With reference to the previous post below - ‘Shadowlands’ - C.S. Lewis believed (and apparently eventually re-believed after his wife’s death) that the purpose of grief was to perfect the soul in this life.
In this he was certainly mistaken. But what, then, is grief actually ‘for’?
Nikolas Lloyd (an evolutionary psychologist with an eclectic site here) wrote that he attended a forum a few years back where pro- and anti- evolutionary psychology advocates battled it out. Here is what happened next.
“One speaker was a social scientist, and a one of such rudeness, such arrogance, and such jaw-dropping ignorance, that I was quite astounded. At one point, this person spoke with heavy scorn about evolutionary psychologists who believed that emotions all had functions. "I can't see the function of grief," said the social scientist, and left it at that.
“Presumably the speaker imagined that the audience would conclude that because a qualified social scientist could not think of a function for grief, then there must be none. In fact, grief is one of the easiest emotions to explain.”
Nikolas then recounts his understanding of the adaptiveness of grief, which seems to me broadly along the right lines, (here). Many emotions seem to have a ‘natural-world’ version and a ‘social-world’ analogue. I suspect grief is the social-world analogue of natural-world pain, with similar cautioning function.
I suspect that C. S. Lewis would have been completely bemused by the discipline of evolutionary psychology. He would surely have found it as incomprehensible as it would have been unacceptable to his concept of God, and of meaning in life.
Monday, January 29, 2007
Sunday, January 28, 2007
Shadowlands
Down to Salisbury Playhouse last night to see ‘Shadowlands’.
C. S. Lewis is the middle-aged Oxford don leading a life of complacent intellectual smugness. His shtick is writing and lecturing about theological issues such as the meaning of suffering. “We are blocks of stone, and the pain we feel is the sculptor, chiselling our shape out of the rock, to make us perfect”. God, that is. And our present life, the sculpting process, is the Shadowland, prefiguring the perfect world to come.
Lewis had met suffering when he was eight years old, when his mother had died of cancer, but had reacted with denial.
Enter Joy Gresham, an American poet with young son in tow, and a huge fan of Lewis. They meet and hit it off. The first part of the play shows Lewis falling in love with Gresham and not knowing it. As Gresham divorces her abusive American husband, Lewis agrees an arranged marriage to enable Joy to stay in the UK.
Now it’s Joy’s turn to be diagnosed with terminal cancer. Almost too late, Lewis realises that he is in love with Joy, a love which infuses his whole being. He has begun to live at last (‘he rejoins the human race’ as a review on Amazon has it) - and then she dies.
His is a searing grief - how can his previous glib thoughts about the necessary role of suffering in Christianity hold up? His clever, but shallow and vacuous intellectual theorisations collapse under the load of his unbearable anguish.
Somehow, his faith remains. We know, by the way, about the aftermath. Lewis wrote up his pain in a brutally honest journal “A Grief Observed” (here).
We thought the play was brilliant - excellent ensemble acting which captured the time (1950s) and attitudes perfectly. Most of Lewis’s misogynistic friends loathed Joy. As she was American, rather ‘in your face’ and had no time for their brittle anti-feminine banter, one can see why.
C. S. Lewis is the middle-aged Oxford don leading a life of complacent intellectual smugness. His shtick is writing and lecturing about theological issues such as the meaning of suffering. “We are blocks of stone, and the pain we feel is the sculptor, chiselling our shape out of the rock, to make us perfect”. God, that is. And our present life, the sculpting process, is the Shadowland, prefiguring the perfect world to come.
Lewis had met suffering when he was eight years old, when his mother had died of cancer, but had reacted with denial.
Enter Joy Gresham, an American poet with young son in tow, and a huge fan of Lewis. They meet and hit it off. The first part of the play shows Lewis falling in love with Gresham and not knowing it. As Gresham divorces her abusive American husband, Lewis agrees an arranged marriage to enable Joy to stay in the UK.
Now it’s Joy’s turn to be diagnosed with terminal cancer. Almost too late, Lewis realises that he is in love with Joy, a love which infuses his whole being. He has begun to live at last (‘he rejoins the human race’ as a review on Amazon has it) - and then she dies.
His is a searing grief - how can his previous glib thoughts about the necessary role of suffering in Christianity hold up? His clever, but shallow and vacuous intellectual theorisations collapse under the load of his unbearable anguish.
Somehow, his faith remains. We know, by the way, about the aftermath. Lewis wrote up his pain in a brutally honest journal “A Grief Observed” (here).
We thought the play was brilliant - excellent ensemble acting which captured the time (1950s) and attitudes perfectly. Most of Lewis’s misogynistic friends loathed Joy. As she was American, rather ‘in your face’ and had no time for their brittle anti-feminine banter, one can see why.
Thursday, January 25, 2007
Altruism and evolutionary psychology
BBC’s NewsNight yesterday (Jan 24th 07) had a quirky feature about heroism. The item featured a guy who had rescued a child and her mother from a burning car, which promptly exploded a few seconds later. He was lucky to have survived.
In the style of news programmes these days, under his name banner across the screen was the role the programme had allocated him. It was the one word: ‘Hero’.
I cringed.
The presenter then raised the question as to why the hero had risked his life in this way. The mother and child were unrelated to him - no genetic advantage seemed to be involved. This was posed to the pundit, a ‘professor in evolutionary biology’ from Imperial College.
The professor gave his opinion that altruism was a ‘mistake’. Brain circuitry which was meant to help closely-related kin had been ‘hijacked’ by these individuals.
I cringed again.
I’ve seen this reductionist argument over and over. It cannot be right. A kin-based altruism which kept making mistakes would have been powerfully-selected against. There is a much better explanation based on the fact that we can’t easily recognise kin.
The same textbooks which have a problem with altruism often observe that children brought up together from a young age observe the incest taboo - they do not form sexual associations, even if genetically unrelated. Why is this relevant? Because we do not have inbuilt DNA-testers, we cannot easily determine our degree of social relatedness to others. We use social-proximity cues to proxy for (close or not-so-close) kin-relatedness.
Most analysts concur that our ‘environment of evolutionary adaptedness’ was an extended kin-group of up to 120 members. In such a group, a random pair of individuals have relatively low genetic overlap and certainly cannot determine the degree of relatedness by observation: the basis of altruism is therefore Trivers’ reciprocal altruism (but based on kin-group selection) as we shall now examine.
