Wednesday, February 18, 2015


ON ROGER PENROSE’S ROAD TO REALITY D. R. Khashaba The demonstration will be to pundits unconvincing, to the wise convincing. Plato, Phaedrus, 245c. Roger Penrose has written a voluminous book, The Road to Reality, 2004. It is not the kind of book I would normally be tempted to tackle, having neither the competence nor the inclination, but a friend has kindly made it available to me. Enticed by the title and being an incorrigible fool, it occurred to me to make some comments on the book, not on the mathematics or the physics: fool though I am, I am not such an imbecile as to opine in areas where I confess myself an ignoramus. I will comment on certain assumptions and certain implications that may slip in unwittingly as they usually do when scientists are oblivious to the limitations of science. Anyway, I know that in this paper I have stuck my neck out by taking on an accomplished man of science. I hope that this does not prove me completely insane, for I am not meeting him on his own ground, which I dare not tread, but on my ground. I begin with two preliminary remarks that I jotted down on first glancing at the title page and the table of contents. A) The book is subtitled “A Complete Guide to the Laws of the Universe”, and the question pops up: Do the laws (mathematical and physical) of the universe constitute reality? Do they reveal reality? What reality? At this point I merely pose these questions as questions and nothing more. In what follows I will clarify the thoughts that impel me to pose these questions. B) Section 1.1 is headed: “The quest of the forces that shape the world”. I suspect a sleight of hand here. The laws have unwarrantably become forces. This is a standing trick of scientists. Science doesn’t know any force, cannot point to any force, since it cannot put any force in a test tube or under a microscope. The laws of the natural world are supposed to work themselves out just by virtue of their being laws decreed by some unknown god, and here they have metamorphosed into forces that shape the world. In doing this, scientists give themselves licence to jump a truly unbridgeable chasm. This is a point I will expand on in what follows. I write down my remarks as I read. This explains the rough edges at certain points and the untidy formation and the many revisions and inserted additions, I am afraid, have added to the disarray. To facilitate reference I will place my remarks under the relevant sections, using the author’s decimal numbering. 1.1 The quest of the forces that shape the world I find in the first paragraph clearly expressed the fallacy I decry in modern scientific thinking. It reads: “What laws govern the universe? How shall we know them? How may this knowledge help us to comprehend the world and hence guide its actions to our advantage?” I find in these words two assumptions implied, one justifiable and the other at best requiring qualification and at worst leading to gross error. But first let us be clear as to what we understand by “laws that govern the universe”. Scientists observe certain regularities, certain patterns, in the natural world; they formulate schemata, always approximate and subject to revision, picturing those regularities and patterns. These ‘laws’ may help us and have been helping us manipulate nature to do our bidding, be it to our advantage or to our doom. This is what I referred to as a justifiable assumption. But how do they help us “to comprehend the world”? It depends on what we mean by ‘comprehend’; if it means simply to know how to manipulate things to our advantage, then the phrase is redundant; but if the word means to give us insight into the reality of the universe, I strongly protest. The trouble is that highly intelligent minds immersed in science have not the least inkling of an idea as to what a philosopher means by understanding reality or insight into reality. I call to my succour Kant who affirmed that all investigation into the natural world studies phenomena but not what is beyond or underneath the phenomena. And before Kant I go for support to Socrates who knew that the investigation of nature cannot yield answers to questions of value, purpose, or ultimate origins. I have been harping on this in all my writings and will mot amplify on it further here. There is in fact in the statement quoted a third questionable assumption lurking in the word ‘govern’: in what sense do scientific laws ‘govern the universe’? There will be scope to examine this in what follows. 1.2 Mathematical truth Again when Penrose speaks of the importance of number and of mathematical concepts “in governing the actions of the physical world” I dread the error into which this seemingly innocuous phrase can mislead us. Mathematical and scientific laws govern our thinking but do not govern the world. They tell us what we may reasonably expect but do not reveal the reason behind the observed process. The notion that the laws of science have an objective existence and constitute a power working within nature is a confused idea breeding much misunderstanding and error. A metaphor is taken literally and thus mistaken for a fact. That we now have non-Euclidean geometry, in my opinion, supports my view that all mathematics and all scientific ‘laws’ are creations of the human mind that confer intelligibility on things but that we cannot affirm to be definitively ‘true’ of the world. The paragraph beginning with the words: “Euclidean geometry is a specific mathematical structure”, in my opinion, lends support to my view. I will not comment on the last paragraph under 1.2 on Plato at this point since it seems there will be ample scope for this under 1.3. 