From stapp@thsrv.lbl.gov Wed Jul 19 10:51:53 2000 Date: Tue, 18 Jul 2000 10:38:59 -0700 (PDT) From: stapp@thsrv.lbl.gov Reply-To: hpstapp@lbl.gov To: piergiorgio odifreddi Cc: hpstapp@lbl.gov, schipani , odifreddi Subject: Re: interview for the italian tv Dear Professor Odifreddi, You have composed a marvelous set of questions. Thank you very much. They provide a wonderful scaffolding that allow me to weave a tale that quickly brings out the main features of my approach. I insert, below, into your letter, my replies to your questions in a written form, They follow generally the verbal answers that I gave on the tv interview. Best regards, Henry On Wed, 12 Jul 2000, piergiorgio odifreddi wrote: > dear professor stapp, > > i'm the math professor in charge of the questions for > your interview. i'm > sorry i couldn't make it to california: i would have > liked to meet you, > since i read your book "mind, matter and quantum mechanics", > and liked it > very much. here in cornell i had a few talks, some years > ago, with david > mermin on the subject of bell's theorem and your versions > of it. > > obviously, in the interview you should try to keep as > informal as you can. > this is going to be a popular program on prime time, and > most people will > not have any scientific or mathematical background. if you > allow me, i will > also publish a version of the interview for a page on > "la repubblica", the > leading italian newspaper. That would be fine. > please answer the questions in > as many words as > you deem necessary: there is always time to edit things > out later on, but > not to add on them! > > the program is called "the other face of science", and is > conceived as > follows. we're after stimulating and novel ideas about the > universe. we > interviewed brian green on his book "the elegant universe", > in particular > about string theory and its applications to the big bang, > including what > might have happened "before". perhaps witten will also > give us an interview > on the same subject. > > we also interviewed frank tipler about theories of the > end of the universe. > we'll balance his (often puzzling) words with freeman > dyson's, who's also > going to talk about some of his provocative ideas about > the origins of life, > as well as space travel and the end of the universe. > > i also hope to get wheeler on the board (till now we've > been unable to > contact him: do you happen to have a recent e-mail or > phone number?). > > we'd like you to talk about the EPR paradox, bell's theorem, > holistic views > of the universe, and the role of consciousness. here is a > list of questions, > which i hope you'll find of your liking. obviously, we'll > have to miss the > chance of any interaction among us, and of reactions to > your words. > > 1) what was einstein trying to accomplish by proposing > his EPR argument? > These three letters, EPR, are the initials of three physicists, Einstein, Podolsky, and Rosen. Podolsky and Rosen were two young colleagues of Einstein, and the three together wrote one of the most famous papers in the history of science. Its title was: "Can Quantum Mechanical Description of Physical Reality Be Considered Complete?" The words ``quantum mechanical description'', mentioned in this title, referred to a new physics developed during the first part of the twentieth century. This new physics was RADICALLY different from what had gone before. The old physics dealt with objects such as planets and cannon balls that were big enough to be seen. However, those big objects were thought to be built out of particles that were too small to be seen, and were just tiny bits of matter. However, that simple idea seemed incompatible with experimental data that physicists were collecting, and physicist made a REVOLUTIONARY change. Instead of speaking directly about the physical reality itself, they made a theory about what human observers CAN KNOW about physical reality. But the question then arises: Can this indirect approach completely describe everything that is out there? Einstein was convinced that the answer was NO! He believed that physicists should try to describe what is ``out there'', rather than what is ``in here''. The EPR argument was designed to PROVE that the new physics did not describe ALL of physical reality. The idea was first to introduce a very reasonable-sounding property of ``physical realty'' and then prove, STARTING FROM THE BASIC PRECEPTS OF THE NEW PHYSICS ITSELF, that this radical new approach left parts of physical reality out. > 2) in plain words, what were the later developments on > this subject, > including bohm's, bell's and your results? > These later developments had to do with the possibility of instantaneous, or faster than light, action at a distance. The key assumption of the EPR argument was that physical reality in one place cannot be influenced INSTANTLY by what someone freely chooses to do in some faraway place. For example, what I choose to do here in Berkeley, right now, cannot effect what is really happening RIGHT NOW in Paris. It takes some FINITE AMOUNT OF TIME for my decision here to have any real effect there. This claim of no instantaneous, or faster-than-light, action at a distance is called the "locality assumption". What David Bohm did was to show that this "locality assumption" was critical. He devised a simple model