Psychologically we have strong emotional drives to identify with a group, and such identification produces a constellation of ‘loyal’ behaviours including altruistic heroism. In a harsh world, the extended kin-group could not cohere and survive without strong loyalties.
if we stir into the mix:
There, how hard was that?
PS. OK, I concede that maybe that was what the professor really meant: it's hard to make any kind of argument when you're restricted to 45 seconds. Still, it came across as stupid. Sorry!
In the style of news programmes these days, under his name banner across the screen was the role the programme had allocated him. It was the one word: ‘Hero’.
I cringed.
The presenter then raised the question as to why the hero had risked his life in this way. The mother and child were unrelated to him - no genetic advantage seemed to be involved. This was posed to the pundit, a ‘professor in evolutionary biology’ from Imperial College.
The professor gave his opinion that altruism was a ‘mistake’. Brain circuitry which was meant to help closely-related kin had been ‘hijacked’ by these individuals.
I cringed again.
I’ve seen this reductionist argument over and over. It cannot be right. A kin-based altruism which kept making mistakes would have been powerfully-selected against. There is a much better explanation based on the fact that we can’t easily recognise kin.
The same textbooks which have a problem with altruism often observe that children brought up together from a young age observe the incest taboo - they do not form sexual associations, even if genetically unrelated. Why is this relevant? Because we do not have inbuilt DNA-testers, we cannot easily determine our degree of social relatedness to others. We use social-proximity cues to proxy for (close or not-so-close) kin-relatedness.
Most analysts concur that our ‘environment of evolutionary adaptedness’ was an extended kin-group of up to 120 members. In such a group, a random pair of individuals have relatively low genetic overlap and certainly cannot determine the degree of relatedness by observation: the basis of altruism is therefore Trivers’ reciprocal altruism (but based on kin-group selection) as we shall now examine.
Psychologically we have strong emotional drives to identify with a group, and such identification produces a constellation of ‘loyal’ behaviours including altruistic heroism. In a harsh world, the extended kin-group could not cohere and survive without strong loyalties.
if we stir into the mix:
- kin-groups;
- strong selection pressure for kin-groups expressing in-group loyalty against those with weak social ties;
- the learned nature of who is in the group;
There, how hard was that?
PS. OK, I concede that maybe that was what the professor really meant: it's hard to make any kind of argument when you're restricted to 45 seconds. Still, it came across as stupid. Sorry!
Sunday, January 21, 2007
Watching the time traveller
Today’s clever discussions about time-travel involve taking you to an alternate universe in the multiverse (David Deutsch - Fabric of Reality) or to somewhere else in ‘Actuality’ (Michael Lockwood - The Labyrinth of Time). However, it is interesting to consider what time travel would look like to ordinary folk if carried out within this universe.
We live our lives in space-time as 4-dimensional ‘world-lines’ (actually hypervolumes) which point forwards at an angle less than 45 degrees in a coordinate system where c=1 and time is ‘up’.
To be a time-traveller requires a world-line which can curve back on itself as in the figure. Call the time-traveller Alice. Watching Alice, the red line, this is what you would see as time ‘flows by’. 'You' are not shown. Image a vertical world-line just to the left of the red s-curve - that's you.
Time A. You see Alice next to you and say hello.
Time B. A copy of Alice suddenly appears across the road and splits into two copies.
Time C. There are now three copies of Alice. Alice-1 is next to you and, maintaining conversational continuity, begins to cross the road. Alice-2 begins to walk backwards from the other side of the road towards Alice-1 (Alice 2 seems to be moving backwards in time - she’s talking backwards). Alice-3, meanwhile begins to walk farther away, turns round and waves to you. She is future-Alice.
Time D. Alice-1, walking forwards, and Alice-2, walking backwards, meet in the middle of the road and merge. They then pop out of existence. As they approached, they seemed to be travelling faster and faster towards each other.
Time E. You and Alice-3 get on with your lives. Alice-3 has lived through more time than you have. Between points B and D, Alice-3 could have told you information about your future.
I don’t comment on issues of conservation of mass-energy, information paradoxes or the fact that Alice travelled faster than light at B and D. Just the observer experience, which to happen this way requires no more than world-line continuity. And there was always only one Alice.
==========================
Roy Simpson writes:
Nigel,
I am not sure whether you are aware of the interesting topics surrounding a paper (summarised here) by Greenberger and Svozil on QM Time Travel? They examine quantum paths which traverse from a later t2 to an earlier t1 (rather than take a non-classical path to later times).
The time travel happens in this universe (a bit like your Alice). The quantum aspect brings in probabilities though.
The trick is to use special 50/50 beam splitters at t1 and t2 respectively, one path of which (at t2) has its particle head back in time (to the t1 splitter as one input). There is a risk of getting stuck in this time loop, I would think. There are consistency conditions here though, so that back at t1 one cannot do anything inconsistent with the t2 one has just left, but freedoms remain at t1.
The classic story is of a man left money from a rich aunt whose money was of uncertain origin. Using the money he builds a quantum Time Machine to find out more from the aunt, and back in time he leaves some money for himself and his aunt using his knowledge of the future stock prices. Hence a consistent history!
Shifting from present-past to future-present the authors suggest that maybe the present is influenced by the future in a similar way. Some things happen the way that they do, to make the future happen as it must. Only some aspects of life would be affected this way though, and so we might not ordinarily notice. So where are these beam splitters then???
Roy
PS. Does anyone read these technical blogs?
Nigel Seel replies:
I read the referenced paper and got the drift. As you say, where ARE the beam splitters? Maybe they are components of the time machine no-one has figured out how to build yet.
I was also reminded that my throwaway remarks about Alice having to travel faster than light are void in general relativity, if the light cones can be sufficiently tipped in the local space-time geometry.
No-one reads the technical postings on this blog (apart from you). But who knows who may in the future? Or the past!
Seriously, one can't expect to contribute to the conceptual state of the art in physics unless one is a fully paid-up researcher. There's just too much going on that one doesn't know about. Intelligent speculation is just for fun, I guess.
We live our lives in space-time as 4-dimensional ‘world-lines’ (actually hypervolumes) which point forwards at an angle less than 45 degrees in a coordinate system where c=1 and time is ‘up’.
To be a time-traveller requires a world-line which can curve back on itself as in the figure. Call the time-traveller Alice. Watching Alice, the red line, this is what you would see as time ‘flows by’. 'You' are not shown. Image a vertical world-line just to the left of the red s-curve - that's you.
