Truth and beauty and love and faith and science. We seek to find the connection...or run from it!
Are you willing to know and face the truth no matter what it is? Have you ever noticed that the truth has a way of being beautiful and elegant? Unless, of course, it is at odds with your own belief system. 2 plus 2 is 4 now and was 4 a thousand years ago. This satisfies both mind and soul.
Do you hunger and thirst for meaning and certainty in life and a standard by which one may live or seek to attain to with conviction and surety? Will you be willing to consider that you are not the answer to your own questions?
Stephen Hawking recently expressed his faith with this statement from his new book, The Grand Design:
Danae's video depends and revolves around the Bible, the Word of God, which is a physical piece of evidence to be considered whether atheists like it or not. Now let us consider the vast distance between the beauty of the concept of God presented by a young teenager versus the cold and uncaring and yet somehow miraculous atheism of Hawking as exposed by the person who perhaps knows him better than anyone else.
McMillan, New York, 2004
Jane Hawking was, for a quarter century, the wife of Stephen Hawking, one of the most famous living scientists of today. Stephen Hawking, now an international celebrity, has sold millions of books, and draws huge crowds wherever he speaks. Cited by Time as the heir to Einstein, only Darwin and Einstein are arguably better known among the public. The first American edition of his best seller, A Brief History of Time, had a press run of ten thousand copies—typical press runs are five hundred to two thousand copies.1 A professor at Cambridge, he occupies the same Lucasian chair that Isaac Newton filled two centuries earlier. Hawking is not only famous as a physicist, but also as one who has overcome obstacles due to the severely disabling neuromuscular disease, Amyotrophic Lateral Sclerosis (ALS), commonly called Lou Gehrig’s Disease.
Jane married Stephen Hawking knowing that he had an incurable disease, but, believing that his life would be short, they hoped to jam as much love and fulfilment into what they thought would be only a few years together (Stephen outlived all expectations, and they were together for over 25 years). They married fairly young, and soon had three children. For years, Jane was an astounding care giver, dealing with Stephen’s progressive physical decline and heavier demands. She managed the household, reared the children, and hauled him around for years before a serious respiratory incident forced them to hire full-time professional nurses. She also recounts her battles with the British health care system, and with Cambridge University for access.
Jane also discusses in detail the anthropic principle, which she calls ‘an important cosmological principle of the twentieth century’ (p. 153). She observed that the strong version has a ‘close philosophical affinity to the medieval cosmos’ where humans were at the center of creation (p. 153). She then concluded that the anthropic principle places humans in a ‘special place at the centre of the universe’, just as did the Ptolemaic system, and that, ‘for the medieval populace, this special position was a strong statement of the unique relationship between human beings and their Creator’ (p. 153). The main intent of early philosophers was to reconcile the
Jane notes,
When asked if he believed in God, ‘Always the answer was the same. No, Stephen did not believe in God and there was no room for God in his universe’ (p. 494). When Stephen gave his usual atheistic answers in Jerusalem, this struck Jane as especially ironic, and she quipped:
As he got older, Stephen became more and more hardened in his atheism. As a result, Jane notes that although in the early days their arguments on religion ‘were playful and fairly light-hearted’, in later years they increasingly
Stephen’s view of the world was a universe ‘which had neither beginning nor end, nor any role for a Creator-God’ (p. 389). And this was a universe in which Jane did not want to live, and which many people increasingly see as not only unreal, but one that avoids reality. Jane summarized her concept of much of the research, of which her husband was in the forefront, as ‘theorizing on abstruse suppositions about imaginary particulars traveling in imaginary time in a looking-glass universe which did not exist except in the mind of the theorists.’ This she described as ‘the demon goddess of physics’ (p. 372).
In an assembly before the Pope, Jane states the Pope said that scientists ‘could study the evolution of the universe’, but ‘should not ask what happened at the moment of Creation at the Big Bang and certainly not before it because that was God’s preserve’ (p. 391). She stated that she was not impressed with this attitude; rather she believed that
The fact that many came to look at Stephen as godlike is discussed in several sections of her book. She stated,
A critical stabilizing factor in Jane’s life was her church. She often talked about her minister’s sermons, and how they helped her to cope with the difficulties of dealing with an invalid husband who required twenty-four-hour-a-day care—he needed to be bathed, have his teeth brushed, have his hair combed, and have his bodily functions taken care of just like a six-month-old baby, yet he attracted worldwide notoriety wherever they went—and they traveled often, which was also a struggle. Jane noted that, as his conditioned deteriorated, she became more like a nurse taking care of a man with a body like a Holocaust victim who had the needs of a child. A concern she had was that ‘Although I derived comfort from my return to the Church, it also posed imponderable questions in my mind.’ One was, ‘What was God really asking of me? How great a sacrifice was required of me?’ (p. 336).
