the-sleeve SETI astronomers and stop transmitting to the aliens!
Of course, there is one bunch of aliens actively hunting for signs of life out there: namely ourselves. It's believed that within a century we will have orbital telescopes able to image the details of extrasolar planets just like spy satellites. Of course, our intentions towards any aliens we find will be nothing short of benevolent, won't they? (I think it was a year ago I was watching that 3D epic Avatar about Pandora).
However, we don't need any such hi-tech observatories to detect alien life: a simple spectrum of the extrasolar planet's atmosphere showing oxygen absorption lines would suffice. How hard is that? Just a few decades away.
Take the earth. It intercepts 0.75 * π * (6 * 106)2 kilowatts from the sun, and with an albedo of 0.3 reflects 30%. That's around 25,000 Terawatts if you work it out. If you can detect that from light years out, you have your spectrum and you know someone's at home.
By comparison, the Arecibo telescope in its radar mode emits 1 Megawatt (I know it's collimated and coherent). Still, if you're sufficient light years away and you can detect Arecibo I reckon you can also detect earth's spectrum. Add us to the list.
So I still think it's a bad idea to holler to those aliens out there: it's capabilities not intentions that you have to worry about. But until we start using Exawatt lasers I agree it just doesn't matter.
Of course, there is one bunch of aliens actively hunting for signs of life out there: namely ourselves. It's believed that within a century we will have orbital telescopes able to image the details of extrasolar planets just like spy satellites. Of course, our intentions towards any aliens we find will be nothing short of benevolent, won't they? (I think it was a year ago I was watching that 3D epic Avatar about Pandora).
However, we don't need any such hi-tech observatories to detect alien life: a simple spectrum of the extrasolar planet's atmosphere showing oxygen absorption lines would suffice. How hard is that? Just a few decades away.
Take the earth. It intercepts 0.75 * π * (6 * 106)2 kilowatts from the sun, and with an albedo of 0.3 reflects 30%. That's around 25,000 Terawatts if you work it out. If you can detect that from light years out, you have your spectrum and you know someone's at home.
By comparison, the Arecibo telescope in its radar mode emits 1 Megawatt (I know it's collimated and coherent). Still, if you're sufficient light years away and you can detect Arecibo I reckon you can also detect earth's spectrum. Add us to the list.
So I still think it's a bad idea to holler to those aliens out there: it's capabilities not intentions that you have to worry about. But until we start using Exawatt lasers I agree it just doesn't matter.
Tuesday, December 28, 2010
Review: "Before I Go To Sleep" by S. J. Watson
This is an Amazon Vine review.
Christine Lucas wakes up each morning believing she is a young woman. So who is this middle-aged man sleeping next to her? And why, when she looks in the mirror, does she see the lines, sags and wrinkles of a 47 year old?
Whatever Christine learns during the day, when she sleeps it will all be erased. Every morning is the same: reset.
She asks questions and is told narratives: about herself, her past, her accident. She was run over; she has a special kind of amnesia; she was a writer. But what she hears from her doctor and her husband don’t cohere - one or both of them are lying. She starts to keep a journal, building multiple explanations for her predicament. Each diverse account makes sense but none of them are grounded. In all the narratives she appears to be safe, so why does she feel so terrified?
This is an extraordinary book by Steven Watson. Written from Christine’s point of view, the level of suspense cranks up in the first few pages and never subsequently abates. It’s that rare thing, a genuine page-turner and one with endless surprises.
The plotting has a family resemblance to the Christopher Nolan film Memento (2000) but the storyline diverges. It kept me completely engrossed and I strongly recommend it. My mother, aged 87, read it over Christmas and could not tear herself away: it clearly appeals to multiple demographics!
A final point: Christine Lucas’s point of view is so authentically sustained that I was sure “S. J. Watson” was a female author. Mr Watson thereby exhibits his profound insight in addition to the other virtues of this excellent first novel.
Christine Lucas wakes up each morning believing she is a young woman. So who is this middle-aged man sleeping next to her? And why, when she looks in the mirror, does she see the lines, sags and wrinkles of a 47 year old?
Whatever Christine learns during the day, when she sleeps it will all be erased. Every morning is the same: reset.
She asks questions and is told narratives: about herself, her past, her accident. She was run over; she has a special kind of amnesia; she was a writer. But what she hears from her doctor and her husband don’t cohere - one or both of them are lying. She starts to keep a journal, building multiple explanations for her predicament. Each diverse account makes sense but none of them are grounded. In all the narratives she appears to be safe, so why does she feel so terrified?
This is an extraordinary book by Steven Watson. Written from Christine’s point of view, the level of suspense cranks up in the first few pages and never subsequently abates. It’s that rare thing, a genuine page-turner and one with endless surprises.
The plotting has a family resemblance to the Christopher Nolan film Memento (2000) but the storyline diverges. It kept me completely engrossed and I strongly recommend it. My mother, aged 87, read it over Christmas and could not tear herself away: it clearly appeals to multiple demographics!
A final point: Christine Lucas’s point of view is so authentically sustained that I was sure “S. J. Watson” was a female author. Mr Watson thereby exhibits his profound insight in addition to the other virtues of this excellent first novel.
Saturday, December 25, 2010
Pix: Christmas lunch
Some pictures from lunchtime today. We had Internet radio from Kamloops running on the PC to remind us of Adrian over in Sun Peaks, Canada (where it was 6 a.m.).
Alex, Clare, Beryl at lunch
Beryl Seel
Alex with the contents of his cracker
Nigel Seel
Beryl and Nigel
Blinded by the light
Christmas Eve, 11.30 p.m. and we're preparing for bed when there's a flash and all the lights go out. Clare and I sit in the living room, faces bathed in residual candlelight and try to absorb it. Has the main fuse gone?
I walk to the window and pull the blinds aside: an icy vista lit by moonlight. OK, it's everyone then. In the distance, I hear the sound of house alarms. Then I realise, my mother is up in her room: 87 years old, in a strange house, in complete darkness. I race to the kitchen and in the gloom retrieve the torch. Now more surefootedly I go up the stairs and knock on her door and enter. She is trying to escape and is in the process of exiting via the wardrobe.
Alex rushes around trying to find further illumination; he unearths a camping light and we all go to bed.
At 12.30 a.m. I am awaked by the interrogator's glare in the face. Groggily I figure it; the power has been restored and we left the bedroom light on. I hear Alex returning from downstairs where he has switched off other lights. I go down myself to check all is well, not fogetting the cat who now has his heated cat-basket restored to use: it's chilly out there.
This morning, Christmas Day, it's bright and clear. Here's a beautiful picture of the sun rising over Wells Cathedral.
I walk to the window and pull the blinds aside: an icy vista lit by moonlight. OK, it's everyone then. In the distance, I hear the sound of house alarms. Then I realise, my mother is up in her room: 87 years old, in a strange house, in complete darkness. I race to the kitchen and in the gloom retrieve the torch. Now more surefootedly I go up the stairs and knock on her door and enter. She is trying to escape and is in the process of exiting via the wardrobe.
Alex rushes around trying to find further illumination; he unearths a camping light and we all go to bed.
At 12.30 a.m. I am awaked by the interrogator's glare in the face. Groggily I figure it; the power has been restored and we left the bedroom light on. I hear Alex returning from downstairs where he has switched off other lights. I go down myself to check all is well, not fogetting the cat who now has his heated cat-basket restored to use: it's chilly out there.
This morning, Christmas Day, it's bright and clear. Here's a beautiful picture of the sun rising over Wells Cathedral.
Thursday, December 23, 2010
Wells Cathedral Carol Service
We walked on the road, mostly. The pavement was a skating rink, a thin film of water spread onto compacted black ice. I said to Clare: if you fall try to crumple and relax otherwise you'll surely break a leg.
Thankfully we were let straight into the Cathedral. If we had had to queue there would have been frozen corpses on the Cathedral Green - snowfield that it now is, -8° plus wind-chill.
Thankfully we were let straight into the Cathedral. If we had had to queue there would have been frozen corpses on the Cathedral Green - snowfield that it now is, -8° plus wind-chill.
A reading at the Carol Service, Wells Cathedral
The Cathedral choir sing very beautifully (they've just won an award as "the best choir in the world"!). At the beginning and end of the hour-long service they paraded along the aisles, fronted by tall, bulky, impassive men wearing secret-police robes with the inscrutable air of secret vices. I must confess I find men in frocks incanting nursery rhyme nonsense deeply creepy: what are they really in it for?
The altar showing scissors arches, Wells Cathedral
The architecture here was, I believe, deeply innovative in its mediaeval day, preventing the walls imploding under the weight of the superstructure.
The Higgs Particle
In 2008 I was at the Open University’s Quantum Mechanics (QM) Summer School. Over coffee I confided to one of the tutors that I was pleased I would be completing the course just in time for new science from the Large Hadron Collider (LHC). This was of course before the accident with the liquid helium which set things back by a year.
The tutor rubbed his chin sagely, trying to think of any overlap between what is covered in a first course in QM and what the LHC was all about. He failed.
This note is the shortest possible explanation of what extra you need to know to understand the main professed objective of the LHC, namely to find and determine the properties of the Higgs boson ...
