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               My diagram of Jesus' mind      Here is my sketch of Jesus's mind based on the ways that he figured things out. See also the diagram above. He was very concerned not to cause others to stumble, and hoped he didn't cause John the Baptist to stumble, but ultimately, he caused his disciples to stumble. He spoke of two gates, the narrow to life and the wide to destruction. He urged people to repent and enter the Kingdom of Heaven, and he spoke to their belief, and some people did believe, and some were ready to die for him. He hoped that the Kingdom of Heaven could be thus established. Yet he accepted God's will to save all of the world, not just some, and so he accepted death and resurrection. So some people accepted him as he was, alive, and others dead, as they wished him, yet resurrected. And so the two branches are made one. Martha gave a great example of the practical work of the courts where the judge ignored the law to do what was right, where the judge gave a woman the right to parent a deaf child because she and her daughters had learned sign language and engaged him whereas his biological father had not. And so if there is nobody to dispute a ruling, then there is healing, there is justice in the most important sense. But if there is somebody to dispute it, then it can go up the system, and the laws can be worked out. Or as in the case of Solomon and the baby, it can become clear, through the process, what was not clear before it, such as who was the real mother. So the law supports a culture but ultimately it must be an internally based culture, and that is the "way", the truth and the life, the branch that Jesus offers, the "gate", the "light".1594

     Pamela McLean, a philosophical portrait      Andrius Kulikauskas, 2011.05.11: Pamela McLean of Dadamac agreed that I draw her philosophical portrait by documenting and sharing her ways of figuring things out. She's a pioneer! Thank you, Pamela!1271

               Keep forgiving so they do not stumble      Luke 17:1 He said to the disciples, "It is impossible that no occasions of stumbling should come, but woe to him through whom they come! 17:2 It would be better for him if a millstone were hung around his neck, and he were thrown into the sea, rather than that he should cause one of these little ones to stumble. 17:3 Be careful. If your brother sins against you, rebuke him. If he repents, forgive him. 17:4 If he sins against you seven times in the day, and seven times returns, saying, 'I repent,' you shall forgive him."1258

          Get behind me, Satan!       Matthew 4:8 Again, the devil took him to an exceedingly high mountain, and showed him all the kingdoms of the world, and their glory. 4:9 He said to him, "I will give you all of these things, if you will fall down and worship me." 4:10 Then Jesus said to him, "Get behind me, Satan! For it is written, 'You shall worship the Lord your God, and you shall serve him only.'"1324

          Jesus' prophesies can keep the disciples from stumbling       John 16:1 These things have I spoken to you, so that you wouldn't be caused to stumble.1374

          Consider what others avoid knowing     What don't people want to know? I decided that if I am to possibly know everything, then God must make that knowledge easy to find and intuit. But others have not yet found it. So it must be a place where people could look, but choose not to. I surmised that it must be the wisdom of life, for there is no science of how to live our lives. Few people seem to wish that there be such a science. 1102

          Ignore the devil      I ignore the devil because I want to live positively, I want to grow positive, and I don't think the devil is relevant. I thereby learn that the devil isn't relevant, at least not for me to live and grow and give fruit forever.1111

          Stay away from what can harm but can't be necessary      I stay away from drugs and am not curious about them. I would tell myself that they can't be necessary for my quest and so they can only hurt me. I stay away from those who want to be degenerate, who want to descend into ruin, who want to involve me in their dysfunctionality.1110

          Suppose that God will make things doable      As a high school student I came to think that physics at the quantum level simply fades the way, and so is not a foundation for knowledge of life. So I concluded that if I am to know everything, God must make that possible. The truth must be at hand, easy for me to find, as if I was to search for a lost key at the foot of a lamp post, where the light happens to be best.1103

        Not shutting ourselves down

Not shutting ourselves down      1142

          Assurance in his own path      Matthew 8:22 But Jesus said to him, "Follow me, and leave the dead to bury their own dead." 1618

          Note the relation between call and response      Matthew 7:7 "Ask, and it will be given you. Seek, and you will find. Knock, and it will be opened for you. 7:8 For everyone who asks receives. He who seeks finds. To him who knocks it will be opened. 1477

