Essay Abstract

To the question 'It from Bit or Bit from It?' this essay replies, 'It from Bit AND Bit from It.' Bringing fun and substance to Wheeler's famous phrase, this wording and emphasis is backed by the creation of a new particle (the first It from Bit) and by the link that ends the EPR-Bell era (fusing EPR's missed Bit with Bell's missed It). Then, proving material objects more fundamental than information, a fresh big Bit from phantasmic It. That is, 'collapse' - so-called, and problematic in QM - is but a short-cut in a new mechanics, wholistic mechanics, wm, with its commonsense philosophy of wholistic-local-realism (WLR) and its aversion to subjectivity (replacing probability with prevalence). WM delivers a whole new particle family, while WLR itself, claiming its EPR-Bell birthright - uniting local-causality (no causal influence propagates superluminally) and physical-realism (some physical properties change interactively) - revives local causality in line with the early hopes of folks like Aspect, Bell, Clauser, Einstein, Podolsky, Rosen. Among findings reported from analysis judged fit for well-taught highschool seniors: Naive realism is a doctrine of limited value, being false in spin-entangled contexts; EPR is vulnerable to a naive-realistic interpretation; Bell's theorems and inequalities are constrained by their basis in naive realism; correlated tests on correlated particles produce correlated results, absent nonlocality, spooky-actions, mystery; like other valued shortcuts, QM wavefunctions and their collapse are abstractions; eliminate collapse, farewell nonlocality, predict with certainty the value of a physical quantity, for there exist elements of physical reality creating that quantity. Suggesting that WLR will feature in the future of physics, that wm will benefit from any and all comments and critiques, this essay invites us to join in the creative fun that goes with such research; and boldly requests: Please respond critically. In a word: Enjoy!

Author Bio

Gordon Watson: Age 11, loves Euclid, girls, a fair go for all; plays rugby, tops geometry, ponders God/Reality. Fitter-Machinist apprentice, maths the best logic, scholarship. UNSW, Mechanical Engineering, more rugby, BE(Hons). Hoffman's quantum classic; he'll study the quantum when It makes sense. Reads Mermin, sends note, that impossible's possible; essay published on EPR-Bell. Given his mother's words, "Gordon was born under the sign of Aries the Ram and has rammed his way through life ever since," it can now be asserted with reasonable confidence that Gordon does not work in a patent office. (PS: Thanks mum.)

Download Essay PDF File

Gordon,

Had you informed me that you were an adult, I would have had no problem describing your essay as being adequately written for people fascinated by abstraction. The fact that you are only 11 leaves me speechless.

As I have gone to great pains to point out in my essay BITTERS, reality is unique. All descriptions of physical reality including yours are unrealistic as you will undoubtedly learn as you get older.

    Dear Joe,

    Your enjoyable essay, BITTERS, was one of the first that I read here. (And I felt for you, given my perception of the title and its context). I was impressed by how close you had come, IMO, to developing an important insight: in so far as the nature of reality is concerned.

    For that reason, please move beyond my Bio. (I was 11 when my wonderful 57 year-old maths teacher gasped -- given my whispered answer to her favourite Euclidean challenge -- "My gosh; you've forced me to change the answer I've been using all these years!")

    Please study the Essay and see how I challenge -- beginning with one simple idea that should resonate with one of your own -- what is, according to many, "the most profound discovery of science."

    In relation to your "familiarity with a real toe" I'm familiar with 20 such; 10 of them being much easier and nicer to access than my own ... . Which might bring us to set theory and a related matter, arising from your closing line

    -- "I have never really been interested in logic" -- .*

    because, unfortunately it seems to me, without some "interest in logic on your part," we will find it difficult to discuss why we appear to differ so significantly re the nature of "abstraction" -- the contrast between the concrete and the abstract, rather than between the absolute and the abstract -- and the use of maths as the best logic.

    For, given you keen focus on fundamentals, I'd be hoping (in a friendly way) to see you contribute more broadly to the study of Reality ... or at least, please, show me more clearly where I go wrong, maybe by expanding on your "All descriptions of physical reality including yours are unrealistic as you will undoubtedly learn as you get older."

    *PS: Hoping you'll enjoy the logic in the attached,

    and with best regards; GordonAttachment #1: 1_Axiom_.pdf

    Dear Gordon,

    If I understand correctly, you are saying that in 1989, when you were 11, you developed the approach in the essay and communicated with David Mermin, to no effect.