[Note: the text has been superceded by an improved version here.]
The tutor rubbed his chin sagely, trying to think of any overlap between what is covered in a first course in QM and what the LHC was all about. He failed.
This note is the shortest possible explanation of what extra you need to know to understand the main professed objective of the LHC, namely to find and determine the properties of the Higgs boson ...
[Note: the text has been superceded by an improved version here.]
Sunday, December 19, 2010
A vole in winter
My mother said on the phone it was sad that we shut the cat in the kitchen overnight. "Poor little freezing thing, it's not as if there were any voles left."
Good point. I said to Clare: "All the voles have either died off or they're buried under a foot of snow. We haven't seen a vole in weeks. You know the cat hates the snow and only goes out when he must. I reckon it would be OK to let him relax overnight in the comfort of the living room, don't you think?"
Clare would have none of it. "We know he goes out at night, we've seen the paw-prints. So we'd have to leave the kitchen door open and then we'd all be frozen in the morning."
So Shadow was duly exiled to the kitchen last night. Lunchtime I was summoned by a shriek from the cooking zone: the vole was scampering along one wall, behind the computer. It was lively and hard to catch: Clare has put cunning obstacles at skirting board level to prevent little rodents from vanishing behind the sink, freezer, refrigerator, tumble-dryer so we never quite lost sight of the varmint.
Finally it was herded to the French windows and out into the snow. At vole-scale the back garden is like those hilly things skiers bounce over (moguls!) and the poor little mite threw itself over the snow-humps like an infantryman fleeing under fire: it made it to the bushes.
I believe it was -8° last night and it's been below zero all day. At these temperatures the very walls suck heat from your body like the cold of outer space.
Good point. I said to Clare: "All the voles have either died off or they're buried under a foot of snow. We haven't seen a vole in weeks. You know the cat hates the snow and only goes out when he must. I reckon it would be OK to let him relax overnight in the comfort of the living room, don't you think?"
Clare would have none of it. "We know he goes out at night, we've seen the paw-prints. So we'd have to leave the kitchen door open and then we'd all be frozen in the morning."
So Shadow was duly exiled to the kitchen last night. Lunchtime I was summoned by a shriek from the cooking zone: the vole was scampering along one wall, behind the computer. It was lively and hard to catch: Clare has put cunning obstacles at skirting board level to prevent little rodents from vanishing behind the sink, freezer, refrigerator, tumble-dryer so we never quite lost sight of the varmint.
Finally it was herded to the French windows and out into the snow. At vole-scale the back garden is like those hilly things skiers bounce over (moguls!) and the poor little mite threw itself over the snow-humps like an infantryman fleeing under fire: it made it to the bushes.
I believe it was -8° last night and it's been below zero all day. At these temperatures the very walls suck heat from your body like the cold of outer space.
Saturday, December 18, 2010
Catholics
Clare had decided to join the church-cleaning brigade this morning: a yearly rite before Christmas. As we had eight inches of snow last night I decided to accompany her - can't have her getting buried in a snowdrift and dying of hypothermia.
After ten minutes of tentative walking we arrived at the Catholic church. At the entrance the old Catholic priest was just leaving, helped by someone a little older than me who I learned was called Peter. The old Catholic priest, a heavy, thickset man who must be in his eighties, can barely walk and was being assisted to his electric cart (or whatever they call those things) prior to making his way home. Given the depth of snow this seemed to be a challenging prospect so I volunteered to help Peter.
We pushed this thing down Chamberlain Street like a miniature snowplough. Things took a turn for the worse as we moved into Union street, the small thoroughfare which leads down to the Library. As I pushed through the packed snow (Peter having gratefully ceded the task to me) my breathing became laboured and exhaustion began to kick-in. After 80 yards of this we both had to turn the cart and push this heavy contrivance up the driveway to the priest's house. With both of us shoving and the electric motor engaged we finally managed to manhandle him to the ramp, which was itself buried in snow. I think it was at this point that I felt incipient backstrain. Great!
Peter now returned to the church to get a spade to clear the ramp. In the spirit of lateral-thinking I meanwhile pushed the snow off the ramp with my trainers. With considerable effort I finally got the priest into his house, helped by his motor.
Now, none of this would be remarkable ... just a bit of neighbourly helping-out in the inclement weather ... except for the remarkable ingratitude and arrogance of the priest. As we turned his mobility cart towards the upward slope leading to his front door he imperiously ordered Peter and myself: "Push me up here!" A little later it was "Clear the snow off that ramp"; then, looking at me, "Push me up the ramp." No 'please', no 'thank you', not even a requestful manner. This is exactly how I imagine the aristocrats of the eighteenth century talked to their peasant serfs. But we don't talk to people like that these days, do we?
I spoke to Clare afterwards about this 'prince of the church'. "Oh yes," she explained, "all the old ones are like that."
I returned to the church where Clare was vacuuming. Afterwards, we all met up for coffee in the back room kitchen where charming Peggy and organised Pam tried to inveigle Clare into joining the Catholic Women's League ("Just once a month at two o'clock, here in the church.").
After ten minutes of tentative walking we arrived at the Catholic church. At the entrance the old Catholic priest was just leaving, helped by someone a little older than me who I learned was called Peter. The old Catholic priest, a heavy, thickset man who must be in his eighties, can barely walk and was being assisted to his electric cart (or whatever they call those things) prior to making his way home. Given the depth of snow this seemed to be a challenging prospect so I volunteered to help Peter.
We pushed this thing down Chamberlain Street like a miniature snowplough. Things took a turn for the worse as we moved into Union street, the small thoroughfare which leads down to the Library. As I pushed through the packed snow (Peter having gratefully ceded the task to me) my breathing became laboured and exhaustion began to kick-in. After 80 yards of this we both had to turn the cart and push this heavy contrivance up the driveway to the priest's house. With both of us shoving and the electric motor engaged we finally managed to manhandle him to the ramp, which was itself buried in snow. I think it was at this point that I felt incipient backstrain. Great!
Peter now returned to the church to get a spade to clear the ramp. In the spirit of lateral-thinking I meanwhile pushed the snow off the ramp with my trainers. With considerable effort I finally got the priest into his house, helped by his motor.
Now, none of this would be remarkable ... just a bit of neighbourly helping-out in the inclement weather ... except for the remarkable ingratitude and arrogance of the priest. As we turned his mobility cart towards the upward slope leading to his front door he imperiously ordered Peter and myself: "Push me up here!" A little later it was "Clear the snow off that ramp"; then, looking at me, "Push me up the ramp." No 'please', no 'thank you', not even a requestful manner. This is exactly how I imagine the aristocrats of the eighteenth century talked to their peasant serfs. But we don't talk to people like that these days, do we?
I spoke to Clare afterwards about this 'prince of the church'. "Oh yes," she explained, "all the old ones are like that."
I returned to the church where Clare was vacuuming. Afterwards, we all met up for coffee in the back room kitchen where charming Peggy and organised Pam tried to inveigle Clare into joining the Catholic Women's League ("Just once a month at two o'clock, here in the church.").
Clare and the cat hunker down
... and this is why
Returning from church...
... it's another winter wonderland for the author
A driveway in winter
Friday, December 17, 2010
A Winter Wonderland
We awoke this morning to a winter wonderland and fought our way to town through a genteel snowfall (we have no other kind in this part of the world: Christmassy, palm-sized, fluffy snowflakes floating through motionless air to earth). Still had to clear the driveway and rock-salt it though. Here are some pictures of Wells in the snow.
Back yesterday from Reading and the Pro4 Christmas dinner at the Malmaison on Wednesday evening (15th). This afternoon it's preparation for a client meeting in the new year on IL2/IL3 accreditation.
Wells Cathedral in the snow
The Market Square
Wells Cathedral with Reindeer
Back yesterday from Reading and the Pro4 Christmas dinner at the Malmaison on Wednesday evening (15th). This afternoon it's preparation for a client meeting in the new year on IL2/IL3 accreditation.
Sunday, December 12, 2010
A vision of woodliness
Not just a designer of telecoms networks; not just an amateur student of theoretical physics: no, he also sculpts in wood. How manly is that? I agree these rather mundane shelves don't totally close the deal.
On the strength of this Clare has suggested I might like to branch out into some kind of "totem pole" tree-trunk sculpture for the back garden. I have currently (in my mind) budgeted around £1,000 worth of workshop cum tools to get me started.
Shelves (obviously!)
However, the rural craft piece shown below, a chic table, surely shows an under-appreciated native genius (at least in not wasting off-cuts)?
A certain rustic charm
Let's not discuss the exposed screws; the raw woodchip ends where the contiboard was inexpertedly sawed; the inexplicable failure to glue the top to the sides before screwing; the over-enthusiastic use of the screwdriver attachment to the drill, resulting in surface fracturing in one corner (now messily glued).On the strength of this Clare has suggested I might like to branch out into some kind of "totem pole" tree-trunk sculpture for the back garden. I have currently (in my mind) budgeted around £1,000 worth of workshop cum tools to get me started.
He's at it again!
It's cold here again today and the cat has reverted to his time-worn ways.