1.3 Is Plato’s mathematical world ‘real’? This section I am afraid is based (first) on the common false understanding of the so-called Platonic ‘Theory of Forms’ and (secondly) on the ambiguity in the terms ‘objective, objectivity’ and ‘existence’ and (thirdly) on the confusion of existence in the natural world with Platonic or metaphysical reality. The supposed ‘separate existence’ of the Platonic Forms in a world of their own is a misconception based partly on Plato’s poetical representation in the Phaedrus of the Forms abiding in a celestial home and partly on Plato’s youthful overemphasis on the immutability of the Forms. The misconception was strengthened by Plato’s early experimentation with various formulations for relating the Forms to the particular multiple things in which the Forms are exemplified; none of these formulations was found satisfactory by Plato. In the first part of the Parmenides he showed their incoherence. In the Sophist he showed the error of excessively dwelling on the immutability and permanence of the Forms. In neither of these later dialogues was Plato altering his original position; he was merely correcting the imbalance in expression bred by his youthful enthusiasm. I have written repeatedly and extensively on this (especially in Plato: An Interpretation, 2005) and do not think I need to go further into it here. Penrose writes: “What I mean by this ‘existence’ is just the objectivity of mathematical truth.” ‘Objectivity’ is a tricky concept. If we mean existence in the outside world then we are begging the question. Though it is not evident that Penrose means this in this particular context, the whole bent of the book shows that this is what he has in mind. His next sentence adds to the confusion. He says, “Platonic existence, as I see it, refers to the existence of an objective external standard that is not dependent upon our individual opinions nor upon our particular culture.” We are entitled to ask: Objective in what sense? External to what? Then we have, “The mathematical assertions that can belong to Plato’s world are precisely those that are objectively true.” Again we ask: What do we mean by ‘objectively true’? If we are agreed on excluding the meaning ‘exist in the outer world’, then in my opinion we are left with the sense ‘intrinsically meaningful, meaningful in themselves’, which, I believe, agrees with Plato’s position but probably not with what Penrose intends. For Plato the Forms (including mathematical notions and structures) are metaphysically real, real in and for the mind, but do not exist in the natural world though they may be exemplified in particular existents. But if “mathematical assertions … are objectively true” is taken in this sense, how does this help Penrose show that mathematical structures reveal the ‘reality’ of the universe? Let us proceed. Penrose is aware that “there will still be many readers who find difficulty with assigning any kind of actual existence to mathematical structures.” How does he meet their difficulty? He asks such readers to “merely broaden their notion of what the term ‘existence’ can mean”. Suppose they mean by ‘existence’ both what is actually in the external world and what Plato means by the term ‘real’. This is not to broaden the motion; this is to choose to ignore a radical distinction. Disregarding that this adds to the confusion, how does it help Penrose? He admits: “The mathematical forms of Plato’s world clearly do not have the same kind of existence as do ordinary physical objects such as tables and chairs.” To my mind this leaves us where we were. Plato’s Forms are a world apart, a world of metaphysical reality, a world in the mind and for the mind; they may confer intelligibility on the outside world; but that outside world remains in itself and by itself a world foreign to the world of the mind; the mind may form a poetical or philosophical vision of the world as a whole but cannot assert the vision to be true of that outside world. When Penrose speaks of the ‘reality’ of the universe I see that as resulting from a confusion of terms and from overlooking the ambiguity in the terms ‘objectivity’ and ‘existence’. Had Penrose been a trained philosopher I would have said that he sophistically manipulates ambiguities; but since he is not, I can only say that he is unaware of the deceptiveness of ambiguous terms; he uses one sense of a term in the premise then slides to a different sense in the conclusion. I hope it is clear I am not critiquing the mathematics or science of the book but only commenting on peripheral notions and assumptions. 