Although Stephen’s state of health was often extremely precarious, modern medicine and twenty-four-hour nursing care (he carried his own mini-hospital with him everywhere) allowed Stephen to pursue a ‘hedonistic way of life, compensating ever more tenaciously for his disability, ever more assured of his own invincibility, mocking the untimely death whose grasp he had evaded’ (p. 476). What sustained Jane was trusting ‘in God through darkness, pain and fear’ (p. 484). When she tried to help Stephen understand the solace she obtained from her faith, and especially the Bible, Stephen ‘was insulted by any mention of compassion; he equated it with pity and religious sentimentality’—something for which he had contempt (p. 485).
Jane discusses her friendship with many well-known cosmologists, many of which were close and personal friends. The theistic evolutionist John Polkinghorne, whom she states she admired, was one of the few who was a great encouragement to her, partly because he helped her realize that ‘atheism was not an essential prerequisite of science and not all scientists were as atheistic as they seemed’ (p. 246). Jane’s assessment is especially critical because she was able to stand back and observe both the worlds of science and religion in order to make objective judgments. Indeed, her book clearly represents an effort to come to grips with some of the central questions of humanity, and why she accepted theism and rejected the atheism of virtually all the leading scientists with whom she spent much of her life, including, especially, her husband. She was the proverbial fly on the wall, giving us insight that can be found nowhere else into the thinking of the world’s leading cosmologists.
However, this does not explain physical evil such as her husband’s illness which only a literal Genesis Creation and Fall, provides.
Much of this work is a contrast between a woman deeply conscious of her Christian spirituality, and a man firmly closed to any theistic spirituality. It is also a sober warning against a Christian becoming unequally yoked with an unbeliever in marriage. Jane concluded that faith is the outward expression of one’s spirituality that ‘can make sense of all the wonders of Creation and of all the suffering in the world’ and give ‘substance to all our hopes. However far-reaching our intelligent achievements and however advanced our knowledge of Creation, without faith and a sense of our own spirituality there is only isolation and despair, and the human race is really a lost cause’ (p. 594).
One cannot read this book without truly admiring Jane and feeling the struggle that she faced. It is an important work for all people interested in not only science/religion conflicts, but also the human needs that so many of us possess.
Do you hunger and thirst for meaning and certainty in life and a standard by which one may live or seek to attain to with conviction and surety? Will you be willing to consider that you are not the answer to your own questions?
I intend to press a point home in the next few days that Darwinism is not science at all, not scientific, but is rather a faith. Darwinism is a religious position and I can prove it. But give me some time to build a little music to a crescendo. Today we present a the first two movements of the symphony of words I wish to write for you.
"Because there is a law such as gravity, the Universe can and will create itself from nothing," the excerpt says. "Spontaneous creation is the reason there is something rather than nothing, why the Universe exists, why we exist. It is not necessary to invoke God to ... set the Universe going."
Design?! Hawking must not have much of a sense of irony. But we will point out later how thoroughly unscientific and religious Hawking's statement actually is later. We'll let his former wife, a brilliant woman hereself, set that stage after the youtube video...
One of our fantastic youth group teens, Danae, made her first youtube video recently as an attempt to express her faith and frankly I was impressed with her presentation of the Christian faith from her own personal point of view. I give you her initial youtube:
Danae's video depends and revolves around the Bible, the Word of God, which is a physical piece of evidence to be considered whether atheists like it or not. Now let us consider the vast distance between the beauty of the concept of God presented by a young teenager versus the cold and uncaring and yet somehow miraculous atheism of Hawking as exposed by the person who perhaps knows him better than anyone else.