Friday, December 10, 2010
Beryl Seel's engagement photo (c. 1947)
In Bristol today doing a number of inconsequential tasks (yet another shelf from B&Q; a supermarket sweep through the M&S Food Hall) plus some rearrangement in my mother's house from whence this rather cute picture taken on the occasion of her engagement, c. 1947.
Added later: here's another of my mother's engagement pictures. Click on it to enlarge.
Beryl Seel engagement photo (c. 1947)
Move over Catherine Middleton!Added later: here's another of my mother's engagement pictures. Click on it to enlarge.
On aiming too high
Apropos the final paragraph of my previous post - my purchase of "Cosmology" by Steven Weinberg, Roy Simpson observes:
Nigel,
The expressions are "bitten off more than you can chew" and - perhaps more appropriately - "eyes larger than stomach" (I blame the Amazon science marketing department myself who really need to know your level of expertise and interests - I have looked at the Amazon entry for the book.) The problem here is that Weinberg has already written a book:--
Gravitation and Cosmology (1972)
which introduces gravitation and applies to cosmology. [Note: costing £120!]
The 1972 book takes about 150 pages to reach Einstein's equations and about 400 pages to reach the Robinson-Walker metric with which your current book begins. So the present book is a "what happened next" - an update 35 years later. So the basics are in the 1972 book which he didn't repeat, although there is an equation summary of that book in Appendix B.
The present book is about things like inertial anisotropy (i.e. irregularities, perturbations from the symmetric Robinson-Walker metric) rather than the core theory. I suspect that this book is for experts in particular contemporary subfields to get hold of specific derivations and data rather than a "read through".
Furthermore I see that the present book (and the 1972 book too I think) are about mainstream Cosmology. This is OK for the purposes above, but if a reader wants some Cosmological excitement in their life, they may have to look elsewhere. One day, for example, in amongst all these Tensors you might learn about something called Torsion.
Torsion is a spin-like property of Tensors which is set = 0 by Einstein (so it is a little bit like the more famous Cosmological Constant Λ, also set = 0 initially). A theory was later developed as a generalisation of Einstein's equations including Torsion, but I cannot see a reference to Torsion in the Index to the 1972 book - when the theory was a live minor alternative to GR.
You can check the present book just in case he refers to it here, but studying what I can of the equations on Amazon I don't see the reference where I would expect it to be.
So I just hope that you have substantially more free bookshelf space than me!
Roy.
-
Yes, I wanted something which talked about the topology of the universe as well as the big bang and inflation. "Cosmology" does discuss all these questions, it's not so "bitty" as you imply, but at a sophisticated level. It's billed as a graduate textbook (which is where I take myself to be: beginning-graduate student) but on scanning it last night I don't think Weinberg intended it for self-study.
I intend to treat it as a target, something the other side of all that differential geometry, tensor analysis and GR. I find that quite motivational, actually.
Nigel,
The expressions are "bitten off more than you can chew" and - perhaps more appropriately - "eyes larger than stomach" (I blame the Amazon science marketing department myself who really need to know your level of expertise and interests - I have looked at the Amazon entry for the book.) The problem here is that Weinberg has already written a book:--
Gravitation and Cosmology (1972)
which introduces gravitation and applies to cosmology. [Note: costing £120!]
The 1972 book takes about 150 pages to reach Einstein's equations and about 400 pages to reach the Robinson-Walker metric with which your current book begins. So the present book is a "what happened next" - an update 35 years later. So the basics are in the 1972 book which he didn't repeat, although there is an equation summary of that book in Appendix B.
The present book is about things like inertial anisotropy (i.e. irregularities, perturbations from the symmetric Robinson-Walker metric) rather than the core theory. I suspect that this book is for experts in particular contemporary subfields to get hold of specific derivations and data rather than a "read through".
Furthermore I see that the present book (and the 1972 book too I think) are about mainstream Cosmology. This is OK for the purposes above, but if a reader wants some Cosmological excitement in their life, they may have to look elsewhere. One day, for example, in amongst all these Tensors you might learn about something called Torsion.
Torsion is a spin-like property of Tensors which is set = 0 by Einstein (so it is a little bit like the more famous Cosmological Constant Λ, also set = 0 initially). A theory was later developed as a generalisation of Einstein's equations including Torsion, but I cannot see a reference to Torsion in the Index to the 1972 book - when the theory was a live minor alternative to GR.
You can check the present book just in case he refers to it here, but studying what I can of the equations on Amazon I don't see the reference where I would expect it to be.
So I just hope that you have substantially more free bookshelf space than me!
Roy.
-
Yes, I wanted something which talked about the topology of the universe as well as the big bang and inflation. "Cosmology" does discuss all these questions, it's not so "bitty" as you imply, but at a sophisticated level. It's billed as a graduate textbook (which is where I take myself to be: beginning-graduate student) but on scanning it last night I don't think Weinberg intended it for self-study.
I intend to treat it as a target, something the other side of all that differential geometry, tensor analysis and GR. I find that quite motivational, actually.
Thursday, December 09, 2010
Bath Christmas Market
To Bath today to visit its celebrated Christmas Market. Our first port of call was the Park and Ride which we reached late morning. Despite its thousand places, it was completely full, with cars bumped up on the kerbs all around the outer perimeter. We chose a spare piece of kerb ourselves.
Transiting via M&S (purchases £90) we finally happened upon the market (pictured below) nestling beneath the flying buttresses of Bath Abbey: a shanty town of timbered shacks, the favela of Bath.
Clare confided over dinner: "The Bath Market was awfully girly, didn't you think? All those trinkets and jewelry, ceramics and posters, arts and crafts? Not a gun in sight."
Yep: no rifles, pistols or semi-automatics; no netbooks or tablets; no smartphones or SatNav. She was spot-on.
"Cosmology" by Steven Weinberg finally arrived, confirming I have seriously bitten off more than I can chew: we hit the Einstein field equations on page 4 (of 563). If only that had been on sale at Bath Christmas Market!
Transiting via M&S (purchases £90) we finally happened upon the market (pictured below) nestling beneath the flying buttresses of Bath Abbey: a shanty town of timbered shacks, the favela of Bath.
Clare confided over dinner: "The Bath Market was awfully girly, didn't you think? All those trinkets and jewelry, ceramics and posters, arts and crafts? Not a gun in sight."
Yep: no rifles, pistols or semi-automatics; no netbooks or tablets; no smartphones or SatNav. She was spot-on.
"Cosmology" by Steven Weinberg finally arrived, confirming I have seriously bitten off more than I can chew: we hit the Einstein field equations on page 4 (of 563). If only that had been on sale at Bath Christmas Market!
Wednesday, December 08, 2010
Snow on the Mendips
We took a walk this morning through Walcombe to the countryside surrounding Pen Hill. There is still snow on the top and the temperature did not exceed freezing point. We spent the early afternoon moving a pile of tree branches from the side of the house into the car and then off to the dump (two car trips). Unlike George Bush we failed to find such brush-clearing particularly relaxing, except insofar as it's a relief to have got it done.
Just finished a re-read of Iain M. Banks' "Use of Weapons" and marvelled yet again at Banks' sheer confidence as an author; his mastery of description and multi-threaded plot development. And did I mention the subtlety of his writing? Yeah, he's good, and to rub it in, it seems effortless.
I also finished "The Two Million-year-old Self" by the renowned Jungian analyst Anthony Stevens. This short book comprises essays linking Jung's thought (centred on his concepts of archetype and the collective unconscious) with more recent thinking from ethology and sociobiology. It may be the case that Jung got there first, and deserves kudos for standing firm against the "blank slate" paradigm which has trashed social science for the last hundred years. Still, there seems little interesting new research being done within the Jungian tradition per se.
The conclusion I drew was that Jung's intuitions were spot-on but only technological advances, especially in brain scanning, can be relied upon to shed more light on the underlying mind-brain conundrums.
Stevens' thoughts on the way in which modern societies violate the psychological "environment of evolutionary adaptation" are interesting and pertinent. His clinical examples are compelling enough although I suspect that agrarian societies have accomplished a little more evolution in the psychological space than he admits: we used to be hunter-gatherers but that was a while (and a fair bit of adaptation) ago.
Pen Hill with TV mast
Snow on the Mendip plateau
Clare and Nigel feeling the cold
Just finished a re-read of Iain M. Banks' "Use of Weapons" and marvelled yet again at Banks' sheer confidence as an author; his mastery of description and multi-threaded plot development. And did I mention the subtlety of his writing? Yeah, he's good, and to rub it in, it seems effortless.
I also finished "The Two Million-year-old Self" by the renowned Jungian analyst Anthony Stevens. This short book comprises essays linking Jung's thought (centred on his concepts of archetype and the collective unconscious) with more recent thinking from ethology and sociobiology. It may be the case that Jung got there first, and deserves kudos for standing firm against the "blank slate" paradigm which has trashed social science for the last hundred years. Still, there seems little interesting new research being done within the Jungian tradition per se.
The conclusion I drew was that Jung's intuitions were spot-on but only technological advances, especially in brain scanning, can be relied upon to shed more light on the underlying mind-brain conundrums.