1.4 Three worlds and three deep mysteries Penrose speaks of three ‘forms of existence’, the mathematical, the mental, and the physical. I do not understand the distinction between the mathematical and the mental. To me both of these have their reality (I reserve ‘existence’ for the physical) in the reality of our subjectivity. Let us see how Penrose relates these three forms of existence, or three worlds, to each other. He dubs the relations between these worlds mysteries. (On reading further I discovered that by ‘mental’ Penrose does not mean the activity of thought as I supposed; he apparently means the biological or physiological undercurrent mediating between his ‘physical’ and his ‘mathematical’ worlds. I wonder why he does not simply say ‘neurological’ and spare us mistaking his meaning. I also realized that my reading of the diagram was too simplistic. However I leave what I have written as it is for what it is worth.) From the schematic representation in Fig. 1.3 it would seem that for Penrose impressions received in the mental sphere go up to the mathematical sphere and from there proceed to the physical sphere. This schema in its bare outline would agree equally with a Platonic as with an Empiricist epistemology. We still have to see if this reveals to us the ‘reality’ of the physical world and if so, how, and in what sense of ‘reality’. Following Fig. 1.3 Penrose writes: “I have imposed upon the reader some of my beliefs, or prejudices, concerning these mysteries.” It is necessary that these beliefs or prejudices should come out plainly for us to decide whether they are justified or not. The figure as it stands could be accepted by Locke as by Plato, by Bertrand Russell as by Kant, which means it does not convey any definite view; the beliefs and prejudices remain hidden. We are told that “only a small part of the world of mathematics need have relevance to the workings of the physical world”. I am still in the dark. I want to know in what way the small part that does have relevance, has relevance. The second mystery, we learn, concerns how mentality comes about in association with certain physical structures (most specifically, healthy, wakeful human brains). On first looking at the figure I did not anticipate any difficulty here. I agree it is a mystery (I only wish physiologists and neurologists would acknowledge that) but I still don’t see how it relates to our knowledge of the ‘reality’ of the physical world. And again we are told that not “the majority of physical structures need induce mentality”. When Penrose follows this by affirming that the brain of a cat may “evoke mentality” but that he does not require the same “for a rock”, I am completely baffled. Leaving aside for the moment the slippery shift from ‘induce’ to ‘evoke’, I ask: In what sense is a rock not required to “evoke mentality”? Obviously not in the sense that it may not be the source of impessions received by a human brain. If we take it to mean that a rock does not have mental states, it is legitimate to ask: How do we know that? Here we have a complete hodgepodge of metaphysical and physical considerations. If you think the notion that ‘inanimate’ objects have ‘mental’ states is absurd, then you are confusing the habitual with the rational. We conventionally assume that a rock has no life and no intelligence, but we deceive ourselves if we believe we have a rational ground for our assumption. I quote below at length a passage from no less a thinker than Francis Bacon: “It is certain that all bodies whatsoever, though they have no sense, yet they have perception: for when one body is applied to another, there is a kind of election to embrace that which is agreeable, and to exclude or expel that which is ingrate; and whether the body is alterant or altered, evermore a perception precedeth operation; for else all bodies would be alike one to another. And sometimes this perception, in some kind of bodies, is far more subtile than sense; so that sense is but a dull thing in comparison of it: we see a weatherglass will find the least difference of the weather in heat or cold, when we find it not. And this perception is sometimes at a distance, as well as upon the touch; as when the loadstone draweth iron; or flame naphtha of Babylon, a great distance off. It is therefore a subject of a very noble enquiry, to enquire of the more subtile perceptions; for it is another key to open nature, as well as the sense; and sometimes better. And besides, it is a principal means of natural divination; for that which in these perceptions appeareth early, in the great effects cometh long after.” (Francis Bacon, Silva Silvarum, as quoted by A. N. Whitehead in Science and the Modern World, pp.55-6.) I confess that what Penrose says n this section of the ‘third mystery’ does not enlighten me in the least, and that is certainly not due to the profundity of the mystery! According to Fig. 1.3, Penrose tells us, the entire physical world is depicted as being governed by mathematical laws. I will not repeat here what I said earlier about the ambiguity and the implicit error in the word ‘governed’ in this context. Scientists should be required to make a careful study of Kant’s Critique of Pure Reason before being permitted to write anything that cannot be put in equations and standard scientific symbols. When they stray outside the sanitized atmosphere of their neat symbols and equations they all, not excluding the admirable Stephen Hawking, write nonsense. Penrose speaks of random behaviour being “governed by strict probabilistic principles”. I wonder, can any probabilistic principle ‘strictly govern’ anything? Is that not incompatible with the very notion of probability? Is it not inbuilt in a ‘probabilistic principle’ that it leaves a margin for divergence? As defence lawyers say, I rest my case! I will not comment on Penrose’s having no problem with his behaviour being controlled by strict mathematical principles. I have dealt elsewhere with the so-called problem of determinism and free will and to go into that here would be out of place. (See “Free Will as Creativity” in The Sphinx and the Phoenix, 2009.) Also I will not comment on what Penrose says about the notion that “all of mentality has its roots in physicality” and the “possibility of physically independent minds”. I maintain that these are questions that are not amenable to scientific methods and I have repeatedly discussed the error of scientists in dealing with these questions. The remaining paragraphs in this section are for mathematicians to discuss, though certain phrases prick me to comment, but I refrain. 1.5 The Good, the True, and the Beautiful The heading suggests that here we are on genuine Platonic ground. But what has mathematics, what has science, indeed what has the physical universe to do with the Good, the True, and the Beautiful? (The True, or at least the word ‘true’ here is confusing: goodness is an intrinsic value; beauty is an intrinsic value; but truth, in the common usage of the term, is an extrinsic relation between thought and actuality.) Plato tells us emphatically that these ideals are not to be found in the natural world and that they are neither visible nor audible nor can they be put to any empirical test. Even the starry heavens that struck Kant with awe are only beautiful to a rational soul. But I am again succumbing to my congenital weakness, letting my thought run at the mere sight of words. Let us see what Penrose has to say. At the outset I have two preliminary remarks. Although Plato was apparently fond of mathematics, yet mathematics does not play a significant role in his philosophy except as a model of Forms and as constituting a principal part in his programme of higher education. Secondly, it is grossly misleading to state simply that mathematics is “crucially concerned with the particular ideal of Truth” unless we specify clearly what we mean by ‘truth’. Truth in mathematics does not mean the same thing as in empirical investigation; ‘truth’ has different meanings in different fields, in history, in judicial testimony. I prefer to say that mathematics is concerned with intrinsic coherence or rationality. The word ‘truth’ should be confined to empirical science and other activities aiming at conformity with an objective (actual) state of affairs. Particularly for Penrose to say that mathematics is concerned with truth is to beg the question since this is just the claim he has to vindicate, namely, that mathematics reveals the nature of the universe. I maintain that mathematics gives us structures (to use Penrose’s term) that enable us to make calculations and predictions but do not reveal the essence of things. (‘Essence’ is not a fortunate term but it helps us avoid circumlocution.) Penrose is “not at all averse” to conceding to Plato the ideals of the Beautiful and the Good. Plato would not have been thrilled: for him the really real is nothing but the mind and the ideals in the mind; and when we say the mind, we decidedly do not mean the brain or anything that can be seen or touched; we mean the living activity of the mind. Penrose refers to “an external Platonic world” that “actually has an existence independent of ourselves”. This is a complete distortion of Plato, even though mainstream academic philosophers endorse it. It misuses his youthful poetical flights of imagination to misrepresent his mature position. To try to justify what I am saying here would be to repeat what I have been expounding in book after book and essay after essay. (See especially Plato: An Interpretation, 2005.) We gather that Penrose’s conviction concerning an external Platonic world “comes from the extraordinary unexpected hidden beauty that the ideas themselves so frequently reveal”. We have no need to go to an external world for this: we learn from Plato that the mind, in itself and by itself, when it communes with its inner reality, begets reality and beauty and understanding (Republic, 490a). This is what Plato otherwise calls giving birth in beauty, tokos en kalôi. Penrose harms himself by mixing science with philosophy. Plato loved mathematics; whether he made any valuable contributions to mathematics I do not know, but when he philosophized he did not confound