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Dec 2005, Changing Times Understanding the Logic of Atheism Creating a Bridge of Understanding Hooman Katirai Table of Contents • Part 1: The Analogies – We create analogies where humans play the role of creator • Part 2: The Harvest – We use the analogies to learn about the creator-created relationship. • Part 3: Proofs of God, we examine two proofs of God – one from Aristotle, the other from William Hatcher. Purpose “If thou wishest the divine knowledge … purify thy heart … and apply thyself to rational and authoritative arguments … then the eye will be opened and will recognize the Sun through the Sun itself.” (Abdu’l-Baha, Baha’i World Faith – Abdu’l-Baha Section, p. 383) The complement of a statement is similar to what Faith we might call an opposite. Types of Faith Belief The complement of “it’sin an Idea in the absence raining” is everything that’s of total not raining. This would proof include, sunny, cloudy, windy, etc .. Blind Faith (commitment to a belief regardless of evidence) Empiricism Belief in an idea because it’s more likely than its complement Some Definitions An Might say … God (or gods) do not exist The question “does God exist?” cannot be proven (or disproven) and is therefore meaningless. Atheist Agnostic Undecided I’m not sure if God exists but I’m open to new evidence. Atheism is difficult to defend Belief: God (or gods) do not exist • To make such a claim one must examine – every part of universe – in case one or more Gods were hiding there. • But atheists have examined only a small part of the universe. • Thus they do not have enough evidence to make the claim “there is no God” TAKEAWAYS: • Atheism is a belief founded on faith. It is not based on logic. Agnostics & Undecideds • Both don’t know if God does or does not exist • Agnostics believe the question can’t be answered • These two groups will be the focus of our discussions! Common Objections to Religion & God Ideas in religion are too outrageous to be true We’ll show ideas like An unknowable creator, Manifestations, etc are all reasonable. Show that existence of God is more likely than non-existence I.e. it is not a fiction. Hatcher’s Proof. Acts of followers ≠ Teachings of religion Religion can be perfect while Followers are not. Precisely why God sends new messengers There can be perfect justice If there is a next world Religion is a fiction adopted by the weak or unhappy (to feel comforted and happy) Religion causes war, and suffering Too much suffering in world for there to be a God. Overcoming Obstacles I don’t believe in religion, which is based on faith I believe in Science We’ll show Science is based on Faith! But a special Kind of faith that can Also be applied in religion. Answering Objection 1: Objection: I don’t believe in religion, which is based on faith I believe in Science We’ll show science is based on a special kind of faith called empiricism that can be used in religion Science is based on Faith! • How do Physicists – discover equations? F F =ma • Simple example: – Newton’s Law (F=ma) Force (F) Mass (M) Frictionless Surface A Takeaway: Even fundamental equations in physics are based on Faith!! Science is based on Faith! (cont’d) • F=ma – equation of a line • Yet, according to math F – Infinite number of points between any two points on a line – Can’t measure Force and Acceleration at all points Takeaway: Science is based on Faith! This faith is differentiated – Yet we assume linear from Blind Faith, and is the act of the scientific rational person. transition holds A Answering Objection 2: Objection: Ideas in religion are too outrageous to be true How we’ll answer it: We’ll show that an unknowable creator, manifestations, etc are all reasonable. Part 1: The Analogies We’ll find situations where we play the role of Creator. These situations will be closely examined in the next part, to learn more about our relationship with God. Humans can create universes • Inside a computer • Like our universe, these universes have – Creatures – Laws • lend insight to – Relationship between creator and created • Case in point – Game of Life (Conway ’70) Game of Life (Conway ’70) • Universe: – A Simple Grid • Creatures: – Yellow cells • Empty Space – Gray cells The Game of Life’s Universal Laws 1. Birth: dead cell with 3 live neighbors becomes alive 2. Survival: live cell with 2-3 live neighbors stays alive 3. Death: all other cases, cell dies or remains dead (loneliness or over-crowding). Game of Life Demo More sophisticated universes • Creatures can learn • Example: – Creature behavior governed by probability matrix – Probabilities updated with experience – Free will simulated by picking behavior according to probabilities • Evolution – Survival of fittest • Programmer does not explicitly write computer program • Instead programmer creates evolutionary environment to evolve solutions. • Process: – Create “population” of randomly generated solutions – Allow solutions to “mate” to yield offspring solutions – Better solutions have higher chance of mating (Darwinian Natural selection) • Outcome of process said to be best solution after many Genetic Programming Link to Additional Slides On GP Genetic Programming Demo Genetic Programming Demo Takeaway: We can create universes in which the creatures can evolve over time! • More than 20 US patents • Several new patents – re-discovered using GP An Automatic Invention Machine? • Genetic Programming has been called • Who is the inventor? – an “Automatic Invention Machine” – discovered using GP – outperform all existing humaninvented solutions – The human or the machine? – “Who is the potter, pray, and who the pot?” –Omar Khayyam Summary of Part 1 • Humans can create universes – Inside a computer – With creatures that can: • Mate • Learn • Evolve • In these universes we play the role of God Part 2: The Harvest ` We’ll use the analogies we studied to draw deductions Suppose you wanted to communicate with your creatures Could you: – enter their world? – turn yourself into a square on the grid? Solution • Since you cannot enter their universe – you must control something in their universe • i.e. speaking to your creatures requires – an intermediary i.e. this man cannot be God Evidence from Christianity Christ is an intermediary who carries actions of God on earth: “I do nothing of myself; but as my Father hath taught me, I speak these things.” -John 8:28 (King James Version) Further evidence of distinction between Christ & God: “But of that day