Darkness

"I was working on my computer, aware of the headlights of oncoming cars. They cause me little bother; in fact, they’re quite reassuring: a communion with other hard workers, getting on with their lives.

"Even an absence can stimulate. I looked up and the window was black. How curious. I stared at the window wondering, why were there no lights? At this time of the evening, it's always a river of white.

"I looked around. The house was as it always was. The lights were on, the rooms well-lit. There was a curious silence. Should anyone else be in the house with me? I wasn’t sure.

"I was now getting somewhat alarmed, something was clearly not right. I believe the feeling is known as dissociation, reminding me of Kafka, one of my favourite authors. But I didn’t think I was dreaming.

"Absurd thoughts came to me. Perhaps I had lived my whole life in a virtual environment. Perhaps this was a ‘glitch in the matrix’, like when that cat reappeared in the film. You blink, you expect reality to come back, but somehow it didn’t. I seemed to be the sole inhabitant of a familiar, well-lighted, but wholly empty world, and I couldn’t quite remember how it had ever been different. I was getting badly frightened.

***

"It’s been a while. Nothing has changed externally, it’s still that long, eternal evening. The house is well-lighted, while outside my window there’s nothing but unrelieved darkness. Curiously, I never seem to leave this room. I don’t seem to get back to my work on the computer either. I just go round in this endless loop.

***

"Here is what I think, though I can’t prove it. I think I must have had a massive stroke. I think I am probably lying in an intensive care ward, tubed to the eyeballs. Large parts of my perceptual brain must have ceased to function, and the higher cortical layers are synthesising this reality out of my memories. A kind of ‘natural virtuality’ if you like. Unfortunately, by definition, I can’t prove this, but what else could it be?

"It’s funny, isn’t it. The basis of this conclusion is Descartes: “I think, therefore I am”. He never realised the elasticity of ‘am’. When I did philosophy at Warwick, I believe I encountered a refutation of Descartes’ argument somewhere.

"Now, if only I could recall it, I’d be out of here.”

Flying justs gets b. & b.

Yesterday was Aberdeen. The flight up wasn’t so bad: we were only delayed an hour. The Geordie pilot confided that they had had mechanical problems earlier (there’s a relief!) and that they would be trying to make up for this all day. His general tone suggested this was unlikely.

I was not late for my meeting, just unable to join the regular weekly team call.

Due to the paucity of flights later in the day from Aberdeen to Southampton, I accompanied a colleague by car down to Edinburgh and arrived at the airport at 6.40 p.m. Good time to check-in, grab a meal, catch-up on email and board the Flybe flight at 8.40 p.m. getting into Southampton at 10.10.

The lady at the Edinburgh check-in was not encouraging. Trouble at Southampton, (something to do with Flybe’s acquisition of BAConnect) and the flight was delayed. We would be going to Bournemouth instead. There would be buses.

S0 I snacked, did email, but mostly waited. 8.40 came and went and it was 10.10 p.m. when we eventually lifted from the Edinburgh runway en route to Bournemouth - the jet was packed by the way, we must have not been the only ones. At least the buses were there. I got home just after 1 a.m.

No amusing people this time. Just folks tired and exasperated, and residual gallows humour (“is this bus going to Edinburgh?”).

Edinburgh airport at 8.40 p.m.

Northanger Abbey

The second Jane Austen adaptation on ITV yesterday evening and what a change from last week’s Mansfield Park!

This was a delight, perfectly capturing the intent of the novel and with beautiful characterisation from all the main players. Worth buying the DVD here.

Next week it’s Persuasion. Let’s hope the new high standard is maintained.

SF books for Adrian

Adrian called yesterday from Whistler, Canada to let us know that on the last snowboarding run of the day, he had broken his collarbone, again.

Adrian flipping more successfully (multiframe)

Local time when he called was 2.30 a.m. and he was all-nighting to take his X-Rays to the course instructor at 8.30 a.m. He had been due to start a week’s supplementary instructor course on ‘park riding’ (jumps, half pipe): this will now have to be substantially postponed, and Adrian is off the slopes pretty much till season-end.