Time A. You see Alice next to you and say hello.
Time B. A copy of Alice suddenly appears across the road and splits into two copies.
Time C. There are now three copies of Alice. Alice-1 is next to you and, maintaining conversational continuity, begins to cross the road. Alice-2 begins to walk backwards from the other side of the road towards Alice-1 (Alice 2 seems to be moving backwards in time - she’s talking backwards). Alice-3, meanwhile begins to walk farther away, turns round and waves to you. She is future-Alice.
Time D. Alice-1, walking forwards, and Alice-2, walking backwards, meet in the middle of the road and merge. They then pop out of existence. As they approached, they seemed to be travelling faster and faster towards each other.
Time E. You and Alice-3 get on with your lives. Alice-3 has lived through more time than you have. Between points B and D, Alice-3 could have told you information about your future.
I don’t comment on issues of conservation of mass-energy, information paradoxes or the fact that Alice travelled faster than light at B and D. Just the observer experience, which to happen this way requires no more than world-line continuity. And there was always only one Alice.
==========================
Roy Simpson writes:
Nigel,
I am not sure whether you are aware of the interesting topics surrounding a paper (summarised here) by Greenberger and Svozil on QM Time Travel? They examine quantum paths which traverse from a later t2 to an earlier t1 (rather than take a non-classical path to later times).
The time travel happens in this universe (a bit like your Alice). The quantum aspect brings in probabilities though.
The trick is to use special 50/50 beam splitters at t1 and t2 respectively, one path of which (at t2) has its particle head back in time (to the t1 splitter as one input). There is a risk of getting stuck in this time loop, I would think. There are consistency conditions here though, so that back at t1 one cannot do anything inconsistent with the t2 one has just left, but freedoms remain at t1.
The classic story is of a man left money from a rich aunt whose money was of uncertain origin. Using the money he builds a quantum Time Machine to find out more from the aunt, and back in time he leaves some money for himself and his aunt using his knowledge of the future stock prices. Hence a consistent history!
Shifting from present-past to future-present the authors suggest that maybe the present is influenced by the future in a similar way. Some things happen the way that they do, to make the future happen as it must. Only some aspects of life would be affected this way though, and so we might not ordinarily notice. So where are these beam splitters then???
Roy
PS. Does anyone read these technical blogs?
Nigel Seel replies:
I read the referenced paper and got the drift. As you say, where ARE the beam splitters? Maybe they are components of the time machine no-one has figured out how to build yet.
I was also reminded that my throwaway remarks about Alice having to travel faster than light are void in general relativity, if the light cones can be sufficiently tipped in the local space-time geometry.
No-one reads the technical postings on this blog (apart from you). But who knows who may in the future? Or the past!
Seriously, one can't expect to contribute to the conceptual state of the art in physics unless one is a fully paid-up researcher. There's just too much going on that one doesn't know about. Intelligent speculation is just for fun, I guess.
Saturday, January 20, 2007
Attack Day
More lazy blogging: another excerpt from my (unpublished) SF novel.
2048-06-30: 1625 GMT. Location: the bridge of the USS Nimitz.
Rear Adm. Samuel J. Scott and his battle group, after three and a quarter hours at 3g, are now a more comfortable 2 million kilometres from the incoming asteroid, at their post-operation coordinates.
While Scott struggled to breathe in his acceleration couch, his similarly-impaired technical staff had been reviewing the telemetry to prepare the briefing the Admiral had ordered, and would surely need.
Now proceeding at 1g in a parking trajectory, Scott gets the picture from his strategy officer.
“They hit us, sir. Hit us with five kinetic energy rounds. We only have it on the fastest imagery, but they launched five antimissiles 114 milliseconds before projected impact. At that time our stealthed warheads were about 115 kilometres out from the asteroid and closing at 1,000 kilometres per second. In the next 14 milliseconds the five hostile antimissiles each covered 100 kilometres and each one scored a direct hit on one of our missiles, totally destroying it.”
Admiral Scott looks nonplussed. Leaving aside considerations of navigation, like how did they know precisely where our missiles were, the timing seems wrong.
“Let me get this straight. They launched kinetic energy kill weapons, which covered 100 kilometres from a standing start in 14 milliseconds?”
“Yes, sir.”
“And how fast were these antimissiles going when they hit our warheads? And what was their acceleration?”
“Sir, we didn’t believe it either, but it comes straight out of the sensor data. Speed of the antimissiles at impact was 4.7 percent of the speed of light. Their acceleration was one hundred million gee.”
=======================
The plot to this point involves an asteroid (from the asteroid belt) being de-orbited on a powered trajectory to impact the earth - clearly a hostile act! Our protagonist has a subtle, psychological attack against the enemy, but the military just want to smash it.
They launch five 12 Gigaton thermonuclear missiles designed to hit the asteroid from orthogonal directions simultaneously at 1,000 km/sec. I did the maths. This would disrupt the asteroid beyond gravitational reassembly.
I wanted the alien attackers to have the best possible defences against such an attack, leaving it to the last possible moment. Here are the antimissile specs.
Antimissile mass = 10 kg
Acceleration: 100 million G (neutronium at 100 billion G)
Time to 100 km = 14 milliseconds
Velocity at 100 km = 14,000 km/sec (4.7% of the speed of light)
KE at 100 km (as tons of TNT) = 0.33 Megatons (+ any remaining antimatter)
Antimatter required to accelerate missile to this velocity >= 12 gm (this is a lower-bound, as the propellant-ejecta will be travelling much faster, but will not mass so much)
According to Joseph Lazio, an astronomer who posts to the web, the largest possible acceleration at the surface of a neutron star before it collapses into a black hole is not known precisely, but it’s somewhere between 250 billion and 1 trillion gee. I’m comfortably inside that limit. I think the kinetic energy kill missile would stay normal matter, not even collapsing to neutronium!
=======================
Joseph Lazio’s note
Re: What is the maximum possible gravity of a neutron star?
Date: Sun Mar 23 07:25:09 2003
Posted By: Joseph Lazio, Radio Astronomer
Area of science: Astronomy
ID: 1047696071.As
I'm going to start by spelling out quite carefully how one arrives at the answer. Neutron stars are sufficiently massive and compact that general relativity has to be taken into account in describing it, which means that answers can differ from the ones to which we are accustomed in our low-gravity experience.