Stephen Hawking: the closed mind of a dogmatic atheist
A review of Music to Move the Stars by Jane HawkingMcMillan, New York, 2004
Courtship and marriage
The book contains much background about Jane’s courtship with Stephen, their marriage, and the problems in their marriage due to the domestic friction that one would expect when a family member is seriously handicapped. Stephen’s pioneering research is clearly explained in simple terms for those lacking a Ph.D. in the mathematical physics of black holes. Even though her Ph.D. was not in science, but Spanish poetry, she explains modern cosmology with almost the same elegance, fluidity, precision and accuracy as that of her world-famous husband. The book provides much insight on the age-old conflicts between science and religion, a subject that Jane discusses in depth. Jane also provides much insight into the minds of the world’s leading scientists, especially cosmologists.Jane married Stephen Hawking knowing that he had an incurable disease, but, believing that his life would be short, they hoped to jam as much love and fulfilment into what they thought would be only a few years together (Stephen outlived all expectations, and they were together for over 25 years). They married fairly young, and soon had three children. For years, Jane was an astounding care giver, dealing with Stephen’s progressive physical decline and heavier demands. She managed the household, reared the children, and hauled him around for years before a serious respiratory incident forced them to hire full-time professional nurses. She also recounts her battles with the British health care system, and with Cambridge University for access.
Jane’s theism vs Stephen’s atheistic faith
One factor that was central to their relationship—and eventual divorce—was religious conflicts. Jane notes that ‘Stephen had no hesitation in declaring himself an atheist despite the strongly Methodist background’ of his family (p. 46). She concluded that his reasoning was, ‘as a cosmologist examining the laws which governed the universe, he could not allow his calculations to be muddled by a confessed belief in the existence in a Creator God’ (p. 46). With candid insights into her private spiritual experiences, Jane draws her own conclusions regarding God’s role in the universe.Jane also discusses in detail the anthropic principle, which she calls ‘an important cosmological principle of the twentieth century’ (p. 153). She observed that the strong version has a ‘close philosophical affinity to the medieval cosmos’ where humans were at the center of creation (p. 153). She then concluded that the anthropic principle places humans in a ‘special place at the centre of the universe’, just as did the Ptolemaic system, and that, ‘for the medieval populace, this special position was a strong statement of the unique relationship between human beings and their Creator’ (p. 153). The main intent of early philosophers was to reconcile the
‘existence of God with the rigours of the laws of science, towards unifying the image of the Creator with the scientific complexity of His Creation. … Conversely, their intellectual heirs, some 800 years later, seemed intent on distancing science as far as possible from religion and on excluding God from any role in Creation. The suggestion of the presence of a Creator God was an awkward obstacle for an atheistic scientist whose aim was to reduce the origins of the universe to an unified package of scientific laws, expressed in equations and symbols. To the uninitiated, these equations and symbols were far more difficult to comprehend than the notion of God as the prime mover, the motivating force behind Creation’ (pp. 154–155).She adds that, as a direct result of the focus of modern cosmologists on mathematics, the concept of a personal God became irrelevant for these scientists because, in their mind, their calculations diminished ‘any possible scope for a Creator’, and
‘they could not envisage any other place or role for God in the physical universe. Concepts which could not be quantified in mathematical terms as a theoretical reflection of physical realities, whether or not the actual existence of those physical realities was proven, were meaningless’ (p. 155).
The nihilism of atheism
Her major concern is that she perceives—and discusses extensively why, based on discussions with her husband and the leading physicists of the world—that the result of the goals of science would eventually result in the situation where‘Human reactions in all their complexities, emotional and psychological, would one day ... be reduced to scientific formulae because, in effect, these reactions were no more than the microscopic chemical interactions of molecules’ (p. 156).The result was that ‘in the face of such dogmatically rational arguments, there was no point in raising questions of spirituality and religious faith, of the soul and of a God who was prepared to suffer for the sake of humanity—questions which ran completely counter to the selfish reality of genetic theory’, evidently referring to the work of Richard Dawkins and others (p. 156).