Surrounded by classics (The Idiot, Bonfire of the Vanities) he is pining for the fast food of classic science fiction. The dilemma - what to order for him from Amazon.ca? Should be good stuff, readable and not something we have at home already.

Here is what I chose.

• The Forever War - Joe Haldeman


• Gateway - Frederik Pohl


• Starship Troopers - Robert Heinlein


• Dune - Frank Herbert

Actually, we already have ST but I couldn’t resist. They should arrive before Easter.

Penny-wise - Pound-foolish

Imagine a cube - 100 pence long, 100 pence wide and 100 pence high. This cube contains one million pennies, and so is worth £10,000.

Of course, since 100p = £1, we could equally well take this cube to be one pound coin long by one pound coin wide by one pound coin high. In other words, a cube containing just one £1 coin.

This proves the old saying of the title.

Another example of the hallucinatory effects of long periods in departure lounges ...

_______________
Postscript: 25/2/07.

You may think the above is quite frivolous. Yes, but also interesting as to what's wrong with the argument. The correct answer has to disentangle the following.

1. The relationship between, centimetres and metres, and cubic centimetres and cubic metres.

2. The relationship between pennies and pounds.

3. Would a correct analogy to (1) work if we had a concept of cubic pennies and cubic pounds?

4. The confusion between the purely logical relationship of (2) and the fact that both pennies and pounds, as coins, are three dimensional physical objects which can be placed in lines, and in the cells of a three dimensional cube: a process which conflates the distinctions of (1-3).

To properly make everything explicit you end up with a nicely elaborated commutative diagram (exercise for the reader).

Airport thoughts

My sister wrote to me about her airport experiences

"Agree your job appears to have some less joyous moments. I guess you just read a lot in airport lounges. I related to your comments about strange pacing man in airport. Saw similar chap in Washington whilst waiting for flight to New York. Was convinced we were all going to die when he boarded same plane. But hey, still here!"

Well, Elaine, I also routinely see people who I suspect of plane-demolishing intentions. However, I reassure myself that even if they did manage to down a Flybe aircraft on an internal flight between two provincial airports, no-one would either notice or care! So why bother.

Sometimes I listen to music on the MP3 function of my mobile phone ... I read a bit. But mostly I just veg out and doze. Sometimes I speculate about what I will do if they cancel the last flight, and I have to overnight at the airport. I surreptitiously try to stake out three seats in a row where I wouldn't be disturbed!

I know it's a well-known truth, but flying regularly brings it home to you just how fundamentally unreliable air travel is.

A very brief tutorial on QM and SR

I write to Roy Simpson (who has an Oxford D.Phil. in the subject under Prof. Roger Penrose).

"... One day I will know enough QM to understand why it isn't mathematically secure! I currently even struggle to understand whether/how the Hilbert space setting of QM handles special relativity conceptually (in the sense of Minkowskian space-time)!"

Roy casually helps me out ... (may be useful to other perplexed individuals out there):

"QM on its own could be mathematically secure.

But QM + Special Relativity = unsecure (or at least uncertain as below)

Remember the Schrodinger equation itself:

H psi = d/dt psi

Here the H (Hamiltonian) might or might not be relativistic, but there is a lone d/dt on the RHS. This singles out "time" for special treatment in the Schrodinger equation different from space (d/dx terms). Any d/dx will be inside the Hamiltonian unrelated to this d/dt. So this is the root of the Newtonian aspect.

Meanwhile the psi lives in a Hilbert space.

Relativity/Minkowski space would prefer a term like:

d/dx + d/dy + d/dz - d/dt,

even better with these components squared.

When this is done we end up with the Dirac equation for a specific type of particle like the electron. Elegant but not the original Schrodinger equation which is somehow also meant to be valid even for a relativistic electron. The Schrodinger aspect gets ignored in physical practice as all the numbers now come from the Dirac equation.

So if you ask too many questions in the relativistic case about the Schrodinger equation you end up in inconsistency. Schrodinger himself kind of knew this, but opted for his equation as it handled the non-relativistic case well - and the relativistic equations came later.

More in that Penrose book."

Yes, I am going to have to go back to it.

