Down to Winchester Cathedral last night for the 6.30 p.m. carol service. The mediaeval cathedral looked magnificent, lit up as it was in the freezing, foggy night. After queuing in the cold for about 20 minutes, we entered, looking for seats. Alas, there were so few, and those taken by the early entrants. We were reduced to stone benches in the side chapel, without a view. 2,000 people had crowded in, apparently.
The choir was breathtakingly beautiful - state-of-the-art plainsong. Competing with the soaring harmonies was a crying baby. A random thought came to mind: “tonight, the crying baby Jesus was ejected from Winchester Cathedral for spoiling the performance of the choir.”
Listening to elderly, distinguished and grown men reciting in portentous voice the advent myths of Judean peasants, as embellished in the early gospels (“this is the Word of the Lord”) I was reminded of Edward Wilson’s remarks about the innate propensity of the human mind to sanctify, endowing all kinds of arbitrary stuff with the aura of unchallengeable authority.
‘How can people say this stuff, or believe it?’ is a kind of category error when faced with religious dogma.
Friday, December 22, 2006
Rabbitcide at Penton Corner
Imagine the shock and horror in the local population when this appalling sight greeted the early riser yesterday.
Investigation sources report that the violence done to the victim seems beyond the capability of the prime suspect: perhaps Mr. Fox had something to do with it.
Wednesday, December 20, 2006
Books in the in-tray
An Introduction to Radio Astronomy by Bernard F. Burke, Francis Graham-Smith.
I find it amazing that it is possible to image the disks of other stars such as Betelgeuse (image here) using synthetic aperture techniques. This book is going to tell me how it all works (albeit in the radio domain, but the theory is the same).
From Jesus to Christianity: How Four Generations of Visionaries & Storytellers Created the New Testament and Christian Faith by L. Michael White.
Having read Dominic Crossan’s books about the historical Jesus (sociological and rooted in the Judaism of the time) I’m interested to see how the flimsy oral legacy became transmuted into a movement with momentum in the face of overpowering Roman repression. The later makeover by Constantine following AD 312 is another story.
The Classical Style: Haydn, Beethoven, Mozart by Charles Rosen. A highly recommended book on the transition from baroque to classical to romantic.
Consilience by E. O. Wilson. After his brilliant ‘On Human Nature’ I couldn’t resist checking out his other major book.
Oh yes, I travel a bit (trains, planes) ...
I find it amazing that it is possible to image the disks of other stars such as Betelgeuse (image here) using synthetic aperture techniques. This book is going to tell me how it all works (albeit in the radio domain, but the theory is the same).
From Jesus to Christianity: How Four Generations of Visionaries & Storytellers Created the New Testament and Christian Faith by L. Michael White.
Having read Dominic Crossan’s books about the historical Jesus (sociological and rooted in the Judaism of the time) I’m interested to see how the flimsy oral legacy became transmuted into a movement with momentum in the face of overpowering Roman repression. The later makeover by Constantine following AD 312 is another story.
The Classical Style: Haydn, Beethoven, Mozart by Charles Rosen. A highly recommended book on the transition from baroque to classical to romantic.
Consilience by E. O. Wilson. After his brilliant ‘On Human Nature’ I couldn’t resist checking out his other major book.
Oh yes, I travel a bit (trains, planes) ...
Sunday, December 17, 2006
Category Theory and Physics
I first met category theory in the early 1980s. I had joined a team at Standard Telecommunications Laboratories (STL) in Harlow, Essex (then part of IT&T) which was developing a computerised system for formal software engineering.
Most systems designers have met abstract data types, the specification-equivalent to ‘objects’ in object-oriented programming. Mathematically, an abstract data type is an algebra: a collection of constants and functions together with equations which determine how the functions work. There are algebras for sets, lists, trees, directed graphs, to name just a few of the building blocks of formal specification.
When we design a system, we compose these basic definitions to create more complex data structures (e.g. lists whose elements are trees). This is where category theory comes in. The objects in category theory are mathematical structures such as sets, lists, trees, vectors, real and complex spaces, etc. The operations of category theory are those which compose and project these spaces. So in a sense, we were building a category theory machine for universal algebra.