Jane notes,
‘at the end of the twentieth century, religion finds its revelationary truths threatened by scientific theory and discovery, and retreats into a defensive corner, while scientists go into the attack insisting that rational argument is the only valid criterion for an understanding of the workings of the universe’ (p. 200).She concludes that the complexity of the cosmologist’s calculations and the admiration their discoveries have caused some people
‘to fall into the trap of believing that science has become a substitute for religion and that, as its great high priests, they can claim to have all the answers to all the questions. However, because of their reluctance to admit spiritual and philosophical values, some of them do not appear to be aware of the nature of some of the questions’ (p. 200).She is especially disheartened with attempts to extrapolate animal-behaviour rules to human behaviour, as illustrated by the evolutionary psychology field. After noting that evolutionary psychologists ascribe altruism solely as a result of natural selection, she adds that
‘scientists still cannot satisfactorily explain why some human beings are prepared to give their lives for others. The complexity of such anomaly lies far outside the scope of their purely mechanical grasp. Nor can they explain why so much human activity operates at a subliminal level. The spiritual sophistication of musical, artistic, politic, and scientific creativity far exceeds that of any primitive function programmed into the brain as a basic survival mechanism’ (p. 200).Although scientists offer explanations, they ‘acknowledge that they are still very far from reaching’ the goal of answering ‘why’, noting that many scientists
‘arrogantly even aspire to become gods themselves by denying the rest of us our freedom of choice and disputing our right to ask the question “Why?” in relation to the origins of the universe and the origins of life. They claim that the question is as … inappropriate, as it would be to ask why Mt. Everest is there. They dismiss the suggestion that the question ‘Why’ is the prerogative of theologians and philosophers rather than scientist because, they say, theologians are engaged in the “study of fantasy”: belief in God can be attributed to “a shortage in the oxygen supply to the brain”. Their theories reduce the whole of Creation to a handful of material components. They complain with a weary disdain of the stupidity of the human race, that human beings are always asking “Why?” Perhaps they should be asking themselves why this is so. Might it not be that our minds have been programmed to ask “Why?” And if this is the case they might then ask who programmed the human computer. The “Why” question is the one which, above all, theologians should be addressing’ (p. 201).She concludes by opining that, since the modes of thought by scientists
‘are dictated by purely rational, materialistic criteria, physicists cannot claim to answer the questions of why the universe exists and why we, human beings, are here to observe it, any more than molecular biologists can satisfactorily explain why, if our actions are determined by the workings of a selfish genetic coding, we sometimes listen to the voice of conscience and behave with altruism, compassion and generosity’ (p. 200).
Their marriage deteriorates
In the latter days of their marriage, her ‘attempts to discuss the profound matters of science and religion with Stephen were met with an enigmatic smile’ (p. 465). Stephen usually ‘grinned’ at the ‘mention of religious faith and belief, though on one historic occasion he actually made the startling concession that, like religion, his own science of the universe’ also required a leap of faith as did theism (p. 465). Jane approvingly quoted scientist-theologian Cecil Gibbons, who concluded that ‘scientific research required just as broad a leap of faith in choosing a working hypothesis as did religious belief’ (p. 465). Although in theory, a leap of faith in science ‘had to be tested against observation’, the problem is that a scientist has to ‘rely on an intuitive sense that his choice was right or he might be wasting years in pointless research with an end result that was definitively wrong’ (p. 465).When asked if he believed in God, ‘Always the answer was the same. No, Stephen did not believe in God and there was no room for God in his universe’ (p. 494). When Stephen gave his usual atheistic answers in Jerusalem, this struck Jane as especially ironic, and she quipped:
‘My life with Stephen had been built on faith—faith in his courage and genius, faith in our joint efforts and ultimately religious faith—and yet here we were in the very cradle of the world’s three great religions, preaching some sort of ill-defined atheism founded on impersonal scientific values with little reference to human experience’ (pp. 494–495).She concludes by saying that the blunt denial by Stephen ‘of all that I believed in was bitter indeed’. Jane was also stuck at the insensitivity of the press to matters of religious faith—they often treated it as something that, if one possesses it, should be kept well hidden (p. 525).
As he got older, Stephen became more and more hardened in his atheism. As a result, Jane notes that although in the early days their arguments on religion ‘were playful and fairly light-hearted’, in later years they increasingly
‘became more personal, divisive and hurtful. It was then apparent that the damaging schism between religion and science had insidiously extended its reach into our very lives: Stephen would adamantly assert the blunt positivist stance which I found too depressing and too limiting to my view of the world because I fervently needed to believe that there was more to life than the bald facts of the laws of physics and the day-to-day struggle for survival. Compromise was anathema to Stephen, however, because it admitted an unacceptable degree of uncertainty when he dealt only with the certainties of mathematics’ (p. 201).