Stevens' thoughts on the way in which modern societies violate the psychological "environment of evolutionary adaptation" are interesting and pertinent. His clinical examples are compelling enough although I suspect that agrarian societies have accomplished a little more evolution in the psychological space than he admits: we used to be hunter-gatherers but that was a while (and a fair bit of adaptation) ago.
Monday, December 06, 2010
Superfast rural broadband
The Government outlined today its plans to roll out "superfast broadband" to rural areas, which the operation of the market continue to undersupply. The obvious problem is that rural population density is low, so that long runs of cable are needed to connect to households. If that cable is copper, attenuation will be so extreme that "broadband" will in reality become narrowband - dial-up modem speeds.
The answer in principle is fibre: to, or near-to the home; but this is very expensive to deploy. An alternative is to use wireless (e.g. 3G Broadband or WiMAX) but again the cost-economics to deploy the necessary base-stations are poor: how often do we fail to get even a 2G mobile signal in rural areas?
Satellite has been mentioned but geostationary satellites are 22,000 miles up and this introduces terrible latency for interactive services such as Skype. Also, due to such distances the equipment is expensive.
So, as usual, it all comes down to cost and therefore subsidies. We are still waiting to see who gets the contract to run this programme on behalf of the Government. My name went forward in November as part of one consortium but unfortunately we were not selected.
After the weekend thaw it's become frigidly arctic again and the cat is increasingly desperate to find warm places to sleep. Mostly he lies out next to the warmest radiator he can find ...
... but walking into our bedroom this morning I was surprised to discover this under the duvet.
The answer in principle is fibre: to, or near-to the home; but this is very expensive to deploy. An alternative is to use wireless (e.g. 3G Broadband or WiMAX) but again the cost-economics to deploy the necessary base-stations are poor: how often do we fail to get even a 2G mobile signal in rural areas?
Satellite has been mentioned but geostationary satellites are 22,000 miles up and this introduces terrible latency for interactive services such as Skype. Also, due to such distances the equipment is expensive.
So, as usual, it all comes down to cost and therefore subsidies. We are still waiting to see who gets the contract to run this programme on behalf of the Government. My name went forward in November as part of one consortium but unfortunately we were not selected.
After the weekend thaw it's become frigidly arctic again and the cat is increasingly desperate to find warm places to sleep. Mostly he lies out next to the warmest radiator he can find ...
... but walking into our bedroom this morning I was surprised to discover this under the duvet.
Saturday, December 04, 2010
Feels warmer
Fourier's law for heat conduction says that if:
- ΔQ/Δt is the rate of heat loss by the house (in watts);
- k is the average heat conductivity of the house (in watts per metre per °K);
- A is the surface area of the house (square metres);
- ΔT is the difference between the inside and outside temperatures (°K = °C);
- Δx is the average width of the walls in metres;
then ΔQ/Δt = -kA ΔT/Δx.
Wrapping k, A and Δx into one constant c we have
ΔQ/Δt = c ΔT.
We tend to keep our house a toasting-warm 23°. When it was absolutely freezing a couple of days ago it was -5° outside giving a ΔT of 28°. Today, however, it's a balmy 2° outside giving a ΔT of 21°.
The ratio of (heat-lossfreezing)/(heat-lossbalmy) is therefore 28/21 = 4/3.
So to keep the house the same temperature, we're using 25% less power today. No wonder we had to turn the heating down.
- ΔQ/Δt is the rate of heat loss by the house (in watts);
- k is the average heat conductivity of the house (in watts per metre per °K);
- A is the surface area of the house (square metres);
- ΔT is the difference between the inside and outside temperatures (°K = °C);
- Δx is the average width of the walls in metres;
then ΔQ/Δt = -kA ΔT/Δx.
Wrapping k, A and Δx into one constant c we have
ΔQ/Δt = c ΔT.
We tend to keep our house a toasting-warm 23°. When it was absolutely freezing a couple of days ago it was -5° outside giving a ΔT of 28°. Today, however, it's a balmy 2° outside giving a ΔT of 21°.
The ratio of (heat-lossfreezing)/(heat-lossbalmy) is therefore 28/21 = 4/3.
So to keep the house the same temperature, we're using 25% less power today. No wonder we had to turn the heating down.
Friday, December 03, 2010
The electric cat
When Alex bought an electric cat-basket for Shadow how we laughed! Well, we're not laughing now.
Shadow has turned into a hibernating creature, curled up in his basket day and night, basking in the electric heat from its base. Occasionally he'll pop out for a snack or to have his ears rubbed or back scratched.
Back in the Egyptian neolithic, 12,000 years ago, the cats had a discussion with their cat-deity: "Shall we stay wild or shall we pretend to give up our independence and throw in our lot with the humans?" they asked. As Shadow peers through the double-glazing at the birds, shivering on their frozen branches, he silently concurs with the way that turned out.
Shadow has turned into a hibernating creature, curled up in his basket day and night, basking in the electric heat from its base. Occasionally he'll pop out for a snack or to have his ears rubbed or back scratched.Back in the Egyptian neolithic, 12,000 years ago, the cats had a discussion with their cat-deity: "Shall we stay wild or shall we pretend to give up our independence and throw in our lot with the humans?" they asked. As Shadow peers through the double-glazing at the birds, shivering on their frozen branches, he silently concurs with the way that turned out.
Review "May 1812" by M. M. Bennetts
This Amazon Vine review is of the novel "May 1812" by M. M. Bennetts and was written by Clare.
A surfeit of romance and soft furnishings: not much decryption [2 stars]
It is a cliché that a book should not be judged by its cover, but the blurb on the back did whet my appetite with the prospect of a historical thriller involving decryption and high-level intelligence operations. However, this novel sheds the light on code-breaking that “Lady Chatterley’s Lover” lavishes on game-keeping; it would rather sit comfortably alongside the Mills and Boon catalogue in content, but might well be rejected on grounds of style.
It’s an overly long telling of a highly implausible love story. The beautiful and handsome couple are beset with misunderstandings and, in the case of the hero, the demands of work (French translation with a smidgeon of code-breaking). The heroine is a perfect, long-suffering and accomplished eighteen year old whose response to neglect and character-assassination at the hands of her husband’s set is to cry and cry, whilst her husband is an emotional child. The tears came so thick and fast in the second part of the story that I felt that the author had been set a challenge to beat some record for their inclusion and was indulging him or herself at the reader’s expense.
In its favour the portrayal of Georgian society in London is credible and entertaining and a counterpoint to the country life portrayed in Jane Austen’s novels. Indeed, this book would perhaps find a place on the shelves of some latter day Catherine Morland (Northanger Abbey).
A surfeit of romance and soft furnishings: not much decryption [2 stars]
It is a cliché that a book should not be judged by its cover, but the blurb on the back did whet my appetite with the prospect of a historical thriller involving decryption and high-level intelligence operations. However, this novel sheds the light on code-breaking that “Lady Chatterley’s Lover” lavishes on game-keeping; it would rather sit comfortably alongside the Mills and Boon catalogue in content, but might well be rejected on grounds of style.
It’s an overly long telling of a highly implausible love story. The beautiful and handsome couple are beset with misunderstandings and, in the case of the hero, the demands of work (French translation with a smidgeon of code-breaking). The heroine is a perfect, long-suffering and accomplished eighteen year old whose response to neglect and character-assassination at the hands of her husband’s set is to cry and cry, whilst her husband is an emotional child. The tears came so thick and fast in the second part of the story that I felt that the author had been set a challenge to beat some record for their inclusion and was indulging him or herself at the reader’s expense.
In its favour the portrayal of Georgian society in London is credible and entertaining and a counterpoint to the country life portrayed in Jane Austen’s novels. Indeed, this book would perhaps find a place on the shelves of some latter day Catherine Morland (Northanger Abbey).
Thursday, December 02, 2010
Why I am not a plumber
A covering of snow last night and a chance to check our loft insulation (below). Compared to some of the other houses, our roof appears happily snow-clad.
Our roof from the south
Our roof from the north
The driveway
I don't have to drive out today. If I did I'd be leaving a trail of ice on the rather steep driveway. We do have some rock salt though.
Drips in the kitchen
Yesterday lunchtime Clare notice rivulets of water running down the kitchen wall by the back door (above). After poking around a bit I came up with an ingenious theory concerning boiler overflows (the boiler is directly above in the back bedroom) and frozen, bursting outlets (below).
Of course we called the builder.
The culprit?
Pete Hutchinson (PAC Construction) came late in the afternoon and investigated. Turns out the problem is with a stuck air-pressure relief valve in the boiler cupboard: nothing whatsoever to do with the cold weather.
Tuesday, November 30, 2010
Snow in Wells
Just a couple of pictures taken from the front bedroom.
By this afternoon when we strolled into town the snow was gone.
By this afternoon when we strolled into town the snow was gone.
Two emails
This morning, as drifting powder snow made Wells a winter wonderland I found two emails waiting for me.
The first was from D. O. Dodd, the author of the novel "Jew" which I reviewed yesterday. Here is what he had to say, together with my reply.
---
"Nigel Seel:
Thank you for the highly perceptive review of my novel, JEW. It was encouraging to read a review with writing of such high calibre.
