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科学与对于上帝的信念 相一致吗? Is Science Consistent With Belief in God? Robert J. Marks II Distinguished Professor Of Electrical and Computer Engineering Abstract 摘要 Some believe those who objectively pursue truth through the scientific method cannot realistically embrace the truth of God. The opposite is true. Indeed, both today and in history, numerous scientists, mathematicians and engineers are motivated in their work by the uncovering of the precise orderliness and wonderful interrelations in God's creations. Recent advances in science have exposed numerous insights into God's existence. We will discuss some of these, including anthropic principles, string theory, and the meanings of phrases like "before the beginning of time", "nothingness" and "infinity". The Question Q: Can a faith in God be consistent with science? Can a scientist believe in God? A: Science & Mathematics offer overwhelming evidence that there is a God. Some Atheist Thoughts about Belief in God… 一些无神论者关于上帝的观点 “Christian theism must be rejected by any person with even a shred of respect for reason” George H. Smith, Atheist Philosopher “[Bible miracles] are very effective with an audience of unsophisticates and children” Richard Dawkins. “Faith is when you believe something no one in their right mind believes.” Archie Bunker Newton on Atheism “Atheism is so senseless and odious to mankind that it never had many professors.” Isaac Newton quoted from Newton’s Philosophy of Nature: Selections From His Writings (Hafner Publishing, 1953) 来自华盛顿邮报的报导 Washington Post article describing international conference on the nature of nature in Washington D.C. in 1989 “Many scientist who were not long ago certain that the universe was created and peopled by accident are having second thoughts and concede the possibility that some intelligent creative force may have been necessary.” ... and what does God tell us about Science? Science and Theology 科学与技术 “[My fellow astronomers are] scaling the mountains of ignorance, … conquering the highest peak, … pulling [themselves] over the final rock … [to be] greeted by a band of theologians who have been sitting there for centuries.” Robert Jastrow, founder and director of NASA's Goddard Institute for Space Examples... 例子: 1. 2. 3. 4. 5. 6. Cosmology: The Big Bang Mathematics: Cantorian Transfinite Number Theory Physics: Fine Tuning of the Universe Biology: Evidence of Design Mathematics & Physics: Dimensionality Engineering: Conservation of Information and Complexity Cosmology: The Big Bang 宇宙论:宇宙大爆炸 1. 2. 3. 4. 5. 6. Cosmology: The Big Bang Mathematics: Cantorian Transfinite Number Theory Physics: Fine Tuning of the Universe Biology: Evidence of Design Mathematics & Physics: Dimensionality Engineering: Conservation of Information and Complexity Cosmology: The Big Bang 宇宙论:宇宙大爆炸 The Possibilities – Static homogeneous universe – Can’t be finite (collapse!) Can’t be infinite (too bright!) Dynamic expanding universe Big Bang Evidence of Old Earth – Hubble’s Red Shift (1929) – Radioactive Dating – Antarctic ice drillings (20-25 Million Years) – Background Radiation (Penzias & Wilson @ Bell Labs, 1965). The Dead Man’s Syndrome... 死人症状 We think in accordance to our presuppositions. Cosmology: The Big Bang 宇宙论:宇宙大爆炸 The Big Bang awoke “Dead Man Syndrome” arguments… “The difficulty of [the theory]… is that it seems to require a sudden and particular beginning of things.” “Philosophically, the notion of a beginning of the present order of Nature is repugnant to me … I should like to find a genuine loophole.” Arthur Eddington (1882-1944) Faith: What do we know and when do we know it? Cosmologists think they know about the big bang from 10-43 seconds. What about before? No one knows! There is lots of guessing. “… all physical theories … break down at the beginning of the universe.” Stephen Hawking Hebrews 11 3 (NIV) By faith we understand that the universe was formed at God's command, so that what is seen was not made out of what was visible. Passage 希 伯 來 書 11:3: 3我们因着信,就知道诸世界是 藉神话造成的;这样,所看见的 ,并不是从显然之物造出来的。 Cosmology: The Big Bang Before, there was “Nothing” 宇宙论:宇宙大爆炸 在那之前,什么都没有… Absence of matter & energy Absence of SPACE Absence of TIME Cosmology: The Big Bang Time was created… 宇宙论:宇宙大爆炸 时间被创造 “…time had a beginning at the big bang, in the sense that earlier times simply would not be defined.” Stephen Hawking Cosmology: The Big Bang Time was created… 宇宙论:宇宙大爆炸 时间被创造 1 Corinthians 2:7 No, we speak of God's secret wisdom, a wisdom that has been hidden and that God destined for our glory before time began. Titus 1:2 a faith and knowledge resting on the hope of eternal life, which God, who does not lie, promised before the beginning of time, Cosmology: The Big Bang 宇宙论:宇宙大爆炸 Some Old Questions Answered… “In the beginning God created the heavens and the earth.” Passage 創 世 記 1:1: 創世記1 1起初, 神创造天地。 