Last night my foot hurt. Let me restate this: last night, in bed, my right foot was extraordinarily painful. My first thought was diagnosis. The entire foot was very tender but nothing about the shape felt odd: no breakages, no swelling.
I reviewed the events of the evening. I had accompanied Clare to six o'clock Saturday Mass so she could watch Andy Murray in the Australian Open final Sunday morning. I must have stepped off a curb awkwardly coming back and not noticed at the time. But God, how it hurt this Saturday night!
My mind wandered to the Spanish practice of bastinado, the beating of prisoners' feet as a form of discreet torture, leaving no marks. I had reflected in the past that maybe this didn't sound so bad, but I was learning just how many nerve endings the foot actually has, all exquisitely tuned for pain.
When I was doing research into Artificial Intelligence in the 1980s, I had read Daniel Dennett on pain. He said that if you concentrated you could make the pain go away. Fine.
So I really thought about it and sensation gradually congealed as a red-hot wire through my foot. Dennet was right: as I focused my attention the pain transformed into mere data. But as he further observed, pain is ultimately so excruciatingly tedious that you can't stay focused forever.
I normally avoid pain-killers. Don't mask the pain, I say to myself, it's your body trying to tell you something. But all my body was communicating at that moment was that I wouldn't be getting any sleep tonight. I put the bedside lamp on - ten past one a.m. - and tried to stand. The pain was shocking and I couldn't put any weight on the foot. Nothing for it, I poked Clare: "You awake?"
She was now. Clare has a bedroom pharmacy of little white tablets: I pleaded for pain-killers. A few minutes later a barely conscious wife offered me two lozenge-shaped pills which I instantly swallowed. God knows what they were, maybe vitamin pills. Within half an hour I was away with the fairies.
This morning with only the slightest twinge I strolled to the paper shop, a twenty minute round trip. What is it with feet?
+++
My three samples were duly posted off to the NHS yesterday for checking. I expect to get a letter telling me whether I have colon cancer or not around February 14th. How romantic is that?
Sunday, January 30, 2011
Thursday, January 27, 2011
Causality in Physics
I took some trouble with my own answer to the following question on Physics StackExchange. So I have copied the details here so it doesn't just get buried. However, all the answers at the question are worth a look.
___
QUESTION
"I have never seen a “causality operator” in physics. When people invoke the informal concept of causality aren’t they really talking about consistency (perhaps in a temporal context)?
For example, if you allow material object velocities > c in Special Relativity (SR) you will be able to prove that at a definite space-time location the physical state of an object is undefined (for example, a light might be shown to be both on and off). This merely shows that SR is formally inconsistent if the v <= c boundary condition is violated, doesn’t it; despite there being a narrative saying FTL travel violates causality?
Note: this is a spinoff from the question: The transactional interpretation of quantum mechanics."
---
MY ANSWER
As the originator of this question I have reviewed and learned something from all the answers posted so far. I would like to summarise my own views here.
Where did this query come from? From a question about the Transactional Interpretation of Quantum mechanics (TIQM), where said theory’s reliance upon “retrocausality” (‘causality’ backwards in time) was held to be a fatal defect. This kind of causality-argument is common in physics: we say that faster-than-light travel in SR is ruled out because it would violate causality.
Such causality arguments are conducted in what you might call the “metalanguage of physics”: technical English which supports and explains formal results. However, the arbiter in the end is the maths, so how do we interpret the notion of causality within the formalism?
Physical theories are defined by mathematical relationships between entities (observed and unobserved) usually expressed by equations (think Schrodinger, Dirac, the Lorentz transformation). If we say that event E1 “causes” event E2, several answers here suggest that the interpretation of causality in the formal theory is that: (i) if E1 is postulated to occur then the theory logically implies that E2 must occur as well; (ii) E2 is within or on the future light-cone of E1 (we say “cause precedes effect”).
However, it’s possible that condition (ii) is too stringent. While logical entailment is obviously an essential part of any formalised theory, our smuggling in of the word “future” is already an extra assumption. Our fundamental theories do not impose a specific past-future direction on the time dimension. This means that if you reverse the film, the events you see are still consistent with our fundamental theories.
Sometimes people use causality-like words in the physics metalanguage without conventional time-ordering condition (ii). For example, a possible Feynman diagram for electron-positron scattering has a narrative that an electron travelling backwards in time from the future encounters a (normal) electron, they exchange a virtual photon and continue on their way scattered. The 'cause' of the scattering event was the arrival of the future electron. Many textbooks mention this way of thinking but we don’t mind because the underlying theory gives consistent results which accord with observation. Perhaps TIQM is like this despite its narrative of retrocausation.