I was still studying undergraduate mathematics at the time, finishing my degree. I had a superficial understanding of the kind of thing category theory was, but it was impossible to penetrate to the underlying motivation. Category theory, which emerged from algebraic topology, abstracts from the deep properties of a number of apparently unrelated mathematical structures. Consequently a deep feel for a lot of mathematics is needed to understand what the theory is trying to achieve. The reward is the profundity of mathematical insight which then emerges.
Although I knew from reading the books by Woit and Smolin that category theory was at the heart of much of the reconceptualisation in physics today, it was not until I stumbled across “A History of n-Categorical Physics” by Baez and Lauda (cached here) that I got a sense of what that meant. The category theorists believe that their discipline is the right framework for structures that the theoretical physicists have been groping towards for decades.
Some interesting points from the paper.
When Heisenberg developed his famous ‘matrix mechanics’ version of quantum theory in 1925 he had never heard of matrices. It was his thesis advisor, Max Born, who had to gently break it to him that he had reinvented matrix multiplication.
The idea of elementary particles (electrons, photons, etc) comes out in the maths in an indirect way. Extending the Lorentz transformations of special relativity with translations (+ some extra QM magic) gives what is called the Poincaré group. The ‘strongly continuous unitary representations’ of this group with positive energy can be built up from irreducible representations, with parameters interpreted as mass, spin etc. It turns out that these are the elementary particles. (I don't pretend to understand this!).
Current work in string theory and loop quantum gravity is investigating mathematical structures where categorical thinking is very influential. This is outlined in the latter part of the paper, where I am way, way out of my depth.
Doing things in a mathematically rigorous way gives a sense of security that you really know what you’re talking about. Physicists pride themselves on being rough and ready: if some complex series expansions is getting the right results, who cares whether it’s always convergent or whether the underlying theory is consistent (or even exists). They say that the mathematics of string theory is so complex that it takes years just to master it. Without yet more years studying the width and depths of pure mathematics, I don’t see how one could master category theory so as to wield it as a creative tool. No wonder Smolin complained that category theory was the hardest thing he had had to study.
Most systems designers have met abstract data types, the specification-equivalent to ‘objects’ in object-oriented programming. Mathematically, an abstract data type is an algebra: a collection of constants and functions together with equations which determine how the functions work. There are algebras for sets, lists, trees, directed graphs, to name just a few of the building blocks of formal specification.
When we design a system, we compose these basic definitions to create more complex data structures (e.g. lists whose elements are trees). This is where category theory comes in. The objects in category theory are mathematical structures such as sets, lists, trees, vectors, real and complex spaces, etc. The operations of category theory are those which compose and project these spaces. So in a sense, we were building a category theory machine for universal algebra.
I was still studying undergraduate mathematics at the time, finishing my degree. I had a superficial understanding of the kind of thing category theory was, but it was impossible to penetrate to the underlying motivation. Category theory, which emerged from algebraic topology, abstracts from the deep properties of a number of apparently unrelated mathematical structures. Consequently a deep feel for a lot of mathematics is needed to understand what the theory is trying to achieve. The reward is the profundity of mathematical insight which then emerges.
Although I knew from reading the books by Woit and Smolin that category theory was at the heart of much of the reconceptualisation in physics today, it was not until I stumbled across “A History of n-Categorical Physics” by Baez and Lauda (cached here) that I got a sense of what that meant. The category theorists believe that their discipline is the right framework for structures that the theoretical physicists have been groping towards for decades.
Some interesting points from the paper.
When Heisenberg developed his famous ‘matrix mechanics’ version of quantum theory in 1925 he had never heard of matrices. It was his thesis advisor, Max Born, who had to gently break it to him that he had reinvented matrix multiplication.
The idea of elementary particles (electrons, photons, etc) comes out in the maths in an indirect way. Extending the Lorentz transformations of special relativity with translations (+ some extra QM magic) gives what is called the Poincaré group. The ‘strongly continuous unitary representations’ of this group with positive energy can be built up from irreducible representations, with parameters interpreted as mass, spin etc. It turns out that these are the elementary particles. (I don't pretend to understand this!).
Current work in string theory and loop quantum gravity is investigating mathematical structures where categorical thinking is very influential. This is outlined in the latter part of the paper, where I am way, way out of my depth.