If God created the universe, then He exists outside of time. If God created us, who created God? The question presupposes the flow of time. It is without meaning. Cosmology: The Big Bang 宇宙论:宇宙大爆炸 God’s Time If God “existed” before time, then God can exist outside the framework of time. – – Movie Analogy Writing Analogy Consequences – – God can have personal relationships with all From God’s perspective, there is no conflict between free will and predestination (fate). Both are temporal concepts. Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 1. 2. 3. 4. 5. 6. Cosmology: The Big Bang Mathematics: Cantorian Transfinite Number Theory Physics: Fine Tuning of the Universe Biology: Evidence of Design Mathematics & Physics: Dimensionality Engineering: Conservation of Information and Complexity Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Georg Ferdinand Ludwig Philipp Cantor Born: 3 March 1845 in St Petersburg, Russia Died: 6 Jan 1918 in Halle, Germany Georg Cantor developed the set theory for transfinite numbers. 2 0 1 3 o ? Georg a Protestant, the religion of his father. Georg's mother was a Roman Catholic Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Cantorian Infinities David Hilbert described Cantor's work as:“...the finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.” "I see it but I don't believe it.” Georg Cantor on his own theory. “…the infinite is nowhere to be found in reality” David Hilbert. Hilbert http://www-gap.dcs.st-and.ac.uk/%7Ehistory/Mathematicians/Cantor.html Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Cantorian Infinities… is not a number – it is a process. is approached, never achieved. limn Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Cantorian Infinities… The set of all counting numbers C={1, 2, 3, 4, …} has cardinality* 0 . Other sets have cardinality* 0 if each element in the set can be placed on a one-to-one correspondence to C. 0 * The number of elements in a set. Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 The Hottentots One Two Three Many (Gamow) Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Cantorian Infinities… The set of even numbers has cardinality 0 E={2, 4, 6, 8, …} Why? Because of the correspondence: C 1 2 3 E 2 4 6 0 … n … 2n Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Hilbert’s Hotel… 0 Rooms – all full. One more person comes. No Problem! Send guest in room 1 to room 2, guest 2 to room 3, etc. This frees room 1 for the new guest. 0 Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Hilbert’s Hotel… 0 Rooms – all full. 0 more person comes. No Problem! Send guest in room 1 to room 2, guest 2 to room 4, 3 to 6, etc. This frees all the odd rooms for the new guests. 0 Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Hilbert’s Hotel… 0 Rooms – all full. 0 guests leave. How many rooms are left occupied? 1. Guests from all rooms leave. 0 - 0 = 0 2. Guests from rooms 4 and higher leave. 0 - 0 = 4 3. Guests from all the even rooms leave, or, guest from every tenth room leaves. 0 - 0 = 0 0 Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Hilbert’s Hotel… http://www.buzzle.com/editorials/9-9-2002-26002.asp Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Hilbert’s Hotel… http://www.buzzle.com/editorials/9-9-2002-26002.asp Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Cantorian Infinities… Numerator 1 Denominator A number is rational number if it can be expressed as the ratio of two integers. The set of rational numbers, R, has cardinality 0. 1 1/1 2 1/2 4 3 4 2/1 3/1 4/1 2/2 1/4 1/5 1/3 2/3 3/3 4/3 1/4 2/4 3/4 4/4 0 3 2 Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Cantorian Infinities… The set of all subsets of a set with 0 elements is of cardinality 1. This is a “bigger” infinity. Example: the set of irrational numbers between 0 and 1 (points on a line) is of cardinality 1. 1 Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Cantorian Infinities… Proof by counterexample: Suppose a mapping exists: 1 0.7568373947578338747575839… 2 0.9585757348938384758439399… 3 0.1938484857657829202938482… 4 0.5000000000000000000000000… 5 0.6549383493904949848484943… 1 Choose any other digit other than the one circled – say the number after. The number 0.86314… is not in the table. Contradiction! Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Cantorian Infinities… The number of points on a line, 1, is the same as the number of points in a square - or in a cube. Consider a unit interval and a unit square. (1,1) For every point, P, in the square, there is a unique corresponding point on the line segment, and visa versa. y P 0 z 1 (0,0) P 1 x The point on the line is z=0.132456754…. Taking every other digit, corresponds to x=0.12574… and y=0.346754… Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Cantorian Infinities… n+1, is the set of all subsets of n . Q: What is an example of 2? A: All the squiggles that can be drawn on a plane. 2 Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Cantorian Infinities… n+1 is the set of all subsets of n . Q: What is an example of 3? A: Like a fifth spatial dimension, this is beyond comprehension. 2 Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Cantorian Infinities… n+1 is the set of all subsets of n . There is no “biggest” infinity. < < 0 1 2 0 Q: Can we use Cantor’s Theory as evidence that the universe must have a beginning? A: Yes, in the sense that otherwise, absurd things happen. Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 William Lane Craig “…since the actual infinite cannot exist and infinite temporal regress of events is an actual infinite, we can be sure that an infinite temporal regress of events cannot exist, that is to say, the temporal regress of events is finite. Therefore, since the temporal regress of events is finite, the universe began to exist.” Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 William Lane Craig Some absurdities of an infinite past: “To try to instantiate an actual infinite progressively in the real world would be hopeless, for one could always add one more element.” (0 versus .) Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 William Lane Craig Some absurdities of an infinite past: Tristram Shandy Paradox (Russell): If Tristram Shandy wrote his autobiography 365 times as slow as he lived life, he could live 0 days and be finished with his autobiography now. Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Tristram Shandy Paradox Writing from t = 0 onward: N years 0 N days t Bummer Tristram will fall further and further behind. Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 Tristram Shandy Paradox Writing from the past to end at t = 0: N years N days No matter how big N, there is always time for Tristram to finish: even if N = 0. Cool t Mathematics: Cantorian Transfinite Number Theory 数学:Cantorian 超限序数论 William Lane Craig “… an infinite temporal regress is absurd.” Thus: Time and the universe are finite. The universe must have been created ex nihilo. Physics: Fine Tuning of the Universe 物理:微调宇宙 1. 2. 3. 4. 5. 6. Cosmology: The Big Bang Mathematics: Cantorian Transfinite Number Theory Physics: Fine Tuning of the Universe Biology: Evidence of Design Mathematics & Physics: Dimensionality Engineering: Conservation of Information and Complexity Physics: Fine Tuning of the Universe Why are constants what they are? 为什么以下常数会有这样的值? Physics: Fine Tuning of the Universe 物理:微调宇宙 John Wheeler Princeton University professor of physics "Slight variations in physical laws such as gravity or electromagnetism would make life impossible . . . the necessity to produce life lies at the center of the universe's whole machinery and design," (Reader's Digest, Sept., 1986). Physics: Fine Tuning of the Universe 物理:微调宇宙 J.L. Mackie, 无神论者 Atheist (Miracle of Theism, p.141) “There is only one actual universe, with a unique set of basic materials and physical constants, and it is therefore surprising that the elements of this unique set-up are just right for life when they might easily have been wrong. This is not made less surprising by the fact that if it had not been so, no one would have been here to be surprised. We can properly envision and consider alternative possibilities which do not include our being there to experience them.” Physics: Fine Tuning of the Universe 物理:微调宇宙 Sir Fred Hoyle,不可知论者 Agnostic (The Intelligent Universe) "Such properties seem to run through the fabric of the natural world like a thread of happy coincidences. But there are so many odd coincidences essential to life that some explanation seems required to account for them." Fred Holye (1915-2001) coined the term “big bang”- mocking the theory. He promoted, instead, the steady state theory. Physics: Fine Tuning of the Universe 物理:微调宇宙 Physics: Fine Tuning of the Universe “Astronomy leads us to a unique event, a universe which was created out of nothing, and delicately balanced to provide exactly the conditions required to support life. In the absence of an absurdly-improbably accident, the observations of modern science seem to suggest an underlying, one might say supernatural, plan.” Arno Penzias, Nobel laureate in Physics Physics: Fine Tuning of the Universe 物理:微调宇宙 Example: Why Three Spatial Dimensions? 