So my conclusion is that we have to be careful about arguments concerning a theory’s validity relying upon causation arguments couched in physics’ metalanguage. It’s not a slam-dunk. Sometimes if a theory violates conventional “cause precedes effect” causation it indicates a breakdown in the underlying mathematics, normally inconsistency. At other times a 'causation' argument is just a way of talking about the entailment of the theory in an innovative or whimsical way, and the theory is actually OK. Go look at the maths.
NOTE: there is a whole separate discussion about why, in natural language, we think so naturally in terms of cause and effect. It links to discussions about the arrow of time and why we do seem to be unhappy about running the film backwards as a valid picture of reality. That is a whole separate issue but still, I suspect, part of physics judging by the number of recent books on the subject.
___
QUESTION
"I have never seen a “causality operator” in physics. When people invoke the informal concept of causality aren’t they really talking about consistency (perhaps in a temporal context)?
For example, if you allow material object velocities > c in Special Relativity (SR) you will be able to prove that at a definite space-time location the physical state of an object is undefined (for example, a light might be shown to be both on and off). This merely shows that SR is formally inconsistent if the v <= c boundary condition is violated, doesn’t it; despite there being a narrative saying FTL travel violates causality?
Note: this is a spinoff from the question: The transactional interpretation of quantum mechanics."
---
MY ANSWER
As the originator of this question I have reviewed and learned something from all the answers posted so far. I would like to summarise my own views here.
Where did this query come from? From a question about the Transactional Interpretation of Quantum mechanics (TIQM), where said theory’s reliance upon “retrocausality” (‘causality’ backwards in time) was held to be a fatal defect. This kind of causality-argument is common in physics: we say that faster-than-light travel in SR is ruled out because it would violate causality.
Such causality arguments are conducted in what you might call the “metalanguage of physics”: technical English which supports and explains formal results. However, the arbiter in the end is the maths, so how do we interpret the notion of causality within the formalism?
Physical theories are defined by mathematical relationships between entities (observed and unobserved) usually expressed by equations (think Schrodinger, Dirac, the Lorentz transformation). If we say that event E1 “causes” event E2, several answers here suggest that the interpretation of causality in the formal theory is that: (i) if E1 is postulated to occur then the theory logically implies that E2 must occur as well; (ii) E2 is within or on the future light-cone of E1 (we say “cause precedes effect”).
However, it’s possible that condition (ii) is too stringent. While logical entailment is obviously an essential part of any formalised theory, our smuggling in of the word “future” is already an extra assumption. Our fundamental theories do not impose a specific past-future direction on the time dimension. This means that if you reverse the film, the events you see are still consistent with our fundamental theories.
Sometimes people use causality-like words in the physics metalanguage without conventional time-ordering condition (ii). For example, a possible Feynman diagram for electron-positron scattering has a narrative that an electron travelling backwards in time from the future encounters a (normal) electron, they exchange a virtual photon and continue on their way scattered. The 'cause' of the scattering event was the arrival of the future electron. Many textbooks mention this way of thinking but we don’t mind because the underlying theory gives consistent results which accord with observation. Perhaps TIQM is like this despite its narrative of retrocausation.
So my conclusion is that we have to be careful about arguments concerning a theory’s validity relying upon causation arguments couched in physics’ metalanguage. It’s not a slam-dunk. Sometimes if a theory violates conventional “cause precedes effect” causation it indicates a breakdown in the underlying mathematics, normally inconsistency. At other times a 'causation' argument is just a way of talking about the entailment of the theory in an innovative or whimsical way, and the theory is actually OK. Go look at the maths.
NOTE: there is a whole separate discussion about why, in natural language, we think so naturally in terms of cause and effect. It links to discussions about the arrow of time and why we do seem to be unhappy about running the film backwards as a valid picture of reality. That is a whole separate issue but still, I suspect, part of physics judging by the number of recent books on the subject.
Wednesday, January 26, 2011
Unable to walk (Cabot Circus)
Down to Bristol today to visit my mother and my brother, Adrian who's currently staying with her. We lunched at Cabot Circus, the new mall in the centre of town.
From the multi-storey car park there's a curious walk-way at level 3 across to the shopping concourse, pictured above. The angled walls and roof create the illusion that the floor is tilted and it's very difficult to walk straight.
As you can see from her expression (click on the picture to make it larger) my mother can't actually cross this bridge with her eyes open. As she stopped, wobbled and flailed for the handrail she whispered "Everyone thinks I'm drunk!" Adrian, also pictured, offers scant sympathy.
We came back at ground level and rejoined the car via the lift.