and that hour knoweth no man, no, not the angels which are in heaven, neither the Son, but the Father.” -Mark 13:32 And Islam • Mohammed is an intermediary that delivers message of God to man: “Even as We have sent unto you a messenger [Mohammed] from among you, who reciteth unto you Our revelations and causeth you to grow, and teacheth you the Scripture and wisdom …” -The Qur’an, 2:151 • “Muhammad is but a messenger, messengers (the like of whom) have passed away before him.” -The Qur’an 3:144 And Judaism • Moses in an intermediary that delivered God’s message to Humankind: • “Remember ye the law of Moses My servant, which I [God] commanded unto him in Horeb for all Israel, even statutes and ordinances.” -Prophets And the Bahá’i Faith • Confirms idea of human intermediary – “since there can be no tie of direct intercourse to bind the one true God with His creation … ” God ordains that “in every age … a pure and stainless Soul be made manifest in the kingdoms of earth and heaven” (Baha’u'llah, The Kitab-i-Aqdas, p. 232) The Holy Spirit “we can understand that the Holy Spirit is the Intermediary between the Creator and the created.” -Abdu’l-Baha, Paris Talks, p. 59 • Anything in between the Created and Created • In our example includes – Computer – Software running universe – Keyboard If you were to speak to your creatures .. • What Language: – English? – their language? “All that I have revealed unto thee … hath been in accordance with thy capacity and understanding, not with My state and the melody of My voice.” -Baha’u'llah, The Hidden Words • Level of communication: – According to our capacity? – Or their capacity? On Miracles • Should not constitute a “proof”: – Except to observers – Even then there are often alternate explanations Miracles • Nonetheless, we can see how – miracles could be easy for creator • Example: Game of Life – can create life simply by flipping a bit from a 0 to a 1 in the grid. – a power creatures do not have So, why not have a miracle side-show to quell all doubts? • If God performed miracles on demand Free Will vs. Miracles – forced to acknowledge him – lose autonomy to recognize (or reject) creator • Suppose instantaneous {punishment, correction, guidance} for ‘wrong’ acts. Puppet -controlled -little or no autonomy -brute -loss of self -no capacity for altruism vs. vs. vs. vs. vs. vs. Growing being guided free will & choice: noble being self capacity for altruism Takeaway: There seems to be a tradeoff between miracles and freewill Why A Human Intermediary? • We discovered we needed – an intermediary to communicate with our creatures • But the intermediary could have been – a talking tree, or a rock that glows in Morse code • Why a human intermediary? Why a Human Intermediary? (cont’d) • A talking tree, or glowing rock constitutes – a miracle – But we’ve established that miracles reduce free-will to accept or reject God. • A human intermediary is ideal because it allows God to – communicate the message, while still providing us with – free will to accept (or deny) God. More on Miracles “… Know that the Word of God … is sanctified from the known elements … It became manifest without an utterance made, or a voice breathed. It is the command of God …” Compilations, Baha’i Scriptures, p. 191, Emphasis added. How might our creatures perceive us? • “The world of our creator so vast that it’s composed of an infinite number of squares.” • “The creator is the source of all life” • “The creator is all-powerful.” • “The creator exists above time. Can see the future; knows the past.” • “The creator is omniscient (all-knowing).” TAKEAWAY: God is unknowable! Any conception we have of God is not God. On Praise: “To have accepted any act or praise from Thy creatures is but an evidence of the wonders of Thy [God’s] grace and bountiful favors, and a manifestation of Thy generosity and providence.” -Baha’u'llah Parallels On Unknowability: “… souls shall be perturbed as they make mention of Me [God]. For minds cannot grasp Me nor hearts contain Me.” -Baha’u'llah, The Arabic Hidden Words But isn’t God All-Powerful? • Can’t God turn himself into a human? • Equivalent question: – “Couldn’t God turn himself into a square in Game of Life?” Power of the Creator (cont’d) • What do we mean by All-Powerful? • In Game of life we are All-Powerful because • We can: – change game’s state to any state – alter universal laws • No creature can stand in our way Meaning of All-Powerful (cont’d) • Though “All-Powerful” in Game of Life – Can we turn ourselves into a square? • 1 bit needed to represent square – Bits required to represent a human? – Information loss Power of God (cont’d) • If humans can’t be represented in 1 bit – Can God? God as Unknowable “… God …can in no wise incarnate His infinite, His unknowable, … Reality in the concrete and limited frame of a mortal being.” -Shoghi Effendi, The World Order of Bahá’u'lláh, p. 112 TAKEAWAY: It’s logically impossible for something to be limited and all-powerful at the same time! Power of God Takeaway: • Even God’s power has limits • All Powerful ≠ Ability to do anything • Specifically God cannot be not God Further Questions Further Questions: • Is humility an attribute of God? Why do we declare our powerlessness in the obligatory prayers everyday? • Is God engaging in some kind of ego trip by requiring us to humble ourselves before him every day? One possible answer to the question: We tend to forget who’s in charge – – we think we are in control hence we need a daily reminder that we are in fact powerless • • • Only when we are mindful of The Source of all power – can we turn unto It, seeking It’s help and guidance. • In sum it seems that God requires us to declare our powerlessness – – for our own benefit To make us aware of reality (that we are powerless) so we can act in an educated manner. What if .. • power withheld from computer for even a few seconds? “.. if for one moment the tide of His mercy and grace were to be withheld from the world, it would completely perish” -Bahá’u'llah, Gleanings from the Writings of Bahá’u'llah, p. 68 Is the universe an abandoned experiment? We are created of love: “… I knew My love for thee; therefore I created thee ….” -Baha’u'llah, The Hidden Words • The loving creator guides us: “… Were it not for the love of God the holy books would not have been revealed. Were it not for the love of God the divine prophets would not have been sent to the world … ” -Abdu’l-Baha, Foundations of World Unity, p. 90 1. Prayer: the creator can communicate with us via inspiration “A servant is drawn unto Me in prayer until I answer him; and when I have answered him, I become the ear wherewith he heareth….