that with mathematics. Leibniz was a great mathematician and a great philosopher who kept the two unmixed. Before him was Descartes who did likewise. In the twentieth century A, N. Whitehead and Bertrand Russell made valuable contributions in both fields but did not make a mixture of the two. Having commented on the five sections of the first chapter, I think I have said all I care to say in this connection. I will glance selectively at some of the remaining chapters for my edification, not for comment; but before that I will look at the final chapter where I may have something to say: in particular 34.6 looks alluringly challenging to me. 34 Where lies the road to reality? Chapter 34 is titled “Where lies the road to reality?” In the first place it is necessary to be clear as to what is meant by ‘reality’. Although in my writings I use the term ‘reality’ in a special, perhaps idiosyncratic, sense, I have no right to impose my usage on anyone else. If the author makes it clear what kind of reality he is seeking the only thing we can comment on is whether the road is well described or not. The trouble is that the author may well describe the road to the kind of reality he has in mind but then implies that that is all the reality we need bother about, or else claims, as is the case here, that that is reality as envisaged by Plato. Indeed our scientists are so innocent of the slightest whiff of suspicion of there being such a thing as metaphysical reality, the kind of reality Plato cared about. And Penrose, although he frequently mentions Plato and seems to make much of Plato’s ‘mathematical world’, is in my opinion quite off the mark in his understanding of Plato. Well, this note, written while I am still at the threshold of Chapter 34 has probably exhausted what I have to say in this connection and on section 34.6 in particular. I will now go directly to that section and see if it helps me make things clearer. — But first a passing thought triggered by the heading of section 34.1. 34.1 Great theories of 20th century physics — and beyond? Scientific theories are conceptual formulations (Penrose’s structures) that “save the appearances”, that confer intelligibility on the appearances, but they are always transitory, can never be final or definitive, and can never disclose the inner reality of things, This is what Kant tried hard to make us grasp. So whatever be the achievements of physics in the past or in the future, these achievements will make us more adept in making use give is more and more detailed information about the ways of nature and the processes of nature but will not reveal what is behind or beneath all that. So the answer to Penrose’s “and beyond?” is “only more of the same”. the knowledge gained by humankind along the millennia from discovering that chippind a stone makes a cutting edge to the latest discoveries of astrophysics has not made us a jot wiser — we are now drowned in knowledge but in dire need for understanding. Passing by the first five sections of Chapter 34 I go to section 34.6 and possibly some of the remaining sections. 34.6 What is reality? I have already asserted that the empiricist conception of reality is totally opposed to the Platonic, and I venture to say that Penrose despite his assumed Platonism is at heart an empiricist. He is so much taken by the objectivity of scence that he barters the subjective coherence of mathematics for the objective truth of physics. Let us see if there is anything to add. Penrose admits that we have not yet “found the true road to reality” though he thinks that extraordinary progress “has been made over three and one half millennia, particularly in the last few centuries”. All I can say is that that progress has been along a way to what I, following Plato, would not call reality. Reality for me, as for Plato, is the mind and what the mind gives birth to. Our mind, the subjectivity of our creative intelligence, is the only reality we know immediately and indubitably. For that reality Plato used the words alêtheia, to on, ho estin, and sometimes ousia, and represented it by the Form of the Good. When he suggested an imaginative cosmogony (in the Timaeus) he presented it openly as a myth that at best may be referred to as a likely tale. At the risk of being tedious I say that I do not object to Penrose or any other scientist pursuing the road to the fullest possible knowledge of the physical world; what I object to is the unjustified identification of that world with Plato’s purely intelligible world. Penrose surmises that some readers may view the road itself as a mirage. In the context of scientific research a mirage is not necessarily a bad thing if it impels us endlessly to move forward without expecting ever to reach the ever receding horizon. It is in expecting to reach a final resting place that scientists are deluded. Philosophers too commit the same fault when they fancy that there can ever be a definitive articulation of the philosophical vision: the philosophical vision is a vision of our inner reality that is strictly ineffable and that must ever be represented anew in imaginative creations. This