Best regards,
-D.O. Dodd "
I replied as follows.
"Yes. I was very surprised by the low quality of the reviews on Amazon. Seems like most of them hadn't actually read the book carefully, let alone engaged with it. None of them appeared to approach understanding.
It's quite dispiriting when you have spent months applying all your thinking and intelligence into a creative work only to have it received with indifference and intellectual shoddiness. What you're doing here is what writers ought to do: engage with universal issues, challenge received shibboleths and do so with art.
I hope your novel gets the wider audience it deserves and has the impact you intended. If so, it's bound to be controversial so I wish you strength with that. "
***
Moving from writing about atrocities to the real thing. Clare makes a small financial contribution to a Catholic Creche in Brazil run by a Father Murphy (in the tradition of Irish missionary priests). Here is what he wrote in his email this morning.
"Hello Creche sponsors,
Carlos Andre Pereira Barros and his brother Carlos Alexandre were both reared at the Creche beginning around 1981, both leaving in the mid-nineties. Carlos Alexandre has a daughter, Carla in the Creche while he lives by selling fruit or flannel towels at the busy road intersections around here.
Carlos Andre had a job with a nearby big car agency, Fiori, which deals in Fiats until last Friday when he was dismissed and paid-off with a lump sum. He had been living with his mother till about a fortnight ago when he decided to rent a place for himself and a male companion on the far outskirts of Reciffe.
That night his place was broken into and he was cruelly killed: his eyes were gouged out and they put one in the sink, the other in the toilet bowl. Only three days later was his disappearance discovered when his companion returned from a visit to the hinterland to his family.
Perhaps his sexual orientation contributed to his being so cruelly killed. May his soul rest in peace.
Frank Murphy (Fr)"
The first was from D. O. Dodd, the author of the novel "Jew" which I reviewed yesterday. Here is what he had to say, together with my reply.
---
"Nigel Seel:
Thank you for the highly perceptive review of my novel, JEW. It was encouraging to read a review with writing of such high calibre.
Best regards,
-D.O. Dodd "
I replied as follows.
"Yes. I was very surprised by the low quality of the reviews on Amazon. Seems like most of them hadn't actually read the book carefully, let alone engaged with it. None of them appeared to approach understanding.
It's quite dispiriting when you have spent months applying all your thinking and intelligence into a creative work only to have it received with indifference and intellectual shoddiness. What you're doing here is what writers ought to do: engage with universal issues, challenge received shibboleths and do so with art.
I hope your novel gets the wider audience it deserves and has the impact you intended. If so, it's bound to be controversial so I wish you strength with that. "
***
Moving from writing about atrocities to the real thing. Clare makes a small financial contribution to a Catholic Creche in Brazil run by a Father Murphy (in the tradition of Irish missionary priests). Here is what he wrote in his email this morning.
"Hello Creche sponsors,
Carlos Andre Pereira Barros and his brother Carlos Alexandre were both reared at the Creche beginning around 1981, both leaving in the mid-nineties. Carlos Alexandre has a daughter, Carla in the Creche while he lives by selling fruit or flannel towels at the busy road intersections around here.
Carlos Andre had a job with a nearby big car agency, Fiori, which deals in Fiats until last Friday when he was dismissed and paid-off with a lump sum. He had been living with his mother till about a fortnight ago when he decided to rent a place for himself and a male companion on the far outskirts of Reciffe.
That night his place was broken into and he was cruelly killed: his eyes were gouged out and they put one in the sink, the other in the toilet bowl. Only three days later was his disappearance discovered when his companion returned from a visit to the hinterland to his family.
Perhaps his sexual orientation contributed to his being so cruelly killed. May his soul rest in peace.
Frank Murphy (Fr)"
Monday, November 29, 2010
Review: "Jew" by D. O. Dodd
This is an Amazon Vine review of "Jew" by D. O. Dodd.
---
This novel seems to have acquired the reputation of atrocity-porn. Not too surprising as the protagonist (it seems quite inappropriate to call him the hero) comes to consciousness naked in a heaped pile of dead bodies. He escapes, and lethally disposing of an officer in a nearby hut, he dumps the body onto the heap, steals his uniform and car and makes for the nearest town. Trauma has wiped his memories: he has no idea who or where he is.
In town he wanders into a coffee-house to the consternation of the clientele – is this a case of mistaken identity? The occupying soldiers soon steer him to his role as commanding officer where he is soon acquiescing in the most brutal atrocities. Thankfully we are spared the most explicit descriptions.
The new commander, as he now is, orders the original heap of bodies to be brought into town. In an eerie recapitulation sequence a naked man crawls out and is promptly captured. Yet the prisoner insists he is the real commander.
The war is now going the wrong way, the occupiers are forced to withdraw and there is a confrontation, followed by an final ironic change of allegiance.
“Jew” is a puzzle wrapped in an enigma. First the puzzle. It becomes clear during the course of the narrative that this is a religious war. Somehow the Jews and the Muslims are involved. But who are the occupiers and who are the occupied? To which faith or ethnic group does the protagonist (the new commander) belong and to which the prisoner who claims to be the real commander?
The writing is deliberately obscure and clues are scattered but it is essential for the reader to get this straight. It helps to know that a Mu’min is an Arab Islamic term meaning a true believer in Islam (p. 134) and that Elohim is the Hebrew term for God (p. 132); to recall the mistaken identity previously alluded to (pp. 29-30); and to realise that the Coalition forces which enter the scene at the end are retreating, not advancing. Anyway, no spoilers here – spend the time and work it out.
The enigma is to fathom what on earth the author is getting at – after all, we already know that soldiers engaged in inter-faith and/or inter-ethnic disputes can behave with unparalleled viciousness. The writing is beautifully allusive conveying a dreamlike quality focusing on the main character’s lack of affect. Motives are never clear, the protagonist seems to be a detached observer of his own actions and of those around him, events which are often deeply symbolic but whose meaning remains elusive. The reader is forced to the conclusion that in the bleak reality of this novel, all honourable courses lead to death and all survival strategies require multi-layered betrayal.
---
This novel seems to have acquired the reputation of atrocity-porn. Not too surprising as the protagonist (it seems quite inappropriate to call him the hero) comes to consciousness naked in a heaped pile of dead bodies. He escapes, and lethally disposing of an officer in a nearby hut, he dumps the body onto the heap, steals his uniform and car and makes for the nearest town. Trauma has wiped his memories: he has no idea who or where he is.
In town he wanders into a coffee-house to the consternation of the clientele – is this a case of mistaken identity? The occupying soldiers soon steer him to his role as commanding officer where he is soon acquiescing in the most brutal atrocities. Thankfully we are spared the most explicit descriptions.
The new commander, as he now is, orders the original heap of bodies to be brought into town. In an eerie recapitulation sequence a naked man crawls out and is promptly captured. Yet the prisoner insists he is the real commander.
The war is now going the wrong way, the occupiers are forced to withdraw and there is a confrontation, followed by an final ironic change of allegiance.
“Jew” is a puzzle wrapped in an enigma. First the puzzle. It becomes clear during the course of the narrative that this is a religious war. Somehow the Jews and the Muslims are involved. But who are the occupiers and who are the occupied? To which faith or ethnic group does the protagonist (the new commander) belong and to which the prisoner who claims to be the real commander?
The writing is deliberately obscure and clues are scattered but it is essential for the reader to get this straight. It helps to know that a Mu’min is an Arab Islamic term meaning a true believer in Islam (p. 134) and that Elohim is the Hebrew term for God (p. 132); to recall the mistaken identity previously alluded to (pp. 29-30); and to realise that the Coalition forces which enter the scene at the end are retreating, not advancing. Anyway, no spoilers here – spend the time and work it out.
The enigma is to fathom what on earth the author is getting at – after all, we already know that soldiers engaged in inter-faith and/or inter-ethnic disputes can behave with unparalleled viciousness. The writing is beautifully allusive conveying a dreamlike quality focusing on the main character’s lack of affect. Motives are never clear, the protagonist seems to be a detached observer of his own actions and of those around him, events which are often deeply symbolic but whose meaning remains elusive. The reader is forced to the conclusion that in the bleak reality of this novel, all honourable courses lead to death and all survival strategies require multi-layered betrayal.
Sunday, November 28, 2010
Christmas Oratorio - J S Bach
Wrapped up like a spaceman against the searing cold, I was fifteen minutes early for Bach's Christmas Oratorio at St. Cuthbert's, Wells last night. Just as well - I got a front seat.
The Oratorio comprises six cantatas, of which four were played last night. The orchestra and Beaumont singers (below) were excellent, despite having to perform in the unheated church.
Highpoints: the violins swooping and gliding over the cello and double-bass; Cressida Nash on cello who never seemed to stop working; the astonishingly high and pure voice of countertenor Simon Clulow.
After the interval a smartly-bearded, black-tied man addressed us from the pulpit.
"Cheapskates! Pennypinchers! Oh you who would cut all funding to the arts!
"No, not you ladies and gentlemen. The sentiments of Johann Sebastian Bach addressing Leipzig Council as they further reduced the stipends available to pay university students to fill in the vacancies in the church orchestras."