“ -Quran 83:28 Can we develop a relationship with an “unknowable God?” “For the core of religious faith is that mystical feeling which unites man with God. This state of spiritual communion can be brought about and maintained by means of meditation and prayer.” Baha’i Writings: Compilations, Lights of Guidance, p. 506 • How do we develop a relationship with an “unknowable God?” (cont’d) Reading – Sacred Scriptures (messages sent by creator) – On spiritual teachings (to understand messages from creator) • Meditation • Striving every day – to bring behavior more into accordance with high standards • Selfless service – to humanity – in carrying on of our trade or profession. Summary of Part 2 • Saw computer universes that have: – Creatures – laws. • Creatures could: – Learn – Evolve • If Computer Generated Universes are comparable to our universe then …. Summary of Part 2 • God is unknowable • You cannot: – fully comprehend or – directly interact with God. • All Powerful ≠ Ability to do anything • Holy Spirit – everything between the Creator and Created • Communication with God – requires an intermediary • Founders of World Religions – intermediaries (messengers) between humankind & God – are not God but are directed by God – hard to imagine another way God could communicate with humankind • without loss of our choice to accept (or reject) God. Part 3: Proofs of God ` We’ll examine and critique two proofs of God • • Suppose you walked into the Amazon jungle and saw some pyramids You would probably immediately attribute these pyramids to an ancient civilization because – – You know the pyramids don’t just create themselves You know pyramids don’t appear out of thin air Cosmological Proof of God (Aristotle) • • In short, you know the pyramids must be preceded by a cause. In other words, in the domain of human created objects, every object is evidence of it’s creator. – – – A chair is evidence of a chair maker A painting is evidence of a painter And so on …. • • • • • Applying this same reasoning to the universe, we ask the question. “Can the existence of the Universe be taken as evidence for a Universe-maker (i.e. God?)” There is a leap of Faith in saying “yes” because we are moving from the domain of human created objects to non-human created ones. Moreover we are moving from causes within the universes, to the cause of the universe itself. Yet at the same time, the answer “yes” seems much more intuitive than the answer of “no” because we have never seen non-causal systems. In fact, the basis of science is that there is a cause for everything and saying no would commit us to the existence of non-causal systems. Returning to our This proof only shows that there exists some kind of creator for the universe; but it doesn’t prove there is only one creator; or if another entity created that creator. Hatcher’s Proof of God • William Hatcher (1935-2005) – Passed Away in Nov. 2005 – Produced the strongest proof of God – You can read more in Hatcher’s Book, Minimalism (ISBN • Why hasn’t his proof been invented yet? – Some basic mathematical tools needed to produce it (Von Neumann Set Theory) hadn’t been invented until the 20th century. – Avicenna, a Muslim philosopher produced a very similar proof using mathematical concepts that were far ahead of their time, but his proof had some subtle errors. – Hatcher fixed Avincenna’s proof and reformulated in modern math. Hatcher’s Proof of God • There are some minor differences between the proof you will find here, and the one presented in Hatcher’s book. • In particular, I have done my best to avoid references to set theory while remaining faithful to Hatcher’s proof. • You can get his original version of the proof which includes references to set theory in his book minimalism. • Another version of the proof appears online here: – http://www.onecountry.org/e102/e10214xs.htm – But this is a book excerpt that may be difficult to understand without the background material provided by previous chapters. Hatcher’s Proof • • • Let V represent all of reality. A phenomenon, is some portion of reality I.e. if the blue ellipse represents V, a phenomenon (illustrated in yellow), is some portion of it. Hatcher’s Proof Continued • We differentiate between two types of phenomena. • Composite phenomena have parts. • Non-composite phenomena have no parts (i.e. they are not divisible). Hatcher’s 3 Principles • P1. All existing phenomena are either self-caused (i.e. AA) or other caused (B A where A≠B) but not both. • P2. If AB, then AE where E is any part of B. • P3. AE cannot hold if E is a component of A. P1 • P1 says there is a reason – for everything • When we write AB we mean “a contains sufficient reason for B” • • There are numerous definitions of causality P2 is Hatcher’s definition of causality. One is the efficient cause in which it’s the straw that breaks the camel’s back” – Hatcher does NOT use this definition • Instead he uses what’s called total causality – Under this notion of causality it’s the 1000 previous straws, the camel, plus the last straw, plus gravity, plus the ground the camel is standing on – and all the other things that would be required to produce the breaking of the camel’s back – that causes the camel to break it’s back. – Put another way to cause a phenomenon, you need to supply everything required to create it to satisfy the definition of causality provided in P2. – That is why when we write AB we say “A contains sufficient reason for B” P3: The Principle of Limitation • P3 is a logical principle. • It says that a composite phenomena cannot be the cause of it’s own components. • A car for example cannot be the cause of it’s steering wheel. • We illustrate P3 in the next slide P3 (Continued) • Every composite phenomena has – parts and – A relationship or structure between these parts Relationship of Parts of Parts to each other Car • A car’s parts laid out on one’s front lawn is not a car • To be considered a car, the parts need to be put together in certain way • This is illustrated in the diagram CAR P3 (Continued) • What P3 is saying is that there is a logical succession from the parts and structure to the car. • I.e. once you have the structure AND parts, you have the car. • This succession is a logical one not a temporal one. I.e. it is not the consequence of the passage of time. – For example the integer 2 following