A more natural way of describing the gravitational acceleration of a body is the gravitational red-shift that it produces. Imagine standing on the surface of an object (or in the case of a black hole being able to hover just above its event horizon). Shine a light of a particular wavelength upward. As the light leaves your beacon, it must lose energy in leaving the gravitational field of the object.
Of course light always travels as the same velocity, about 300,000 km/s, so as it loses energy it cannot slow down. Rather, its wavelength increases. The difference between the wavelength emitted at the surface and the wavelength received by a distant observer divided by the emitted wavelength is the gravitational red-shift or
z = (wave-length-emitted - wave-length-received)/wave-length-emitted.
For reference, here are the gravitational red-shifts from the surfaces of various objects.
Sun 0.000002
white dwarf ~ 0.0002
neutron star ~ 0.35
black hole ~ to infinity
So what does this mean in terms of the gravitational acceleration at its surface? Provided that the red-shift z is "small," i.e., much less than 1, we can use the standard Newtonian formula for the gravitational acceleration.
The neutron star gravitational red-shift is large enough, though, that we have to use the general relativistic formula, which Pons et al. (2002, Astrophysical Journal, vol. 564, p. 981) give as
g = GM / R^2 sqrt (1 - 2GM/ [Rc^2])
Using the canonical values of M = 1.4 solar masses and R = 10 km (and making sure that one does the calculation in consistent units!), I find g = 2.4 x 1012 m/s^2, or expressed in units of the gravitational acceleration at the Earth's surface (which is 9.8 m/s^2),
I find 250 billion g's. If anything, your science fiction story used too low a value!
If a neutron star acquires too much mass, it is not stable against collapse into a black hole. The current best estimates are that this happens around 3 solar masses. The formula for the gravitational acceleration is not linear in the mass, because the mass appears in the square root in the denominator. As a result, as the mass of the neutron star approaches its maximum value, the gravitational red-shift will increase rapidly.
The "canonical" values for the neutron star mass and radius seem reasonable, based on the limited observational evidence that we have, e.g., Thorsett and Chakrabarty (1999, Astrophysical Journal, vol. 512, p. 288). However, if one wants to be extremely cautious and take into account all of the possible theoretical uncertainty, the maximum mass of a neutron star could be as large as about 6 solar masses before it collapsed into a black hole. As one can see from above, that means the gravitational acceleration could be more than four times larger than what I cite as the "canonical" value. A TRILLION GEES.
For more, though quite technical, reading, see Shapiro and Teukolsky, Black Holes, White Dwarfs, and Neutron Stars (1983, John Wiley and Sons, Co.).
2048-06-30: 1625 GMT. Location: the bridge of the USS Nimitz.
Rear Adm. Samuel J. Scott and his battle group, after three and a quarter hours at 3g, are now a more comfortable 2 million kilometres from the incoming asteroid, at their post-operation coordinates.
While Scott struggled to breathe in his acceleration couch, his similarly-impaired technical staff had been reviewing the telemetry to prepare the briefing the Admiral had ordered, and would surely need.
Now proceeding at 1g in a parking trajectory, Scott gets the picture from his strategy officer.
“They hit us, sir. Hit us with five kinetic energy rounds. We only have it on the fastest imagery, but they launched five antimissiles 114 milliseconds before projected impact. At that time our stealthed warheads were about 115 kilometres out from the asteroid and closing at 1,000 kilometres per second. In the next 14 milliseconds the five hostile antimissiles each covered 100 kilometres and each one scored a direct hit on one of our missiles, totally destroying it.”
Admiral Scott looks nonplussed. Leaving aside considerations of navigation, like how did they know precisely where our missiles were, the timing seems wrong.
“Let me get this straight. They launched kinetic energy kill weapons, which covered 100 kilometres from a standing start in 14 milliseconds?”
“Yes, sir.”
“And how fast were these antimissiles going when they hit our warheads? And what was their acceleration?”
“Sir, we didn’t believe it either, but it comes straight out of the sensor data. Speed of the antimissiles at impact was 4.7 percent of the speed of light. Their acceleration was one hundred million gee.”
=======================
The plot to this point involves an asteroid (from the asteroid belt) being de-orbited on a powered trajectory to impact the earth - clearly a hostile act! Our protagonist has a subtle, psychological attack against the enemy, but the military just want to smash it.
They launch five 12 Gigaton thermonuclear missiles designed to hit the asteroid from orthogonal directions simultaneously at 1,000 km/sec. I did the maths. This would disrupt the asteroid beyond gravitational reassembly.
I wanted the alien attackers to have the best possible defences against such an attack, leaving it to the last possible moment. Here are the antimissile specs.
Antimissile mass = 10 kg
Acceleration: 100 million G (neutronium at 100 billion G)
Time to 100 km = 14 milliseconds
Velocity at 100 km = 14,000 km/sec (4.7% of the speed of light)
KE at 100 km (as tons of TNT) = 0.33 Megatons (+ any remaining antimatter)
Antimatter required to accelerate missile to this velocity >= 12 gm (this is a lower-bound, as the propellant-ejecta will be travelling much faster, but will not mass so much)
According to Joseph Lazio, an astronomer who posts to the web, the largest possible acceleration at the surface of a neutron star before it collapses into a black hole is not known precisely, but it’s somewhere between 250 billion and 1 trillion gee. I’m comfortably inside that limit. I think the kinetic energy kill missile would stay normal matter, not even collapsing to neutronium!
=======================
Joseph Lazio’s note
Re: What is the maximum possible gravity of a neutron star?
Date: Sun Mar 23 07:25:09 2003
Posted By: Joseph Lazio, Radio Astronomer
Area of science: Astronomy
ID: 1047696071.As
I'm going to start by spelling out quite carefully how one arrives at the answer. Neutron stars are sufficiently massive and compact that general relativity has to be taken into account in describing it, which means that answers can differ from the ones to which we are accustomed in our low-gravity experience.
A more natural way of describing the gravitational acceleration of a body is the gravitational red-shift that it produces. Imagine standing on the surface of an object (or in the case of a black hole being able to hover just above its event horizon). Shine a light of a particular wavelength upward. As the light leaves your beacon, it must lose energy in leaving the gravitational field of the object.
