Friday night: an apeology

Can I say about Friday night how very sorry I am that you have none of you have yet apologised to me for your behaviour. What a disgraceful shower, and carrying on like that in Club Derrig!

Top Team......?

After spending a few days shacked up in the lap of luxury in the middle of the English countryside - dull, eh, readers? - a right bunch of reprobates are now self-declared 'losers'.

Look at them - smug, self-satisfied, and stuffed to the gills with the finest foods and wines available from Grantham's 'Victor Value' supermarket.

Why wasn't I asked?

Clever Clogs

I am delighted, but not at all surprised, that I have been approached to put together an elite team for the wacky BBTV show quiz "Smartarses".

I can, of course, answer on pretty much any subject you care to engage upon me with. The downside is that I am unable to be considered a team on my own.

Having cast around Club Derrig for likely team members I identified the Lady Jojojo, Jools Hallam, Tallulah and the Twins of Evil (on a job share basis) as those with the most potential.

Armed with this information I gathered them together in a state of heightened anticipationing and awarded them team membership.

Unfortunately, not only did they all start getting a tad iffy when the Lady Jojojo revealed that her legions of past boyfriends would be alarmed to see her present state of decrepitude, and that TV adds around half a stone to one's appearance, but I also discovered that between them they were a coven of blithering fools.

The putative Team CD had taken a right royalist knock and no mistake!

I looked at the dregs of humanity slumped drooling against the bar - men at their lowest ebb, and only the vainest hope of charitable support - and chose Bertuchi, Evans, Oestreicher, and Mr"." Thomas, with the Genius Amanuensis along for the ride.

Between us we could fill a bucket with what we don't know.

Keep 'em peeled for our possible televisual appearance.

Stage genius identity query

A star-spotter writes:
Dear Uncle Colin
Vic Olivier? Who?
A mum

Uncle Colin advises such and thuslike:

Short, sharp, and to the point - just how I like my mums.

Let me roll back into the mists of time to when all our heroes pranced about in tights on the silver stage, poinards in hand, and dripping in painted grease in front of the raw crowds of hoi-polloi.

Vic Olivier,(born 8 July 1898 in Kingston upon Hull, East Riding of Yorkshire, England) is a long-serving comedian. He is best known for his legendary 'faulty handshake' routine and for his amazingly lifelike gibbon impressions (a part he has now played in all 37 of Shakespeare's plays on stage, never making a successful transition to the silvery screen).

He is also, of course, the older brother of the lesser-known failed ventriloquist Larry Olivier.

Olivier grew up in Doncaster in a working-class family. While working at BP's chemical factory, he started making all sorts of noises, making his workmates laugh with improvised comic routines during breaks (and all too often outside them). Encouraged by his line managers, he started to work the northern workingmen's club scene, with steady success through the 1930s. He first came to national media attention after a successful appearance at the Royal Variety Command Performance in 1951. Though occasionally appearing on television thereafter, he made his main reputation on the northern club circuit, and was highly regarded by many fellow comics. (Notably Frank Carson, Bobby DeNiro, Michael Caine, Prince Philip, Les Dawson, and 'Little Ann Large', who was a regular house, and family wedding, guest.)

To casual television viewers, he is best known for two routines: one in the guise of a northern club compere whose handshake works intermittently; another adopting the noises, gestures and movements of a gibbon, using his outturned jacket to suggest the mighty creature's wings. However, the 'soundbite' demands of television work have never reflected the detailed and large-scale routines that have characterised Olivier's club work and which brought him enormous success through the 1950s and 1960s. (He was never a participant, for example, in the 1970s ITV gagfest series The Professionals.)

His reputation among working-class clubgoers and fellow professional comedians has always been somewhat tarnished by his habit of staeling drinks from the tables of patrons; however, those who have never ventured inside a working men's club and imagine they know the comic's work from a few unrepresentative minutes of television are, like everyone else, totally bamboozled as to how he has stayed constantly in demand for over 40 years.

In 1970 he won an ITV series called Get Off, You're Rubbish, in which club entertainers were pitted against each other, performing their full routines in front of a panel of judges. Olivier was easily knocked out in the first round by a unanimous decision of the panel.

His style is very much in the traditional northern-comic school, based on absurdist situational monologues and the phrase 'sock-drawer', rather than a 'series of jokes', and shows a notable influence of the 1950s star Al Martino. Unlike some comedians of the 1930s, Olivier did not rely on any racist material; however, his zany set-pieces have often drawn on northern working-class archetypes, for which he was often punched.

He has been married eleven times to the same woman, who is getting thoughly sick of it. He has twenty-eight children scattered around Yorkshire, several hundred grandchildren, and an ever-vaster number of great-grandchildren who make up most of the population of Hebden Bridge. He lives in Penury, a rundown village west of Hull.

I hope that clears it all up.

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Liquid diet consumption foolishness

A cavalier-cum-King Charles' spaniel writes:

Dear Uncle Colin,
I keep seeming to need a fresh change of clothes whenever I partake of that delightful contemporary comestible "the smoothie". Any hints?
Mutt

Uncle Colin advises such and thuslike:

Oh Mutt, Mutt, Mutt, Mutt, Mutt, Mutt, Mutt, Mutt, Mutt, Mutt, Mutt. Crazy name, crazy guy!

It's a problem more common than one might think amongst those who have damaged their brains with Wee, PPS, XXX-Box, Zeldo and Audio Hedgehog, not to mention those Spanish electrician twins. A regular input of these serves only to enflabbergast the brain parts that deal with operational sequencing, leading to all sorts of embarrassing problems, such as sticking one's head out of unopened windows.