          People are saved by their faith      Luke 7:47 Therefore I tell you, her sins, which are many, are forgiven, for she loved much. But to whom little is forgiven, the same loves little." 7:48 He said to her, "Your sins are forgiven." 7:49 Those who sat at the table with him began to say to themselves, "Who is this who even forgives sins?" 7:50 He said to the woman, "Your faith has saved you. Go in peace."1366

          Specific case follows from general principle      Matthew 7:7 "Ask, and it will be given you. Seek, and you will find. Knock, and it will be opened for you. 7:8 For everyone who asks receives. He who seeks finds. To him who knocks it will be opened. 1478

               Axiom of the empty set      Wikipedia: There is a set such that no set is a member of it.1162

          Notation      Adding notation is typically referencing everything with regard to an origin, a reference point. We need some "notation". Let us assume that there is a universal coordinate system, such as longitude and latitude, so that we can refer to the "same" location on any planet. For example, if the planets were little balls floating in a room, the location "north pole" would mean the point on a planet which was closest to the ceiling. Given such a universal coordinate system, what can we say about a planet P which has a private point at location x? pg. 64 The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1520

          Accepting God's assertion      I am in love with a woman who God told me I will marry. I don't pray that she marry me because God assures me that she will. I prayed with her that her aunt get well from cancer and God consistently assured me that she would. I asked if I should keep praying, if I should offer myself to him in some way, but he said no. She died, though. Yet they reported that just before she died she bore witness that God truly is, that he had greeted her, and she said that she loved them all very much, and she passed away. I didn't know what to make of this, and when I ask God, he doesn't say.1233

          What can or can't be removed?      Conversing with: the unthinkable As a freshman at the University of Chicago, I was trying to explain how the concept of everything was an absolute. We seem to all have the concept, but perhaps others might not. One question that helped was to ask whether we could get rid of the concept of everything? My personal answer is no, I don't conceive of how I could let go of such a concept. Thus this supports the property of everything that it is a required concept.1224

          What must I believe?      Conversing with: my ability to believe As a child, I pondered, what must I accept and believe so that I don't go astray in my thinking? and think evil things? I thought I should believe, as Jesus teaches, to believe God, and then also, to love my neighbor as myself, and for good measure, to believe that Jesus is God.1222

        Rooting ourselves in our inner world

Rooting ourselves in our inner world      1669

          Give away what I have      I ultimately collected about two hundred classics of rock music but it was getting difficult to buy albums and CDs were very pricey. So I gave away my collection, mostly to some rock musicians from Lithuania. It was nice that they appreciated the albums.1013

          Replying to Scripture with Scripture      In Matthew, the devil cites the Scripture in tempting Jesus, and Jesus responds with Scripture, and only Scripture, except for "Get behind me Satan!" with his last reply. Jesus seems to accord to Scripture greater assurance than anything he could say with his own mind.1319

          What is the law and the prophets?      Matthew 7:12 Therefore whatever you desire for men to do to you, you shall also do to them; for this is the law and the prophets. 1482

               127 people in a tennis tournament      If 127 people play in a singles tennis tournament, prove that at the end of the tournament, the number of people who have played an odd number of games is even. ... each game has exactly two people playing it... the sum counts every game that has been played exactly twice! ... the sum above is even, and is a sum of an odd number (127) of elements. If an odd number of them were odd, the sum would not be even... pg. 102, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1644

               Parity problem: Dominos on a chessboard      Remove the two diagonally opposite corner squares of a chessboard. Is it possible to tile this shape with thirty-one 2 x 1 "dominos"? ... At first, it seems like a geometric/combinatorial problem with many cases and subcases. But it is really just a question about counting colors. The two corners that were removed wre both (without loss of generality) white, so the shape we are interested in contains 32 black and 30 white squares. Yet any domino, once it is placed, will occupy exactly one black and one white square. The 31 dominos thus require 31 black and 31 white squares, so tiling is impossible. pg. 60 The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1509

        Presuming others likewise

Presuming others likewise      1670

        Appreciate others

Appreciate others      As we give, we appreciate what others can and do give, for we may have them give on our behalf.1081

          Take family stories to heart      After the war in Soviet-occupied Lithuania there was not much food and our relatives ate from one bowl and they say the children who ate slower ended up smaller.1071