Of course light always travels as the same velocity, about 300,000 km/s, so as it loses energy it cannot slow down. Rather, its wavelength increases. The difference between the wavelength emitted at the surface and the wavelength received by a distant observer divided by the emitted wavelength is the gravitational red-shift or
z = (wave-length-emitted - wave-length-received)/wave-length-emitted.
For reference, here are the gravitational red-shifts from the surfaces of various objects.
Sun 0.000002
white dwarf ~ 0.0002
neutron star ~ 0.35
black hole ~ to infinity
So what does this mean in terms of the gravitational acceleration at its surface? Provided that the red-shift z is "small," i.e., much less than 1, we can use the standard Newtonian formula for the gravitational acceleration.
The neutron star gravitational red-shift is large enough, though, that we have to use the general relativistic formula, which Pons et al. (2002, Astrophysical Journal, vol. 564, p. 981) give as
g = GM / R^2 sqrt (1 - 2GM/ [Rc^2])
Using the canonical values of M = 1.4 solar masses and R = 10 km (and making sure that one does the calculation in consistent units!), I find g = 2.4 x 1012 m/s^2, or expressed in units of the gravitational acceleration at the Earth's surface (which is 9.8 m/s^2),
I find 250 billion g's. If anything, your science fiction story used too low a value!
If a neutron star acquires too much mass, it is not stable against collapse into a black hole. The current best estimates are that this happens around 3 solar masses. The formula for the gravitational acceleration is not linear in the mass, because the mass appears in the square root in the denominator. As a result, as the mass of the neutron star approaches its maximum value, the gravitational red-shift will increase rapidly.
The "canonical" values for the neutron star mass and radius seem reasonable, based on the limited observational evidence that we have, e.g., Thorsett and Chakrabarty (1999, Astrophysical Journal, vol. 512, p. 288). However, if one wants to be extremely cautious and take into account all of the possible theoretical uncertainty, the maximum mass of a neutron star could be as large as about 6 solar masses before it collapsed into a black hole. As one can see from above, that means the gravitational acceleration could be more than four times larger than what I cite as the "canonical" value. A TRILLION GEES.
For more, though quite technical, reading, see Shapiro and Teukolsky, Black Holes, White Dwarfs, and Neutron Stars (1983, John Wiley and Sons, Co.).
Thursday, January 18, 2007
Fence redux
As forecast, winds gusting to 70 mph hit us today, and by this afternoon it was the usual story in the back garden. Our neighbour, who owns the fence on that side, has just visited in a familiar state of depression.
Here is where the missing panels ended up, once we had bravely ventured out to stack them. It was a bit like grass wind-surfing once the wind caught them.
A cat may look at a printer
So here is the dilemma. Is the cat showing some genuinely creative intelligence here - interest in printers, or maps perhaps?
Or is this the application of an evolutionarily-ancient module - Kitty believes the printer is a bush or something, and the emerging paper is some kind of small prey animal?
Or is this the application of an evolutionarily-ancient module - Kitty believes the printer is a bush or something, and the emerging paper is some kind of small prey animal?
Nature or nurture? ... The dilemma of modern evolutionary psychology ...
====================
Roy Simpson writes: "The cat may just be applying the principle that as the paper is a moving object, there must be some unseen force involved. A hidden mouse perhaps?"
Nigel Seel replies: "It could be applying a hidden variable theory ... or maybe it's just accepted an intrinsic indeterminacy in the printer's actions. Given it's all down to Windows XP, we will never know..."
Monday, January 15, 2007
More on N-category theory
My former colleague at STL, Roy Simpson, wrote to set me straight (or at least straighter) on N-category theory, mentioned in a previous post here. I quote from his email.
-------------------------
“Nigel,
I hadn’t heard of N-category theory before, but I have had a look at that and a couple of other papers by J. Baez. What this paper is actually doing (as a summary) is taking category theory up into "higher dimensions". Thus the category theory of abstract data types and of set theory is really just 1-category theory, in this terminology. Things appear to have moved on from there now though (at least during the 1990s).
So (1-)categories have objects and morphisms between them (plus maybe a few rules like association). 2-Categories have "morphisms between morphisms". These 2-morphisms have association rules too, but they can be composed "vertically - i.e. the underlying 1-morphisms" or "horizontally - i.e. as 2-morphisms" as they can be viewed more as 2-dimensional objects. There is a giant commutative diagram showing how this association would work.
Much of "known applications" seems to be at this 2-category level. However the development continues into 3-categories ... on to the general N-category and there is even an upper limit of an omega-category.
One key attraction seems to be that in category theory one doesn’t have equations like:
a = b (meaning a is exactly b), but rather
a ~ b (meaning a is b "up to isomorphism"),
then the "rules" defining what an N-isomorphism is are set at the N+1-category level. Hence the journey to the omega-category. As you know vectors are equal "given a choice of basis" and sets can be isomorphic - yet not have identical elements.
In terms of computer science there are two areas of application mentioned:
1. Baez refers to the high level morphisms as "processes between processes between processes....."
I have yet to find if any computer scientist has done anything with this idea though.
2. N-Categories have been described as a "semantics for higher order type theory". There are papers from - as usual - Edinburgh University on this.
On the physics side we find Baez (another regular blogger on physics by the way) referring to e.g. Feynman path integrals as morphisms. String theory takes it all into higher dimension. Despite all the enthusiasm he spouts for this area I have yet to see exactly where he is going with it though. More study required here I suppose!
Finally it is remarkable the statements he makes about N-category theory. At one point he says that quantum mechanics was Nature's way to make science pay attention to N-categories. At another point he describes the scientific "drop" from the omega-category to the 1-category of sets as like the Gnostic description of Mankind's fall.
So the overall diagram seems to be:
(QM) Physics
<--->
N-Categories
<--->
Computer Science (e.g. type semantics)”
-------------------------
Back to me again. So ... there folks, clearer now?
Anti-intellectualism aside, I guess it makes some sense. A process is a running program. An example of a process which maps processes to processes might be an operating system scheduler. To move up a level we might consider an adaptive operating system which modifies its own process-scheduling algorithms (e.g. under load). The analogy with higher-order functions (and therefore higher-order type semantics) is fairly clear. Sadly I’m not qualified to debate the take on physics.
A less kind thought is that if you have a hammer, everything in the world looks remarkably like a nail.
Put it down to that I’m a little bit jaundiced that I don’t get paid to do this for a living any more!