of physical reality that met all other requirements, but was blatantly nonlocal. Specifically, he showed, by means of a simple explicit example, that one COULD make theory of physical reality itself, provided one were willing to abandon this locality assumption. But physicists were not prepared to abandon locality. Einstein himself, who wanted to have a theory of reality, called Bohm's model "too cheap". I asked David about this remark by Einstein, and he replied that he COMPLETELY AGREED! But the question that then arises is whether it is possible to make a satisfactory theory that is similar to Bohm's, but is "local". That is where John Bell came in. He showed that ANY theory that is like Bohm's theory MUST BE NONLOCAL. However, Bell's proof was not really satisfactory. That is because his proof rested on an assumption that directly violated a key premise of the new physics. So from the point of view of an orthodox quantum theorist Bell's theorem merely confirmed that the quantum principles were sound: it proved nothing about nonlocality. That is where I came in: I showed, STARTING DIRECTLY FROM THE PRINCIPLES OF THE NEW PHYSICS, that any theory of reality agrees with the predictions of quantum theory must violate the locality assumption. This means that physicist are face with the option of either: 1) Abandoning the possibility of describing a physical reality that agrees with what know about it, or 2) Abandoning the locality assumption. The Copenhagen position is, essentially, that it is better to renounce completely, and permanently, the possibility of describing reality, rather than allow a violation of the locality assumption. > 3) have there been experimental results related to these results? Yes. Many such experiments have been performed. The arguments about nonlocality are theoretical arguments. They are based on what the new physics predicts, in certain special cases, about two experiments performed at the same time in different places. Thus the question arises: Are these prediction valid? To answer these questions experimental testing is required. Many such experiments have been performed over the past twenty years and it is now abundantly clear that the predictions of the new physics are accurate with very high precision. In some recent experiments the distance between the two experiments was more than ten kilometers. So we are talking here about connections that extend over distances that are huge on the atomic scale. > > 4) do people agree on their outcomes, or is there room > to speculate? > It is now clear the the predictions of the new physics are borne out to high precision in the relevant experiments. > 5) what is the world view that follows from bell's theorem > and its variants? > Failure of this locality assumption would means that, at some deep underlying level, the universe is much more closely interconnected than the old physics had led people to believe. The universe seems to be a giant structure such that any change in one place requires instant adjustments in faraway places. > 6) can we draw any connection with the holistic world view > that has been > proposed in various (mostly eastern) philosophies? > Niels Bohr and Erwin Schroedinger, two of the founders of the new physics, had noticed connections of this sort. But the important thing is that the physics that I am speaking about is expressed in a solid mathematical structure that is erected upon the results of scientific experiments. And it arises within the analytical traditions of Western science. Thus both the origin and detailed content of the new insights differ greatly from those of the older traditions. > 7) do we have to change our view of the world, and > how difficult is it to do for the layman? > If one is interested in bettering his understanding the reality that lies behind the world of human experiences, then a profound change in world view is certainly required. It is not difficult to do this. The mind of man is amazingly facile: it can easily grasp counterintuitive ideas if they are rationally coherent. An example is the classical physics idea that a solid rock is mostly empty space. Similarly, it is not hard to grasp the idea that the world behind our evanescent experiences is really more "solid'' and "interlocked" than it appears to be, particularly the new concept is if it is backed up by a rationally coherent mathematical theory supported by empirical evidence. > 8) how is science still possible, if all things are > really interconnected? > The problem raised here is that if faraway events can effect what is happening here, then how can we ever get a grip on causation. The answer is that the new physics specifies probabilities, and that these probabilities follow more normal laws of causation. Thus although the cause of individual events may be difficult to trace out, the constraints on probabiliies often allow one to predict with good accuracy what will happen under specified conditions. All of the causal connection specified by the old physics come out of the new physics in this way. > 9) is modern physics telling us something about consciousness > and its role, as well? in particular, can we separate > observer and observed as neatly as we used to do in > the 1800's? A big problem with the physics of the 1800's is that it made the separation between observer and observed TOO neat. The