As regards the smoothie, try printing off the following and sticking it on your refrigerator so it may be consulted before creating havoc:

Smoothie operating instructions

1. Open refrigerator

2. Locate smoothie

3. Remove from refrigerator

4. Shake smoothie vigorously to ensure even distribution of contents

5. AND ONLY NOW TAKE THE BLOODY LID OFF, YOU TWIT.

6. Position bottle opening at mouth.

7. Consume responsibly.

8. Dispose of smoothie bottle in recycling bin.

On no accounts reverse the order of operations 4 and 5.

I think you will find this advice will see a reduction in your laundry bills.

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Homme superieur?

A genius and auto-didact scribes:
Dear Uncle Colin,
I see that Morrison, clearly a representative of higher beings sent to grace us with his gorgeous presence, has been apologised unto by a 'music magazine' for allegations made thereunto him. How think you on this?
Yours in awe of your mighty figurine collection and sterling crop of locks,
Anonymous

Uncle Colin advises such and thuslike:
I am always delighted to get such important and thought-provocating messages from people who are clearly on a par with me mentality-speaking.

I do not wish to recount the many times I have seen the hairy-chested giant of pop, and will reserve that for my readers' pleasure on another occasion.

I will say, though, that this man - so unfairly maligned, misrepresented, and abused by the MNE, the Words, his former band-mates in The Smurfs (God rest that beautiful band of brothers), the judge at the royalties trial, the entire reggae industry, and all the others - is nothing less than a God descended to earth in human form.

Who could fail to be stirred by his ripe quiff? His sturdy and inviting musculature? His simpering chops and ambrosaical way with a melody line? The way he removes his jacket whilst he sneers, exposing his self-knit chunky cable-stitch top? The rocking chair? His grandfather's clock? The delicate lace doilies? The poodles? Half a pound of sausages, a packet of Daz, two large aubergines, and a handful of dolly mixtures. And a trout, if you wouldn't mind doing the descaling and top and tailing it for me I'd very grateful?

If only more of us could be like him!

A very good question indeed. More like this please.

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Breakfast element equivalence conundrum

An entrepreneur writes:

Dear Uncle Colin,
I have a great idea for providing breakfasts for drivers at road-side cafes. Don't laugh - it's an idea whose time has come. I seriously think it has potential to be a real moneyspinner.

The only flaw in my plan is quite how the elements of a breakfast relate to one another commensurateness-wise. For example - the mighty fried egg. A lovely way to get your protein slathered in grease, but not everyone's cup of tea. If a punter should ask for the set breakfast (sausage, fried egg, beans, fried bread, black pudding, chips, tomato, toast and tea or coffee) but request no fried egg, preferring a replacement, commensurate element, just what should the replacement element be?
Your soon-to-be-wealthy admirer
Ricky Dicky

Uncle Colin advises such and thuslike:

An important issue, as I have learned to my cost in many of the fine restaurants I have frequented down the years. You would think it is simply a matter of the cost of the element, but there are other factors to take into account: overall nutritional balance of the meal; the weight of the item; the aesthetics of how the elements meld together to create the breakfast.

I've given it a great deal of thought and believe it comes down to the following simple table.

1 fried egg = 1 sausage and a portion of black pudding
1 tomato = 80 beans
6 chips = 1 slice fried bread

Follow this golden rule and you'll be rolling in the moolah in a matter of months.

Detection overload strain problem

A spiv writes:
Dear Uncle Colin,
I have exhausted my reserves through deployment of my wizard detective skills in solving the case of the missing fiver and the few bob. I am trying to relax and recuperate my sleuthing abilities, but simply can't get the time what with work and the lady wife's demands. Can you show me a simple way of getting some quality chill-out time so I can get back to being a top 'tec and spiv?
Sam O'Striker

Uncle Colin advises thus and suchlike:

We need more like you on our team! Yes, I'm glad to be of help. Next time you have five minutes free, stare solidly for two minutes at the graphic at the top of this post. Sit close to the screen and do not let your concentration slip. After two minutes, look away quickly at a blank sheet of paper (best to have this prepared beforehand and not go stumbling around trying to find one as it'll mean having to start all over again) and - out of nothing - POOF! - an image of a very famous event will appear.

It's a fantastic illusion, but also an amazing way of giving the brainstuff what amounts to an oilbath and relaxing old massage.

(And, in the spirit of generosity, there's a prize for every reader who identifies the event correctly!)

Tricky philosophicality

Dear Uncle Colin,

So what do you make of this idea that social and cultural scientists have anything to contribute to the 'hard' disciplines of mathematics, physics, and so on?

The President, The Lady Josephine Whelan of Whelan-Whelan

Uncle Colin advises such and thuslike:

You come round here with your fancy Liverpudlian banter and think I've nothing to say about the subject. Ha! Why do you think I keep experts such as top scientist and baby-maker Paul Wacko on the staff team? I've had a word with him and he thought about it a bit last night and he phoned me up this morning and said:

Morning, Col. How's the leg?

("Not bad" I said.)

Good (he said). Well, I had a bit of mull last night just before bed. Then I got in and had think about the conundrum you set me. Well, there are many natural scientists, and especially physicists, who continue to reject the notion that the disciplines concerned with social and cultural criticism can have anything to contribute, except perhaps peripherally, to their research. Still less are they receptive to the idea that the very foundations of their worldview must be revised or rebuilt in the light of such criticism. Rather, they cling to the dogma imposed by the long post-Enlightenment hegemony over the Western intellectual outlook, which can be summarized briefly as follows: that there exists an external world, whose properties are independent of any individual human being and indeed of humanity as a whole; that these properties are encoded in ``eternal'' physical laws; and that human beings can obtain reliable, albeit imperfect and tentative, knowledge of these laws by hewing to the ``objective'' procedures and epistemological strictures prescribed by the (so-called) scientific method.