From the multi-storey car park there's a curious walk-way at level 3 across to the shopping concourse, pictured above. The angled walls and roof create the illusion that the floor is tilted and it's very difficult to walk straight.
As you can see from her expression (click on the picture to make it larger) my mother can't actually cross this bridge with her eyes open. As she stopped, wobbled and flailed for the handrail she whispered "Everyone thinks I'm drunk!" Adrian, also pictured, offers scant sympathy.
We came back at ground level and rejoined the car via the lift.
Tuesday, January 25, 2011
The King's Speech
Finally saw it this afternoon. I was prepared to be sceptical, after all the hype but it's a very fine experience with brilliant acting by Colin Firth as King George VI, Helena Bonham Carter as Queen Elizabeth and Geoffrey Rush as Lionel Logue (the Australian speech therapist).
It turns out that King George VI died of a coronary thrombosis, brought on by heavy smoking, in 1952 after only 15 years on the throne.
It turns out that King George VI died of a coronary thrombosis, brought on by heavy smoking, in 1952 after only 15 years on the throne.
Monday, January 24, 2011
Ed vs. Ed
What does psychological type theory tell us about the future evolution in the relationship between Ed Miliband, Leader of the Labour Party and Ed Balls, his new Shadow Chancellor?
Ed Miliband is an interesting case: he's most likely INFJ although he might score a low E. An INFJ is driven by a strong set of personal values, gives and respects loyalty and comes across as empathic and warm (extraverted F). This orientation to the human, emotional side comes at the expense of analytic skills and an interest in the logic of policies.
Ed Balls is the very picture of an ENTJ. Extraverted, intellectual and judgemental with an underdeveloped extraverted feeling (F) function (his weakest function - see here). Ed is superlative at mapping out a grand strategy and marshalling forces to accomplish it - but without much regard for casualties along the way, collateral or otherwise.
As a male-female partnershipo ENTJ and INFJ could work although there would be plenty of arguing (too many Js). As a male-male subordinate-boss relationship the dynamics are unstable.
Ed can only operate through a strategy which makes sense to him. If people get in the way of its execution he will simply work to eliminate them. This requires him to "tame" Miliband and bind him to the strategy. At that point, for Balls, Miliband has a function - which is to go play nursemaid to the wounded egos left in the wake of Mr Balls' operations, while being a publicist/frontman for the touchy-feely media.
INFJs are hopeless at strategy and focus instead on harmony which is why Miliband's trades union sponsors elected him in the first place, to 'harmonise' with their particular interests and to be a public lobbyist for them. However, Ed Balls' "no cuts" strategy is even more closely aligned with the special interests of Labour's core constituencies (especially the public sector unions who pay the bills) so if Ed Miliband is looking for help in that direction he can forget it.
In this fascinating opera to come, Ed Balls is like an evil spirit who for his very existence has to take over and possess the soul of young Ed Miliband, making him his puppet. It will be fascinating and horrible to watch.
___
If David Miliband had become leader, he would have found Ed Balls an equally difficult character. David Miliband has the same personality type as Tony Blair (ENTP), while Ed Balls is an extraverted version of Gordon Brown (who is INTJ). So you would have had a reprise of the Blair-Brown poisonous relationship but with added public venom.
Ed Miliband is an interesting case: he's most likely INFJ although he might score a low E. An INFJ is driven by a strong set of personal values, gives and respects loyalty and comes across as empathic and warm (extraverted F). This orientation to the human, emotional side comes at the expense of analytic skills and an interest in the logic of policies.
Ed Balls is the very picture of an ENTJ. Extraverted, intellectual and judgemental with an underdeveloped extraverted feeling (F) function (his weakest function - see here). Ed is superlative at mapping out a grand strategy and marshalling forces to accomplish it - but without much regard for casualties along the way, collateral or otherwise.
As a male-female partnershipo ENTJ and INFJ could work although there would be plenty of arguing (too many Js). As a male-male subordinate-boss relationship the dynamics are unstable.
Ed can only operate through a strategy which makes sense to him. If people get in the way of its execution he will simply work to eliminate them. This requires him to "tame" Miliband and bind him to the strategy. At that point, for Balls, Miliband has a function - which is to go play nursemaid to the wounded egos left in the wake of Mr Balls' operations, while being a publicist/frontman for the touchy-feely media.
INFJs are hopeless at strategy and focus instead on harmony which is why Miliband's trades union sponsors elected him in the first place, to 'harmonise' with their particular interests and to be a public lobbyist for them. However, Ed Balls' "no cuts" strategy is even more closely aligned with the special interests of Labour's core constituencies (especially the public sector unions who pay the bills) so if Ed Miliband is looking for help in that direction he can forget it.