    In remembrance of Ray Munroe, a number of us here believe that "Have Fun" is a good credo. However in the context of Bell's theorem I wonder if the lighthearted approach, such as your confusing bio, is well advised. You don't want to lend a sort of 'Sokal affair' air to your essay. You will be attacked enough without giving your opponents extra ammunition.

    On first reading I found no obvious problems, but of course there many places in your essay where one can stumble.

    I am somewhat confused by your p(lambda_sub_n_plus_i) as the 'It Bell missed'. Are you seriously proposing a new particle? You seem to be: ("WM delivers a whole new particle family,") and ("backed by the creation of a new particle.") If so, it seems that you might have developed more physics of the new particle, rather than focusing on Bell's logic -- which does not take into account any new particle. So let me be specific: is a new particle, as yet undiscovered, necessary for your scheme to work?

    You repeatedly ask for critical response, so I'm responding. It seems a lot of work for a joke. Do you claim that you wrote most of this at age 11, or have you reworked it considerably? It's a lot to ask your readers to plow through for a joke. I have plowed through it, and plan to again.

    I did find your "fill in the figure" approach interesting, and it did cause me to have an idea while contemplating it.

    In short, I believe that Bell's theorem is an incorrect analysis, and I believe it is the *only* reason that so many people are taking "it from bit" seriously. So it is serious business, as, in my opinion, it is leading physicists far astray. The essay sends mixed signals. On the one hand the analysis is impressive. On the other hand there are incongruous elements that throw off anyone capable of working through your logic. Perhaps these are simply remnants of your 11-year-old effort. If so, I think you should rewrite it in a more conventional style. This will deflect criticism and give your supporters more confidence that it is a serious challenge to Bell.

    Anyway, that's my immediate reaction to your impressive essay.

    I look forward to your response.

    Edwin Eugene Klingman

      Dear Edwin,

      Thank you for your welcome and well-structured response! I've copied it **below** and will insert what I trust will be helpful and clarifying responses -- R#. I'm delighted that you also follow the credo: "Where there's confusion, let there be questions."

      **Dear Gordon,

      If I understand correctly, you are saying that in 1989, when you were 11, you developed the approach in the essay and communicated with David Mermin, to no effect.**

      R1: Oops! Not quite! In my Bio, various life-phases are separated by full-stops. So what I did when 11 was go the highschool, love Euclid, etc. Had more words been allowed I'd have closed that phase with "continues to ponder God/Reality."

      Then there's a sentence about my post-highschool phase. Then one on my Uni phase; etc.

      NB: In that it was a Bio and not a CV, I thought it best to convey something of my nature ... and not of my achievements.

      R2: Then, in 1989, I did call David Mermin; communicating my view that Bell's theorem was wrong, etc. This was an immediate response to his essay -- Mermin, N. D. (1988). Spooky actions at a distance: Mysteries of the quantum theory. The Great Ideas Today 1988. M. J. Adler. Chicago, Encyclopædia Britannica Inc: 2-53 -- which, to me, included many challenges (on which I thrive), all of which could be easily understood and answered.

      R3: One such Mermin challenge is this (p.23): "The data I have described may well be the most profoundly disturbing ever to have been collected in an experiment, or derived from a valid scientific theory." Another (p.26): "At this point it would be well for you to pause and try to invent [a mechanism to explain the data] ... Unless you are well versed in quantum theory, I can guarantee that you will fail ..."

      R4: NB: A guarantee to FAIL!? Having next to zero knowledge of QM, I was the perfect antidote. And thus I responded: offering Mermin the solution, thinking that he would run with it.

      **In remembrance of Ray Munroe, a number of us here believe that "Have Fun" is a good credo. However in the context of Bell's theorem I wonder if the lighthearted approach, such as your confusing bio, is well advised. You don't want to lend a sort of 'Sokal affair' air to your essay. You will be attacked enough without giving your opponents extra ammunition.**

      R5: I'd like to learn more about Ray and his credos. Also about that "number of us" and that "here" please; me trusting that the Bio is much less confusing already. [Please email me directly re any non-public info.] As for those prophesied attacks -- and there being enough of them -- let's see. In the meantime let us sort out our own positions and differences to the max.