But deep conceptual shifts within twentieth-century science have undermined this Cartesian-Newtonian metaphysics; revisionist studies in the history and philosophy of science have cast further doubt on its credibility; and, most recently, feminist and poststructuralist critiques have demystified the substantive content of mainstream Western scientific practice, revealing the ideology of domination concealed behind the façade of ``objectivity''. It has thus become increasingly apparent that physical ``reality'', no less than social ``reality'', is at bottom a social and linguistic construct; that scientific ``knowledge", far from being objective, reflects and encodes the dominant ideologies and power relations of the culture that produced it; that the truth claims of science are inherently theory-laden and self-referential; and consequently, that the discourse of the scientific community, for all its undeniable value, cannot assert a privileged epistemological status with respect to counter-hegemonic narratives emanating from dissident or marginalized communities. These themes can be traced, despite some differences of emphasis, in Aronowitz's analysis of the cultural fabric that produced quantum mechanics; in Ross' discussion of oppositional discourses in post-quantum science; in Irigaray's and Hayles' exegeses of gender encoding in fluid mechanics; and in Harding's comprehensive critique of the gender ideology underlying the natural sciences in general and physics in particular.

I wanted to take this further by taking account of recent developments in quantum gravity: the emerging branch of physics in which Heisenberg's quantum mechanics and Einstein's general relativity are at once synthesized and superseded. In quantum gravity, as we shall see, the space-time manifold ceases to exist as an objective physical reality; geometry becomes relational and contextual; and the foundational conceptual categories of prior science -- among them, existence itself -- become problematized and relativized. This conceptual revolution, I believe, has profound implications for the content of a future postmodern and liberatory science.

To do this I'll first review very briefly some of the philosophical and ideological issues raised by quantum mechanics and by classical general relativity. Next I will sketch the outlines of the emerging theory of quantum gravity, and discuss some of the conceptual issues it raises. Finally, I will comment on the cultural and political implications of these scientific developments. It should be emphasized that this is all of necessity tentative and preliminary; I do not pretend to answer all of the questions that are raised. My aim is, rather, to make the key points, and to sketch as best I can their philosophical and political implications. I have endeavored here to keep mathematics to a bare minimum.

It is not my intention to enter here into the extensive debate on the conceptual foundations of quantum mechanics. Suffice it to say that anyone who has seriously studied the equations of quantum mechanics will assent to Heisenberg's measured (pardon the pun) summary of his celebrated uncertainty principle:

We can no longer speak of the behaviour of the particle independently of the process of observation. As a final consequence, the natural laws formulated mathematically in quantum theory no longer deal with the elementary particles themselves but with our knowledge of them. Nor is it any longer possible to ask whether or not these particles exist in space and time objectively ...

When we speak of the picture of nature in the exact science of our age, we do not mean a picture of nature so much as a picture of our relationships with nature. ... Science no longer confronts nature as an objective observer, but sees itself as an actor in this interplay between man [sic] and nature. The scientific method of analysing, explaining and classifying has become conscious of its limitations, which arise out of the fact that by its intervention science alters and refashions the object of investigation. In other words, method and object can no longer be separated.

Along the same lines, Niels Bohr wrote:

An independent reality in the ordinary physical sense can ... neither be ascribed to the phenomena nor to the agencies of observation.
Stanley Aronowitz has convincingly traced this worldview to the crisis of liberal hegemony in Central Europe in the years prior and subsequent to World War I.
A second important aspect of quantum mechanics is its principle of complementarity or dialecticism. Is light a particle or a wave? Complementarity ``is the realization that particle and wave behavior are mutually exclusive, yet that both are necessary for a complete description of all phenomena.''

More generally, notes Heisenberg, the different intuitive pictures which we use to describe atomic systems, although fully adequate for given experiments, are nevertheless mutually exclusive. Thus, for instance, the Bohr atom can be described as a small-scale planetary system, having a central atomic nucleus about which the external electrons revolve. For other experiments, however, it might be more convenient to imagine that the atomic nucleus is surrounded by a system of stationary waves whose frequency is characteristic of the radiation emanating from the atom. Finally, we can consider the atom chemically. ... Each picture is legitimate when used in the right place, but the different pictures are contradictory and therefore we call them mutually complementary.

And once again Bohr: A complete elucidation of one and the same object may require diverse points of view which defy a unique description. Indeed, strictly speaking, the conscious analysis of any concept stands in a relation of exclusion to its immediate application.

This foreshadowing of postmodernist epistemology is by no means coincidental. The profound connections between complementarity and deconstruction have recently been elucidated by Froula and Honner, and, in great depth, by Plotnitsky.

A third aspect of quantum physics is discontinuity or rupture: as Bohr explained,
[the] essence [of the quantum theory] may be expressed in the so-called quantum postulate, which attributes to any atomic process an essential discontinuity, or rather individuality, completely foreign to the classical theories and symbolized by Planck's quantum of action.

A half-century later, the expression ``quantum leap'' has so entered our everyday vocabulary that we are likely to use it without any consciousness of its origins in physical theory.

Finally, Bell's theorem and its recent generalizations show that an act of observation here and now can affect not only the object being observed -- as Heisenberg told us -- but also an object arbitrarily far away (say, on Andromeda galaxy). This phenomenon -- which Einstein termed ``spooky'' -- imposes a radical reevaluation of the traditional mechanistic concepts of space, object and causality, and suggests an alternative worldview in which the universe is characterized by interconnectedness and (w)holism: what physicist David Bohm has called ``implicate order''. New Age interpretations of these insights from quantum physics have often gone overboard in unwarranted speculation, but the general soundness of the argument is undeniable. In Bohr's words, ``Planck's discovery of the elementary quantum of action ... revealed a feature of wholeness inherent in atomic physics, going far beyond the ancient idea of the limited divisibility of matter.''