Postscript: March 29th 2007

When I raised the query at the top of the page, I was thinking of a Minkowskian metric over the Hilbert space. Wrong! The Hilbert space is an abstract space, not space-time. In fact, space-time is just a particular basis out of many, corresponding to event-positional observables (although, as Roy pointed out, time is 'special').

In fact, the way Special Relativity comes into Quantum Mechanics is by way of Quantum Field Theory, as described in 'Deep Down Things' which I reviewed here.

I find QM and SR one vast jigsaw puzzle and the pieces are only slowly coming together as I study more.

Mansfield Park redux ... again!

Patricia Rozema brought us 'feisty Fanny' in the 2000 film . Then there was the original BBC six-parter which, nominally true to Ms Austen's script, brought us 'dowdy, plain-jane Fanny' and a difficult-to-believe final romance. And last night ITV presented 'Tardis Fanny', as Billie Piper scampered around the 90 minutes of film and 30 minutes of adverts constituting the latest Mansfield Park.

The use of just the one set obviously saved money, and the deletion of Fanny's exile to Portsmouth saved both time and money. What was left of Ms Austen's complex tapestry? Sadly just plot #5 in the standard lexicon:

"Girl loves boy, boy fancies other-girl, other-boy takes unwanted fancy to girl, other-boy shown to be a bad lot, other-girl found to be a bad lot, boy sees error of ways, girl marries boy."

With nothing left going for it, the plot jolted and shuddered its way through the required algorithm, jettisoning pieces of superfluous Austen back-story en route. It finally disolved into a sickly cloud of sugar.

Trivia point: Billie Piper looks quite decorous from some angles, but when she smiles, images of a large mare come inescapably to my mind. She may have topical street cred with ITV's target audience right now but I'm really not sure about her shelf life. To be fair, her acting was by no means the worst (which might be reserved for the actor playing Edmund).

And another thing, I'm really not sure about cousin marriages!

Next week the delights of the 'reduced Austen company' doing Northanger Abbey. We then get Persuasion and a repeated version of Emma (details here).

Chick Flix

When I was up in Edinburgh last week (previous post "fog") I took coffee and cakes with two colleagues. The discussion turned around to wives, and each of them proudly showed a picture from their wallets of their equally gorgeously-attractive partners.

Needless to say, I had no such picture. However, a quick check this weekend with my Sony-Ericsson K750i camera-phone manual showed that I could replace the current anodyne screen wallpaper/screensaver with pictures of my choice. Ransacking my collection of photos I came up with the following.

This is the basic phone 'wallpaper'

This shows as the camera goes to standby.

Reserved for jetlag and 'the morning after'

In fact I originally planned to use the picture below, but as it dates back to 1980, only a few years after we got married, I was promptly forbidden.

AI modelling with undefined state

Roy Simpson, a colleague back at STL in the 1980s where we were doing Artificial Intelligence (AI) and Computer Science (CS) research, wrote to me about some work he was doing which touched on my Ph. D. research here. This is what he said.

"Some years ago I found some theorems and related ideas in the logical basis of CS & AI which looked like they would have interesting implications. Grouped together these ideas got dubbed: "TTM-Network Theory" - the working claim being that it provides the best ever logical foundation for Computational Network theory. A big claim for a small set of results - so the challenge has been to confront well known areas of CS with the TTM ideas to see if the established areas can be improved (& maybe the TTM side improved as well).

Anyway after some encouraging initial results, last year I decided to turn attention to the SRS Model (and Reactive Systems Theory in general). Again the question was: Do the TTM ideas cause any form of re-evaluation of the SRS Model and/or its conclusions? The SRS Model as presented, for example on your website.

The answer was that an ambiguity has been identified in the basic presentation of the SRS Model. The crux of the problem is that we dont get told whether or not the object update functions f1 etc are total or partial. From this ambiguity a series of issues concerning the formal presentation of the material then unwind, these issues may also spill over into the general conclusions (see below).

A possible view is that the functions are total - this is certainly how all the examples are laid out: SCP, L-R, etc. But totality of the functions is a restriction and not the general case - so why should these functions be total? If it is any consolation none of the books or articles I have read on "Computation and Physics" address this question - they all silently assume that such functions will be total. As you can imagine another branch of the TTM research is whether it could make physical (especially quantum) sense to allow partial functions here.