例子:为什么空间是三维的? Schrodinger’s equation only gives stable, bound energy levels for 3-D or less universe. Maxwell’s equations are only valid for a 3-D universe. High fidelity transmission of light and sound is optimized in a 3-D universe. Physics: Fine Tuning of the Universe 物理:微调宇宙 Another Example 另外一个例子 “[If the attraction of gravity] went down faster with distance, the orbits of the planets would … spiral into the sun, If it went down slower, the gravitation forces from distant stars would dominate over that from earth.” Stephen Hawking Physics: Fine Tuning of the Universe 物理:微调宇宙 Hawking “... why should we live in a four dimensional world, and not eleven, or some other number of dimensions... [In] two spatial dimensions, are not enough for complicated structures, like intelligent beings. On the other hand, four or more spatial dimensions would mean that gravitational and electric forces would fall off faster than the inverse square law. In this situation, planets would not have stable orbits around their star, nor electrons have stable orbits around the nucleus of an atom. Thus intelligent life, at least as we know it, could exist only in four dimensions.” Physics: Fine Tuning of the Universe 物理:微调宇宙 Hawking’s Flat Dog 3-D is fit for human & animal life A 2-D dog would drift apart in 2 Dimensions Physics: Fine Tuning of the Universe 物理:微调宇宙 The Anthropic Principal: Week & Strong Stephen Hawking What is “the Anthropic Principle?” http://www.hawking.org.uk “Many physicists dislike the Anthropic Principle. They feel it is messy and vague, it can be used to explain almost anything, and it has little predictive power. I sympathize with these feelings, but the Anthropic Principle seems essential in quantum cosmology.” Physics: Fine Tuning of the Universe 物理:微调宇宙 Stephen Hawking “Why is the universe so close to the dividing line between collapsing again and expanding indefinitely?...If the rate of expansion one second after the big bang had been less by one part in 1010 , the universe would have collapsed in a few million years. If it had been greater by one part in 1010 , the universe would have been essentially empty….One has either appeal to the anthropic principle or find some physical explanation for why the universe is the way it is.” Biology: Evidence of Design 生物:设计的证据 1. 2. 3. 4. 5. 6. Cosmology: The Big Bang Mathematics: Cantorian Transfinite Number Theory Physics: Fine Tuning of the Universe Biology: Evidence of Design Mathematics & Physics: Dimensionality Engineering: Conservation of Information and Complexity Evidence of Design: Irreducible Complexity 设计的证据:不可简化的复杂性 Darwin’s Black Box by Michael Behe Premise: Irreducibly complex machinery cannot evolve. Mathematics & Physics: Dimensionality 数学与物理: 维度 1. 2. 3. 4. 5. 6. Cosmology: The Big Bang Mathematics: Cantorian Transfinite Number Theory Physics: Fine Tuning of the Universe Biology: Evidence of Design Mathematics & Physics: Dimensionality Engineering: Conservation of Information and Complexity Mathematics & Physics: Dimensionality 数学与物理: 维度 The Hottentots One Two Three Many (Gamow) Mathematics & Physics: Dimensionality 数学与物理: 维度 Dimensions 维数 One Dimension = A Line • Two Dimensions = A Plane Mathematics & Physics: Dimensionality 数学与物理: 维度 Dimensions 维数 Three Dimensions = Space • Four (Spatial) Dimensions = ??????? “It is impossible to envision a four dimensional space” Stephen Hawking • Time as a dimension Mathematics & Physics: Dimensionality 数学与物理: 维度 Time As A Dimension 将时间作为一维 Need 4 numbers to specify a point (ball) in time and space… time Mathematics & Physics: Dimensionality 数学与物理: 维度 How Long is a Second? 一秒有多久? 