-------------------------
“Nigel,
I hadn’t heard of N-category theory before, but I have had a look at that and a couple of other papers by J. Baez. What this paper is actually doing (as a summary) is taking category theory up into "higher dimensions". Thus the category theory of abstract data types and of set theory is really just 1-category theory, in this terminology. Things appear to have moved on from there now though (at least during the 1990s).
So (1-)categories have objects and morphisms between them (plus maybe a few rules like association). 2-Categories have "morphisms between morphisms". These 2-morphisms have association rules too, but they can be composed "vertically - i.e. the underlying 1-morphisms" or "horizontally - i.e. as 2-morphisms" as they can be viewed more as 2-dimensional objects. There is a giant commutative diagram showing how this association would work.
Much of "known applications" seems to be at this 2-category level. However the development continues into 3-categories ... on to the general N-category and there is even an upper limit of an omega-category.
One key attraction seems to be that in category theory one doesn’t have equations like:
a = b (meaning a is exactly b), but rather
a ~ b (meaning a is b "up to isomorphism"),
then the "rules" defining what an N-isomorphism is are set at the N+1-category level. Hence the journey to the omega-category. As you know vectors are equal "given a choice of basis" and sets can be isomorphic - yet not have identical elements.
In terms of computer science there are two areas of application mentioned:
1. Baez refers to the high level morphisms as "processes between processes between processes....."
I have yet to find if any computer scientist has done anything with this idea though.
2. N-Categories have been described as a "semantics for higher order type theory". There are papers from - as usual - Edinburgh University on this.
On the physics side we find Baez (another regular blogger on physics by the way) referring to e.g. Feynman path integrals as morphisms. String theory takes it all into higher dimension. Despite all the enthusiasm he spouts for this area I have yet to see exactly where he is going with it though. More study required here I suppose!
Finally it is remarkable the statements he makes about N-category theory. At one point he says that quantum mechanics was Nature's way to make science pay attention to N-categories. At another point he describes the scientific "drop" from the omega-category to the 1-category of sets as like the Gnostic description of Mankind's fall.
So the overall diagram seems to be:
(QM) Physics
<--->
N-Categories
<--->
Computer Science (e.g. type semantics)”
-------------------------
Back to me again. So ... there folks, clearer now?
Anti-intellectualism aside, I guess it makes some sense. A process is a running program. An example of a process which maps processes to processes might be an operating system scheduler. To move up a level we might consider an adaptive operating system which modifies its own process-scheduling algorithms (e.g. under load). The analogy with higher-order functions (and therefore higher-order type semantics) is fairly clear. Sadly I’m not qualified to debate the take on physics.
A less kind thought is that if you have a hammer, everything in the world looks remarkably like a nail.
Put it down to that I’m a little bit jaundiced that I don’t get paid to do this for a living any more!
Sunday, January 14, 2007
Miss Potter
We went to see said film this evening at Salisbury. Miss Renée Zellweger managed to do that gloopy smile thing quite often. The tale was a largely linear narrative of a talented and intelligent woman (Beatrix Potter) set in the first decade of the twentieth century. Her conventional, society-focused mother has been trying to marry her off to a succession of rich/titled dunderheads. She won't play ball. Her publisher by contrast is smart, empathic and gentle ... but by definition a tradesman. Cue parental disapproval to marriage but she wins a delayed permission ... only to have him die on her. But we all know the story.
Driving home, Clare was debating Beatrix Potter vs. Jane Austen. There are plenty of similarities: smart women trying to do their thing in a rigidly circumscribed man's world. Miss Potter had more social room to breathe and made more money, which as always bought her independence.
Clare pointed out that Beatrix was basically an illustrator/painter, and the stories were just what you had to do as a linking narrative between pictures. And she thought that Jane Austen was scarier.
Driving home, Clare was debating Beatrix Potter vs. Jane Austen. There are plenty of similarities: smart women trying to do their thing in a rigidly circumscribed man's world. Miss Potter had more social room to breathe and made more money, which as always bought her independence.
Clare pointed out that Beatrix was basically an illustrator/painter, and the stories were just what you had to do as a linking narrative between pictures. And she thought that Jane Austen was scarier.
Friday, January 12, 2007
Asteroid impact effects
A while ago, I wrote an (unpublished) science-fiction novel. Here is an extract where the two main characters are discussing what a grazing asteroid impact on the earth would look and feel like.
---
They both turn round on the log, and, with the sun on their backs, look towards London. Right on the horizon, Stephen can just make out tiny skyscrapers, a distant toytown.
“That’s right,” says Emma, “you can just see the towers at Canary Wharf, next to the Thames in East London. Do you know how far away they are? About 30 kilometres from here.”
Emma is warming to her theme.
“You’re trying to divert the asteroid to just miss the earth - what we call a grazing trajectory. You want to leave it as late as possible to minimise the chances of countermeasures, so you’re going for a very, very close encounter, right?”
Steven nods. That’s exactly the plan.
“Suppose you get things a little wrong. Suppose the asteroid were to come in over London, for example, with the ultimate grazing trajectory. It just comes really close to the ground and then flies out of the atmosphere again. Do you know whether that would be good or bad? What the effects would be?”
Steven hasn’t thought about it in detail. He considers: it’s two kilometres wide, weighs 33 billion tons and is travelling at 53 kilometres per second.
“It’s going to create one massive fireball and shockwave, and cause huge localised damage.”
“It’s twelve seconds to closest approach, Steven, and this is your first real sight of the asteroid. Look there, out over London.” she points. “ It’s currently 640 kilometres out, right there on the horizon, and it’s just hit the top of the atmosphere, 30 kilometres up. It looks like a brilliant point of light. That’s the plasma shock in front of it.
“Nine seconds to go now. It’s 18 kilometres up and 480 kilometres out. The asteroid now sits behind a 6 kilometres wide plasma disk at 6,000 degrees centigrade - the bow-shock. It looks like the sun, but it’s 50% wider, and it already feels twice as hot. It’s so hot you can barely stand it .
“Two seconds to closest approach now, Stephen and although it’s still 75 kilometres away and 440 metres up, it looks nine times wider than the sun and it’s beginning to loom. Another half a second and you burst into flames ... it’s eighty times the heat of the sun and all around you, the countryside is on fire.
“That’s right,” says Emma, “you can just see the towers at Canary Wharf, next to the Thames in East London. Do you know how far away they are? About 30 kilometres from here.”
Emma is warming to her theme.