        Hear

Hear      136

          Add his faith where faith is lacking      Matthew 8:23 When he got into a boat, his disciples followed him. 8:24 Behold, a violent storm came up on the sea, so much that the boat was covered with the waves, but he was asleep. 8:25 They came to him, and woke him up, saying, "Save us, Lord! We are dying!" 8:26 He said to them, "Why are you fearful, O you of little faith?" Then he got up, rebuked the wind and the sea, and there was a great calm.1620

          What does it take for people to repent?      People may repent if they wrong the righteous. Matthew 23:33 You serpents, you offspring of vipers, how will you escape the judgment of Gehenna? 23:34 Therefore behold, I send to you prophets, wise men, and scribes. Some of them you will kill and crucify; and some of them you will scourge in your synagogues, and persecute from city to city; 23:35 that on you may come all the righteous blood shed on the earth, from the blood of righteous Abel to the blood of Zachariah son of Barachiah, whom you killed between the sanctuary and the altar. 1576

          What will Jesus give to those who are burdened      Matthew 11:28 "Come to me, all you who labor and are heavily burdened, and I will give you rest. 1917

        Learn what is fair

Learn what is fair      1082

          Realizing the basis for leadership      When I started my business I wanted my colleagues in Lithuania to earn the same as me. But then I realized that I am the one investing, sticking my neck out, running the risk. And they themselves stated that first I need to make money, and then they can.1062

        Healing

Healing      Jesus heals many people and they are made whole and do not stumble because of him. Yet others are upset that he heals on the Sabbath and thus stumble because of him. Jesus keeps believers from stumbling. God gives the reward, and the reward is Jesus. The good does not receive the reward, because they had the good from the beginning, for the reward is sharing in all things, and so Jesus appreciates the logic, for Jesus had appreciated the wealth of God from the beginning, and received it likewise, and so could have no reward, except through those who were given to him by God.1364

          Am I causing others to stumble?      Jesus doesn't want others to stumble because of him, yet it may happen, and yet he suggests that there are those who he doesn't cause to stumble, and thus more fundamentally, people need not stumble. Luke 7:19 John, calling to himself two of his disciples, sent them to Jesus, saying, "Are you the one who is coming, or should we look for another?" ... Go and tell John the things which you have seen and heard: that the blind receive their sight, the lame walk, the lepers are cleansed, the deaf hear, the dead are raised up, and the poor have good news preached to them. 7:23 Blessed is he who finds no occasion for stumbling in me.1363

          What are the consequences of believing?      Matthew 7:24 "Everyone therefore who hears these words of mine, and does them, I will liken him to a wise man, who built his house on a rock. 7:25 The rain came down, the floods came, and the winds blew, and beat on that house; and it didn't fall, for it was founded on the rock.1496

          What is more relevant?      Spiritual health is more relevant than physical health. Jesus naturally is alert to a person's spiritual well being and focuses on that rather on their physical well-being. Thus he takes liberty to interpret the person's sadness or happiness as regarding his sins, not his illness. Matthew 9:2 Behold, they brought to him a man who was paralyzed, lying on a bed. Jesus, seeing their faith, said to the paralytic, "Son, cheer up! Your sins are forgiven you." 1653

        Include - Care

Include - Care      176

          I-Thou dialogue      Bob Lichtenbert writes up a dialogue where one person is the Seeker and the other is the Tipper (typical person). Then volunteers read that dialogue out loud. Then they pause discuss. This yields a more interdisciplinary approach to questions because the audience is from different fields and aren't philosophers.1443

        Invest in giving

Invest in giving      Invest in a culture of giving1083

          Recognizing who is there for me      I went to school in Chicago in part to be closer to my relatives, all of whom lived in the area. Some of them would say how family was much more important than friends because in the end you always counted on family. But that never bore out. Partly, my mother didn't want me to ever have or discuss any money issues with anybody in our extended family. And simply in practice, whenever I discussed my business needs or for loans or leads or mentors, there was no help. Whereas I have good friends who backed me up with significant long term or short term loans. In general, different people helped or not in different ways, as they were able and felt comfortable.1050