separation was so neat that my thoughts are rendered unable to cause my tongue to move so that I can describe to you my thoughts. The experienced fact that my thoughts can influence my actions, which lies at the base of our human existence, must be, if one is in the grip of the fundamentally false ideas of the 1800's, be regarded as a mysterious illusion, or vast confusion. The new physics, on the other hand, is essentially a description of the dynamical two-way connection between the thoughts of participant-observers and activities in of their brains, with thoughts described in psychological language and brains described in the language of the new physics. > 10) how were your views influenced by heisenberg's > interpretation of the > world according to quantum mechanics, in particular by his > notion of > "potentia"? > I was greatly influenced by this idea. Heisenberg was the most important founder of the new physics, and he generally adhered to the orthodox philosophy, which said that the new physics was just a set of mathematical rules connecting bits of human knowledge, and that we should not try to look deeper. But on one occasion he did addressed the question of what was "really happening". He referred to the concept of "potentia" in Aristelian philosophy, and said that in nature one must distinguish "possible" from "actual", and that the transitions from "possible" to "actual" are governed by "potentia", which are "objective tendencies" This point of view converts the new physics from a mere set of computional rules that human beings find useful, into a way of describing physical reality. But this physical reality is completely different in character from the physical reality imagined to exist in the old physics. Now it was a churning caldron of "urges" for EVENTS to occur, where these events were sudden transitions from possible to actual. > 11) how were your views influenced by william james' > philosophy and psychology? William James was both psychologist and philosopher. As a psychologist he was interested in such things as our conscious thoughts, sensations, and feelings. He recognized, and strongly emphasized in his writings, that these things come to us, in sudden EVENTS, or happenings, as complex wholes. Thus James identified complex EVENTS in the psychological realm that could be seen as parallels to the physical events that Heisenberg spoke about. > 12) von neumann and wigner thought that the collapse of > the wave function is > the result of consciousness. could you first spell their > views, and then tell > us if you agree with them? > John von Neumann was one of the most brilliant mathemations and logicians of his time. He, and nobel laureate Eugene Wigner, provided the mathematical structure that allowed the psychological events of James to be dynamically linked to the physical events of Heisenberg. Their work gives the mathematical foundation of a theory of reality that that is built upon the dynamical interaction between minds and brains. > 13) can you tell us about your proposal of defining > man's consciousness in terms of physical events? The connection is through the brain. The brain constructs possible courses of action for the person to follow in his current situation. But the new physics requires, in connection with each event, TWO CHOICES that are not determined by the mathematical rules of the theory. One of these choices can be ascribed to Nature, and THAT choice is constrained by certain statistical or probabilistic rules. But the other choice is a free choice on the part of the PERSON. This personal, or subjective, choice can be the choice to CONSENT or NOT CONSENT to a course of action prepared by the brain. This personal choice is needed to make the quantum machinery work, but it is not constrained by the rules of the new physics. It can be identified as a CONSCIOUS CHOICE. The content of the associated conscious event is an image of the proposed course of action that is made ``actual'' by the physical event. > 14) is it actually possible to define a universal > consciousness, of which man's own would just be a > manifestation? According to the new physics, the state of the universe is a "compendium" of the increments of subjective knowledge of all the observers. Thus it is made out of the same kind of stuff as human conscious experience. Each subjective increment of knowledge can be regarded as a addition to the objective state of knowledge that constitutes the universe. > 15) is this a way of reintegrating man into the cosmos, > and of undoing the separation proposed by bacon and > descartes? Francis Bacon was one of the great early proponents of science, and he saw science as a way of putting nature to work in the service of man. This is indeed what occurred. Just consider how our understanding of electricity has been put to use. But this idea that of man enslaving nature has dangers. It can lead, for example, to the rape of the environment. The new physics places man more securely IN nature, and presents the connection of human beings to nature as more of a cooperative venture, not one of master and slave. Descartes' name is generally associated with a complete disjunction of the worlds of mind and matter: mind stands apart from the physical morld of matter, and observes it without being able to influence it in any way. (Actually, Descartes himself