The man then read a ten-page memo written in 1730 in which Bach itemises the poor quality of the singers and instrumentalists at his disposal (naming names!), his lack of funds and his resentment at the incessant sniping he's receiving from the Council. All good knockabout stuff, typical of the man and eerily presaging contemporary concerns.
And then it was back to Cantata III and the glittering roller-coaster of baroque counterpoint.
The Oratorio comprises six cantatas, of which four were played last night. The orchestra and Beaumont singers (below) were excellent, despite having to perform in the unheated church.
Highpoints: the violins swooping and gliding over the cello and double-bass; Cressida Nash on cello who never seemed to stop working; the astonishingly high and pure voice of countertenor Simon Clulow.
After the interval a smartly-bearded, black-tied man addressed us from the pulpit.
"Cheapskates! Pennypinchers! Oh you who would cut all funding to the arts!
"No, not you ladies and gentlemen. The sentiments of Johann Sebastian Bach addressing Leipzig Council as they further reduced the stipends available to pay university students to fill in the vacancies in the church orchestras."
The man then read a ten-page memo written in 1730 in which Bach itemises the poor quality of the singers and instrumentalists at his disposal (naming names!), his lack of funds and his resentment at the incessant sniping he's receiving from the Council. All good knockabout stuff, typical of the man and eerily presaging contemporary concerns.
And then it was back to Cantata III and the glittering roller-coaster of baroque counterpoint.
Dynamics of Personality Type
This is a "problem-solving" review of Linda Berens' self-study booklet "Dynamics of Personality Type". To view all diagrams below full-size, click on them: preferably open them with a right-click in a new tab so as not to lose the text.
By way of introduction, many people first learn about their Myers-Briggs "type indicator" (MBTI) through taking a 'personality assessment' and getting a code: example, my MBTI is INTP.
There is a "boxy" way of understanding this. Psychological type defines a four-dimensional personality space and each type is a vector within it. If you proceed in this manner you get a good correlation with academic psychology's "Big-5" five-factor model (FFM) and it's common to hear that the MBTI is the FFM without the "Emotional-Stability -- Neuroticism" dimension.
But to view psychological type like this is to take the snapshot when you could be getting the movie. In the Jungian view, personality is about the active interplay of psychological functions or processes. Jung and Myers talked about the Dominant, Auxiliary, Tertiary and Inferior hierarchy of processes (each of which could appear as introverted or extraverted).
Subsequently Beebe, and later Berens, proposed extending the model with explicit consideration of subconscious processes (itemised as 5th, 6th, 7th and 8th). The priority-ranking of the processes for an INTP are shown below: only the 1st to the 4th are conscious.
So what does this mean? My dominant function is Ti which means an orientation to theorising, modelling, looking for patterns, spotting inconsistencies. You don't see this because it's interiorised, introverted, but ask yourself: why else am I writing this stuff?
The Ne is extraverted iNtuition which you do see ... as the generation of creative new ideas in response to here-and-now stuff: present situation, conversation etc.
The tertiary Si is introverted Sensation, corresponding to memories, past experiences and stored knowledge. This is less central in driving my interior life but forms a backcloth to the Thinking function. Again, you don't see it directly.
The Fe is extraverted Feeling which you do see: a kind of rather unsophisticated cameraderie used in engaging with others. Let's not short-change myself here: there is a certain amount of warmth but it's subservient to stronger internal masters.
So what this amounts to is that the interior Ti provides the hidden core of my personality-processes, backed up with Si, while the external public form or wrapping is provided by an ideas-oriented, affable persona NeFe.
There, that wasn't so hard, was it?
The functions 5-8, my conscious orientations operating in their non-preferred way, are both weak in influence and unconscious.They are collectively called "the Shadow" and might manifest themselves in my behaviour if I lost control of myself. People might say things like "He behaved totally out of character," and it's a possible defence in a court of law (let's hope it never comes to that).
If you know your own Myers-Briggs type you can read your process hierarchy above (click on the image to make it larger). If you don't know it yet, discover your type by taking the assessment here.
Here is a more structured description of what the process-letters mean, first for Perceiving functions ...
... and here for Judging functions.
Now Beren's analysis starts to get really interesting as she considers communication and relationships between types. When any type meets their type-counterpart - someone else of the same type - then all their cognitive preferences are aligned. They often become friends because communication seems so natural.
So for example, in the diagram above, when an INTP meets another INTP they have a shared interior life of systems building and theorising. They both delight in the generation of ideas and the exploration of consequences, and they both share a general affability. The arrows go across horizontally.
They may enjoy a chat but do they care much about each other as people? No, not much. That Fe function is the inferior function and is not much of a driver in the psyche.
INTP with INFP: these two types are close to my heart as Clare is INFP. Her dominant process is Fi which in plain English describes a drive for positive ethical outcomes, harmony and spirituality.
Note where that is in my list! And note where Ti is in hers!
So the model predicts that we have common ground in ideas, concepts and shared experiences. But if my logical analysis and her moral values come into conflict we're never going to resolve things. And neither of us is much driven by Se which you can read as either a lack of concern for the minutiae of the world around us, or as no common sense whatsoever. In the conversational domain, Se equates to smalltalk and we both conspicuously lack that.
Here's a relationship where meaningful communication is "interesting". I mention this because my mother is ISFP. The combination of SeFi, the latter dominant and introverted can be glossed as a strong orientation to moral values wrapped up in a common-sense reference system, robustly delivered (inferior Te): not however very susceptible to analytic disputation.
Of course, with Linda Berens' instruction you can do this with your own relationships and those of others. Above is my diagram for ISTJ - ISFP, only showing those interactions where both parties are using their conscious processes (there are some more lines you can draw but if an arrow lands on one party's subconscious process communication is very difficult). My late father was ISTJ so it's an interesting exercise to translate this diagram into plain English.
To read more about Myers-Briggs Type Theory and brain architecture click here.
By way of introduction, many people first learn about their Myers-Briggs "type indicator" (MBTI) through taking a 'personality assessment' and getting a code: example, my MBTI is INTP.
There is a "boxy" way of understanding this. Psychological type defines a four-dimensional personality space and each type is a vector within it. If you proceed in this manner you get a good correlation with academic psychology's "Big-5" five-factor model (FFM) and it's common to hear that the MBTI is the FFM without the "Emotional-Stability -- Neuroticism" dimension.
But to view psychological type like this is to take the snapshot when you could be getting the movie. In the Jungian view, personality is about the active interplay of psychological functions or processes. Jung and Myers talked about the Dominant, Auxiliary, Tertiary and Inferior hierarchy of processes (each of which could appear as introverted or extraverted).
Subsequently Beebe, and later Berens, proposed extending the model with explicit consideration of subconscious processes (itemised as 5th, 6th, 7th and 8th). The priority-ranking of the processes for an INTP are shown below: only the 1st to the 4th are conscious.
The eight functions for an INTP
So what does this mean? My dominant function is Ti which means an orientation to theorising, modelling, looking for patterns, spotting inconsistencies. You don't see this because it's interiorised, introverted, but ask yourself: why else am I writing this stuff?
The Ne is extraverted iNtuition which you do see ... as the generation of creative new ideas in response to here-and-now stuff: present situation, conversation etc.
The tertiary Si is introverted Sensation, corresponding to memories, past experiences and stored knowledge. This is less central in driving my interior life but forms a backcloth to the Thinking function. Again, you don't see it directly.
The Fe is extraverted Feeling which you do see: a kind of rather unsophisticated cameraderie used in engaging with others. Let's not short-change myself here: there is a certain amount of warmth but it's subservient to stronger internal masters.
So what this amounts to is that the interior Ti provides the hidden core of my personality-processes, backed up with Si, while the external public form or wrapping is provided by an ideas-oriented, affable persona NeFe.
There, that wasn't so hard, was it?
The functions 5-8, my conscious orientations operating in their non-preferred way, are both weak in influence and unconscious.They are collectively called "the Shadow" and might manifest themselves in my behaviour if I lost control of myself. People might say things like "He behaved totally out of character," and it's a possible defence in a court of law (let's hope it never comes to that).
The prioritised functions for the 16 types
If you know your own Myers-Briggs type you can read your process hierarchy above (click on the image to make it larger). If you don't know it yet, discover your type by taking the assessment here.
Description of the Perceiving processes
Here is a more structured description of what the process-letters mean, first for Perceiving functions ...
Description of the Judging processes
... and here for Judging functions.
INTP talks to INTP
Now Beren's analysis starts to get really interesting as she considers communication and relationships between types. When any type meets their type-counterpart - someone else of the same type - then all their cognitive preferences are aligned. They often become friends because communication seems so natural.
So for example, in the diagram above, when an INTP meets another INTP they have a shared interior life of systems building and theorising. They both delight in the generation of ideas and the exploration of consequences, and they both share a general affability. The arrows go across horizontally.
They may enjoy a chat but do they care much about each other as people? No, not much. That Fe function is the inferior function and is not much of a driver in the psyche.
INTP talks to INFP
INTP with INFP: these two types are close to my heart as Clare is INFP. Her dominant process is Fi which in plain English describes a drive for positive ethical outcomes, harmony and spirituality.