The Galileo irony
Ironically, Stephen’s hero was Galileo—‘a devout Catholic’ (p. 200). Stephen launched a personal campaign for Galileo’s reinstatement, which was eventually successful. But it ‘was nevertheless seen as a victory for the rational advance of science over the hidebound antiquated forces of religion rather than as a reconciliation of science with religion’ (p. 202). Indeed, Galileo’s main problem was the dogmatism of the Aristotelian scientific establishment of his day! The intransigence of Stephen on religion is in dramatic contrast to the many changes he made in his theories and ideas—for example, the conclusion that ‘contrary to all previously held theories on black holes, a black hole could radiate energy’ (p. 236).Dogmatic boffins
As Stephen became more famous, his associations changed to more and more eminent scientists, which Jane had to admit she did not find appealing. The contrast between her old friends and the world’s leading scientists who became their friends (as Stephen became increasingly renowned in his field) was enormous. Their old friends were able to talk intelligently about many things and show a ‘human interest in people and situations’. In contrast, as a whole, their new friends were ‘a dry, obsessive bunch of boffins’, little concerned with people, but rather very concerned with their personal scientific reputations. She adds, ‘They were much more aggressively competitive than the relaxed, friendly relativists with whom we had associated in the past’ (p. 296). Their old friends’ dedication to science verged on the dilettante in comparison with the ‘driving fanaticism’ of their new friends (p. 296). Jane stresses that she concluded that‘Nature was powerless to influence intellectual beings who were governed by rational thought, [but] who could not recognize reality when it stood, bared before them, pleading for help. They appeared to jump to conclusions, which distorted the truth to make it fit their preconceptions’ (p. 312).
Jane’s solace in religion
Religion permeated Jane’s world, as is obvious from her extensive discussions. This world, though, her husband did not want any part of, nor did most of his friends. It was a world that Jane eventually left, partly because the antagonism of Stephen and his atheistic friends. She concluded that most famous scientists, her former husband among them, were dogmatic atheists, unwilling to even reason on the evidence for design in the universe. Jane even called physics a ‘demon goddess’. Such scientists, in turn, saw someone such as Jane, who believed in God, as an ignorant person who inhabited a world that they were not part of, nor did they want to be part of.Stephen’s view of the world was a universe ‘which had neither beginning nor end, nor any role for a Creator-God’ (p. 389). And this was a universe in which Jane did not want to live, and which many people increasingly see as not only unreal, but one that avoids reality. Jane summarized her concept of much of the research, of which her husband was in the forefront, as ‘theorizing on abstruse suppositions about imaginary particulars traveling in imaginary time in a looking-glass universe which did not exist except in the mind of the theorists.’ This she described as ‘the demon goddess of physics’ (p. 372).
In an assembly before the Pope, Jane states the Pope said that scientists ‘could study the evolution of the universe’, but ‘should not ask what happened at the moment of Creation at the Big Bang and certainly not before it because that was God’s preserve’ (p. 391). She stated that she was not impressed with this attitude; rather she believed that
‘Instead of embracing the modern scientific quest for truth to its ultimate objective and glorying in the even deeper layers of mystery thus revealed, the Vatican still viewed cosmological science as a contentious issue, a threat to religious stability, which had to be contained’ (p. 391).She concluded that the Pope’s prohibition was misdirected, and what is dangerous is the misinterpretation of, and the use to which, these discoveries are put—especially those who have an axe to grind, such as many eminent scientists.
The fact that many came to look at Stephen as godlike is discussed in several sections of her book. She stated,
‘I found myself telling him that he was not God. The truth was that supercilious enigma of that smile which Stephen wore whenever the subjects of religious faith and scientific research came up was driving me to my wit’s end. It seemed that Stephen had little respect for me as a person and no respect at all for my beliefs and opinions’ (p. 536).One of her strongly held opinions was that ‘reason and science alone could not furnish all of the answers to the imponderable mysteries of human existence’ (p. 536). Yet this ‘simple and fairly obvious’ truth was ‘most unpalatable to those people who had come to believe in Stephen’s immortality and infallibility’ (p. 537). The fact is, in the minds of many people, Stephen’s scientific theories became ‘the basis for a new religion’ (p. 537). Nonetheless, she concluded that ‘Religion for me had to be a personal relationship with God and through it … I found the germinating seeds of an incipient peace and a wholeness which I had not known for a very long time’ (p. 572).