In this fascinating opera to come, Ed Balls is like an evil spirit who for his very existence has to take over and possess the soul of young Ed Miliband, making him his puppet. It will be fascinating and horrible to watch.
___
If David Miliband had become leader, he would have found Ed Balls an equally difficult character. David Miliband has the same personality type as Tony Blair (ENTP), while Ed Balls is an extraverted version of Gordon Brown (who is INTJ). So you would have had a reprise of the Blair-Brown poisonous relationship but with added public venom.
Saturday, January 22, 2011
The Black Swan (film)
We braved the freezing wind and zero temperature and walked to the Wells Film Centre this afternoon, orginally to see The King's Speech. But, Satuday and all that, it was sold out. So we opted instead for The Black Swan.
Now all the bleating from the ballet "community" about how this film bad-mouths behind-the-scenes goings-on in their art is ridiculous. The film is about an immature 28 year old ballerina Nina who is an OCD perfectionist but dances from the head, not from the heart. In her new top role as the Swan Queen (in Swan Lake) she is required to dance the part of the black swan, a seductive temptress, as well as the virginal princess white swan.
Nina can, of course, do white swans with her eyes shut, but letting her emotional side hang-out seems beyond her. Under a combination of the stress, the well-meaning efforts of her friends to help her loosen up and some slipped drugs, she starts to crack up.
The film starts puzzling, then it flips a few red herrings to mislead you it's going to follow the usual shop-worn cliches, then the tension ratchets up and it all gets totally surreal.
We enjoyed it.
___
* In reviews, some fuss has been made about explicit sex and drug use. Relax: it's not that explicit and no horses were frightened in the viewing of this film.
** We're down to see The King's Speech later in the week.
Now all the bleating from the ballet "community" about how this film bad-mouths behind-the-scenes goings-on in their art is ridiculous. The film is about an immature 28 year old ballerina Nina who is an OCD perfectionist but dances from the head, not from the heart. In her new top role as the Swan Queen (in Swan Lake) she is required to dance the part of the black swan, a seductive temptress, as well as the virginal princess white swan.
Nina can, of course, do white swans with her eyes shut, but letting her emotional side hang-out seems beyond her. Under a combination of the stress, the well-meaning efforts of her friends to help her loosen up and some slipped drugs, she starts to crack up.
The film starts puzzling, then it flips a few red herrings to mislead you it's going to follow the usual shop-worn cliches, then the tension ratchets up and it all gets totally surreal.
We enjoyed it.
___
* In reviews, some fuss has been made about explicit sex and drug use. Relax: it's not that explicit and no horses were frightened in the viewing of this film.
** We're down to see The King's Speech later in the week.
Friday, January 21, 2011
Even more physics questions
I posted some more questions at the ever-more-addictive Physics StackExchange site.
* A flyby of orbiting supermassive black holes.
* Photon wave packets from distant stars.
* A flyby of orbiting supermassive black holes.
* Photon wave packets from distant stars.
Thursday, January 20, 2011
Avicide
We were only out for about half an hour this afternoon. Just popped down to the shops to buy some milk plus a bag of "insect feast" (sic) and a carton of fat-balls for the birds.
This was the sight which greeted us when we got back: the evidence of a crime against the avian community.
Once a sparrow, now through murderous intent transformed into one more piece of "goodness" for the garden. Clare buried it near the rose bush: it was still warm.
A trivial piece of detective work unmasks the perpetrator, his reputation as a bird-lover now transformed for ever.
This was the sight which greeted us when we got back: the evidence of a crime against the avian community.
Once a sparrow, now through murderous intent transformed into one more piece of "goodness" for the garden. Clare buried it near the rose bush: it was still warm.
A trivial piece of detective work unmasks the perpetrator, his reputation as a bird-lover now transformed for ever.
More physics questions!
I posted two more, frankly populist questions on the Physics StackExchange site and got good answers. My reputation now stands at 42! (Clare asks wearily "Is it all men on this site?").
First question: "Is there a maximum possible acceleration?"
Second question: "What would happen if a large relativistic object hit the earth?"
Click on the links to see the full questions and the rather interesting answers.
--
Mundane news: our replacement DVD player arrived today, accompanied by The Brothers Karamazov.
First question: "Is there a maximum possible acceleration?"
Second question: "What would happen if a large relativistic object hit the earth?"
Click on the links to see the full questions and the rather interesting answers.
--
Mundane news: our replacement DVD player arrived today, accompanied by The Brothers Karamazov.
Subscribe to:
Posts (Atom)