        Others' limits

Others' limits      164

        Our outer world

Our outer world      1668

        Taking

Taking      1097

          Somebody suggests to Jesus what Jesus might want      Matthew 8:2 Behold, a leper came to him and worshiped him, saying, "Lord, if you want to, you can make me clean." 8:3 Jesus stretched out his hand, and touched him, saying, "I want to. Be made clean." Immediately his leprosy was cleansed. 8:4 Jesus said to him, "See that you tell nobody, but go, show yourself to the priest, and offer the gift that Moses commanded, as a testimony to them." 1601

          What is the way to destruction?      The gate of "belief" leads to life; the gate of "caring" leads to destruction. We can distinguish the gates by seeing who goes through them. Matthew 7:13 "Enter in by the narrow gate; for wide is the gate and broad is the way that leads to destruction, and many are those who enter in by it. 7:14 How narrow is the gate, and restricted is the way that leads to life! Few are those who find it. 1487

               Prove that the sum of the interior angles of any n-gon is 180(n-2) degrees      Weitz, pg.501499

          Observing what is going on around me      As a nearsighted child, I noticed "floaters" that moved across my eye, chains of blocks. I learned about cells in my biology, and then, one day, sitting in a dentist's chair, I thought, the floaters must be chains of cells which I can see because they are close up, right on my eyeball. My mother said no. But later an optometrist confirmed that, yes, indeed they were! I thought it was wonderful that I could see human cells with my own naked eyes!1235

     Noting what we find no analogue for      1532

          Unexpected recording of unconscious      Keith Richards of the Rolling Stones came up with the riff for the song "Satisfaction" in his sleep, recorded it unexpectedly, and woke up to find it on the tape. Fresh Air: In an interview on Fresh Air, Richards recounts how he woke up just long enough to record the famous opening riff of "Satisfaction" on a cassette player he'd placed next to his bed. "I go to bed as usual with my guitar, and I wake up the next morning, and I see that the tape is run to the very end," Richards tells Terry Gross. "And I think, 'Well, I didn't do anything. Maybe I hit a button when I was asleep.' So I put it back to the beginning and pushed play and there, in some sort of ghostly version, is [the opening lines to 'Satisfaction']. It was a whole verse of it. And after that, there's 40 minutes of me snoring. But there's the song in its embryo, and I actually dreamt the damned thing."1714

          Distinguish direct and indirect importance      Matthew 6:25 Therefore I tell you, don't be anxious for your life: what you will eat, or what you will drink; nor yet for your body, what you will wear. Isn't life more than food, and the body more than clothing? 6:26 See the birds of the sky, that they don't sow, neither do they reap, nor gather into barns. Your heavenly Father feeds them. Aren't you of much more value than they? 1450

          Relative comparison      Mark 12:43 ... "Most certainly I tell you, this poor widow gave more than all those who are giving into the treasury, 12:44 for they all gave out of their abundance, but she, out of her poverty, gave all that she had to live on."1410

          Use of extreme principle with induction      Often, problems involve the extreme principle plus a particular argument style, such as contradiction or induction. A common tactic is to use the extremes to "strip down" a problem into a smaller version ... The formal argument then uses induction. ... Several positive integers are written on a blackboard. One can erase any two distinct integers and write their greatest common divisor and least common multiple instead. Prove that eventually the numbers will stop changing. pg.85, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1633

          Well-Ordering Principle      Every non-empty set of positive integers has a least element. pg.83, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1631

          Reading a book that somebody recommends      I've learned quite a bit from several books that others recommended that I read. An IrDA member from Oregon introduced me to Christopher Alexander's "The Timeless Way of Building". It's a wonderfully poetic book and I rank Alexander along with Plato and Kant for his insightful theory and practice of pattern languages. Malcolm Duerod recommended that I read "The Shack", a book depicting God's relationship with himself as the Holy Trinity, but it got me thinking that, in my imagination, God is alone. June Terry recommended "A Purpose Driven Life" and I've just read the first chapter, but it made me realize that, as a child, I appreciated that my happy life did not come from my own merits, yet it was I who appreciated that, and I who decided to apply myself, and I who engaged God regarding that, as I myself thought best.1299