      **On first reading I found no obvious problems, but of course there many places in your essay where one can stumble.**

      R6: The essay is written to be stumble-free, even typo free, to thus help the interested Reader persist and learn from slips and mistakes. And, in so doing, sort me and others out along the way. NB: If even some small thing jolts you or gives pause -- let me know.

      TO BE continued -- Preview Post Text NOT WORKING with full reply! Is there a word limit?

      Edwin; continuing:

      **I am somewhat confused by your p(lambda_sub_n_plus_i) as the 'It Bell missed'. Are you seriously proposing a new particle? You seem to be: ("WM delivers a whole new particle family,") and ("backed by the creation of a new particle.") If so, it seems that you might have developed more physics of the new particle, rather than focusing on Bell's logic -- which does not take into account any new particle. So let me be specific: is a new particle, as yet undiscovered, necessary for your scheme to work?**

      R7: The new particles are NEW to the extent that they have not been announced heretofore. In this Essay, they arise from a rigorous analysis of Bell's boundary conditions, but they are plain and simple spin-half particles.

      R7A: Edwin, you need to understand how their "naming = numbering" keeps account of what actually happens in experiments -- and not what is assumed to happen via BS -- "Bellian-style" -- maths, so to speak.

      So the adjective "new" was thought by me to the best way to introduce them. I'm not aware of anything like them in the Bell literature. PS: I can see you slapping you forehead when you catch on!

      **You repeatedly ask for critical response, so I'm responding. It seems a lot of work for a joke. Do you claim that you wrote most of this at age 11, or have you reworked it considerably? It's a lot to ask your readers to plow through for a joke. I have plowed through it, and plan to again.**

      R8: Yes, critical responses are vital. And, Edwin, I do apologise for your wrestling with my text under the cloud of a hoax. It is NOT such. It is a claimed refutation of what so many believe to be "the most profound discovery of science" -- not just physics but Science!! It goes on to show what follows when nonsense and nonlocality are removed from view. Please continue to be critical -- that's the missing link here, the essence of helpful and cooperative communication, for me.

      **I did find your "fill in the figure" approach interesting, and it did cause me to have an idea while contemplating it.**

      R9: This is good news to me, and I thank you for it. The "fill-in" approach is akin to asking open questions in an area where the facts are so straightforward that there's reduced opportunity for creativity.

      **In short, I believe that Bell's theorem is an incorrect analysis, and I believe it is the *only* reason that so many people are taking "it from bit" seriously. So it is serious business, as, in my opinion, it is leading physicists far astray. The essay sends mixed signals. On the one hand the analysis is impressive. On the other hand there are incongruous elements that throw off anyone capable of working through your logic. Perhaps these are simply remnants of your 11-year-old effort. If so, I think you should rewrite it in a more conventional style. This will deflect criticism and give your supporters more confidence that it is a serious challenge to Bell.**

      R10: Really great to see those two opening sentences here. BUT there should be NO mixed signals in the Essay itself. Rest assured that I am serious; me trusting that the mixed-signals are seen to arise from perceptions of lighthearted fun not from the central facts. And me certainly hoping that we'll enjoy a productive correspondence involving a creative mix of fact and fun.

      **Anyway, that's my immediate reaction to your impressive essay.**

      R11: Your immediate reaction is very welcome and much appreciated.

      **I look forward to your response.

      Edwin Eugene Klingman**

      R12: And Me-Too, to your next, Edwin; and maybe some from your group there;

      with my thanks again; Gordon

      Gordon,

      Thank you for your reply. I will study your answer about the 'new' particle(s) and hope to end up slapping my head.

      My remark about stumbling was based on the sheer number of equations to plow through and the number of key symbols in your glossary. Impossible to grasp in one reading. I plan to re-read it, perhaps several times.

      Serious challenges to Bell are attacked, often viciously, and the last to do so, Joy Christian, has been attacked for years. That is why I suggest that the unconventional bio and any other departure from 'standard, boring, dry' papers will not be rewarded. That was my caution about 'lighthearted fun'.

      Ray Munroe was the author of several FQXi essays and often (usually) signed his comments with 'Have Fun'. He died last year, but is well remembered and missed.

      I'm trying to read all essays and a number have been posted in the last few days, but I will try to find time before long to re-read yours. I would also invite you to read my essay.