Note where that is in my list! And note where Ti is in hers!
So the model predicts that we have common ground in ideas, concepts and shared experiences. But if my logical analysis and her moral values come into conflict we're never going to resolve things. And neither of us is much driven by Se which you can read as either a lack of concern for the minutiae of the world around us, or as no common sense whatsoever. In the conversational domain, Se equates to smalltalk and we both conspicuously lack that.
INTP talks to ISFP (or not)
Here's a relationship where meaningful communication is "interesting". I mention this because my mother is ISFP. The combination of SeFi, the latter dominant and introverted can be glossed as a strong orientation to moral values wrapped up in a common-sense reference system, robustly delivered (inferior Te): not however very susceptible to analytic disputation.
ISTJ talks to ISFP
Of course, with Linda Berens' instruction you can do this with your own relationships and those of others. Above is my diagram for ISTJ - ISFP, only showing those interactions where both parties are using their conscious processes (there are some more lines you can draw but if an arrow lands on one party's subconscious process communication is very difficult). My late father was ISTJ so it's an interesting exercise to translate this diagram into plain English.
To read more about Myers-Briggs Type Theory and brain architecture click here.
Saturday, November 27, 2010
Review: The Manticore – Robertson Davies
In Fifth Business, the first volume of The Deptford Trilogy we learned the story of Boy Staunton, obnoxious youth who became the foremost tycoon in second world-war Canada before dying mysteriously in an apparent suicide.
In this second volume, The Manticore, attention shifts to his son David Staunton. The story opens in Zürich where David Staunton is starting a course of psychotherapy following the death of his father. He believes he is going mad.
As the therapy progresses we examine in detail Staunton’s relationship with his mother and step-mother, his sister Caroline, nurse Netty, schoolmaster Dunstan Ramsay (the narrator of Fifth Business), David’s first girlfriend Judy and centrally Boy Staunton himself. It rapidly becomes clear to the reader that David Staunton has been psychologically overwhelmed by his dominant father. In a classic love-hate relationship David has judged everyone else through the distorting lens of his own idolised view of his father while simultaneously trying to distance himself in his own life and career.
As the narrative advances through a recapitulation of David Staunton’s biography we see him gradually re-evaluating his relationships under the skilful hand of his therapist. In fact this book is a wonderful advertisement for the Jungian approach. In a final escapade in the Swiss mountains (in the reunited company of Dunstan Ramsay, Liesl Vitzliputzli and Magnus Eisengrim) David undergoes a symbolic “rebirthing”: we leave confident that he can progress the rest of his life developing his new-found maturity.
I am now looking forwards to the final volume, World of Wonders, where we learn more about the magician Magnus Eisengrim.
A Manticore, by the way, is a mythical being with the face of a man, the body of a lion and a stinging tail. It is the image David Staunton’s unconscious chooses for himself.
In this second volume, The Manticore, attention shifts to his son David Staunton. The story opens in Zürich where David Staunton is starting a course of psychotherapy following the death of his father. He believes he is going mad.
As the therapy progresses we examine in detail Staunton’s relationship with his mother and step-mother, his sister Caroline, nurse Netty, schoolmaster Dunstan Ramsay (the narrator of Fifth Business), David’s first girlfriend Judy and centrally Boy Staunton himself. It rapidly becomes clear to the reader that David Staunton has been psychologically overwhelmed by his dominant father. In a classic love-hate relationship David has judged everyone else through the distorting lens of his own idolised view of his father while simultaneously trying to distance himself in his own life and career.
As the narrative advances through a recapitulation of David Staunton’s biography we see him gradually re-evaluating his relationships under the skilful hand of his therapist. In fact this book is a wonderful advertisement for the Jungian approach. In a final escapade in the Swiss mountains (in the reunited company of Dunstan Ramsay, Liesl Vitzliputzli and Magnus Eisengrim) David undergoes a symbolic “rebirthing”: we leave confident that he can progress the rest of his life developing his new-found maturity.
I am now looking forwards to the final volume, World of Wonders, where we learn more about the magician Magnus Eisengrim.
A Manticore, by the way, is a mythical being with the face of a man, the body of a lion and a stinging tail. It is the image David Staunton’s unconscious chooses for himself.
Friday, November 26, 2010
Computing the weather
On 24 November 2010 19:24, Roy Simpson wrote:
I have just noticed a Met Office link on your blog (scrolling down, on the right), so I think it must have been added recently? Maybe there is now an increased interest in weather details down there in Wells? Looking at the site I would estimate that the atmospheric pressure at Wells is about 1009 right now, which is a slight low.
Maybe this link also presages some blog items on weather science: here is a quote from that site on their current Global Unified Model to get this started:
"The latest version of the atmospheric model uses non-hydrostatic dynamics with semi-Lagrangian advection and semi-implicit time stepping. It is a grid-point model with the ability to run with a rotated pole and variable horizontal grid. A number of sub-grid scale processes are represented, including convection, boundary layer turbulence, radiation, cloud, microphysics and orographic drag. It can be run as a global model, or a limited area."
I will have to explain later what this means ... unless you get there first on a Blog item ...
Roy.
-----
Sadly my knowledge of computational fluid dynamics (CFD) is just about zero so I'll have to wait for further enlightenment ... Nigel.
-----
Well I have spent some time on CFD and Numerical Weather Prediction (NWP) - and an interesting journey it is...
Firstly NWP isn’t really CFD at all. Perhaps it could be, but NWP is a slightly different discipline at the moment, as it involves modelling global weather phenomena explicitly: this gives rise to thermodynamic equations as well as fluid equations. Furthermore the Navier-Stokes equation (around which CFD is aimed) gives rise to phenomena which are local (and which would interfere with final significant global solutions). So the Navier-Stokes needs to be simplified out. In fact many phenomena need to be simplified out. A good example I found was the question of wave height prediction (in windy conditions). The wave height is really determined by the tides on a multi-hour basis, but the instantaneous values of the waves on the shore provide no clue to any theory of predicting the wave height over the day. So these "high frequency" components need to be removed from observation and theory.
You have read the book about Fry Richardson (Turbulence), who made a prediction that pressure would rise by 100 mb in 6 hrs, which was wrong because similar "high frequency" components (of pressure changes) in his calculation were irrelevant.
Anyway, down to explaining that paragraph from the Met web site (which is a very good site). So let’s introduce the fundamental issue - the grid.
The model will include a discretized grid of 3D space points plus of course a time step. Call the space distance ΔX and the time step ΔT, then we notice the following.
ΔX/ΔT has dimensions of a velocity. It turns out that this "velocity" is key to much of the validity of using the grid successfully. In particular it is necessary that any physical effect (such as the speed of sound 300 m/s) < ΔX/ΔT. This principle is known as the CFL theorem.
However CFL has the unfortunate consequence that if we have such a grid working successfully and we wish to double the resolution so that ΔX' = 1/2 ΔX, to preserve the validity of that equation (in 3 dimensions) we would need to decrease the time step by 8. This results in 8 times more computation - and so a solution has to be found to bypass the CFL theorem. More below....
Now we shall parse the Met Office NWP statement:
“The latest version of the atmospheric model uses non-hydrostatic dynamics”
Given a model atmosphere a "parcel of air" will exert pressure up and down. In hydrostatic dynamics the pressures between neighbouring parcels are equal:
Pressure(N) up = Pressure(N+1) down + gravity(N+1).
So there is no net vertical flow and the system is in equilibrium. This is the model which works for large scale objects like the global atmosphere. In fact the pressure decrease that this implies is a negative exponential of height as discovered by Laplace / Pascal.
This approximation breaks down as we approach smaller grid scales (ΔX). In particular at the 10 km level (mesoscale) convection-like effects start to appear - resulting in rising/falling air, and so to incorporate these the model needs to be non-hydrostatic.
“with semi-Lagrangian advection”
Advection is the transport of properties (like heat) along with a fluid flow (wind flow). The advection equation is a square root of the wave equation. There is a problem with solving it numerically however: that CFL condition mentioned above. So the solution has been to introduce the distinction between an explicit solution (using the grid and time-step) and an implicit solution. In an implicit solution the value of a quantity T= N+1 is a function of the solution at N and also N+1. Hence the equation is implicit and might be solvable directly as is possible with advection equations. This sort of bypasses the CFL problem which really only applies to the time step grid approach (where T’= N+1 is calculated from T = N), but at the price of a false rendering of fast moving phenomena. So the trick is to do both explicit and implicit in the same calculation hence:
“and semi-implicit time stepping.”
Semi-implicit means do the sensitive bits explicitly and directly and do the less physically important bits implicitly. This somewhat bypasses the CFL theorem and has allowed a speed up so that in most NWP systems a time-step of 2 minutes has been extended to 15 minutes.
“It is a grid-point model with the ability to run with a rotated pole”
The grid formulation is itself a large topic. The problem again is that CFL theorem and that fact that a standard latitude-longitude grid would all converge towards the North and South Poles. This results in a need to vary the ΔX parameter near the North or South Poles which then runs into the CFL theorem again. So the solution is simple: move the poles out of the way so that the earth region you are modelling has no poles and the grids are of uniform size here.