Doing things in a mathematically rigorous way gives a sense of security that you really know what you’re talking about. Physicists pride themselves on being rough and ready: if some complex series expansions is getting the right results, who cares whether it’s always convergent or whether the underlying theory is consistent (or even exists). They say that the mathematics of string theory is so complex that it takes years just to master it. Without yet more years studying the width and depths of pure mathematics, I don’t see how one could master category theory so as to wield it as a creative tool. No wonder Smolin complained that category theory was the hardest thing he had had to study.
Saturday, December 16, 2006
The Xmas house (redux) and thoughts of Iraq
Clare complained that the previous picture of the house didn't do justice to the latest round of Xmas lights. So here is our house at dusk.
We were debating how the Romans would have handled the present Iraq situation. The American game plan seems to be to push the Shiite leadership into concessions which could bring the Sunni Baathists on-side, isolating the Islamic fundamentalist who could then be crushed.
The problem is that the assumed political middle ground doesn't exist. The Shiites hate the Sunnis for past wrongs, and those sentiments are reciprocated by the Sunnis big-time. The politicians being pressurised by the Americans are themselves detached from the militias, the tribal and religious groups who are carrying out the violence.
The New York Times carried a report that the Saudis threated the Americans that if they pulled out and the Iraqi Sunnis were then involved in a civil war with the majority Shias, the Saudis would intervene militarily on the side of their Sunni kinsmen. The Saudis stated that they would also increase production of oil to halve the world price, thereby bankrupting the Shia Iranian regime, currently flush with oil revenues.
The standard Roman response to this kind of situation would be to build a wall around Iraq to seal the borders, then send the legions in to destroy all resistance and disarm the local populations. The fact that this would involve genocidal levels of killing would not deter them.
However, this option doesn't seem open to the Americans, not simply due to modern moral scruples, but because of the fact that none of Iraq's neighhbours could passively observe such a scenario without being drawn in. The consequences of the subsequent global Islamic radicalisation can also scarcely be imagined.
As far as I can see, whether the Americans get out over the next year or so, trying to manage a resolution of the situation along the natural fault lines, or whether they 'surge' another 30-50,000 troops into Baghdad to 'freeze' the situation for a while is hardly decisive. The eventual outcome is no longer under their control as their political project is no longer realisable. A sufficiently slow-motion resolution along the natural fault lines may (and only may) avoid a hot regional conflict.
This could have been, and was, predicted at the very start of this adventure by just about everyone who knew anything at all about the region.
And here is what it looks like as the sun vanishes.
We were debating how the Romans would have handled the present Iraq situation. The American game plan seems to be to push the Shiite leadership into concessions which could bring the Sunni Baathists on-side, isolating the Islamic fundamentalist who could then be crushed.
The problem is that the assumed political middle ground doesn't exist. The Shiites hate the Sunnis for past wrongs, and those sentiments are reciprocated by the Sunnis big-time. The politicians being pressurised by the Americans are themselves detached from the militias, the tribal and religious groups who are carrying out the violence.
The New York Times carried a report that the Saudis threated the Americans that if they pulled out and the Iraqi Sunnis were then involved in a civil war with the majority Shias, the Saudis would intervene militarily on the side of their Sunni kinsmen. The Saudis stated that they would also increase production of oil to halve the world price, thereby bankrupting the Shia Iranian regime, currently flush with oil revenues.
The standard Roman response to this kind of situation would be to build a wall around Iraq to seal the borders, then send the legions in to destroy all resistance and disarm the local populations. The fact that this would involve genocidal levels of killing would not deter them.
However, this option doesn't seem open to the Americans, not simply due to modern moral scruples, but because of the fact that none of Iraq's neighhbours could passively observe such a scenario without being drawn in. The consequences of the subsequent global Islamic radicalisation can also scarcely be imagined.
As far as I can see, whether the Americans get out over the next year or so, trying to manage a resolution of the situation along the natural fault lines, or whether they 'surge' another 30-50,000 troops into Baghdad to 'freeze' the situation for a while is hardly decisive. The eventual outcome is no longer under their control as their political project is no longer realisable. A sufficiently slow-motion resolution along the natural fault lines may (and only may) avoid a hot regional conflict.
This could have been, and was, predicted at the very start of this adventure by just about everyone who knew anything at all about the region.