      I hope you have a good challenge to Bell. I meant those two sentences you liked.

      Best regards,

      Edwin Eugene Klingman

      Gordon,

      Thank you for your gracious answer to my somewhat boorish comments. I did not wish to use the term "unrealistic" disparagingly. I know everything in the Universe is unique, once and I was merely trying to emphasize that as all abstractions are recurring, they cannot be unique and therefore, they can only be unrealistic. This must not be taken as me asserting that abstractions do not have an important utility. Obviously properly constructed abstractions when recorded correctly as stated in your essay can be extremely useful for anyone wishing to become more knowledgeable.

      Edwin, thanks for that additional information; I appreciate the points you make so clearly (me having a bit to learn in this field). As for Joy Christian's work, that warrants two numbered responses:

      R13: I leave it to others to formally assess Joy's work but I personally doubt that he has succeeded in disproving Bell. For I'm not aware that Joy's work makes the following connections directly or simply: In my work, one equation handles both spin-half particles and (spin-one) photons logically and readily right from the start. That is, they differ in their intrinsic spins (respectively s = 1/2, s = 1) and that difference -- in the context of the relevant correlations issuing from the Source, of course -- accounts for their differing behaviour in Bell-tests.

      That, to me, is how the physics should go.

      R14: I'd welcome serious and critical correspondence with any and all Bell supporters. So if there are some that I should contact directly, please let me know. Thanks.

      With thanks again; Gordon

      Many thanks Joe; that nicely clarifies our differences somewhat. But I continue to wonder: Am I reading you correctly?

      So, trusting that you'll excuse me here (maybe) pushing for another friendly opportunity to encourage you to move beyond your central theme -- everything in the Universe is unique -- how should I understand this, from you:

      "Abstractions when recorded correctly ... can be extremely useful for anyone wishing to become more knowledgeable."

      Are you saying that you personally have no wish to become more knowledgable?

      For I still have this spinning in my head: "I [Joe] have never really been interested in logic."

      Are you maybe suggesting that we should join you in the set of such?

      FOR I can see clear benefits flowing from such a worldview: extra time for gardening, walking, sleeping, ..., which are not to be sneezed at, that's for sure! Though all such would surely be improved by us each abstracting and becoming more knowledgable? And our sharing some of that? Yes?

      Anyway Joe, such puzzlement has me putting on hold my sales-pitch re the benefits that "ABSTRACTION" brings us; and temporarily suspending a challenge to your phrasing: "all abstractions are recurring, they cannot be unique and therefore, they can only be unrealistic."

      Looking forward to your clearing my head somewhat, yours cordially; Gordon

      Gordon,

      I wish I had your manners.

      "Abstractions when recorded correctly ... can be extremely useful for anyone wishing to become more knowledgeable."

      Are you saying that you personally have no wish to become more knowledgable?

      For I still have this spinning in my head: "I [Joe] have never really been interested in logic."

      I regret my abysmal lack of a formal education. As I have admitted elsewhere at this site: I never had self awareness. From my birth to the present no matter in which direction I faced, I have only been able to see humanly fabricated structures or humanly explored terrains. My nostrils have only ever received wafts of humanly compromised fumes. My mouth has only tasted humanly adulterated food and liquids. Man made sounds have constantly drowned out any bird songs or dog barks or cock crows. Only fabricated materials have ever touched me.

      There is no me here. I have three options. I can be a conventional, consistent, or conspicuous conformist.

      If I am right about my assertion that one real Universe could only be eternally occurring in one real infinite dimension, once, That means that Copernicus, Newton, Einstein, and Hawking had to have gotten it wrong.

      I am sorry. I cannot answer your questions.

      • [deleted]

      • Post #12

      PS: Just dropping by on my way to Edwin's essay.

      "There is no me here. I have three options. I can be a conventional, consistent, or conspicuous conformist."

      To the me that is not there; to the I that sees but three options; to the one making assertions: Talk to Joe Fisher, the gloriously curious non-conformist.

      Hello Gordon,

      The BIT I can say is that your essay is well organized. Because of the high mathematical content I may not be able to comment as much as I would have wanted unless you bring out the logic behind the math used.

      Having said that, for completeness it is good for you to mention that the EPR paradox afflicts only the particle picture. The wave picture of light does not require superluminal signaling to know the direction of a second wave's polarization by measuring that of the first.