after 1 – but this does not involve the passage of time. Relationship of Parts of Parts to each other Car (Structure) CAR P3 (Continued) • The car can’t cause the steering wheel (a part), because the car doesn’t exist until all the parts (including the steering wheel exist) and until such parts are put in the right form. • Put another way, the parts and structure logically precede the car. • It is possible that the car and it’s parts come into being simultaneously BUT it’s not possible for the car to cause it’s own component. Relationship of Parts of Parts to each other Car (Structure) CAR Proof of a Universal Cause • Now that we’ve established the 3 principles, the proof follows. • With respect to V, we know (from P1) that ONLY ONE of the following two statements is true: a) That V is self caused (i.e. VV) I.e. that reality contains sufficient reason for it’s own existence b) That V is other-caused (i.e. there exists some GV) That is some portion of reality, which we call G, is the ultimate cause of everything. Proof of a Universal Cause • Suppose Statement (a) is true i.e. VV • By P2, the statement VV implies that VA for every A which is a component of V – but this contradicts P3 which says a composite phenomena cannot be a cause of one of it’s components. • From the above contradiction we know statement (a) must be false • But according to P1 if (a) is false, then (b) must be true. • Thus there exists a G, which is the ultimate cause of everything (i.e. GV) Proof that G has no components • • • – – We know that GV According to P2, this means GG (since G is a part of V). Either one of the following two statements must hold: G1. G has components G2. G has no components • • G1 cannot hold for the same reasons that VV does not hold (i.e. it would violate P3). This means G has no components. Proof of G’s Uniqueness • Here we will prove that there can only be one universal cause. • We already showed there exists a universal cause, G but lets suppose there exists another universal cause, which we’ll call G’ • Because G’ is a universal cause, we know G’V • By P2, this implies that G’ causes everything including G’ itself; i.e. G’G’ (i.e. G’ is self-caused) (1) • But we also know that the other universal cause, G, causes V i.e. G V. But according to P2, this means G causes everything in V including G’; i.e. GG’ (which means G’ is other caused) (2) • According to statement (1), G’ is self-caused, but according to statement (2), G’ is also other caused. • But this violates P1, which says that G’ must be either self caused, or other caused but not both. • The only way to avoid a contradiction is for G’=G • Thus there is only one universal cause. Hatcher’s Proof • Put together, we have shown that there exists a unique (i.e. there’s only one), universal (i.e. the cause of everything), self-caused (i.e. it contains sufficient reason for it’s own existence) cause. This cause is distinct from the universe, but is the cause of everything within it. • The proof doesn’t require this G to be the immediate cause of everything; but it does say that God is the ultimate cause of everything. • The proof does not tell you if this G, is the same as the God of Christianity, Islam, or the Baha’i Faith – but the findings of the proof are consistent with the God of those religions. Critique of Hatcher’s Proof • – Hatcher used first order logic most well understood and accepted form of logic • As a result there are only three possible ways to attack his proof all of which are very difficult to defend. These attacks are: – – To attack logic itself (not the act of a reasonable person) To show that one or more principles do not hold (this approach is also very difficult to defend – see next slide) Critiquing Hatcher’s Proof If you accept logic, you can only use attack 2. Attack 2 requires one to negate one or more of the 3 principles, but in practice this very difficult to defend; lets go over each principle: – P1 says there is a cause for everything, and that the question “why?” is always meaningful. Negating this principle is difficult because P1 – which says that there is an explanation for everything – is one of the core ideas in Science. ; i.e. that every phenomena is preceded by a cause. Further, those who deny P1, commit themselves to the existence of non-causal systems – something humanity has never observed. – P2 is just a definition of causality – P3 is simply a logical idea. It too is difficult to attack. • • • As introduced at the beginning of this presentation, Science picks as true, statements that are more probable than their complement. It would seem that all 3 of Hatcher’s principles pass this test Thus this proof shifts the burden of proof to people to show there isn’t a God. Dec 2005, Changing Times Understanding the Logic of Atheism QUESTIONS Hooman Katirai (hooman@alumni.mit.edu in 2006) Backup Slides ` More details on Genetic Programming Final Questions • What could we possibly offer our creator that it doesn’t already have? – Thankfulness Nature Vs. Genetic Programming • Survival of Fittest • A Fitness function tells you how well any given solution solves the problem A technique called Tournament selection mimics this phenomenon Parents mate to produce fratenal twins, with genetic code from the parents BUT parent’s immediately die after doing so. Mutation operator Genetic Code = Parse Trees • Several Males will compete to mate with one female or viceversa Parents mate to produce offspring whose genetic makeup a combination of parents • • • • • Offspring contain some genetic code independent of parents Genetic Code = DNA • • Parse Trees: The DNA of Solutions A Simple Example + 2 5 + 5 4 2 7 A More Complicated Example + / 8 7 5 Parse Trees: The DNA of Solutions + A More Complicated Example / Freq(“Huge Savings”) Freq(“Credit Card”) 4 • The parse trees shown in previous slides are somewhat boring – – They always reduced to the same answer More interesting is when we add feature detectors which allow the result to change according to some input. For example the parse tree above will give you a different answer according to how many times the phrases “credit card” and “huge savings appears in a document. Indeed, parse trees using feature detectors have been used to filter junk e-mail with greater than 90% accuracy (See Katirai, “Filtering Junk Email,” 1999). – How two solutions can be mated to produce “children” solutions * + / 8 4 + Gives 5 Mated with 2 2 * + 7 7 5 And 2 2 + / 8 4 To Mate two solutions We swap two randomly selected