allowed for interaction via the human pineal gland, but the laws of Newton mechanics excludes any action of mind on matter.) But the new physics, interpreted in the Heisenberg/James/vonNeumann-Wigner way, specifies the nature of the two-way causal connection between the aspects of nature that we describe in these two different ways. > > 16) how does this relate to the problems of free will and determinism? > The essential point is that the new physics has two separate elements of freedom. One is a choice on the part of nature. This choice is constrained by a statistical rule. The second element of freedom is a choice on the part of the human participant. This latter choice is not constrained, within the framework of the laws and rules set forth in the new physics. This second element of freedom is the analog in von Neumann's quantum theory of the free choice, on the part of the experimenter, as to which experiment he will perfom. This choice is an essential ingredient in the quantum machinery. This choice puts before nature some specific Yes-No question. This choice---of which question to put to Nature---is absolutely essential to the mathematical machinery, yet is not specified by that machinery. This element of freedom given to the human participant by the quantum machinery provide an opening for what we feel to be our freedom to consent, or reject, courses of action that present themselves to us. > 17) are physics in general, and your views in particular, > giving a precise meaning to such venerable notions as the > presocratics' intelligence of the world, the stoics' > pneuma, and the christian's holy spirit? > These venerable notions all ascribe to nature herself, in some objective sense, properties similar to our own psychological qualities. The new physics represents nature as a "compendium" of bits of human-type knowledge, and gives to nature a quality of "potentia", which is akin to a pschological "urge". And the new physics builds the universe out of complex macroscopic whole events---not out of bits of matter---in much the same way as a human stream of consciousness is built out of a sequence of complex whole events, rather than a collection of moving material particles. But these "psychological" properties of nature are encoded in a well defined mathematical structure that conforms to rules that can be empirically tested. > 18) how do your views related to eccles' and penrose's? in particular, what > do you think of psychons and microtubula as mechanisms for consciousness to > act on the brain? Eccles' theory adds `spirit entities' onto the new physics whereas I build directly upon the structure and rules of that theory as it already exist: I introduce nothing that is not already an integral part of the new physics. Eccles allows his spirit entities to bias, hence violate, the quantum laws, whereas I adhere strictly to those laws. The quantum structure is an intricate structure of amazing internal logical coherence, hence violating any part of it opens the door to pandemonium, and unconstrained speculation. Penrose's dependence upon microtubula require a certain property of brains called `macroscopic coherence'. Most physicists expect this propery to disappear in a warm wet brain in something like one nth of a second, where n is 1 followed by 23 zeros. I share that general expectation, and in fact not only embrace but make important use of the expected macroscopic decoherence. > 19) how do your views relate to bohm's and josephson's? in > particular, what do you think of the implicate order, and > of the possibility of experiencing it through meditation > techniques? Bohm's concept of implicate order is rather vague. I prefer to build directly on the clear and well tested mathematical structure that defines contemporary physics, and the findings of psychologists and neuroscientists. I do not meditate, and rely on the testable ideas that have emerged from the objective techniques of Western science. > ********************************** > > Piergiorgio Odifreddi > Dipartimento di Matematica > Via Carlo Alberto 10 > 10123 Torino (Italy) > > tel. +39-11-898.5253 > fax +39-11-670.2878 > > e-mail: piergior@dm.unito.it > > From stapp@thsrv.lbl.gov Wed Jul 19 10:52:40 2000 Date: Wed, 19 Jul 2000 10:46:14 -0700 (PDT) From: stapp@thsrv.lbl.gov Reply-To: hpstapp@lbl.gov To: Stanley Klein Subject: Re: interview for the italian tv (fwd) On Wed, 19 Jul 2000, Stanley Klein wrote: > Henry, that was a really wonderful interview. I hope an English > speaking paper picks it up. My only complaint is that there is > nothing at all for me to complain about. I agree with it all. By > explicitly avoiding the specific Zeno mechanism you have converted > your approach to one that I think is unassailable. I see no need for > Mr. Zeno whatsoever. It holds together beautifully as it is. > > (But if you are still advocating Zeno, I will continue to pester you > about how the mind is able to do the big one msec collapse following > all the nanosec entanglements with the environment. I think that is > an ugly thing for the mind to do. I would need to see how a human > experimenter could do such a thing.). > > Stan > I did not mention QZE, but it is essential. The point is that if one does not use it, then the freedom of choice that QT gives to the person to pick which question to ask---i.e., which aspect of nature