is the thought behind the title of my Tne Sphinx and the Phoenix: the Sphinx ever posing new questions and the Phoenix, symbolizing the articulated philosophies, ever consumed in fire, that from the ashes new imaginative representations of the ineffable reality may arise: philosophy is nothing but ceaselessly philosophizing, living in intelligent creativity. Both philosophers and scientists have nothing to lose and everything to gain if they renounce the idolatry of that false god, truth, and realize that it is the quest that is true life; it is the journey that is the end; the end of the journey is death. I do not find it necessary to comment on the rest of this paragraph and the following couple of pages although I was tempted to say something on the difference between ‘what’, ‘how’, and ‘why’ questions and to emphasize that these belong to radically different worlds of thought, but I have taken this up in many of my writings and I did not think it needful to reiterate at this point what I said there. In page 1028 Penrose says that “modern physicists invariably describe(s) things in terms of mathematical models”. That is just the point. A mathematical model is as different from the reality of the thing as an excellent architectural blueprint of a house is different from the house to live in. The chemist’s H2O does not quench my thirst; the actual thing represented by the chemist’s symbol does. To mistake the model for the actual thing is the delusion Whitehead debunked, naming it the Fallacy of Misplaced Concreteness. Penrose adds, “It is as though they seek to find ‘reality’ within the Platonic world of mathematical ideals.” Plato never imagined he would find the physical world (Penrose’s ‘reality’) within mathematical or any other ideals. For him the ideals are all the reality; the whole of the physical world is a fleeting shadow. Besides, I repeat a question I asked before: Can mathematical models, mathematical structures, subsist independently of a rational mind? Can they in themselves and by themselves constitute an actual world, physical or non-physical? Plato’s ideal world is not independent of mind; it is the phronêsus, the ongoing activity of living, creative mind. Penrose continues, “Such a view would seem to be a consequence of any proposed ‘theory of everything’, for then physical reality would appear merely as a reflection of purely mathematical laws.” Would you rather say that the physical world is in itself nothing but mathematical equations (‘structures’) or affirm with Kant that our knowledge of the natural world is merely conceptual representation of phenomena and that we cannot know the noumena, what things are in themselves? Neither Plato nor Kant lessens the jurisdiction of science over the things of nature but they both say that reality (in Kant’s lingo ‘the noumenon’) is to be sought elsewhere. I find Penrose at fault both in thinking that mathematical formulations can lead us to reality when that ‘reality’ is nothing but fleeting shadows, and in presuming that the mathematical formulations actually constitute that reality. The first fault may be reduced to a difference in terminological usage, but the second fault, to put it most mildly, is quite serious. I have to remind the reader that what I have been saying throughout this paper has nothing to do with the mathematics and the physics in the book; I am only commenting on the assumptions and implications hidden in the extra-scientific matter, I will not throw myself into the hornet’s nest by speaking of ‘the theory of everything’ (although I could say something meaningful without pretending to have any scientific knowledge) but I have to put in a word about Penrose’s statement that “the more deeply we probe Nature’s secrets, the more profoundly we are driven into Plato’s world of mathematical ideals”. I cannot pass this without protesting that this amounts to a grievous corruption of Plato’s thought. I think I have shown amply in what went before why it is so. This goes for the rest of this section. I am afraid I have to be bluntly crude. When Penrose says that “physical reality itself is constructed merely from abstract notions” or that “the Platonic world may be the most primitive … since mathematics is a kind of necessity, virtually conjuring its very self into existence through logic alone” — I do not see in this mystery but absurdity and, muddled thinking, bred by our failure to confess our ignorance. I cannot picture to myself any absurdity more gross than fancying abstract notions as a kind of necessity “conjuring its very self into existence through logic alone” — this is as monstrous as the monotheistic idea of God suddenly obeying a whim to create the world out of nothing. Apparently the abstract notions and the logic existed before they conjured themselves into existence; how else could they conjure up anything? We do not and can not know the ‘reality’ of the natural world. The only reality we know, the only understanding we can have, is within us, in the subjectivity of our inner being. I would accept and admire Penrose’s statements were they to come from Meister Eckhart