Dec 2005, Changing Times Understanding the Logic of Atheism Creating a Bridge of Understanding Hooman Katirai Table of Contents • Part 1: The Analogies – We create analogies where humans play the role of creator • Part 2: The Harvest – We use the analogies to learn about the creator-created relationship. • Part 3: Proofs of God, we examine two proofs of God – one from Aristotle, the other from William Hatcher. Purpose “If thou wishest the divine knowledge … purify thy heart … and apply thyself to rational and authoritative arguments … then the eye will be opened and will recognize the Sun through the Sun itself.” (Abdu’l-Baha, Baha’i World Faith – Abdu’l-Baha Section, p. 383) The complement of a statement is similar to what Faith we might call an opposite. Types of Faith Belief The complement of “it’sin an Idea in the absence raining” is everything that’s of total not raining. This would proof include, sunny, cloudy, windy, etc .. Blind Faith (commitment to a belief regardless of evidence) Empiricism Belief in an idea because it’s more likely than its complement Some Definitions An Might say … God (or gods) do not exist The question “does God exist?” cannot be proven (or disproven) and is therefore meaningless. Atheist Agnostic Undecided I’m not sure if God exists but I’m open to new evidence. Atheism is difficult to defend Belief: God (or gods) do not exist • To make such a claim one must examine – every part of universe – in case one or more Gods were hiding there. • But atheists have examined only a small part of the universe. • Thus they do not have enough evidence to make the claim “there is no God” TAKEAWAYS: • Atheism is a belief founded on faith. It is not based on logic. Agnostics & Undecideds • Both don’t know if God does or does not exist • Agnostics believe the question can’t be answered • These two groups will be the focus of our discussions! Common Objections to Religion & God Ideas in religion are too outrageous to be true We’ll show ideas like An unknowable creator, Manifestations, etc are all reasonable. Show that existence of God is more likely than non-existence I.e. it is not a fiction. Hatcher’s Proof. Acts of followers ≠ Teachings of religion Religion can be perfect while Followers are not. Precisely why God sends new messengers There can be perfect justice If there is a next world Religion is a fiction adopted by the weak or unhappy (to feel comforted and happy) Religion causes war, and suffering Too much suffering in world for there to be a God. Overcoming Obstacles I don’t believe in religion, which is based on faith I believe in Science We’ll show Science is based on Faith! But a special Kind of faith that can Also be applied in religion. Answering Objection 1: Objection: I don’t believe in religion, which is based on faith I believe in Science We’ll show science is based on a special kind of faith called empiricism that can be used in religion Science is based on Faith! • How do Physicists – discover equations? F F =ma • Simple example: – Newton’s Law (F=ma) Force (F) Mass (M) Frictionless Surface A Takeaway: Even fundamental equations in physics are based on Faith!! Science is based on Faith! (cont’d) • F=ma – equation of a line • Yet, according to math F – Infinite number of points between any two points on a line – Can’t measure Force and Acceleration at all points Takeaway: Science is based on Faith! This faith is differentiated – Yet we assume linear from Blind Faith, and is the act of the scientific rational person. transition holds A Answering Objection 2: Objection: Ideas in religion are too outrageous to be true How we’ll answer it: We’ll show that an unknowable creator, manifestations, etc are all reasonable. Part 1: The Analogies We’ll find situations where we play the role of Creator. These situations will be closely examined in the next part, to learn more about our relationship with God. Humans can create universes • Inside a computer • Like our universe, these universes have – Creatures – Laws • lend insight to – Relationship between creator and created • Case in point – Game of Life (Conway ’70) Game of Life (Conway ’70) • Universe: – A Simple Grid • Creatures: – Yellow cells • Empty Space – Gray cells The Game of Life’s Universal Laws 1. Birth: dead cell with 3 live neighbors becomes alive 2. Survival: live cell with 2-3 live neighbors stays alive 3. Death: all other cases, cell dies or remains dead (loneliness or over-crowding). Game of Life Demo More sophisticated universes • Creatures can learn • Example: – Creature behavior governed by probability matrix – Probabilities updated with experience – Free will simulated by picking behavior according to probabilities • Evolution – Survival of fittest • Programmer does not explicitly write computer program • Instead programmer creates evolutionary environment to evolve solutions. • Process: – Create “population” of randomly generated solutions – Allow solutions to “mate” to yield offspring solutions – Better solutions have higher chance of mating (Darwinian Natural selection) • Outcome of process said to be best solution after many Genetic Programming Link to Additional Slides On GP Genetic Programming Demo Genetic Programming Demo Takeaway: We can create universes in which the creatures can evolve over time! • More than 20 US patents • Several new patents – re-discovered using GP An Automatic Invention Machine? • Genetic Programming has been called • Who is the inventor? – an “Automatic Invention Machine” – discovered using GP – outperform all existing humaninvented solutions – The human or the machine? – “Who is the potter, pray, and who the pot?” –Omar Khayyam Summary of Part 1 • Humans can create universes – Inside a computer – With creatures that can: • Mate • Learn • Evolve • In these universes we play the role of God Part 2: The Harvest ` We’ll use the analogies we studied to draw deductions Suppose you wanted to communicate with your creatures Could you: – enter their world? – turn yourself into a square on the grid? Solution • Since you cannot enter their universe – you must control something in their universe • i.e. speaking to your creatures requires – an intermediary i.e. this man cannot be God Evidence from Christianity Christ is an intermediary who carries actions of God on earth: “I do nothing of myself; but as my Father hath taught me, I speak these things.” -John 8:28 (King James Version) Further evidence of distinction between Christ & God: “But of that day and that hour knoweth no man, no, not the angels which