“You’re trying to divert the asteroid to just miss the earth - what we call a grazing trajectory. You want to leave it as late as possible to minimise the chances of countermeasures, so you’re going for a very, very close encounter, right?”
Steven nods. That’s exactly the plan.
“Suppose you get things a little wrong. Suppose the asteroid were to come in over London, for example, with the ultimate grazing trajectory. It just comes really close to the ground and then flies out of the atmosphere again. Do you know whether that would be good or bad? What the effects would be?”
Steven hasn’t thought about it in detail. He considers: it’s two kilometres wide, weighs 33 billion tons and is travelling at 53 kilometres per second.
“It’s going to create one massive fireball and shockwave, and cause huge localised damage.”
“It’s twelve seconds to closest approach, Steven, and this is your first real sight of the asteroid. Look there, out over London.” she points. “ It’s currently 640 kilometres out, right there on the horizon, and it’s just hit the top of the atmosphere, 30 kilometres up. It looks like a brilliant point of light. That’s the plasma shock in front of it.
“Nine seconds to go now. It’s 18 kilometres up and 480 kilometres out. The asteroid now sits behind a 6 kilometres wide plasma disk at 6,000 degrees centigrade - the bow-shock. It looks like the sun, but it’s 50% wider, and it already feels twice as hot. It’s so hot you can barely stand it .
“Two seconds to closest approach now, Stephen and although it’s still 75 kilometres away and 440 metres up, it looks nine times wider than the sun and it’s beginning to loom. Another half a second and you burst into flames ... it’s eighty times the heat of the sun and all around you, the countryside is on fire.
“Do you know when it reaches London, right there on your far horizon? Just 570 milliseconds before it gets to you. At that point, the bottom of the plasma shock disk is only 70 metres above London’s streets and the disk is 23 times the size of the sun. It’s dominating your northern horizon. You’re already toast, of course, but steel structures around you are melting under 500 times normal solar intensity.
“In the next few tenths of a second, your remains will have the privilege of encountering the heart of a thermonuclear fireball, as the plasma shock fills the entire sky.
“It goes without saying that London would be completely destroyed, by the thermal effects, and then the blast wave. Most of southern England would be set ablaze and flattened in fact. And that’s an asteroid miss. Although the plasma shock front itself touches down, the asteroid never got closer than two kilometres up.”
“I should say, though, for completeness that the asteroid semi-disintegrates in this scenario. The combination of searing heat and heavy aerodynamic loading as it hits the denser atmosphere causes the surface to ablate and tear off. The asteroid tumbles and fragments, and pieces impact the earth at 50 kilometres per second despite the main bulk missing us. There are going to be a lot of Meteor Craters in Southern England and Northern France. "
Saturday, January 06, 2007
Paul Murphy
We went up to Liverpool yesterday to attend a Requiem Mass for Paul Murphy. Paul was married to Cathy, who is Clare’s cousin. He died on Boxing Day from a brain tumour.
I was surprised: there were hundreds of people at the Mass. I had met Paul only a few times - he seemed smart and energetic, but hopelessly at sea with small talk.
Clare’s family, who mostly still live in Merseyside, are Catholics from working-class stock and many would say that they operate as an extended kin-group; ‘Tribal’ is another word. It’s hard for the in-laws to deal with this, especially the male in-laws, when five of the Youells are men. I think Paul found it the hardest.
I had him typologically flagged as ENTJ. He was clearly extravert: ‘He could talk for England on any subject, whether he knew anything about it or not,’ was quoted at the Mass. He ran clubs, enjoyed multiple sports and was a stalwart of something called the Warrington Catenian Association. He utterly lacked a common touch and I sometimes winced at his attempts at chit-chat at family parties. I personally found him amiable enough, although we had little in common.
Paul went to his death with full knowledge, courage and faith. I must say the Catholic Church does death awfully well. 2,000 years of practice have led to an hour-long ritual which carefully orchestrates both the feelings of the bereaved as well as the Catholic meaning of death for the broader community of the faithful.
Those of us who don’t even want to be atheists because the word contains a concept of God lack the corresponding, purely humanist ritual, let alone a hall where the community can gather round and collectively come to terms with terminal absence. I was talking to Clare as we drove back down south. Does the Catholic Church do a form of Requiem Mass for confirmed unbelievers? I will have to check.
Postscript: Paul organised all the aspects of the Mass before he died. As the priests and congregation departed the church at the end of the Mass, they did so to the strains of Abba’s “Thank You for the Music” played from a ghetto blaster parked on a bench behind the pews. Naff to the end? I like to think he did it on purpose.
[See also this].
I was surprised: there were hundreds of people at the Mass. I had met Paul only a few times - he seemed smart and energetic, but hopelessly at sea with small talk.
Clare’s family, who mostly still live in Merseyside, are Catholics from working-class stock and many would say that they operate as an extended kin-group; ‘Tribal’ is another word. It’s hard for the in-laws to deal with this, especially the male in-laws, when five of the Youells are men. I think Paul found it the hardest.
I had him typologically flagged as ENTJ. He was clearly extravert: ‘He could talk for England on any subject, whether he knew anything about it or not,’ was quoted at the Mass. He ran clubs, enjoyed multiple sports and was a stalwart of something called the Warrington Catenian Association. He utterly lacked a common touch and I sometimes winced at his attempts at chit-chat at family parties. I personally found him amiable enough, although we had little in common.
Paul went to his death with full knowledge, courage and faith. I must say the Catholic Church does death awfully well. 2,000 years of practice have led to an hour-long ritual which carefully orchestrates both the feelings of the bereaved as well as the Catholic meaning of death for the broader community of the faithful.
Those of us who don’t even want to be atheists because the word contains a concept of God lack the corresponding, purely humanist ritual, let alone a hall where the community can gather round and collectively come to terms with terminal absence. I was talking to Clare as we drove back down south. Does the Catholic Church do a form of Requiem Mass for confirmed unbelievers? I will have to check.
Postscript: Paul organised all the aspects of the Mass before he died. As the priests and congregation departed the church at the end of the Mass, they did so to the strains of Abba’s “Thank You for the Music” played from a ghetto blaster parked on a bench behind the pews. Naff to the end? I like to think he did it on purpose.
[See also this].
Monday, January 01, 2007
A review of 'Consilience' by Edward Wilson
Edward Wilson, the founder of sociobiology and evolutionary psychology, is now retired. This has given him time to absorb himself in the social sciences and arts: literature, sociology, anthropology, theology, psychology and economics. What would these be like if they were informed by the concept that individual and social behaviour is constrained by an evolutionary history, whose drivers are increasingly understood?