A critical stabilizing factor in Jane’s life was her church. She often talked about her minister’s sermons, and how they helped her to cope with the difficulties of dealing with an invalid husband who required twenty-four-hour-a-day care—he needed to be bathed, have his teeth brushed, have his hair combed, and have his bodily functions taken care of just like a six-month-old baby, yet he attracted worldwide notoriety wherever they went—and they traveled often, which was also a struggle. Jane noted that, as his conditioned deteriorated, she became more like a nurse taking care of a man with a body like a Holocaust victim who had the needs of a child. A concern she had was that ‘Although I derived comfort from my return to the Church, it also posed imponderable questions in my mind.’ One was, ‘What was God really asking of me? How great a sacrifice was required of me?’ (p. 336).
Although Stephen’s state of health was often extremely precarious, modern medicine and twenty-four-hour nursing care (he carried his own mini-hospital with him everywhere) allowed Stephen to pursue a ‘hedonistic way of life, compensating ever more tenaciously for his disability, ever more assured of his own invincibility, mocking the untimely death whose grasp he had evaded’ (p. 476). What sustained Jane was trusting ‘in God through darkness, pain and fear’ (p. 484). When she tried to help Stephen understand the solace she obtained from her faith, and especially the Bible, Stephen ‘was insulted by any mention of compassion; he equated it with pity and religious sentimentality’—something for which he had contempt (p. 485).
Jane discusses her friendship with many well-known cosmologists, many of which were close and personal friends. The theistic evolutionist John Polkinghorne, whom she states she admired, was one of the few who was a great encouragement to her, partly because he helped her realize that ‘atheism was not an essential prerequisite of science and not all scientists were as atheistic as they seemed’ (p. 246). Jane’s assessment is especially critical because she was able to stand back and observe both the worlds of science and religion in order to make objective judgments. Indeed, her book clearly represents an effort to come to grips with some of the central questions of humanity, and why she accepted theism and rejected the atheism of virtually all the leading scientists with whom she spent much of her life, including, especially, her husband. She was the proverbial fly on the wall, giving us insight that can be found nowhere else into the thinking of the world’s leading cosmologists.
The enigma of evil
Evil was a subject with which she had to deal because of Stephen’s progressing illness, which caused endless hospital stays and almost insurmountable obstacles necessary to live a life that resembles normalcy. With much insight, she notes that if ‘belief in God were automatically decreed by the Creator, the human race would simply be a breed of automatons’ (p. 461). The world God created provided motivation for discovery, and a sense of wonder due to freedom of choice. Jane recognized that, given this freedom, therein lies the heart of the source of suffering and evil. God could eliminate evil, but if He did, freedom of choice also would be eliminated. She stresses that most evil is often reducible ‘to human greed and selfishness’ (p. 461).However, this does not explain physical evil such as her husband’s illness which only a literal Genesis Creation and Fall, provides.
Jane abandoned by Stephen
Although many other women might have left Stephen because of his intolerable attitude toward her, and especially what she represented, she stuck by her husband through everything. It was he who left her for another woman. She tried in vain to reconcile with Stephen—his terms were, he would live at home with his family for part of the week, and the rest of the week he would live ‘with his ladylove’ (p. 574). This was unacceptable to Jane. His selfishness and hedonism had shown through again.Much of this work is a contrast between a woman deeply conscious of her Christian spirituality, and a man firmly closed to any theistic spirituality. It is also a sober warning against a Christian becoming unequally yoked with an unbeliever in marriage. Jane concluded that faith is the outward expression of one’s spirituality that ‘can make sense of all the wonders of Creation and of all the suffering in the world’ and give ‘substance to all our hopes. However far-reaching our intelligent achievements and however advanced our knowledge of Creation, without faith and a sense of our own spirituality there is only isolation and despair, and the human race is really a lost cause’ (p. 594).
One cannot read this book without truly admiring Jane and feeling the struggle that she faced. It is an important work for all people interested in not only science/religion conflicts, but also the human needs that so many of us possess.
Reference
- As a point comparison, the first American edition of Jonathan Sarfati’s best sellers Refuting Evolution and Refuting Evolution 2 had a press run of 19,472 and 22,494 copies, respectively. Return to text.