          What would make things more likely?      In China, one night in bed, I was thinking to myself ... that if I lived in Lithuania, it would make it more likely that I could fall in love with a Lithuanian woman, as my unconscious was not allowing me otherwise, for I had grown up in a Lithuanian family and was committed to being Lithuanian. 1591

          Are you making people better?      Matthew 23:15 Woe to you, scribes and Pharisees, hypocrites! For you travel around by sea and land to make one proselyte; and when he becomes one, you make him twice as much of a son of Gehenna as yourselves. 1568

          Looking for exceptions      Matthew 7:9 Or who is there among you, who, if his son asks him for bread, will give him a stone? 7:10 Or if he asks for a fish, who will give him a serpent? 1479

          Who is the teacher?      Matthew 23:8 But don't you be called 'Rabbi,' for one is your teacher, the Christ, and all of you are brothers. 1551

          Wisdom is expressed through many styles      Wisdom caters to all styles, yet those who wish will reject each style. Luke 7:31 ... To what then will I liken the people of this generation? What are they like? 7:32 They are like children who sit in the marketplace, and call one to another, saying, 'We piped to you, and you didn't dance. We mourned, and you didn't weep.' 7:33 For John the Baptizer came neither eating bread nor drinking wine, and you say, 'He has a demon.' 7:34 The Son of Man has come eating and drinking, and you say, 'Behold, a gluttonous man, and a drunkard; a friend of tax collectors and sinners!' 7:35 Wisdom is justified by all her children.1365

          Finite Injury Priority Method      Muchnik [1956] and Friedberg [1957] invented a computable approximation to this forcing argument, called the finite injury method , where they allow a requirement to finitely often be injured (i.e, previous progress to be destroyed), and then they begin again to satisfy the given requirement, until after it is finally satisfied and never injured thereafter. We present finite injury priority arguments and a solution to Post's problem of c.e. sets A and B of incomparable Turing degree. Robert Soare's upcoming book, "Computability Theory and Applications: The Art of Classical Computability".1660

          Ask for help with a formality      During the independence movement, the dollar was worth a lot and I could hire an organizer. I paid him for one or two months but then he needed his labor book to be signed by somebody official. So I suggested that we go the reform movement's office, that they could do that formality, and I was surprised that they refused.1060

          Ask neighbors for donations      In high school we used to raise money for our swim team by having a swimathon. We would go door to door and ask for a penny or more per lap that we swam. We ended up swimming 200 laps. It was good practice asking people for support and quite surprising how supportive people were.1065

          What happens to the bad tree?      Matthew 7:19 Every tree that doesn't grow good fruit is cut down, and thrown into the fire.1490

          What is possible for man and God      God can change one's heart. Luke 18:26 Those who heard it said, "Then who can be saved?" 18:27 But he said, "The things which are impossible with men are possible with God."2073

          What is the ultimate outcome?      Matthew 24:1 Jesus went out from the temple, and was going on his way. His disciples came to him to show him the buildings of the temple. 24:2 But he answered them, "You see all of these things, don't you? Most certainly I tell you, there will not be left here one stone on another, that will not be thrown down." 1560

          Who is our Father?      Matthew 23:9 Call no man on the earth your father, for one is your Father, he who is in heaven.1554

          Infinite Injury Priority Method      Shoenfield [1961] and Sacks independently [1963a,b,c] invented the infinite injury method for computable constructions in which a given requirement may be injured infinitely often, but only computably so, and still somehow succeed. Yates, Martin, and Lachlan extended and refined this method and added others such as the minimal pair construction of a pair of noncomputable c.e. sets A and B whose degree have infimum degree 0 the degree of the computable sets. By the end of the initial period of computability 1930--1970 the constructions and proofs had become so complicated that it had become very difficult to obtain any intuition about them. Fortunately, Lachlan introduced: (1) the method of games in computability Lachlan [1970a] (see Chapter on Lachlan Games); (2) the topology of priority arguments Lachlan [1973], which gave rise to the true stages method for infinite injury (refined in Chapter 8); and (3) the use trees in Lachlan [1975] to divide a strategy for a priority argument into a collection of strategies, one assigned to each node of the tree, and each equipped with a guess about the outcome of higher priority strategies. Lachlan's original use of trees [1975] for a 0''' argument was very complicated, but the tree method with simplifications was presented in Soare [1985] and is further refined in this book in Chapters 9 and 10. It has been used very extensively in computability theory ever since. These three improvements and their refinements allow the reader of this book to help keep in mind what Leo Harrington calls the mountain top view of the proof: a small number of key elements, their interaction, how we resolve conflicts between conflicting requirements, and the underlying beauty of the proof. Robert Soare's upcoming book, "Computability Theory and Applications: The Art of Classical Computability".1661