In the Newtonian mechanistic worldview, space and time are distinct and absolute. In Einstein's special theory of relativity (1905), the distinction between space and time dissolves: there is only a new unity, four-dimensional space-time, and the observer's perception of ``space'' and ``time'' depends on her state of motion. In Hermann Minkowski's famous words (1908): Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

Nevertheless, the underlying geometry of Minkowskian space-time remains absolute.
It is in Einstein's general theory of relativity (1915) that the radical conceptual break occurs: the space-time geometry becomes contingent and dynamical, encoding in itself the gravitational field. Mathematically, Einstein breaks with the tradition dating back to Euclid (and which is inflicted on high-school students even today!), and employs instead the non-Euclidean geometry developed by Riemann. Einstein's equations are highly nonlinear, which is why traditionally-trained mathematicians find them so difficult to solve. Newton's gravitational theory corresponds to the crude (and conceptually misleading) truncation of Einstein's equations in which the nonlinearity is simply ignored. Einstein's general relativity therefore subsumes all the putative successes of Newton's theory, while going beyond Newton to predict radically new phenomena that arise directly from the nonlinearity: the bending of starlight by the sun, the precession of the perihelion of Mercury, and the gravitational collapse of stars into black holes.

General relativity is so weird that some of its consequences -- deduced by impeccable mathematics, and increasingly confirmed by astrophysical observation -- read like science fiction. Black holes are by now well known, and wormholes are beginning to make the charts. Perhaps less familiar is Gödel's construction of an Einstein space-time admitting closed timelike curves: that is, a universe in which it is possible to travel into one's own past!

Thus, general relativity forces upon us radically new and counterintuitive notions of space, time and causality; so it is not surprising that it has had a profound impact not only on the natural sciences but also on philosophy, literary criticism, and the human sciences.

For example, in a celebrated symposium three decades ago on Les Langages Critiques et les Sciences de l'Homme, Jean Hyppolite raised an incisive question about Jacques Derrida's theory of structure and sign in scientific discourse: When I take, for example, the structure of certain algebraic constructions [ensembles], where is the center? Is the center the knowledge of general rules which, after a fashion, allow us to understand the interplay of the elements? Or is the center certain elements which enjoy a particular privilege within the ensemble? ... With Einstein, for example, we see the end of a kind of privilege of empiric evidence. And in that connection we see a constant appear, a constant which is a combination of space-time, which does not belong to any of the experimenters who live the experience, but which, in a way, dominates the whole construct; and this notion of the constant -- is this the center?

Derrida's perceptive reply went to the heart of classical general relativity: The Einsteinian constant is not a constant, is not a center. It is the very concept of variability -- it is, finally, the concept of the game. In other words, it is not the concept of something -- of a center starting from which an observer could master the field -- but the very concept of the game ...

In mathematical terms, Derrida's observation relates to the invariance of the Einstein field equation under nonlinear space-time diffeomorphisms (self-mappings of the space-time manifold which are infinitely differentiable but not necessarily analytic). The key point is that this invariance group ``acts transitively'': this means that any space-time point, if it exists at all, can be transformed into any other. In this way the infinite-dimensional invariance group erodes the distinction between observer and observed; the of Euclid and the G of Newton, formerly thought to be constant and universal, are now perceived in their ineluctable historicity; and the putative observer becomes fatally de-centered, disconnected from any epistemic link to a space-time point that can no longer be defined by geometry alone.

However, this interpretation, while adequate within classical general relativity, becomes incomplete within the emerging postmodern view of quantum gravity. When even the gravitational field -- geometry incarnate -- becomes a non-commuting (and hence nonlinear) operator, how can the classical interpretation of as a geometric entity be sustained? Now not only the observer, but the very concept of geometry, becomes relational and contextual.

The synthesis of quantum theory and general relativity is thus the central unsolved problem of theoretical physics; no one today can predict with confidence what will be the language and ontology, much less the content, of this synthesis, when and if it comes. It is, nevertheless, useful to examine historically the metaphors and imagery that theoretical physicists have employed in their attempts to understand quantum gravity.

The earliest attempts -- dating back to the early 1960's -- to visualize geometry on the Planck scale (about centimeters) portrayed it as ``space-time foam'': bubbles of space-time curvature, sharing a complex and ever-changing topology of interconnections. But physicists were unable to carry this approach farther, perhaps due to the inadequate development at that time of topology and manifold theory (see below).

In the 1970's physicists tried an even more conventional approach: simplify the Einstein equations by pretending that they are almost linear, and then apply the standard methods of quantum field theory to the thus-oversimplified equations. But this method, too, failed: it turned out that Einstein's general relativity is, in technical language, ``perturbatively nonrenormalizable''. This means that the strong nonlinearities of Einstein's general relativity are intrinsic to the theory; any attempt to pretend that the nonlinearities are weak is simply self-contradictory. (This is not surprising: the almost-linear approach destroys the most characteristic features of general relativity, such as black holes.)

In the 1980's a very different approach, known as string theory, became popular: here the fundamental constituents of matter are not point-like particles but rather tiny (Planck-scale) closed and open strings. In this theory, the space-time manifold does not exist as an objective physical reality; rather, space-time is a derived concept, an approximation valid only on large length scales (where ``large'' means ``much larger than centimeters''!). For a while many enthusiasts of string theory thought they were closing in on a Theory of Everything -- modesty is not one of their virtues -- and some still think so. But the mathematical difficulties in string theory are formidable, and it is far from clear that they will be resolved any time soon.

More recently, a small group of physicists has returned to the full nonlinearities of Einstein's general relativity, and -- using a new mathematical symbolism invented by Abhay Ashtekar -- they have attempted to visualize the structure of the corresponding quantum theory. The picture they obtain is intriguing: As in string theory, the space-time manifold is only an approximation valid at large distances, not an objective reality. At small (Planck-scale) distances, the geometry of space-time is a weave: a complex interconnection of threads.
Finally, an exciting proposal has been taking shape over the past few years in the hands of an interdisciplinary collaboration of mathematicians, astrophysicists and biologists: this is the theory of the morphogenetic field. Since the mid-1980's evidence has been accumulating that this field, first conceptualized by developmental biologists, is in fact closely linked to the quantum gravitational field: (a) it pervades all space; (b) it interacts with all matter and energy, irrespective of whether or not that matter/energy is magnetically charged; and, most significantly, (c) it is what is known mathematically as a ``symmetric second-rank tensor''. All three properties are characteristic of gravity; and it was proven some years ago that the only self-consistent nonlinear theory of a symmetric second-rank tensor field is, at least at low energies, precisely Einstein's general relativity.