are in heaven, neither the Son, but the Father.” -Mark 13:32 And Islam • Mohammed is an intermediary that delivers message of God to man: “Even as We have sent unto you a messenger [Mohammed] from among you, who reciteth unto you Our revelations and causeth you to grow, and teacheth you the Scripture and wisdom …” -The Qur’an, 2:151 • “Muhammad is but a messenger, messengers (the like of whom) have passed away before him.” -The Qur’an 3:144 And Judaism • Moses in an intermediary that delivered God’s message to Humankind: • “Remember ye the law of Moses My servant, which I [God] commanded unto him in Horeb for all Israel, even statutes and ordinances.” -Prophets And the Bahá’i Faith • Confirms idea of human intermediary – “since there can be no tie of direct intercourse to bind the one true God with His creation … ” God ordains that “in every age … a pure and stainless Soul be made manifest in the kingdoms of earth and heaven” (Baha’u'llah, The Kitab-i-Aqdas, p. 232) The Holy Spirit “we can understand that the Holy Spirit is the Intermediary between the Creator and the created.” -Abdu’l-Baha, Paris Talks, p. 59 • Anything in between the Created and Created • In our example includes – Computer – Software running universe – Keyboard If you were to speak to your creatures .. • What Language: – English? – their language? “All that I have revealed unto thee … hath been in accordance with thy capacity and understanding, not with My state and the melody of My voice.” -Baha’u'llah, The Hidden Words • Level of communication: – According to our capacity? – Or their capacity? On Miracles • Should not constitute a “proof”: – Except to observers – Even then there are often alternate explanations Miracles • Nonetheless, we can see how – miracles could be easy for creator • Example: Game of Life – can create life simply by flipping a bit from a 0 to a 1 in the grid. – a power creatures do not have So, why not have a miracle side-show to quell all doubts? • If God performed miracles on demand Free Will vs. Miracles – forced to acknowledge him – lose autonomy to recognize (or reject) creator • Suppose instantaneous {punishment, correction, guidance} for ‘wrong’ acts. Puppet -controlled -little or no autonomy -brute -loss of self -no capacity for altruism vs. vs. vs. vs. vs. vs. Growing being guided free will & choice: noble being self capacity for altruism Takeaway: There seems to be a tradeoff between miracles and freewill Why A Human Intermediary? • We discovered we needed – an intermediary to communicate with our creatures • But the intermediary could have been – a talking tree, or a rock that glows in Morse code • Why a human intermediary? Why a Human Intermediary? (cont’d) • A talking tree, or glowing rock constitutes – a miracle – But we’ve established that miracles reduce free-will to accept or reject God. • A human intermediary is ideal because it allows God to – communicate the message, while still providing us with – free will to accept (or deny) God. More on Miracles “… Know that the Word of God … is sanctified from the known elements … It became manifest without an utterance made, or a voice breathed. It is the command of God …” Compilations, Baha’i Scriptures, p. 191, Emphasis added. How might our creatures perceive us? • “The world of our creator so vast that it’s composed of an infinite number of squares.” • “The creator is the source of all life” • “The creator is all-powerful.” • “The creator exists above time. Can see the future; knows the past.” • “The creator is omniscient (all-knowing).” TAKEAWAY: God is unknowable! Any conception we have of God is not God. On Praise: “To have accepted any act or praise from Thy creatures is but an evidence of the wonders of Thy [God’s] grace and bountiful favors, and a manifestation of Thy generosity and providence.” -Baha’u'llah Parallels On Unknowability: “… souls shall be perturbed as they make mention of Me [God]. For minds cannot grasp Me nor hearts contain Me.” -Baha’u'llah, The Arabic Hidden Words But isn’t God All-Powerful? • Can’t God turn himself into a human? • Equivalent question: – “Couldn’t God turn himself into a square in Game of Life?” Power of the Creator (cont’d) • What do we mean by All-Powerful? • In Game of life we are All-Powerful because • We can: – change game’s state to any state – alter universal laws • No creature can stand in our way Meaning of All-Powerful (cont’d) • Though “All-Powerful” in Game of Life – Can we turn ourselves into a square? • 1 bit needed to represent square – Bits required to represent a human? – Information loss Power of God (cont’d) • If humans can’t be represented in 1 bit – Can God? God as Unknowable “… God …can in no wise incarnate His infinite, His unknowable, … Reality in the concrete and limited frame of a mortal being.” -Shoghi Effendi, The World Order of Bahá’u'lláh, p. 112 TAKEAWAY: It’s logically impossible for something to be limited and all-powerful at the same time! Power of God Takeaway: • Even God’s power has limits • All Powerful ≠ Ability to do anything • Specifically God cannot be not God Further Questions Further Questions: • Is humility an attribute of God? Why do we declare our powerlessness in the obligatory prayers everyday? • Is God engaging in some kind of ego trip by requiring us to humble ourselves before him every day? One possible answer to the question: We tend to forget who’s in charge – – we think we are in control hence we need a daily reminder that we are in fact powerless • • • Only when we are mindful of The Source of all power – can we turn unto It, seeking It’s help and guidance. • In sum it seems that God requires us to declare our powerlessness – – for our own benefit To make us aware of reality (that we are powerless) so we can act in an educated manner. What if .. • power withheld from computer for even a few seconds? “.. if for one moment the tide of His mercy and grace were to be withheld from the world, it would completely perish” -Bahá’u'llah, Gleanings from the Writings of Bahá’u'llah, p. 68 Is the universe an abandoned experiment? We are created of love: “… I knew My love for thee; therefore I created thee ….” -Baha’u'llah, The Hidden Words • The loving creator guides us: “… Were it not for the love of God the holy books would not have been revealed. Were it not for the love of God the divine prophets would not have been sent to the world … ” -Abdu’l-Baha, Foundations of World Unity, p. 90 1. Prayer: the creator can communicate with us via inspiration “A servant is drawn unto Me in prayer until I answer him; and when I have answered him, I become the ear wherewith he heareth….