          Surprising interaction      Bob Lichtenbert's aphorisms: "I'm so glad when other people respond to me." Somebody responded to me and I was surprised that they didn't change the subject.1441

          Consider what I need to do myself      And given that I need to pay taxes in both Lithuania and the United States I think that I should do all the paperwork myself because I need to be on top of it myself and there is nobody here who knows both systems anyways.1054

               Millstone in Matthew      Matthew 18:1 In that hour the disciples came to Jesus, saying, "Who then is greatest in the Kingdom of Heaven?" 18:2 Jesus called a little child to himself, and set him in their midst, 18:3 and said, "Most certainly I tell you, unless you turn, and become as little children, you will in no way enter into the Kingdom of Heaven. 18:4 Whoever therefore humbles himself as this little child, the same is the greatest in the Kingdom of Heaven. 18:5 Whoever receives one such little child in my name receives me, 18:6 but whoever causes one of these little ones who believe in me to stumble, it would be better for him that a huge millstone should be hung around his neck, and that he should be sunk in the depths of the sea.1254

        Align

Align      1072

          How will you be judged?      Matthew 7:1 "Don't judge, so that you won't be judged. 7:2 For with whatever judgment you judge, you will be judged; and with whatever measure you measure, it will be measured to you. 1467

          Who is more valuable      Matthew 6:25 Therefore I tell you, don't be anxious for your life: what you will eat, or what you will drink; nor yet for your body, what you will wear. Isn't life more than food, and the body more than clothing? 6:26 See the birds of the sky, that they don't sow, neither do they reap, nor gather into barns. Your heavenly Father feeds them. Aren't you of much more value than they? 1452

          Stretching things      Three women check into a motel room which advertises a rate of $27 per night. They each give $10 to the porter, and ask her to bring back 3 dollar bills. The porter returns to the desk, where she learns that the room is actually only $25 per night. She gives $25 to the motel desk clerk, returns to the room, and gives the guests back each one dollar, deciding not to tell them about the actual rate. Thus the porter has pocketed $2, while each guest spent 10-1 = $9, a total of 2 + 3 x 9 = $29. What happened to the other dollar? ... try stretching things a bit: what if the actual room rate had been $0? Then the porter would pocket $27 and the guests would spend $27, which adds up to $54! pg. 22, 102, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1649

          Topologically equivalent      ... the original problem was almost immediately equivalent to the modified easier version. That happened for a mathematical reason: the problem was a "topological" one. This "trick" of mutating a diagram into a "topologically equivalent" one is well worth remembering. pg.19, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1418

        Pursue

Pursue      1073

          Considering a principle's consequences      513

          Are works truly good?      Matthew 7:22 Many will tell me in that day, 'Lord, Lord, didn't we prophesy in your name, in your name cast out demons, and in your name do many mighty works?' 7:23 Then I will tell them, 'I never knew you. Depart from me, you who work iniquity.' 1494

          Do they make life easier or harder?      Matthew 23:4 For they bind heavy burdens that are grievous to be borne, and lay them on men's shoulders; but they themselves will not lift a finger to help them. 1549

          No good tree brings forth rotten fruit      Luke 6:43 For there is no good tree that brings forth rotten fruit; nor again a rotten tree that brings forth good fruit. 6:44 For each tree is known by its own fruit. For people don't gather figs from thorns, nor do they gather grapes from a bramble bush. 1359

          The tree is known by the fruit.      Matthew 7:15 "Beware of false prophets, who come to you in sheep's clothing, but inwardly are ravening wolves. 7:16 By their fruits you will know them. Do you gather grapes from thorns, or figs from thistles? 7:17 Even so, every good tree produces good fruit; but the corrupt tree produces evil fruit. 7:18 A good tree can't produce evil fruit, neither can a corrupt tree produce good fruit. 7:19 Every tree that doesn't grow good fruit is cut down, and thrown into the fire. 7:20 Therefore by their fruits you will know them.1489