to probe: which projection operator P to use---produces no net statistical effect on behaviour of a system that has already been reduced by environmental decoherence to an ensemble of quasi-classical systems, when P picks out a subset of these quasi-classical systems. Without exploiting the suppression of the linear-in-time term the system becomes essentially classical, and in the classical case the capacity to choose which question to ask has no effect on the statistical ensemble: one must add the contributions from the two possible answers to the question, Yes or No, and this leaves the statistical ensemble unchanged. An ugly thing for mind to do? I find it rather beautiful, and in any case natural. The brain-body is (represented by) Tr_{-b} S(t). So the posing of a question by a person's mind ought to be represented by choosing a projection operator P that depends only on the variables that specify the person's body-brain, and that acts only on those variables. You ask how the mind is able to do the big one msec collapse following all the nanosecond entanglements with the environment. The absolutely essential thing about the reduction, via entanglement with the environment, to the ensemble of quasi-classical state is that this is generated by the Schroedinger equation alone, and hence no actual reduction has occurred to any one of the quasi-classical states: the brain is the entire ensemble. It is true that if one is interested only in calculating expectation values of operators that do not depend on the environment, then the fact that the state of the brain, Tr_{-b}S(t), has this form means that the computation is the same AS IF the brain were in one of quasi-classical states, but we don't know which one, but do know the relative probabilities. That is the basis of the Copenhagen approach, where one settles for practical rules that work. But at the ontological level of von Neumann, which is also the level of Zurek and the others who want to go beyond the Copenhagen interpretation and explain why classical concepts come naturally into QM, the full state of the universe S(t) is the basic physical reality, and hence the state of the brain-body is the full ensemble Tr_{-b} S(t). You are not entitled to imagine that the brain is really just ONE of the quasi-classical states, except for the particular purpose of computing expectation values of observables that depend only on the variables that characterize the body-brain. It would be worthwhile for you to look at Zurek's paper in Progress of Theoretical Physics, 89, 281-312 (1993) to see him wrestling with this point, and admitting that environmental decoherence does not really solve the problems, but that one needs a theory of consciousness. He says: "Such model of consciousness is presently not available". That is the essential point. One needs a theory of consciousness to make sense of quantum theory: trying to understand quantum theory without recognizing that it can only be understood within the context of a theory of consciousness is a nonstarter. The environmental decoherence is indeed important in understanding the importance in QT of classical concepts. But one must then bite the bullet and face the problem of consciousness. The first important thing to recognize clearly is that the environmental decoherence does not by itself reduce the brain to ONE quasi-classical state: it reduces it to an entire ensemble of such states. Thus those nanosecond reductions are merely a first stage of the process. They set the stage for the real problem. Henry From stapp@thsrv.lbl.gov Wed Jul 19 12:56:33 2000 Date: Wed, 19 Jul 2000 12:53:49 -0700 (PDT) From: stapp@thsrv.lbl.gov Reply-To: hpstapp@lbl.gov To: Bruce Rosenblum Cc: Subject: Re: interview for the italian tv (fwd) On Wed, 19 Jul 2000, Bruce Rosenblum wrote: > Henry, > > I too found your interview for Italian TV wonderfully concise. But maybe > you would comment on a point that I find confusing (and so, I'll bet, would > Italian viewers). You say: > > "According to the new physics, the state of the universe > is a "compendium" of the increments of subjective knowledge > of all the observers. Thus it is made out of the same kind > of stuff as human conscious experience. Each subjective increment > of knowledge can be regarded as an addition to the > objective state of knowledge that constitutes the universe." > > Should I take this as a sort of (objective) idealism--all that exists are > minds? Sometimes I believe you say the state vector of the universe > REPRESENTS the knowledge. > REPRESENTS = IS? And there's nothing else? > > If your answer is simply "yes," I could not say you deviate from standard > qm here. The wavefunction of an atom represents (= is?) our knowledge of > the atom. And there's presumably no atom out there as something in > addition to the wavefunction (Bohm aside). So you're saying nothing more > confusing than standard qm. But standard qm has always confused me, at > least whenever I take it seriously. If you have a few words to throw light > on this--even to merely confirm that you really mean "IS," and mean that > there's nothing else, I'd appreciate it--and continue to ponder. > > Bruce > One must distinguish the Copenhagen view (Quantum theory is a practical set of rules that we use) from the vN view (The quantum state of the universe represents/is physical reality