      Then in your bio, you mentioned your fascination with Euclid. You may wish to check out my take on the relationship between his definitions and reality in my essay, 'On the road not taken'. Will appreciate your comments.

      Wish you the best in the contest.

      Regards,

      Akinbo

        Message to Gordon, ...come in Gordon,

        What Akinbo said just now...

        He's right you know that? (name that quote). His essay is good. Long live reality!

        But back to this unequal war. I've got my flank well covered and I think I got a major hit with my new prototype spin bomb. With what looked like another big hit from your own secret weapon I think we've got them pinned down, but I don't really know how much damage mine can do yet. You may have a better view than me, can you do a recce, observe and report?

        I'm couldn't read your codes and don't seem to have the right code book so I didn't get a complete view of your own hit, but I have to say it sounded bang on target and at least as effective as mine. It may be that together the force is irresistible? You'll have to give me a critical view of my own. I'm sure were probably looking at the very same thing from our very different local vantage points.

        I've called on back up from another Aspect, but it's tricky to know which side some of those guys are really on. While the troglodytes outnumber us there's probably still a lot of relative uncertainty about. I've also sent a dispatch to Joy but no news yet. It's a bit spooky. I fear the worst.

        I know Edwin has a good position across the other side so we can avoid action at a distance and have a complete ring with all the angles covered. I think if we keep up the momentum the core of the resistance may fade away. Let me know how good a hit you think mine was, and if looks like our weapons can be co-ordinated.

        I think I feel a top score coming on from this side. Let me know how it looks from there.

        Best of luck

        Peter

        PS. They seem to have got your Figures. No probs I have spare stash. Tell me which ones you like.

        PPS. If there are any typo's above I apologise sincerley but I'm afraid I'm a Captain and certainly not a typist.

          • [deleted]

          • Post #16

          To: Senior Counsel, Atomistic Enterprises Inc. Attention: Dr Akinbo Ojo

          From: DOPE! Subject: Thou shalt not out-plateau Plato!

          Sir: We object to your provocative communique and have this hour lodged an appeal to the Eternal Court of Arbitration. They are stuffed by our clients as you well-know, so prepare for overturn and defeat. As previously advised: It is not permitted anywhere at anytime to use non-conformist thinking against our aged Founder; nor his adherents.

          Sincerely; Defenders of Platonists Everywhere!

          Hello Akinbo, with a big welcoming wOJOw! WOW! Many thanks for bringing your delightful essay to my attention; it is a wonderful work and an inspiring read; in a word -- brilliant.

          It also gives me confidence that you will have little trouble with my maths, except maybe a little rustiness for a while; for it is essentially the basic trigonometry of your highschool mates. So if you have a go at the maths, I will happily support your efforts with the accompanying logic.

          I see your monads (maybe just slightly tweaked) situated between Euclid's wonderful points (beautiful and helpful abstractions) and the limits of Planck's constant of action (my focus area).

          It is in this latter regard I'd welcome your clarification of this: "The wave picture of light does not require superluminal signaling to know the direction of a second wave's polarization by measuring that of the first." For it may reflect an underlying misunderstanding.

          Note that the the photons are UN-polarized in their entangled state (Bell 2004:82). And as my essay shows: NO superluminal signalling is required anywhere.

          PS: Indeed, Euclid remains a hero of mine with his clear axiomatic approach to analysis.

          Looking forward to many more fruitful exchanges, please do not hesitate to question the maths, logic, etc; Gordon

          Dear Gordon,

          Again, welcome to FQXi. I would like to point out that an accepted use of the blogs associated with each essay is to expand upon the points of the essay which were constrained by the nine page limit. I always try to make good use of my comments in this fashion. [I'm starting a new thread for visibility.]

          To kick this off I would suggest you expand upon the meaning of the hidden variable lambda in your equations 3 through 6, particularly your statement about the impossibility of Bell's treatment.