          Whether they succeed      Matthew 17:19 Then the disciples came to Jesus privately, and said, "Why weren't we able to cast it out?" 17:20 He said to them, "Because of your unbelief. For most certainly I tell you, if you have faith as a grain of mustard seed, you will tell this mountain, 'Move from here to there,' and it will move; and nothing will be impossible for you. 17:21 But this kind doesn't go out except by prayer and fasting."2045

          Who is worthy?      Matthew 10:11 Into whatever city or village you enter, find out who in it is worthy; and stay there until you go on.1783

          Geometric series tool      Let 1=a0=a1=a2=... Then the corresponding generating function is just 1 + x + x**2 + x**3 + ... This is an infinite geometric series which converges to 1/(1-x), provided that |x|<1 pg.144, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.2165

          Appreciating that I could have been born anybody      As a child, I realized that I was profoundly happy, but that it was not of my own merits. I could have been born in Cambodia, defenseless and left to die or be killed. Therefore I thought that my happiness, gifts and talents were not meant simply to serve me, to keep me happy, but rather, to serve absolutely everybody, for I could have been anybody. How could I serve us all? What would others want me to do?1300

          What is fruitful is positive      Sometimes, as my debts grew, I would wonder if I should have foresworn from ever going into debt. But time and again I realized that the pressure of my debts kept me from sitting still, from stagnating, and forced me to be enormously creative in ways that I probably would not have been otherwise. I realized that it was good, just as negative numbers are good, because they open up more possibilities.1108

          Learning from experience whether something was worthwhile      When I was seven years old my parents gave me seventy five cents and I decided to spend it to go up the Space Needle. It was something I really wanted to do. But then I cried and they asked why, wasn't I happy? And I said, yes, it was good but it wasn't worth seventy five cents. I had thought that it would be a life time experience and then felt disappointed that it wasn't and it was over and I could have gotten some army soldiers instead.1040

        Let things unfold

Let things unfold      150

          Analogy of God to us as parent to children      Matthew 7:11 If you then, being evil, know how to give good gifts to your children, how much more will your Father who is in heaven give good things to those who ask him!1480

          Are we the same or different?      Matthew 23:8 But don't you be called 'Rabbi,' for one is your teacher, the Christ, and all of you are brothers. 1552

          Planning      Matthew 16:18 I also tell you that you are Peter, and on this rock I will build my assembly, and the gates of Hades will not prevail against it. 16:19 I will give to you the keys of the Kingdom of Heaven, and whatever you bind on earth will have been bound in heaven; and whatever you release on earth will have been released in heaven."1328

          The Jewish prophets are the Kingdom of Heaven      Jesus calls the Jewish people "the children of the Kingdom of Heaven" and says that Abraham, Isaac and Jacob will be in the Kingdom of Heaven. But this means that Abraham, Isaac and Jacob are already in the Kingdom of Heaven and even define the Kingdom of Heaven. Therefore the "children" ethnically are not necessarily the children spiritually. Jesus is, it seems, discovering this distinction. Note also that Isaac is the child of Abraham, and Jacob is the child of Isaac. Matthew 8:11 I tell you that many will come from the east and the west, and will sit down with Abraham, Isaac, and Jacob in the Kingdom of Heaven, 8:12 but the children of the Kingdom will be thrown out into the outer darkness. There will be weeping and gnashing of teeth.1606

          Whether Jesus or Satan has them      Jesus prayed that Peter's faith not fail. Luke 22:31 The Lord said, "Simon, Simon, behold, Satan asked to have you, that he might sift you as wheat, 22:32 but I prayed for you, that your faith wouldn't fail. You, when once you have turned again, establish your brothers."2075

          Who revealed this      Matthew 16:15 He said to them, "But who do you say that I am?" 16:16 Simon Peter answered, "You are the Christ, the Son of the living God." 16:17 Jesus answered him, "Blessed are you, Simon Bar Jonah, for flesh and blood has not revealed this to you, but my Father who is in heaven. 16:18 I also tell you that you are Peter, and on this rock I will build my assembly, and the gates of Hades will not prevail against it. 16:19 I will give to you the keys of the Kingdom of Heaven, and whatever you bind on earth will have been bound in heaven; and whatever you release on earth will have been released in heaven."1998