186,000 miles/sec 1 sec = 186,000 miles Mathematics & Physics: Dimensionality 数学与物理: 维度 Building Dimensions 建立维数 A POINT (Zero Dimensions) has no width, height or length. Here is a representation: • A LINE (1-D) is a sequence of points • A LINE (1-D) has length, but no width or height. It is infinitely thin! Mathematics & Physics: Dimensionality 数学与物理: 维度 Building Dimensions 建立维数 A PLANE (2 Dimensions) is a sequence of lines: • An infinite number of lines is needed to make a plane. The plane has NO thickness, Mathematics & Physics: Dimensionality 数学与物理: 维度 Building Dimensions 建立维数 SPACE (3 Dimensions) is a sequence of planes: • An infinite number of planes is needed to make space. Mathematics & Physics: Dimensionality 数学与物理: 维度 Building Dimensions 建立维数 FOUR Spatial dimensions is a sequence of spaces: • PARALLEL UNIVERSES . • What of five, six, seven or an infinite number of dimensions? • Reality or Theory? Mathematics & Physics: Dimensionality 数学与物理: 维度 Building Dimensions: Time as a Dimension 建立维数 将时间作为一维 SPACE – TIME (4 Dimensions) is a sequence of spaces: time • TIME is different. It only can be traversed in one direction. Mathematics & Physics: Dimensionality 数学与物理: 维度 坝上 (Flatland) -- Edwin A. Abbott (1884) 一则关于维数的中篇小说 Two Dimensional Creatures & the Theory of “UP” Mathematics & Physics: Dimensionality 数学与物理: 维度 坝上 -- by Edwin A. Abbott Strange Visitation Mathematics & Physics: Dimensionality 数学与物理: 维度 Properties of High Dimensions 多维的性质 Lefties in Flatland Once a lefty – always a lefty. Mathematics & Physics: Dimensionality 数学与物理: 维度 Properties of High Dimensions 多维的性质 Once a lefty – always a lefty? Not if you can flip in three dimensions. Mathematics & Physics: Dimensionality 数学与物理: 维度 Application to Baseball 在棒球中的应用 Flip into the fourth dimension & back… Mathematics & Physics: Dimensionality 数学与物理: 维度 Breaking Chains 断链 Chains in Flatland Links can be separated in three dimensions. Mathematics & Physics: Dimensionality 数学与物理: 维度 断链 Breaking Chains: Chains linked in three dimensions can be separated in four. Passage 使 徒 行 傳 12:6-7: Acts 12:6 The night before Herod was to bring him to trial, Peter was sleeping 6希律将要提他出来 between two soldiers, bound with two 的前一夜,彼得被两条 chains, and sentries stood guard at the entrance. 7 Suddenly an angel of the Lord appeared and a light shone in the cell. He struck Peter on the side and woke him up. "Quick, get up!" he said, and the chains fell off Peter's wrists. YES Maybe 铁炼锁着,睡在两个兵 丁当中;看守的人也在 门外看守。 7忽然,有主的一个 使者站在旁边,屋里有 光照耀,天使拍彼得的 肋旁,拍醒了他,说: 快快起来!那铁炼就从 他手上脱落下来。 Mathematics & Physics: Dimensionality 数学与物理: 维度 Walking Through Walls 穿墙而过 Locked in a box in Flatland Mathematics & Physics: Dimensionality 数学与物理: 维度 3-D walls are no obstacle in four spatial dimensions 在四维空间中,三维的墙算不上障碍物 • John 20:26 A week later his disciples were in the house again, and Thomas was with them. Though the doors were locked, Jesus came and stood among them and said, "Peace be with you!" YES Maybe Passage 約 翰 福 音 20:26: 26 过 了 八 日 , 门徒又在屋里, 多马也和他们同 在,门都关了。 耶稣来,站在当 中说:愿你们平 安! Mathematics & Physics: Dimensionality 数学与物理: 维度 Consequences 结果 … A higher dimensional entity – – – Can be infinitely close without physical appearance Is able to intersect our universe at will Is able to see inside you Explanation of certain “miracles” – Walking through walls – Chains dropping Mathematics & Physics: Dimensionality 数学与物理: 维度 Dimensions In Math 数学中的维数 Multidimensional spaces are common mathematical models. Some mathematical spaces contain an infinite number of dimensions (e.g. certain Hilbert Spaces.) These spaces are not physical spaces. Mathematics & Physics: Dimensionality 数学与物理: 维度 Are Extra Dimensions “Real?” Strings & Dimensions Atoms, Protons, Quarks & Strings “[Strings work only] if space-time has either ten or twenty-six dimensions” Stephen Hawking Q: Where are the other dimensions? A: Compactified. They were never birthed in the big bang. Only three spatial dimensions and time were. Mathematics & Physics: Dimensionality 数学与物理: 维度 Hawking’s Flat Dog 3-D is fit for human & animal life A 2-D dog would drift apart in Flatland Engineering: Conservation of Information and Complexity 工程: 信息与复杂的结合 1. 2. 3. 4. 5. 6. Cosmology: The Big Bang Mathematics: Cantorian Transfinite Number Theory Physics: Fine Tuning of the Universe Biology: Evidence of Design Mathematics & Physics: Dimensionality Engineering: Conservation of Information and Complexity Engineering: Conservation of Information and Complexity 工程: 信息与复杂的结合 See my presentation... “Does Evolution Require External Information? Some Lessons from Computational Intelligence” Summary 总结 1. 2. 3. 4. 5. 6. Cosmology: The Big Bang Mathematics: Cantorian Transfinite Number Theory Physics: Fine Tuning of the Universe Biology: Evidence of Design Mathematics & Physics: Dimensionality Engineering: Conservation of Information and Complexity