“and variable horizontal grid.”
This means that you can "zoom in" to a sub-region. So you have ΔX at 1000 km for the wider region and 10 km for the area of interest. Of course this is also needed to solve the "boundary condition" problem when modelling a region. If you just had a model for Wells area then how does the weather get into Wells? You cannot use the same micromodel for the rest of the world here (and it would be time consuming) so the ROW is modelled by these larger 1000 km cells.
”A number of sub-grid scale processes are represented, including convection, boundary layer turbulence, radiation, cloud, microphysics .”
Remember the grid size ΔX? Well the best UK model is called UK4. This means that ΔX is 4 km in that model. Good but not great. Some weather phenomena (such as cloud formations) are actually at the 1 km scale. And we want to model clouds don’t we? Until we have a 1 km model (under research at the Met Office if you check the page) we still have to account for 1 km physics. That is we cannot allow "under the radar" phenomena to affect our weather model (otherwise it would be like a telecoms company missing IP technology because it was under the radar). The under-the-radar phenomena (listed there) are called "sub-grid scale processes". They are accounted for by so called fixed parameters which adjust values in each cell to make it more "realistic" than otherwise.
“and orographic drag.”
Orographic means surface bumps like mountains and hills. So orographic drag is obviously the air friction effect of any mountains/hills in that particular cell.
“It can be run as a global model, or a limited area."
An interesting bunch of slides on NWP is
www.ral.ucar.edu/general/events/2007/part2_warner.ppt
Every major country in the world believes that their model is the best. Still the Met Office does put out a good research programme.
It is ironic that the research frontier for these models is the 1 km level at which clouds form: because Cloud technology is just where IT systems theory is at too ... and don’t ask about Grids :-)
Another question that has occurred to me is how much of this has been applied to planets like Jupiter and Venus? Global waves can be very non-intuitive with the phase velocity going in a different direction to the group velocity and so on. Apparently Europa is like that ... and maybe the Earth's core too (called inertial waves).
Roy.
I have just noticed a Met Office link on your blog (scrolling down, on the right), so I think it must have been added recently? Maybe there is now an increased interest in weather details down there in Wells? Looking at the site I would estimate that the atmospheric pressure at Wells is about 1009 right now, which is a slight low.
Maybe this link also presages some blog items on weather science: here is a quote from that site on their current Global Unified Model to get this started:
"The latest version of the atmospheric model uses non-hydrostatic dynamics with semi-Lagrangian advection and semi-implicit time stepping. It is a grid-point model with the ability to run with a rotated pole and variable horizontal grid. A number of sub-grid scale processes are represented, including convection, boundary layer turbulence, radiation, cloud, microphysics and orographic drag. It can be run as a global model, or a limited area."
I will have to explain later what this means ... unless you get there first on a Blog item ...
Roy.
-----
Sadly my knowledge of computational fluid dynamics (CFD) is just about zero so I'll have to wait for further enlightenment ... Nigel.
-----
Well I have spent some time on CFD and Numerical Weather Prediction (NWP) - and an interesting journey it is...
Firstly NWP isn’t really CFD at all. Perhaps it could be, but NWP is a slightly different discipline at the moment, as it involves modelling global weather phenomena explicitly: this gives rise to thermodynamic equations as well as fluid equations. Furthermore the Navier-Stokes equation (around which CFD is aimed) gives rise to phenomena which are local (and which would interfere with final significant global solutions). So the Navier-Stokes needs to be simplified out. In fact many phenomena need to be simplified out. A good example I found was the question of wave height prediction (in windy conditions). The wave height is really determined by the tides on a multi-hour basis, but the instantaneous values of the waves on the shore provide no clue to any theory of predicting the wave height over the day. So these "high frequency" components need to be removed from observation and theory.
You have read the book about Fry Richardson (Turbulence), who made a prediction that pressure would rise by 100 mb in 6 hrs, which was wrong because similar "high frequency" components (of pressure changes) in his calculation were irrelevant.
Anyway, down to explaining that paragraph from the Met web site (which is a very good site). So let’s introduce the fundamental issue - the grid.
The model will include a discretized grid of 3D space points plus of course a time step. Call the space distance ΔX and the time step ΔT, then we notice the following.
ΔX/ΔT has dimensions of a velocity. It turns out that this "velocity" is key to much of the validity of using the grid successfully. In particular it is necessary that any physical effect (such as the speed of sound 300 m/s) < ΔX/ΔT. This principle is known as the CFL theorem.
However CFL has the unfortunate consequence that if we have such a grid working successfully and we wish to double the resolution so that ΔX' = 1/2 ΔX, to preserve the validity of that equation (in 3 dimensions) we would need to decrease the time step by 8. This results in 8 times more computation - and so a solution has to be found to bypass the CFL theorem. More below....
Now we shall parse the Met Office NWP statement:
“The latest version of the atmospheric model uses non-hydrostatic dynamics”
Given a model atmosphere a "parcel of air" will exert pressure up and down. In hydrostatic dynamics the pressures between neighbouring parcels are equal:
Pressure(N) up = Pressure(N+1) down + gravity(N+1).
So there is no net vertical flow and the system is in equilibrium. This is the model which works for large scale objects like the global atmosphere. In fact the pressure decrease that this implies is a negative exponential of height as discovered by Laplace / Pascal.
This approximation breaks down as we approach smaller grid scales (ΔX). In particular at the 10 km level (mesoscale) convection-like effects start to appear - resulting in rising/falling air, and so to incorporate these the model needs to be non-hydrostatic.
“with semi-Lagrangian advection”
Advection is the transport of properties (like heat) along with a fluid flow (wind flow). The advection equation is a square root of the wave equation. There is a problem with solving it numerically however: that CFL condition mentioned above. So the solution has been to introduce the distinction between an explicit solution (using the grid and time-step) and an implicit solution. In an implicit solution the value of a quantity T= N+1 is a function of the solution at N and also N+1. Hence the equation is implicit and might be solvable directly as is possible with advection equations. This sort of bypasses the CFL problem which really only applies to the time step grid approach (where T’= N+1 is calculated from T = N), but at the price of a false rendering of fast moving phenomena. So the trick is to do both explicit and implicit in the same calculation hence:
“and semi-implicit time stepping.”
Semi-implicit means do the sensitive bits explicitly and directly and do the less physically important bits implicitly. This somewhat bypasses the CFL theorem and has allowed a speed up so that in most NWP systems a time-step of 2 minutes has been extended to 15 minutes.
“It is a grid-point model with the ability to run with a rotated pole”
The grid formulation is itself a large topic. The problem again is that CFL theorem and that fact that a standard latitude-longitude grid would all converge towards the North and South Poles. This results in a need to vary the ΔX parameter near the North or South Poles which then runs into the CFL theorem again. So the solution is simple: move the poles out of the way so that the earth region you are modelling has no poles and the grids are of uniform size here.
“and variable horizontal grid.”
This means that you can "zoom in" to a sub-region. So you have ΔX at 1000 km for the wider region and 10 km for the area of interest. Of course this is also needed to solve the "boundary condition" problem when modelling a region. If you just had a model for Wells area then how does the weather get into Wells? You cannot use the same micromodel for the rest of the world here (and it would be time consuming) so the ROW is modelled by these larger 1000 km cells.
”A number of sub-grid scale processes are represented, including convection, boundary layer turbulence, radiation, cloud, microphysics .”
Remember the grid size ΔX? Well the best UK model is called UK4. This means that ΔX is 4 km in that model. Good but not great. Some weather phenomena (such as cloud formations) are actually at the 1 km scale. And we want to model clouds don’t we? Until we have a 1 km model (under research at the Met Office if you check the page) we still have to account for 1 km physics. That is we cannot allow "under the radar" phenomena to affect our weather model (otherwise it would be like a telecoms company missing IP technology because it was under the radar). The under-the-radar phenomena (listed there) are called "sub-grid scale processes". They are accounted for by so called fixed parameters which adjust values in each cell to make it more "realistic" than otherwise.
“and orographic drag.”
Orographic means surface bumps like mountains and hills. So orographic drag is obviously the air friction effect of any mountains/hills in that particular cell.
“It can be run as a global model, or a limited area."
An interesting bunch of slides on NWP is
www.ral.ucar.edu/general/events/2007/part2_warner.ppt
Every major country in the world believes that their model is the best. Still the Met Office does put out a good research programme.
It is ironic that the research frontier for these models is the 1 km level at which clouds form: because Cloud technology is just where IT systems theory is at too ... and don’t ask about Grids :-)
Another question that has occurred to me is how much of this has been applied to planets like Jupiter and Venus? Global waves can be very non-intuitive with the phase velocity going in a different direction to the group velocity and so on. Apparently Europa is like that ... and maybe the Earth's core too (called inertial waves).
Roy.
Wednesday, November 24, 2010
Wearyall Hill
A walk to the top of Wearyall Hill south-west of Glastonbury this morning - before we hit Morrison's. It was a bit hazy but the views were spectacular.
Glastonbury Tor from Wearyall Hill
Looking out over the Somerset levels
Glastonbury west
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