Tuesday, December 12, 2006
Stanza as heard today in a BT building in London
At the end of a poorly-lit corridor
a woman tries resisting doors
complains to her companion
"Why would I want to be contactable, day or night, anywhere in the world?" ....
a woman tries resisting doors
complains to her companion
"Why would I want to be contactable, day or night, anywhere in the world?" ....
Monday, December 11, 2006
Discussion on “Remembering the future”
Some emails resulting from the posting earlier. Roy Simpson worked with me at Standard Telecommunications Laboratories in the late 1980s on AI topics. His background is physics. As usual with email, read from the bottom up.
*****
Nigel,
On the issue of the physics - QM (quantum mechanics) link and the branching aspect of time, an interesting gap appears in QM as discussed in Penrose's Road to Reality. Accordingly the area is "Multi-body Relativistic QM" - it sounds a mouthful, but the reason it hasn’t been developed is because it would seem to introduce multi-dimensional time -which no-one can make sense of.... and yet this area needs developing..... For various reasons I begin to think that there is a "Worldview" issue involved here. Worldviews are essentially psychological so maybe there is a connection here too.
Thus it seems likely that the psychological aspect of time will be closely linked to AI and also to the physics of time (and its perception). All these components need to converge on a good explanation.
Roy.
___________________________
nigel.seel@interweave-consulting.com wrote:
Roy,
I was more interested in the 'psychology' of time-past and time-future. I appreciate your point and the arguments work I think with directed graphs in general. The concept of 'time' comes in with the idea of an order relation on events, I suppose, but it doesn't have to be a total order. Note the diverse models of the various modal logics which have been applied to time modelling - forwards and backwards branching time as well as linear time.
The underlying physics would be the real boundary condition, but it's not clear to me that you get a good answer. The ontology behind QM is completely obscure (there are no classical events, only amplitudes). Since classical (Einsteinian)physics is effectively time-reversible, then I guess you have a total order. But perhaps it all breaks down again at the Planck length or something, where space-time meets quantum effects.
The piece was really a note to self, and would need a fair bit of work to reach conference paper standard, even if there was a place to put it. I DO think that the 'AI level' has something to add to the discussion of the 'psychological arrow of time', especially given the inadequacy of the treatment given by physicists who normally write about this stuff and who lack AI-based formal models.
Nigel.
----- Original Message ----
From: Roy Simpson
To: Nigel Seel
Sent: Sunday, December 10, 2006 10:52:10 AM
Subject: Recent Blog on Time Asymmetry
Nigel,
I am not clear whether the article notes that there is a distinction forward and reverse in Turing Machine operation.
If we consider a TM obeying function f so that e.g. f(1)=5, f(2)=6,f(3)=7,f(4)=5, ... then we can film a (any) sequence of inputs and the corresponding outputs. We run the film in reverse to observe the non-functional relation g. Non-functional since g(5)= 4 and g(5)=1.
So there is an asymmetry between f and g. To restore g to being a function (and so the reverse flow looks behaviourally like the forward flow) it is necessary to introduce another parameter - the Order - into the type and description of g. So f: Nat --> Nat, but g: Nat X Nat --> Nat, but g is now functional.
Arguments like this might suggest that the origin of temporal properties is fundamentally a computational one rather than a physical one, as commonly assumed.
Roy.
*****
Nigel,
On the issue of the physics - QM (quantum mechanics) link and the branching aspect of time, an interesting gap appears in QM as discussed in Penrose's Road to Reality. Accordingly the area is "Multi-body Relativistic QM" - it sounds a mouthful, but the reason it hasn’t been developed is because it would seem to introduce multi-dimensional time -which no-one can make sense of.... and yet this area needs developing..... For various reasons I begin to think that there is a "Worldview" issue involved here. Worldviews are essentially psychological so maybe there is a connection here too.
Thus it seems likely that the psychological aspect of time will be closely linked to AI and also to the physics of time (and its perception). All these components need to converge on a good explanation.
Roy.
___________________________
nigel.seel@interweave-consulting.com wrote:
Roy,
I was more interested in the 'psychology' of time-past and time-future. I appreciate your point and the arguments work I think with directed graphs in general. The concept of 'time' comes in with the idea of an order relation on events, I suppose, but it doesn't have to be a total order. Note the diverse models of the various modal logics which have been applied to time modelling - forwards and backwards branching time as well as linear time.