Thus, if the evidence for (a), (b) and (c) holds up, we can infer that the morphogenetic field is the quantum counterpart of Einstein's gravitational field. Until recently this theory has been ignored or even scorned by the high-energy-physics establishment, who have traditionally resented the encroachment of biologists (not to mention humanists) on their ``turf''. However, some theoretical physicists have recently begun to give this theory a second look, and there are good prospects for progress in the near future.

It is still too soon to say whether string theory, the space-time weave or morphogenetic fields will be confirmed in the laboratory: the experiments are not easy to perform. But it is intriguing that all three theories have similar conceptual characteristics: strong nonlinearity, subjective space-time, inexorable flux, and a stress on the topology of interconnectedness.

Unbeknownst to most outsiders, theoretical physics underwent a significant transformation -- albeit not yet a true Kuhnian paradigm shift -- in the 1970's and 80's: the traditional tools of mathematical physics (real and complex analysis), which deal with the space-time manifold only locally, were supplemented by topological approaches (more precisely, methods from differential topology) that account for the global (holistic) structure of the universe. This trend was seen in the analysis of anomalies in gauge theories; in the theory of vortex-mediated phase transitions; and in string and superstring theories. Numerous books and review articles on ``topology for physicists'' were published during these years.

At about the same time, in the social and psychological sciences Jacques Lacan pointed out the key role played by differential topology:

This diagram [the Möbius strip] can be considered the basis of a sort of essential inscription at the origin, in the knot which constitutes the subject. This goes much further than you may think at first, because you can search for the sort of surface able to receive such inscriptions. You can perhaps see that the sphere, that old symbol for totality, is unsuitable. A torus, a Klein bottle, a cross-cut surface, are able to receive such a cut. And this diversity is very important as it explains many things about the structure of mental disease. If one can symbolize the subject by this fundamental cut, in the same way one can show that a cut on a torus corresponds to the neurotic subject, and on a cross-cut surface to another sort of mental disease.

As Althusser rightly commented, ``Lacan finally gives Freud's thinking the scientific concepts that it requires''. More recently, Lacan's topologie du sujet has been applied fruitfully to cinema criticism and to the psychoanalysis of AIDS. In mathematical terms, Lacan is here pointing out that the first homology group of the sphere is trivial, while those of the other surfaces are profound; and this homology is linked with the connectedness or disconnectedness of the surface after one or more cuts. Furthermore, as Lacan suspected, there is an intimate connection between the external structure of the physical world and its inner psychological representation qua knot theory: this hypothesis has recently been confirmed by Witten's derivation of knot invariants (in particular the Jones polynomial) from three-dimensional Chern-Simons quantum field theory.

Analogous topological structures arise in quantum gravity, but inasmuch as the manifolds involved are multidimensional rather than two-dimensional, higher homology groups play a role as well. These multidimensional manifolds are no longer amenable to visualization in conventional three-dimensional Cartesian space: for example, the projective space , which arises from the ordinary 3-sphere by identification of antipodes, would require a Euclidean embedding space of dimension at least 5. Nevertheless, the higher homology groups can be perceived, at least approximately, via a suitable multidimensional (nonlinear) logic.

Luce Irigaray, in her famous article ``Is the Subject of Science Sexed?'', pointed out that the mathematical sciences, in the theory of wholes [théorie des ensembles], concern themselves with closed and open spaces ... They concern themselves very little with the question of the partially open, with wholes that are not clearly delineated [ensembles flous], with any analysis of the problem of borders [bords] ...

In 1982, when Irigaray's essay first appeared, this was an incisive criticism: differential topology has traditionally privileged the study of what are known technically as ``manifolds without boundary''. However, in the past decade, under the impetus of the feminist critique, some mathematicians have given renewed attention to the theory of ``manifolds with boundary'' [Fr. variétés à bord]. Perhaps not coincidentally, it is precisely these manifolds that arise in the new physics of conformal field theory, superstring theory and quantum gravity.
In string theory, the quantum-mechanical amplitude for the interaction of n closed or open strings is represented by a functional integral (basically, a sum) over fields living on a two-dimensional manifold with boundary. In quantum gravity, we may expect that a similar representation will hold, except that the two-dimensional manifold with boundary will be replaced by a multidimensional one. Unfortunately, multidimensionality goes against the grain of conventional linear mathematical thought, and despite a recent broadening of attitudes (notably associated with the study of multidimensional nonlinear phenomena in chaos theory), the theory of multidimensional manifolds with boundary remains somewhat underdeveloped.

Nevertheless, physicists' work on the functional-integral approach to quantum gravity continues apace, and this work is likely to stimulate the attention of mathematicians.

As Irigaray anticipated, an important question in all of these theories is: Can the boundary be transgressed (crossed), and if so, what happens then? Technically this is known as the problem of ``boundary conditions''. At a purely mathematical level, the most salient aspect of boundary conditions is the great diversity of possibilities: for example, ``free b.c.'' (no obstacle to crossing), ``reflecting b.c.'' (specular reflection as in a mirror), ``periodic b.c.'' (re-entrance in another part of the manifold), and ``antiperiodic b.c.'' (re-entrance with twist). The question posed by physicists is: Of all these conceivable boundary conditions, which ones actually occur in the representation of quantum gravity? Or perhaps, do all of them occur simultaneously and on an equal footing, as suggested by the complementarity principle?