“ -Quran 83:28 Can we develop a relationship with an “unknowable God?” “For the core of religious faith is that mystical feeling which unites man with God. This state of spiritual communion can be brought about and maintained by means of meditation and prayer.” Baha’i Writings: Compilations, Lights of Guidance, p. 506 • How do we develop a relationship with an “unknowable God?” (cont’d) Reading – Sacred Scriptures (messages sent by creator) – On spiritual teachings (to understand messages from creator) • Meditation • Striving every day – to bring behavior more into accordance with high standards • Selfless service – to humanity – in carrying on of our trade or profession. Summary of Part 2 • Saw computer universes that have: – Creatures – laws. • Creatures could: – Learn – Evolve • If Computer Generated Universes are comparable to our universe then …. Summary of Part 2 • God is unknowable • You cannot: – fully comprehend or – directly interact with God. • All Powerful ≠ Ability to do anything • Holy Spirit – everything between the Creator and Created • Communication with God – requires an intermediary • Founders of World Religions – intermediaries (messengers) between humankind & God – are not God but are directed by God – hard to imagine another way God could communicate with humankind • without loss of our choice to accept (or reject) God. Part 3: Proofs of God ` We’ll examine and critique two proofs of God • • Suppose you walked into the Amazon jungle and saw some pyramids You would probably immediately attribute these pyramids to an ancient civilization because – – You know the pyramids don’t just create themselves You know pyramids don’t appear out of thin air Cosmological Proof of God (Aristotle) • • In short, you know the pyramids must be preceded by a cause. In other words, in the domain of human created objects, every object is evidence of it’s creator. – – – A chair is evidence of a chair maker A painting is evidence of a painter And so on …. • • • • • Applying this same reasoning to the universe, we ask the question. “Can the existence of the Universe be taken as evidence for a Universe-maker (i.e. God?)” There is a leap of Faith in saying “yes” because we are moving from the domain of human created objects to non-human created ones. Moreover we are moving from causes within the universes, to the cause of the universe itself. Yet at the same time, the answer “yes” seems much more intuitive than the answer of “no” because we have never seen non-causal systems. In fact, the basis of science is that there is a cause for everything and saying no would commit us to the existence of non-causal systems. Returning to our This proof only shows that there exists some kind of creator for the universe; but it doesn’t prove there is only one creator; or if another entity created that creator. Hatcher’s Proof of God • William Hatcher (1935-2005) – Passed Away in Nov. 2005 – Produced the strongest proof of God – You can read more in Hatcher’s Book, Minimalism (ISBN • Why hasn’t his proof been invented yet? – Some basic mathematical tools needed to produce it (Von Neumann Set Theory) hadn’t been invented until the 20th century. – Avicenna, a Muslim philosopher produced a very similar proof using mathematical concepts that were far ahead of their time, but his proof had some subtle errors. – Hatcher fixed Avincenna’s proof and reformulated in modern math. Hatcher’s Proof of God • There are some minor differences between the proof you will find here, and the one presented in Hatcher’s book. • In particular, I have done my best to avoid references to set theory while remaining faithful to Hatcher’s proof. • You can get his original version of the proof which includes references to set theory in his book minimalism. • Another version of the proof appears online here: – http://www.onecountry.org/e102/e10214xs.htm – But this is a book excerpt that may be difficult to understand without the background material provided by previous chapters. Hatcher’s Proof • • • Let V represent all of reality. A phenomenon, is some portion of reality I.e. if the blue ellipse represents V, a phenomenon (illustrated in yellow), is some portion of it. Hatcher’s Proof Continued • We differentiate between two types of phenomena. • Composite phenomena have parts. • Non-composite phenomena have no parts (i.e. they are not divisible). Hatcher’s 3 Principles • P1. All existing phenomena are either self-caused (i.e. AA) or other caused (B A where A≠B) but not both. • P2. If AB, then AE where E is any part of B. • P3. AE cannot hold if E is a component of A. P1 • P1 says there is a reason – for everything • When we write AB we mean “a contains sufficient reason for B” • • There are numerous definitions of causality P2 is Hatcher’s definition of causality. One is the efficient cause in which it’s the straw that breaks the camel’s back” – Hatcher does NOT use this definition • Instead he uses what’s called total causality – Under this notion of causality it’s the 1000 previous straws, the camel, plus the last straw, plus gravity, plus the ground the camel is standing on – and all the other things that would be required to produce the breaking of the camel’s back – that causes the camel to break it’s back. – Put another way to cause a phenomenon, you need to supply everything required to create it to satisfy the definition of causality provided in P2. – That is why when we write AB we say “A contains sufficient reason for B” P3: The Principle of Limitation • P3 is a logical principle. • It says that a composite phenomena cannot be the cause of it’s own components. • A car for example cannot be the cause of it’s steering wheel. • We illustrate P3 in the next slide P3 (Continued) • Every composite phenomena has – parts and – A relationship or structure between these parts Relationship of Parts of Parts to each other Car • A car’s parts laid out on one’s front lawn is not a car • To be considered a car, the parts need to be put together in certain way • This is illustrated in the diagram CAR P3 (Continued) • What P3 is saying is that there is a logical succession from the parts and structure to the car. • I.e. once you have the structure AND parts, you have the car. • This succession is a logical one not a temporal one. I.e. it is not the consequence of the passage of time. – For example the integer 2 following after 1 – but this does not involve the passage of