The underlying physics would be the real boundary condition, but it's not clear to me that you get a good answer. The ontology behind QM is completely obscure (there are no classical events, only amplitudes). Since classical (Einsteinian)physics is effectively time-reversible, then I guess you have a total order. But perhaps it all breaks down again at the Planck length or something, where space-time meets quantum effects.
The piece was really a note to self, and would need a fair bit of work to reach conference paper standard, even if there was a place to put it. I DO think that the 'AI level' has something to add to the discussion of the 'psychological arrow of time', especially given the inadequacy of the treatment given by physicists who normally write about this stuff and who lack AI-based formal models.
Nigel.
----- Original Message ----
From: Roy Simpson
To: Nigel Seel
Sent: Sunday, December 10, 2006 10:52:10 AM
Subject: Recent Blog on Time Asymmetry
Nigel,
I am not clear whether the article notes that there is a distinction forward and reverse in Turing Machine operation.
If we consider a TM obeying function f so that e.g. f(1)=5, f(2)=6,f(3)=7,f(4)=5, ... then we can film a (any) sequence of inputs and the corresponding outputs. We run the film in reverse to observe the non-functional relation g. Non-functional since g(5)= 4 and g(5)=1.
So there is an asymmetry between f and g. To restore g to being a function (and so the reverse flow looks behaviourally like the forward flow) it is necessary to introduce another parameter - the Order - into the type and description of g. So f: Nat --> Nat, but g: Nat X Nat --> Nat, but g is now functional.
Arguments like this might suggest that the origin of temporal properties is fundamentally a computational one rather than a physical one, as commonly assumed.
Roy.
Friday, December 08, 2006
Remembering the future
Why do we remember the past and not the future? A saloon-bar response is that the future hasn’t happened yet, but this is to glibly avoid all the real issues. Yesterday morning I failed to remember yesterday afternoon - but, from my vantage point now, yesterday has ‘happened’ in its entirety: I remember both the morning and the afternoon. So what was my problem yesterday morning? .... more.
Coming home to this?
As Clare came back from the shops lunchtime, she noticed this. Not our wall, but a neighbour's, around the corner. A certain amount of forensic camera work identifies the muddy tyre-tracks of the lorry which reversed into the wall - now long gone.
The police may make something of the paint samples left behind, and let's hope the insurance company doesn't try to weasel out of it.
Wednesday, December 06, 2006
The Xmas House
Our Christmas HouseIn America, our house had an illuminated reindeer family to shock and awe passers-by. Back in England, we have more modest objectives: our lit-up bush cheers walkers down our dark street.
You have no idea of the engineering resources which went into this. We have no outside electricity socket, so we planned to feed the outdoor lights from the garage. This is about 30 metres away at the bottom of our back garden. We had no wiring long enough, so we had to go to the hardware shop and buy outside extension cabling. Then there were issues in getting this cabling from the inside to the outside of the garage.
When we (read Clare) put the lights on the tree, we discovered the lighting flex was so thin that it easily goes between the kitchen window and window frame and into a power point in the kitchen.
Next year we may run to a small illuminated hedgehog ...
Monday, December 04, 2006
Homage to 'Permutation City'
You are in a dark, silent room. Lying back in comfort, you see, hear, smell, taste and feel absolutely nothing. Suddenly there is a sharp pain in your thumb. Ouch! You feel the pain and wonder what caused it. Meanwhile, five seconds pass.
Assume a space-time view. Your brain is circumscribed by a cube with sides, say, 15 cm. Using the speed of light as time-into-space translation, 5 seconds = 15 x 1010 cm.
So that five seconds of conscious experience is encompassed by a block of space-time measuring 15 x 15 x 15 x 15 x 1010 = 5 x 1014 cm4.
Now, neuron simulation models typically sample at a time resolution of 100 microseconds. That five seconds of painful experience comes down to 50,000 brain-state samples. Through advanced engineering, whilst you were in that room experiencing that brief pain, your brain was being sampled non-invasively: that five second experience is now all on disk.
Note that the four dimensional hypercuboid which circumscribed your brain during those five seconds has now been spread out in space as 50,000 ‘instantaneous-brain-state’ cuboids (mapped into storage), each invariantly ‘travelling through time’ at its own behest.