At this point my summary of developments in physics must stop, for the simple reason that the answers to these questions -- if indeed they have univocal answers -- are not yet known. In the remainder of this essay, I propose to take as my starting point those features of the theory of quantum gravity which are relatively well established (at least by the standards of conventional science), and attempt to draw out their philosophical and political implications.

Over the past two decades there has been extensive discussion among critical theorists with regard to the characteristics of modernist versus postmodernist culture; and in recent years these dialogues have begun to devote detailed attention to the specific problems posed by the natural sciences. In particular, Madsen and Madsen have recently given a very clear summary of the characteristics of modernist versus postmodernist science. They posit two criteria for a postmodern science: A simple criterion for science to qualify as postmodern is that it be free from any dependence on the concept of objective truth. By this criterion, for example, the complementarity interpretation of quantum physics due to Niels Bohr and the Copenhagen school is seen as postmodernist.

Clearly, quantum gravity is in this respect an archetypal postmodernist science.

Secondly, the other concept which can be taken as being fundamental to postmodern science is that of essentiality. Postmodern scientific theories are constructed from those theoretical elements which are essential for the consistency and utility of the theory.

Thus, quantities or objects which are in principle unobservable -- such as space-time points, exact particle positions, or quarks and gluons -- ought not to be introduced into the theory.

While much of modern physics is excluded by this criterion, quantum gravity again qualifies: in the passage from classical general relativity to the quantized theory, space-time points (and indeed the space-time manifold itself) have disappeared from the theory.

However, these criteria, admirable as they are, are insufficient for a liberatory postmodern science: they liberate human beings from the tyranny of ``absolute truth'' and ``objective reality'', but not necessarily from the tyranny of other human beings. In Andrew Ross' words, we need a science ``that will be publicly answerable and of some service to progressive interests.''

From a feminist standpoint, Kelly Oliver makes a similar argument:
... in order to be revolutionary, feminist theory cannot claim to describe what exists, or, ``natural facts.'' Rather, feminist theories should be political tools, strategies for overcoming oppression in specific concrete situations. The goal, then, of feminist theory, should be to develop strategic theories -- not true theories, not false theories, but strategic theories.

How, then, is this to be done?

In what follows, I would like to discuss the outlines of a liberatory postmodern science on two levels: first, with regard to general themes and attitudes; and second, with regard to political goals and strategies.

One characteristic of the emerging postmodern science is its stress on nonlinearity and discontinuity: this is evident, for example, in chaos theory and the theory of phase transitions as well as in quantum gravity. At the same time, feminist thinkers have pointed out the need for an adequate analysis of fluidity, in particular turbulent fluidity. These two themes are not as contradictory as it might at first appear: turbulence connects with strong nonlinearity, and smoothness/fluidity is sometimes associated with discontinuity (e.g. in catastrophe theory); so a synthesis is by no means out of the question.

Secondly, the postmodern sciences deconstruct and transcend the Cartesian metaphysical distinctions between humankind and Nature, observer and observed, Subject and Object. Already quantum mechanics, earlier in this century, shattered the ingenuous Newtonian faith in an objective, pre-linguistic world of material objects ``out there''; no longer could we ask, as Heisenberg put it, whether ``particles exist in space and time objectively''. But Heisenberg's formulation still presupposes the objective existence of space and time as the neutral, unproblematic arena in which quantized particle-waves interact (albeit indeterministically); and it is precisely this would-be arena that quantum gravity problematizes. Just as quantum mechanics informs us that the position and momentum of a particle are brought into being only by the act of observation, so quantum gravity informs us that space and time themselves are contextual, their meaning defined only relative to the mode of observation.

Thirdly, the postmodern sciences overthrow the static ontological categories and hierarchies characteristic of modernist science. In place of atomism and reductionism, the new sciences stress the dynamic web of relationships between the whole and the part; in place of fixed individual essences (e.g. Newtonian particles), they conceptualize interactions and flows (e.g. quantum fields). Intriguingly, these homologous features arise in numerous seemingly disparate areas of science, from quantum gravity to chaos theory to the biophysics of self-organizing systems. In this way, the postmodern sciences appear to be converging on a new epistemological paradigm, one that may be termed an ecological perspective, broadly understood as ``recogniz[ing] the fundamental interdependence of all phenomena and the embeddedness of individuals and societies in the cyclical patterns of nature.''

A fourth aspect of postmodern science is its self-conscious stress on symbolism and representation. As Robert Markley points out, the postmodern sciences are increasingly transgressing disciplinary boundaries, taking on characteristics that had heretofore been the province of the humanities: Quantum physics, hadron bootstrap theory, complex number theory, and chaos theory share the basic assumption that reality cannot be described in linear terms, that nonlinear -- and unsolvable -- equations are the only means possible to describe a complex, chaotic, and non-deterministic reality. These postmodern theories are -- significantly -- all metacritical in the sense that they foreground themselves as metaphors rather than as ``accurate'' descriptions of reality. In terms that are more familiar to literary theorists than to theoretical physicists, we might say that these attempts by scientists to develop new strategies of description represent notes towards a theory of theories, of how representation -- mathematical, experimental, and verbal -- is inherently complex and problematizing, not a solution but part of the semiotics of investigating the universe.

From a different starting point, Aronowitz likewise suggests that a liberatory science may arise from interdisciplinary sharing of epistemologies: ... natural objects are also socially constructed. It is not a question of whether these natural objects, or, to be more precise, the objects of natural scientific knowledge, exist independently of the act of knowing. This question is answered by the assumption of ``real'' time as opposed to the presupposition, common among neo-Kantians, that time always has a referent, that temporality is therefore a relative, not an unconditioned, category. Surely, the earth evolved long before life on earth. The question is whether objects of natural scientific knowledge are constituted outside the social field. If this is possible, we can assume that science or art may develop procedures that effectively neutralize the effects emanating from the means by which we produce knowledge/art. Performance art may be such an attempt.