time. Relationship of Parts of Parts to each other Car (Structure) CAR P3 (Continued) • The car can’t cause the steering wheel (a part), because the car doesn’t exist until all the parts (including the steering wheel exist) and until such parts are put in the right form. • Put another way, the parts and structure logically precede the car. • It is possible that the car and it’s parts come into being simultaneously BUT it’s not possible for the car to cause it’s own component. Relationship of Parts of Parts to each other Car (Structure) CAR Proof of a Universal Cause • Now that we’ve established the 3 principles, the proof follows. • With respect to V, we know (from P1) that ONLY ONE of the following two statements is true: a) That V is self caused (i.e. VV) I.e. that reality contains sufficient reason for it’s own existence b) That V is other-caused (i.e. there exists some GV) That is some portion of reality, which we call G, is the ultimate cause of everything. Proof of a Universal Cause • Suppose Statement (a) is true i.e. VV • By P2, the statement VV implies that VA for every A which is a component of V – but this contradicts P3 which says a composite phenomena cannot be a cause of one of it’s components. • From the above contradiction we know statement (a) must be false • But according to P1 if (a) is false, then (b) must be true. • Thus there exists a G, which is the ultimate cause of everything (i.e. GV) Proof that G has no components • • • – – We know that GV According to P2, this means GG (since G is a part of V). Either one of the following two statements must hold: G1. G has components G2. G has no components • • G1 cannot hold for the same reasons that VV does not hold (i.e. it would violate P3). This means G has no components. Proof of G’s Uniqueness • Here we will prove that there can only be one universal cause. • We already showed there exists a universal cause, G but lets suppose there exists another universal cause, which we’ll call G’ • Because G’ is a universal cause, we know G’V • By P2, this implies that G’ causes everything including G’ itself; i.e. G’G’ (i.e. G’ is self-caused) (1) • But we also know that the other universal cause, G, causes V i.e. G V. But according to P2, this means G causes everything in V including G’; i.e. GG’ (which means G’ is other caused) (2) • According to statement (1), G’ is self-caused, but according to statement (2), G’ is also other caused. • But this violates P1, which says that G’ must be either self caused, or other caused but not both. • The only way to avoid a contradiction is for G’=G • Thus there is only one universal cause. Hatcher’s Proof • Put together, we have shown that there exists a unique (i.e. there’s only one), universal (i.e. the cause of everything), self-caused (i.e. it contains sufficient reason for it’s own existence) cause. This cause is distinct from the universe, but is the cause of everything within it. • The proof doesn’t require this G to be the immediate cause of everything; but it does say that God is the ultimate cause of everything. • The proof does not tell you if this G, is the same as the God of Christianity, Islam, or the Baha’i Faith – but the findings of the proof are consistent with the God of those religions. Critique of Hatcher’s Proof • – Hatcher used first order logic most well understood and accepted form of logic • As a result there are only three possible ways to attack his proof all of which are very difficult to defend. These attacks are: – – To attack logic itself (not the act of a reasonable person) To show that one or more principles do not hold (this approach is also very difficult to defend – see next slide) Critiquing Hatcher’s Proof If you accept logic, you can only use attack 2. Attack 2 requires one to negate one or more of the 3 principles, but in practice this very difficult to defend; lets go over each principle: – P1 says there is a cause for everything, and that the question “why?” is always meaningful. Negating this principle is difficult because P1 – which says that there is an explanation for everything – is one of the core ideas in Science. ; i.e. that every phenomena is preceded by a cause. Further, those who deny P1, commit themselves to the existence of non-causal systems – something humanity has never observed. – P2 is just a definition of causality – P3 is simply a logical idea. It too is difficult to attack. • • • As introduced at the beginning of this presentation, Science picks as true, statements that are more probable than their complement. It would seem that all 3 of Hatcher’s principles pass this test Thus this proof shifts the burden of proof to people to show there isn’t a God. Dec 2005, Changing Times Understanding the Logic of Atheism QUESTIONS Hooman Katirai (hooman@alumni.mit.edu in 2006) Backup Slides ` More details on Genetic Programming Final Questions • What could we possibly offer our creator that it doesn’t already have? – Thankfulness Nature Vs. Genetic Programming • Survival of Fittest • A Fitness function tells you how well any given solution solves the problem A technique called Tournament selection mimics this phenomenon Parents mate to produce fratenal twins, with genetic code from the parents BUT parent’s immediately die after doing so. Mutation operator Genetic Code = Parse Trees • Several Males will compete to mate with one female or viceversa Parents mate to produce offspring whose genetic makeup a combination of parents • • • • • Offspring contain some genetic code independent of parents Genetic Code = DNA • • Parse Trees: The DNA of Solutions A Simple Example + 2 5 + 5 4 2 7 A More Complicated Example + / 8 7 5 Parse Trees: The DNA of Solutions + A More Complicated Example / Freq(“Huge Savings”) Freq(“Credit Card”) 4 • The parse trees shown in previous slides are somewhat boring – – They always reduced to the same answer More interesting is when we add feature detectors which allow the result to change according to some input. For example the parse tree above will give you a different answer according to how many times the phrases “credit card” and “huge savings appears in a document. Indeed, parse trees using feature detectors have been used to filter junk e-mail with greater than 90% accuracy (See Katirai, “Filtering Junk Email,” 1999). – How two solutions can be mated to produce “children” solutions * + / 8 4 + Gives 5 Mated with 2 2 * + 7 7 5 And 2 2 + / 8 4 To Mate two solutions We swap two randomly selected
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