Here are the questions.
1. If we load brain-state samples [1 ... 50,000] into a computer, in sequence, in real time, is there - within the simulation - your feeling of puzzlement and pain. In other words, have we recreated your conscious experience as described at the start of this note above? (Think of it like a movie).
If you think the answer is no, why not exactly? After all, we are reproducing every single neuron of your brain in its exact behaviour: what else could there be to your experience?
2. If we load the sequence [1 ... 50,000] slower (or faster) than realtime into the computer, does the conscious experience of the simulation change? If so, why? The brain has no internal clock which is different than the firing of neurons.
3. If we run the sequence out of order, does that change anything? Each sample is independent of all the others. When it runs, it ‘doesn’t know’ which sample was previous and which will be next. No sample, after all, is changed in the process.
4. Suppose we don’t ‘run’ the sequence at all, but merely leave it on disk. Does the conscious experience still happen? And then in what order or all at once? The point here is that deceptive word ‘run’. When we ‘run’ a particular sample ‘on the computer’ we are doing nothing special - we’re simply copying the sample-content from one piece of storage (on ‘disk’) into another piece of storage (in the computer RAM). How does this meaningless, low-level act, change anything?
5. In the original space-time hypercuboid of your brain in five seconds of real time, all those instants continue to exist as space-like slices through that specific volume of space-time. Does this mean that the discussion around Question 4 also applies?
I would like to think that all these points are original - what they imply about consciousness is scary - but they were all anticipated (and more) in Greg Egan’s book Permutation City.
Assume a space-time view. Your brain is circumscribed by a cube with sides, say, 15 cm. Using the speed of light as time-into-space translation, 5 seconds = 15 x 1010 cm.
So that five seconds of conscious experience is encompassed by a block of space-time measuring 15 x 15 x 15 x 15 x 1010 = 5 x 1014 cm4.
Now, neuron simulation models typically sample at a time resolution of 100 microseconds. That five seconds of painful experience comes down to 50,000 brain-state samples. Through advanced engineering, whilst you were in that room experiencing that brief pain, your brain was being sampled non-invasively: that five second experience is now all on disk.
Note that the four dimensional hypercuboid which circumscribed your brain during those five seconds has now been spread out in space as 50,000 ‘instantaneous-brain-state’ cuboids (mapped into storage), each invariantly ‘travelling through time’ at its own behest.
Here are the questions.
1. If we load brain-state samples [1 ... 50,000] into a computer, in sequence, in real time, is there - within the simulation - your feeling of puzzlement and pain. In other words, have we recreated your conscious experience as described at the start of this note above? (Think of it like a movie).
If you think the answer is no, why not exactly? After all, we are reproducing every single neuron of your brain in its exact behaviour: what else could there be to your experience?
2. If we load the sequence [1 ... 50,000] slower (or faster) than realtime into the computer, does the conscious experience of the simulation change? If so, why? The brain has no internal clock which is different than the firing of neurons.
3. If we run the sequence out of order, does that change anything? Each sample is independent of all the others. When it runs, it ‘doesn’t know’ which sample was previous and which will be next. No sample, after all, is changed in the process.
4. Suppose we don’t ‘run’ the sequence at all, but merely leave it on disk. Does the conscious experience still happen? And then in what order or all at once? The point here is that deceptive word ‘run’. When we ‘run’ a particular sample ‘on the computer’ we are doing nothing special - we’re simply copying the sample-content from one piece of storage (on ‘disk’) into another piece of storage (in the computer RAM). How does this meaningless, low-level act, change anything?
5. In the original space-time hypercuboid of your brain in five seconds of real time, all those instants continue to exist as space-like slices through that specific volume of space-time. Does this mean that the discussion around Question 4 also applies?
I would like to think that all these points are original - what they imply about consciousness is scary - but they were all anticipated (and more) in Greg Egan’s book Permutation City.
Sunday, December 03, 2006
Book about to be published ...
My book will now be published (in the UK) on Wednesday Dec. 6th.
Successful authors have launch parties with the glitterati: Clare and myself may raise a glass in that cosmopolitan centre which is Penton Corner. You can buy it, of course, here.
We were hit by 80 mph gales last night, and as is traditional, the fence gave way.
Here is another view.
Apparently more of the same to come this evening.