Finally, postmodern science provides a powerful refutation of the authoritarianism and elitism inherent in traditional science, as well as an empirical basis for a democratic approach to scientific work. For, as Bohr noted, ``a complete elucidation of one and the same object may require diverse points of view which defy a unique description'' -- this is quite simply a fact about the world, much as the self-proclaimed empiricists of modernist science might prefer to deny it. In such a situation, how can a self-perpetuating secular priesthood of credentialed ``scientists'' purport to maintain a monopoly on the production of scientific knowledge? (Let me emphasize that I am in no way opposed to specialized scientific training; I object only when an elite caste seeks to impose its canon of ``high science'', with the aim of excluding a priori alternative forms of scientific production by non-members.)

The content and methodology of postmodern science thus provide powerful intellectual support for the progressive political project, understood in its broadest sense: the transgressing of boundaries, the breaking down of barriers, the radical democratization of all aspects of social, economic, political and cultural life.

Conversely, one part of this project must involve the construction of a new and truly progressive science that can serve the needs of such a democratized society-to-be. As Markley observes, there seem to be two more-or-less mutually exclusive choices available to the progressive community: On the one hand, politically progressive scientists can try to recuperate existing practices for moral values they uphold, arguing that their right-wing enemies are defacing nature and that they, the counter-movement, have access to the truth. [But] the state of the biosphere -- air pollution, water pollution, disappearing rain forests, thousands of species on the verge of extinction, large areas of land burdened far beyond their carrying capacity, nuclear power plants, nuclear weapons, clearcuts where there used to be forests, starvation, malnutrition, disappearing wetlands, nonexistent grass lands, and a rash of environmentally caused diseases -- suggests that the realist dream of scientific progress, of recapturing rather than revolutionizing existing methodologies and technologies, is, at worst, irrelevant to a political struggle that seeks something more than a reenactment of state socialism.

The alternative is a profound reconception of science as well as politics: [T]he dialogical move towards redefining systems, of seeing the world not only as an ecological whole but as a set of competing systems -- a world held together by the tensions among various natural and human interests -- offers the possibility of redefining what science is and what it does, of restructuring deterministic schemes of scientific education in favor of ongoing dialogues about how we intervene in our environment.

It goes without saying that postmodernist science unequivocally favors the latter, deeper approach.

In addition to redefining the content of science, it is imperative to restructure and redefine the institutional loci in which scientific labor takes place -- universities, government labs, and corporations -- and reframe the reward system that pushes scientists to become, often against their own better instincts, the hired guns of capitalists and the military. As Aronowitz has noted, ``One third of the 11,000 physics graduate students in the United States are in the single subfield of solid state physics, and all of them will be able to get jobs in that subfield.'' By contrast, there are few jobs available in either quantum gravity or environmental physics.

But all this is only a first step: the fundamental goal of any emancipatory movement must be to demystify and democratize the production of scientific knowledge, to break down the artificial barriers that separate ``scientists'' from ``the public''. Realistically, this task must start with the younger generation, through a profound reform of the educational system. The teaching of science and mathematics must be purged of its authoritarian and elitist characteristics, and the content of these subjects enriched by incorporating the insights of the feminist, queer, multiculturalist and ecological critiques.

Finally, the content of any science is profoundly constrained by the language within which its discourses are formulated; and mainstream Western physical science has, since Galileo, been formulated in the language of mathematics.

But whose mathematics? The question is a fundamental one, for, as Aronowitz has observed, ``neither logic nor mathematics escapes the `contamination' of the social.'' And as feminist thinkers have repeatedly pointed out, in the present culture this contamination is overwhelmingly capitalist, patriarchal and militaristic: ``mathematics is portrayed as a woman whose nature desires to be the conquered Other.'' Thus, a liberatory science cannot be complete without a profound revision of the canon of mathematics. As yet no such emancipatory mathematics exists, and we can only speculate upon its eventual content. We can see hints of it in the multidimensional and nonlinear logic of fuzzy systems theory; but this approach is still heavily marked by its origins in the crisis of late-capitalist production relations. Catastrophe theory, with its dialectical emphases on smoothness/discontinuity and metamorphosis/unfolding, will indubitably play a major role in the future mathematics; but much theoretical work remains to be done before this approach can become a concrete tool of progressive political praxis. Finally, chaos theory -- which provides our deepest insights into the ubiquitous yet mysterious phenomenon of nonlinearity -- will be central to all future mathematics.

And yet, these images of the future mathematics must remain but the haziest glimmer: for, alongside these three young branches in the tree of science, there will arise new trunks and branches -- entire new theoretical frameworks -- of which we, with our present ideological blinders, cannot yet even conceive.

But that's as far as I really got. Will that do?

"Of course," I said. "That'll be one up the throat for her blinking ladyship! Good work, Wacko!"

Underling management frustration

A Boss Lady writes:

Dear Uncle Colin,

Please help me, I’m desperate.

I head up a multi-disciplinary team in an organisation of world-wide renown. I pride myself on my professionalism as a manager and as a “can do” type, and I have a robust reputation as someone who delivers on time, within budget, and often without moaning.

I am immensely proud of my team and their contribution to the success of the organisation. They are a reasonably well-rounded bunch, with an amazing span of talents (give or take), able to mesh together and stump up the goods as a unit even with heavy delivery requirements and against the tightest deadlines. (Although obviously I need to crack the whip every now and then.) Every single one of them is worth more than their weight in gold, and each one will tell you they deserve to earn more than they can ever expect to be paid.

Except one.

I inherited him from my predecessor who was, shall we say, rather less disciplined than myself on appointing minions.

I have absolutely no idea what he does all day, other than stroke his stylus over his diminutive organ, and phone up women. He seems to have a remarkable social life, but no job description of any sort. He breezes in and out like he owns the place and as if he is without a care in the world.

I have regular meetings with him to review work and development, and after the meeting I can remember not a jot of what was discussed, and have merely a vague recollection of him staring into my eyes, after which I go all warm and fuzzy. It's a complete blank after that, except I always find a note in his handwriting reminding me about giving him a more impressive job title.