or Giordano Bruno, because a mystic does not speak of the actual world but projects her or his inner reality, expresses her or his vision of Reality, in symbol and myth. The Muslim mystic Al-Hallaj said, “I am the Truth” and was put to death for saying it; he was giving expression to the final Reality wherein we have our personal reality and that gives us all our worth. But a scientist who said what Al-Hallaj said would rightfully be confined to a mental asylum. I do not expect to find in the remaining sections much to evoke any new comment, but I will run through them, just in case. 34.7 The roles of mentality in physical theory Here again we have a mixture of questions that should not be mixed. To ask about the role of mentality in physical theory is silly but legitimate (if we take the word in its common sense); we may wish to distinguish the roles of thought and imagination or even superstition and taboo in constructing physical theories; these notions belong to one realm. But to ask about the role of mentality in the physical world (and with Penrose the question can surreptitiously turn into this) is illegitimate: neither science nor philosophy can give a true answer to this question, though philosophers can and do offer imaginative visions answering the question for their own satisfaction but cannot claim that the answer is factual or that the vision represents an actuality. I have already discussed this in my comments under 1.4 in connection with Penrose’s contention about a rock not ‘evoking’ mentality. “Any universe”, Penrose writes, “that can be ‘observed’ must, as a logical necessity, be capable of supporting conscious mentality, since consciousness is precisely what plays the ultimate role of ‘observer’.” This is basically a tautology that tells us nothing. It amounts to saying that in any universe where consciousness observes we will find consciousness that observes. So what? Is this consciousness in the world outside us? In a sense it is in the world since it is in us and we are part of the world; but is it in the world outside us, independently of the human mind? These two questions have to be separated. Dear reader, pardon me. I will once again repeat what I have already said above because I think it important to drive it home. Here we have a question that science cannot answer and that philosophy answers imaginatively but is not entitled to say that the answer is true of the natural world. A scientist may philosophize but is not entitled to dress her or his philosophical vision in the garb of science or to smuggle it in, in the interstices of his scientific work. This book should have been split into two completely separate ones: one surveying the contributions of mathematics to physics; this would be for scientists to evaluate; and the other giving an imaginative vision of the universe, a vision that can neither be empirically verified nor deductively inferred but can only be appreciated on the merit of its coherence and intelligibility as a creative work of imagination. The science should not be mixed with philosophical speculation and the philosophy should not pretend to be supported by the results of scientific research. The radical separation of science and philosophy is needed to spare us the errant vagrancy of scientists and the foolish dogmatism of philosophers. Penrose refers to the notion of a spatially infinite universe. Here I will audaciously expose myself to ridicule. I know that mathematics has invented the notion of an infinite series. Ignorant as I am I would say that a completed infinite series is a contradiction in terms, so that in this sense an infinite series can never be an actuality. What about a spatially infinite universe? Is an actual spatially infinite universe possible? Is it conceivable? These questions are not for me to delve in. Or does the notion simply translate into that of an endlessly expanding universe? What would ‘expanding’ here mean? Can there be expansion into a non-existent outer space? Would not the expansion simply be relative to contracting constituents of the universe? These are puzzles that may serve for idling away an hour but not for serious study. Should we not rather say that the idea of a spatially infinite universe is just another useful scientific fiction that enables us to make certain calculations? Anyway, all of this is neither here nor there for my purpose. I have simply been foolishly enticed into this digression in an area where I have no right to trespass. What Penrose says about the role played by consciousness in interpretations of quantum mechanics is forbidden ground for me but I think I am within my rights in remarking on the statement that “almost all the ‘conventional’ interpretations of quantum mechanics ultimately depend upon the presence of a ‘perceiving being’, and therefore seem to require that we know what a perceiving being actually is!” I will naively say: Yes we do know, but do not scientifically know, what a perceiving being is. Fortunately a scientific knowledge of what a perceiving being is. is not needed for the perceiving being to continue perceiving and continue