itself.) In Copenhagen quantum theory the quantum state can properly be called, and often IS called, a representation (within our human-consructed theory) of "our knowledge": it IS a mathematical structure, existing within our thoughts, that REPRESENTS our knowledge. It REPRESENTS a compendium of the increments of knowledge that we have put into this state. In the final analysis all of our theories are ideas that exist in our thoughts. But vN quantum theory moves in the direction of trying to make the theoretical concepts accurate images in our thoughts of aspects of what really exists in nature. We can imagine that Nature herself has aspects that really do have structural qualities of a kind that we can grasp and represent in a mathematical form that exists in our thoughts. According to this scenario the structure that we express in our mathematical formulas is isomorphic to a structure that exists in Nature herself. Thus we can, in the usual way, use this isomorphism to allow us to speak as if the mathematical structure that we postulate in our thoughts is the structure that exists in the physical world itself. Whether we say the quantum state REPRESENTS reality or IS reality is not significant, if this isomorphism really exists. The Copenhagen view is not puzzling in itself: we have useful rules that work. It only becomes puzzling if we try to understand what is really happening, which the Copenhagen approach instructs you not to do. The vN approach likewise is not puzzling if you accept that nature has the behaviour that vN/W QT says it has. This behaviour is a behaviour appropriate to a world that is formed as an accumulation of bits of knowledge. The appropriate language is the language appropriate to this behaviour. The physical world IS made out of bits of knowledge: it IS a compendium of these bit of knowledge. But it evolves according to mathematical laws that entail all of the connections between the our experiences that classical physical theory correctly predicts, plus a lot more. But I have not said that there is nothing more that these bits of knowledge: present-day quantum theory does not explain how nature makes her choices. Nor does it specify exactly how we make our "free" choices. But present-day quantum theory does slice the mind-brain problem in a different way. It formulates the problem explicitly in terms of two aspects of nature that are described in two different languages, one physical, the other psychological, and specifies the dynamical connections between the two aspects. And this dynamical connection leads naturally to the sorts of connections that we experience, first of all in our perceptions pertaining to connections between, say, motions of planets and falling apples, and secondly in the power of our thoughts to direct our bodily actions and mental processes. Henry From stapp@thsrv.lbl.gov Sun Jul 23 04:40:42 2000 Date: Sun, 23 Jul 2000 04:34:02 -0700 (PDT) From: stapp@thsrv.lbl.gov Reply-To: hpstapp@lbl.gov Subject: Re: experientialism (fwd) ---------- Forwarded message ---------- Date: Sun, 23 Jul 2000 04:26:28 -0700 (PDT) From: stapp@thsrv.lbl.gov Reply-To: hpstapp@lbl.gov To: zznobo Subject: Re: experientialism On Sat, 22 Jul 2000, zznobo wrote: ... > While at your webpage, I read your exchanges with Klein and Rosenblum > regarding the Odifreddi interview. Two questions came to mind. First, > would it be compatible with your views to contrue subjectivity as > objectivity in the making? Dear Jorge, Yes! But I do associate subjectivity with some sort of physical system. > Second, do you equate knowledge and > information? or would you be willing to say that all > knowledge is > information, but not all information is knowledge? > (On the other hand, > all information must be in principle knowable, though not > necessarily by us.) That does seem to be a good way to put it. > It seems to me that, with the Copenhagen view, > the quantum state does > "represent a compendium of knowledge that we have put > into this state." > On the other hand, in the vN/W view, it may be better to > say that the > physical world is made out of bits of information, only > some of which > are bits of human knowledge. Excellent! > I am shooting in the dark here, but, without going > into details, I am > trying to see whether there is some fit between my > metaphysics and your > physics. For me, treating human knowledge as a special > case of > information is metaphysically desirable, lest we make > human knowings way > too special. Also, as a bit of terminological strategy, > your audience is > less likely to bolt up the wrong tracks with the claim > that the world is > an accumulation of bits of information than with the > claim that it is an > accumulation of bits of knowledge. > Regards, > Jorge > Right! I do want to use "knowledge" to tie it into the Copenhagen position, both in terms of the terminology that the Copenhageners use, and in terms of the meaning appropriate to their pragmatic point of view. But I need to allow for precursers to human knowledge, and then "information" seems better. It is also better suited to the objective vN position, and, as you mention, more reasonable-sounding, and metaphysically neutral, as an objective property of nature. I think we see this terminological issue in a very similar way, and that your way of resolving it is very good. Henry