There seems little I can do as he is adored and protected by my own manager. It seems as if he has a map showing the location of some of the corpses for which she is rumoured to be responsible.

Is there anything at all I can do? I am tearing my hair out!

Uncle Colin advises thus and suchlike:

No. Except maybe buy a wig.

Outlandish claim quandary

The years of success, with his popular new romantic beat combo

Jon "Leggings Akimbo" Richards, a self-confessed "Senior National Officer" writes:

Dear Uncle Colin,

I have a friend who likes to go on the lash and is particularly addicted to sweet and sickly cocktails or luminescent liqueurs with strange sounding names such as aftershock. Additionally he can sometimes be found participating in strange ritualistic drinking games. Should I be worried or is this normal behaviour for a be-quiffed bon viveur?

Uncle Colin advises thus and suchlike:

"I have a friend..." Ha! That's an old formula, isn't it? Who are you really talking about, I wonder?

And if you are going to stick to this absurd and wild assertion about having a friend I expect to see documentary evidence before I even consider whether to reply to this jumped-up suit-wearing South-of-the-river excuse-for-a-failed-80s-pop-star.

Yours comfortingly,
Uncle Colin, the agoniser's friend

Total situation misjudgement lunacy

A drug-crazed serial fantasist writes

Dear Uncle Colin

A friend of mine has fallen out with a long standing friend over something trivial. They are both too proud and pig headed to make the first move to try to repair the friendship. How do I get them to see sense and make-up?
Please can you help?

Anon

Uncle Colin advises such and thuslike:

Firstly can I say that I think you need to question yourself as to whether you are jumping to conclusions about the triviality of the issue at the heart of this matter. It could easily be - and I do not feel I am overstating things here - a matter the like of which would cause a schism in any established organisation, not to mention the possibility of all-out thermo-nuclear war. Think on, will you?

Now, using all my skills as a rooter-out of all kinds of relationship problems, and my gifts for empathy and understanding, I can read between the lines of your tear-streaked email and see that one of these 'friends' is a headstrong galoot and not worth the fuss you are making about him. You really shouldn't be upsetting yourself over this as it seems he's made up his mind to build up the breach beyond any bridging, and I am sure will live to regret his buffoonish ways and his appalling behaviour viz. the other.

After all, the other is clearly a fine and handsome member of the community, with a wealth of taste, good judgement and wit, and not fit to have his boots licked clean by the likes of the friendship-wrecking boor. Yes, I can see it all now, quite clearly. This fine chap has a magnificent head of hair, and an even finer collection of figurines. He has a winning way with the laydeez, and an iron grip, which he knows they like. He knows when his mind is made up, and being a man of principle will let neither information nor sense alter his firmness of purpose. I feel nothing but admiration for the chap.

Yes, I think you've misinterpreted it all, but fear not - it is something many laydeez of a certain age and in need of some hard loving often do.

And this giant among men I've described - well, to be blunt - you'd be a fool to let this one go. His only fault is his generosity and his romantically-inclined nature. He's a real catch and you truly should be grateful you've got the chance of a crack at him. Forget all this other rot about his clearly unlikeable friend (someone he has no doubt lavished kindness and attention on over the years, only to be repaid with gripes and chuntering abuse) and clasp this God among men to your breast, and plead with him to make you happy and bring you bliss by the bucketload.

I think that you would benefit greatly from a private consultation with yours truly for a spot of the old mermerism. By this means I would be able to exploit the opportunities provided by your drowsiness AND discover the source of your inability to understand what is really going on around you. Drop me a line at the usual address and let me know your rates.

Comfortingly yours
Uncle Colin, the agoniser's friend

Batty Uncle Torment

A Twin of Evil writes:

Our Uncle, recently arrived from Saltzburg, seems to be paying a lot of very special attention to my twin sister and I. We suspect that he has been watching us covertly as we go about our daily business and only yesterday I noticed him drooling when we returned from a vigorous ride and I took off my scarf upon entering the house. We do not have much contact with society and don’t know whether we are right to be concerned or whether these are the normal attentions of a male in the prime of life. Please help!

Uncle Colin advises thus and suchlike:

In my time I have uncled-up to many a young laydee and it seems that such behaviour goes with the territory. If you wish to dissuade him from his dribbling, and feverish oglingery, I would make the following practical suggestions:

1. Prevention is better than cure - remove the source of temptation: always lock the door when going about your daily business;

2. Use concealing anti-perspirants and deodorants to obscure the most obvious of your womanly charms;

3. Remember, an uncle's drives are unpredictable and may need a variety of attentions to still his inflammations. Treat him kindly, as you would your favourite steed.

Do write again with more details and/or pictures.

Yours comfortingly
Uncle Colin, the agoniser's friend

I'm here to help

Mature, sensitive, and unceasingly compassionate.

For some time now I've been thinking about how much more I could be helping humankind.

I know I do a lot (far too much they say) already - my unmentionable, soul-destroying and utterly thankless non-profit-making charity work; running Club Derrig; and, of course, providing laydeez everywhere with regular bouts of bliss - but I know I could do more.

So I am embarking on a special project to try and help even more, by putting my immense brain into the service of poor souls who have lost their way and need the benefit of my wisdom, guidance, and compassion.

Yes, I'm setting up as an Agonising Uncle. (For the next two weeks, on a pilot basis to see if your problems are actually worth my while.)

No query or quandary is too small. No life-event too painful. No detail too explicit.

And it's totally free.*

Simply email your moaning or misery to me at

cpaderrigAThotmail.co.uk

and I will not laugh myself stupid - rather, I will don the silky cape of Vlad the Empathiser and open my brains to you.

It's a once in a lifetime offer.

*All rights reserved to publish your problems in my forthcoming book "Stop being a loser, you miseryguts".