interpreting the secrets of quantum mechanics. That we are conscious, perceiving, thinking beings is a mystery that will remain a mystery. Scientists had better acknowledge that this mystery is not amenable to investigation by scientific methods. When Penrose says that he takes the ‘phenomenon of consciousness’ to be “a real physical process, arising ‘out there’ in the physical world”, I have to say that here again we have a presumptuous jump over the chasm between scientific thinking and philosophical thinking. Science can describe the process accompanying the appearance of consciousness, whether on the level of biological evolution or on the level of embryological development, but cannot identify that consciousness with the physical process or assert that it is an outcome of the process. Again this is a subject I have dealt with frequently in my writings and do not find it needful to amplify on it here. It is the same with the presumption of neurologists who think that their observations of the brain can explain the mind. This paper is already longer than I anticipated and probably if I continue I will merely be repeating again comments I have already made repeatedly. So I will pass over the remaining sections of this chapter only stopping at 34.9 with its intriguing title. 34.9 Beauty and miracles Penrose repeatedly speaks of the ‘Platonic mathematical world’ when he means his own conception of a mathematical world that somehow ‘governs’ the physical world. This is misleading. Plato spoke of a world of Forms of which mathematical forms were a part. In Plato’s scheme of education in the Republic the study of mathematics is a discipline to prepare the mind for the contemplation of the Forms; but mathematics has no direct relation to the physical world; knowledge of the physical world, even when under Forms given by the mind, does not rise to the highest order of knowledge which Plato reserves for the philosophical consideration of first principles. These first principles themselves are subjected to dialectic that regularly destroys their ground assumptions. Penrose had no need for Plato; his own mathematical world stands on its own feet. Plato could give him no support and no help and would, in my opinion, have evinced no interest in Penrose’s so-called ‘Platonic’ world. Obviously Penrose has a very special meaning for the term ‘miracle’. (In writing this sentence I have betrayed my ignorance. I now see that Penrose is not responsible for introducing the term in this special sense. Apparently it has already become standard scientific jargon.) Let us see what the concept behind the term is and what use he makes of it. Penrose gives an instance. (I will cut out all the scientific substance as far as possible, reducing Penrose’s statement to its basic linguistic schema, since it is the logic of the statement, and not its scientific content, that concerns me.) We are told that under certain conditions we have certain non-renormalizable divergences which “miraculously cancel out” when supersymmetry is introduced. Couldn’t we have replaced the word ‘miraculously’ here by ‘suddenly’, ‘unexpectedly’, ‘spontaneously’, or even ‘luckily’? You might say, what’s in a word? But I am sure that some ignorant, dogmatic person, especially where I live, will readily pounce on the word, crying out for all the world to hear, “See! Science confirms the occurrence of miracles!” So, at least to let Hume’s bones rest in his gtave, let us choose another word for these lucky windfalls in scientific research. (I wrote this thinking Penrose invented the term, Alas! I now find it has already been sanctified by pundits and there is no hope of its being replaced.) Throughout this paper my remarks have been mainly critical. I hope that it will be clear to readers that my criticism applies exclusively to extra-scientific and extra-mathematical matter. I am not qualified to speak of Penrose’s mathematics and physics. The stupendous range and depth of the physics and the mathematics in the book most probably make it a valuable contribution to the ongoing research into the puzzles and the mysteries of the physical universe and students and researchers in this field may well find the book a real help. I only hope that they will not be misled by Penrose’s extra-scientific and extra-mathematical excursions which should be judged on their own merit purely by philosophical criteria. I have said my say. To recapitulate would be to say it all over again. But there is no harm in putting the moral of the tale in a few words. Truth is a Holy Grail. Philosophy is to philosophize; science is to search. In philosophizing and in searching we live intelligently, exercising our proper virtue as human beungs. To have that as an end is o be wise; to seek an end beyond that end is folly and vanity of vanities. T. S. Eliot has wisely spoken when he said: We shall never cease from exploration And the end of all our exploring Will be to arrive where we started And know the place for the first time. T. S. Eliot – “Little Gidding”, Four Quartets. Cairo, 18 February, 2015.


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