So maybe the SRS update functions are partial? In that case a world like the following can arise:

w(3) = {(a,(1,1),f1),(b,(2,2),f2),(c,(3,U),f3),(d,(4,4),f4)}

- here object c has its external state undefined as a result of the non-termination of its update function from an earlier time.

The next formal problem is how to we define Next to get to w(4)?

Next could be strict so that w(4)=U. This does not seem the proper way to model such a situation (because object c might be independent of the others), so I would argue for Next to be non-strict. We have to be more careful in our formal analysis though, because non-computable functions are also non-strict.....

This was where I left the situation last year (except I checked out current theories of Reactive systems - but that is another story). Recently I have returned to the SRS model to see whether and how these issues might ripple deeper into the SRS model - and another discovery (at least for me) was awaiting!

The problem now is with the PTL (Propositional Temporal Logic) definitions - specifically the valuation function. Consider any predicate on worlds like:

P (w) = For all objects in world w. internal state value=external state value.

Condition P is nearly satisfied by w(3) above except for object c. The undefined value for object c's external state makes the valuation function here undefined. The common solution is to introduce 3-valued logic to model possible non-termination logics (as we know). If we stick to a 2-valued valuation function then the valuation function is non-computable. Anyway I then realised that PTL is actually a Modal Logic and I was now considering a 3 - valued Modal logic for the SRS Model! Except I had never heard of 3-valued Modal logic before! None of the standard references (Hughes, Cresswell, etc) cover it.

I have had to do a Web search for papers on 3-valued (nowadays n-valued or even Heyting algebra valued) Modal Logics. I can see that it is an area that is evolving - with some similarities and differences with the two valued case. Specifically duality between necessity and possibility modal operators is in general lost - they have to be defined separately.

So my recent objective has again been achieved - to show that the theorems which drive the TTM work can open up new areas.

As far as the SRS Theory is concerned there would need to be a re-examination to see how the arguments above affects your conclusions. I am aware that a key part of this re-examination is the question: Does the computational (ie non-termination option) of the model's functions actually help in Cognitive Modelling (ditto physical modelling)? Does the model really just want reliable total functions?

Interestingly your final conclusion is that the multi-agent extension collapsed into well known Protocol theory. Well I wonder if that is still true in the 3-valued case? Three valued Modal logic isnt well known. Then again maybe Protocol theory isnt that general either - another target for my TTM work one day."

--------------------- and my reply

"I think this is quite interesting and would make only three points in response.

1. The SRS model is probably too constrained to be the most suitable structure for the mathematical analysis of either synchronous automata with undefined state-elements or three-valued modal logics. The extra structure in the model is there to handle psychological states. However, I am sure there is some really interesting maths in the addition of undefined elements in automata theory/modal logic, as you suggest.

2. In my naive ontology, which I was getting at with the SRS model, I put in the minimum necessary structure for a multi-object/multi-agent world with non-transparent behaviour (via hidden, private state) which would allow the introduction of intentional modelling (epistemic, doxastic, conative operators). My intuitions did not extend to situations where object next-states would be undefined (and still don't!). If you get any fresh insights at the intentional level please let me know. Of course, in physics terms, the SRS model is hopeless: absolute simultaneity is structurally built-in, plus complete determinacy. It's through-and-through Newtonian!

3. My Ph.D research, as written up on my site, was really modelling bacterium/insect levels of behaviour (despite references to rats and Skinner boxes). I was obviously interested to see to what extent the approach could be extended to human-level cognition, and was led to concerns about ‘what problem does human-level cognition actually solve’. This is now the field of evolutionary psychology, but my stuff was before that.

Just adding in a requirement to communicate doesn't help much, because once you define a 'distributed communications problem' the answer is to design a communications protocol. You gets ants, not people. I concluded that I couldn't easily find a simple framework which transcended this and which led to a tractable model saying something about human cognition, and then time ran out at STL as we became BNR.

I think the fact that this is a really hard problem is evident in the lack of progress since - I suspect that we need lots more brain-scan type data on brain architecture and function before we will have the insights as to what specifically the human brain does differently than, say, that of an insect or a rat - most notably in the consciousness space."