Wilson believes they would be a great deal different, and Consilience is his attempt to imagine the future reconceptualisation of the humanities within an overarching scientific (Darwinian) framework. Does it work? Yes, mostly, if you are scientifically trained: probably not at all if you are not.
I suspect most adherents to the ‘Standard Social Science Model’ will simply conclude that Wilson is just making endless category errors in trying to insert sociobiological constraints into the high domains of culture, ethics and theology. But sometimes you have to just come off the fence: they would be wrong in this judgement. Nevertheless, the current generation of social science academics will never accept Wilson’s approach. The eventual triumph of sociobiology (if anyone will still be using the term) will be the end-point of generations of research.
Where does Wilson fall short of his own high standards within his own paradigm? I think in a couple of areas.
1. On p. 127 the philosopher David Chalmers is quoted as distinguishing the ‘easy’ from the ‘hard’ problems of consciousness research. Everything is hard of course, but investigating how, for example, vision works is a research programme in signal processing and pattern recognition which has been producing results for more than thirty years. This is one of Chalmers ‘easy’ problems. A ‘hard’ problem is the experience of agonising pain. We think, for example, we know in principle how to make a robot which could see: there are few people who believe they could sketch out an architecture for a computer which could honestly be said to experience pain (and thus be tortured). Wilson completely fails to address this issue in his glib assertion that ‘the hard problem is conceptually easy to solve’ (p. 128). No it’s not.
2. One of the shocking consequences of an evolutionary analysis of humanity is that there is no point to any person’s life, or to humanity as a whole, other than the successful reproduction of genetic material - something we share with any bacterium. Even as we know this to be true, we instinctively shy away from it, looking for deep meaning here, there, anywhere ... . We never find it, but we ‘know’ it must be somewhere. One of the triumphs of evolutionary psychology is to identify the ‘instinct’ for deep meaning in life with the sanctification of tribal or community life, which is a powerful asset in group cohesion, and therefore strongly selected for. The dilemma is that even though we understand scientifically why we feel this way, that understanding does nothing to address the emotional need. Somehow we need a deep belief in the meaning of life (usually expressed through some kind of religion or group values) even though scientifically we know this is simply an effective adaptation for group cohesion. Wilson concurs that there is absolutely no solution to this problem, but still, mysteriously, dabbles in ‘deism’.
A key dilemma which will confront future generations, not so far away, is the power to change the human genetic code. But if there is no point to human existence, there can be no guides as to which way to change it (once obvious defects have been fixed). Wilson accepts the point but limits speculation - there is a whole book’s worth of thinking to do about this issue, but perhaps it’s too early for it to be written.
People have been kind about Wilson’s merits as a stylist. I didn’t find the book a gripping read: the writing is rather discursive and lacks bite. In this it shows its own ancestry as a compilation of articles and talks. ‘On Human Nature’ is much better, as it seems to have real emotion around it - a response to his critics - and a more polemical style.
Wilson is currently a lobbyist for conservation and against climate change. The final chapter on this topics is superb, and a welcome antidote to over-familiar ‘save the planet’ narratives driven by inaccurate science and fuzzy emotionalism.
Wilson believes they would be a great deal different, and Consilience is his attempt to imagine the future reconceptualisation of the humanities within an overarching scientific (Darwinian) framework. Does it work? Yes, mostly, if you are scientifically trained: probably not at all if you are not.
I suspect most adherents to the ‘Standard Social Science Model’ will simply conclude that Wilson is just making endless category errors in trying to insert sociobiological constraints into the high domains of culture, ethics and theology. But sometimes you have to just come off the fence: they would be wrong in this judgement. Nevertheless, the current generation of social science academics will never accept Wilson’s approach. The eventual triumph of sociobiology (if anyone will still be using the term) will be the end-point of generations of research.
Where does Wilson fall short of his own high standards within his own paradigm? I think in a couple of areas.
1. On p. 127 the philosopher David Chalmers is quoted as distinguishing the ‘easy’ from the ‘hard’ problems of consciousness research. Everything is hard of course, but investigating how, for example, vision works is a research programme in signal processing and pattern recognition which has been producing results for more than thirty years. This is one of Chalmers ‘easy’ problems. A ‘hard’ problem is the experience of agonising pain. We think, for example, we know in principle how to make a robot which could see: there are few people who believe they could sketch out an architecture for a computer which could honestly be said to experience pain (and thus be tortured). Wilson completely fails to address this issue in his glib assertion that ‘the hard problem is conceptually easy to solve’ (p. 128). No it’s not.
2. One of the shocking consequences of an evolutionary analysis of humanity is that there is no point to any person’s life, or to humanity as a whole, other than the successful reproduction of genetic material - something we share with any bacterium. Even as we know this to be true, we instinctively shy away from it, looking for deep meaning here, there, anywhere ... . We never find it, but we ‘know’ it must be somewhere. One of the triumphs of evolutionary psychology is to identify the ‘instinct’ for deep meaning in life with the sanctification of tribal or community life, which is a powerful asset in group cohesion, and therefore strongly selected for. The dilemma is that even though we understand scientifically why we feel this way, that understanding does nothing to address the emotional need. Somehow we need a deep belief in the meaning of life (usually expressed through some kind of religion or group values) even though scientifically we know this is simply an effective adaptation for group cohesion. Wilson concurs that there is absolutely no solution to this problem, but still, mysteriously, dabbles in ‘deism’.
A key dilemma which will confront future generations, not so far away, is the power to change the human genetic code. But if there is no point to human existence, there can be no guides as to which way to change it (once obvious defects have been fixed). Wilson accepts the point but limits speculation - there is a whole book’s worth of thinking to do about this issue, but perhaps it’s too early for it to be written.
People have been kind about Wilson’s merits as a stylist. I didn’t find the book a gripping read: the writing is rather discursive and lacks bite. In this it shows its own ancestry as a compilation of articles and talks. ‘On Human Nature’ is much better, as it seems to have real emotion around it - a response to his critics - and a more polemical style.
Wilson is currently a lobbyist for conservation and against climate change. The final chapter on this topics is superb, and a welcome antidote to over-familiar ‘save the planet’ narratives driven by inaccurate science and fuzzy emotionalism.