          As I understand it the problem you point out is that, while invoking the third particle c, Bell uses the same hidden variable, lambda, as was used for the original pair of particles, (a,b), despite having already declared that "it is a matter of indifference... whether lambda denotes a single variable or a set, or even a set of functions, and whether the variables are discrete or continuous". Unless and until someone shows how a third particle can be produced, with exactly the same generalized, unconstrained hidden variable that applied to the pair a and b, then this is, as you say, unphysical, i.e., impossible. Consider, as an example only, that lambda is a 'phase angle' of the wave function common to the particles a and b. There may, of course exist an analogous phase angle in another entangled pair (a',c). But there is no way to measure these phase angles (except statistically via 'weak' measurement) and no grounds to assume that they are equal from a to a'. But this is implied by Bell's use of only one lambda in 14(a) and 14(b) while you clearly and correctly label these lambda_sub_i and lambda_sub_n_plus_i.

          It's a forehead slapper all right.

          Any fine points you'd like to comment on before I work further into your essay?

          Best,

          Edwin Eugene Klingman

            Dear Edwin,

            Thanks indeed for the welcome, the very helpful guidance,* and the hopeful news that your forehead-slapping is behind us; just one small uppercut needed now -- under the chin -- "small" given my appreciation of your own views and engagement on these matters.

            For I think it not good to refer to any particle by the unit vector -- "invoking the third particle c" -- associated with the relevant SGD. It gets quite messy and confusing in what, IMO, should really be a very simple matter. (Some, as you probably know, even refer to the particles as Alice and Bob -- the SGD operators -- such is the confusion greeting newcomers to this important subject.)

            I know and appreciate what you mean but I like to make this subject as easy as possible for newcomers -- and to be especially free to discuss those interesting hypothetical cases where Alice and Bob freely and independently select the same or antiparallel orientations.

            * I should also explain that I'm working my way into FQXi via a new and troublesome internet upgrade, so your advice should soon be reflected in my expanded involvement here. (AND, playing safe, I might go with a series of short replies for a while.) PS: While I'm at it: every sentence of mine comes with an implicit IMO!

            So, on the subject of particle identification, I suggest we stick with selections from the pwn+i family -- introduced at equation (22) but with lambda not used in this text here for convenience -- it being understood that each particle carries a unique lambda, correspondingly identified: NO two particles the same!

            That is: particle p'wn+i carries a lambda' (lambda-prime) antiparallel to the lambda of its twin pwn+i -- that antiparallel relation here a consequence of the symmetry associated with the conservation of total angular momentum in the production of each pair.

            Note in passing: In this way, pwn+i brings Joe Fisher's primary theme (the uniqueness of Reality) into mathematical form -- and hence into the best logic -- and hence into the Bell story.

            Following your suggestion: Let's now expand upon the meaning of the Bellian lambda that is introduced into the maths at equation (3): Let's follow the clue -- "Bell's hint" -- in equation (1) and see how far we can take it.

            So, since Bell's 1964:(1) and our (1) allow that 'a' is a unit vector, let lambda be one too. And, since we are working with spin and SGDs -- and always subject to Bell's (1964) boundary conditions -- let lambda be the most general unit vector in the space of 'a' -- a unit vector in 3-space.

            Then, since lambda is beyond our control -- a truly random variable in 3-space -- and recognising that no two can be the same: we must label them accordingly. NB: Not here (yet) relating the lambda label to a particle label.

            Equations (3)-(7) thus follow, and the source of Bell's famous inequality is revealed:

            In general: Bell's 1964:(14b) IS NOT EQUAL TO Bell's 1964:(14a)! QED.

            Noting that any difficulties for newcomers probably reside in the common but rigorous notation, which is soon easily grasped; especially if they ask questions.

            THUS: The first IT from BIT!

            For we started with BIT (information, essentially provided by Bell and his boundary conditions) and we discover a fairly sensational IT (one missed by the whole Bellian community, as far as I know).

            That IT is particle pn+i!

            NB: pn+i is a crucially different particle because, carrying a crucially different lambda, it cannot POSSIBLY be paired with particle pi in the manner of Bell's maths -- 1964:(14b) = 1964:(14a) -- as Bell and many others would have us believe.

            Hence the IMPOSSIBILITY of Bell's manoeuvre. And hence the downfall -- per that equation (22) -- of all CHSH-style inequalities: here simply, theoretically; and (importantly), as confirmed experimentally -- as you yourself stress.

            AND hence the wonder -- given the conclusions drawn (and so forcefully promulgated) re nonlocality and the impossibility of common-sense local realism -- that not one of Bell's supporters critically revisited his maths posthaste.

            To be continued:

            With my thanks again; please don't hesitate to interpose remarks -- even swift uppercuts -- at any stage; Gordon