          Geometric symmetry      The simplest geometric symmetries are rotational and reflectional. pg. 71 The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1582

          Invariant with respect to transformations      this topic [symmetry] is logically contained within the concept of invariants. If a particular object (geometrical or otherwise) contains symmetry, that is just another way of saying that the object itself is an invariant with respect to some transformation or set of transformations. For example, a square is invariant with respect to rotations about its center of 0, 90, 180 and 270 degrees. pg. 103, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1646

     Capture with a personal expression      1589

          Consider how a word is used in other passages     Is God good? Jesus in the Gospels seems to speak in a private language, a personal code, much as I think in my philosophy. I find that about a third of his sayings are unclear as to their meaning. I look for other passages where he uses the same word or image or idea and that helps me decode what I think he means. In the Gospel of John, I traced down that the "Son of Man" means one who is taught by man, and man teaches by making an example out of him. I did a comprehensive review of Jesus's words in the Gospel of John and how he uses and explains his words, I chased them down and found that they centered on doing the will of God, which is that we have eternal life. With further contemplation, I concluded that "life is the fact that God is good, but eternal life is understanding that fact, that God need not be good." Similarly, I've tried to decode Kant's Critique of Pure Reason and the beginning of Heidegger's Being and Time. As I do that, I look for approaches and structures that I myself have uncovered in my own thinking. I think a similar approach led to the decoding of the Rosetta stone and of the Egyptian hieroglyphics as well as many others.1725

          Visualizing my feelings      In 1992, I was devastated because the woman I loved with all my heart, but hadn't been in love with me, returned to her home in Lithuania and married a man she loved, but who hadn't been in love with her. Sometimes I would visualize how I felt. I felt that I was in a deep abyss, so far down that I couldn't even see or imagine the light above, and the abyss went down, down, down. But over the months, as I chugged along, I started to feel the light; I started to imagine the edge of the cliff; I was still down below, but I knew there was a pasture above that edge; that was about six months later. And then one day I felt that I was over the edge.1230

        Match inner and outer worlds through person-in-general

Match inner and outer worlds through person-in-general      1525

          Defining basic terms      Bob Lichtenbert, Seekers' Dialogue on Motivating For More Meaning Let's start at the same place that we always ought to and do begin, namely, with a definition of boundary setting on basic terms. Now by "motivating" I shall primarily mean "moving another person to care or be interested or do in anything". I am mostly interested in personal motivation in the psychological and philosophical (or value) senses. So "motivation" as I mean it here in general is "to arouse others toward goal-directed behavior".1712

          Make myself vulnerable to others' standards of behavior      I would lend money to my friends and have them pay off my own loans, thus hurting my credit rating. I felt that I was helping by letting them make good use of my credit. And that I shouldn't have to be after them as they should be on top of things. But none of them were perfect as to that. I suppose it's important to keep on top of the use of credit if you're going to share it, you have to manage that.1057

        Our message

Our message      153

        Valuation

Valuation      Giving and Taking are in sync when we Live As If We Were All One Person. We can then substitute for ourselves with Valuation. Such a substitution (much like a model substituting for reality) takes place on four levels:

  • Peace of mind (A decision substitutes for the decision maker.)
  • Motivation (External motivation substitutes for internal motivation.)
  • Money (Compensation substitutes for disparity in contributions.)
  • Humility (Autonomy substitutes for morality)
In the case of "peace of mind", we conflate ourselves with our avatar, which is to say, as decision maker we are one with our decisions. Whereas, in "humility", we divorce ourselves from our avatar. If people truly want to hang themselves, or be fat, drunk, stupid, mean, sick, ugly, filthy, destructive, uptight, hurtful, if they truly want that, then we'll sell them the rope in whatever color they want. (Yes, I get stuck at that point. Perhaps I doubt if they are truly free.)1101

          Compassion for what they may suffer      Matthew 15:32 Jesus summoned his disciples and said, "I have compassion on the multitude, because they continue with me now three days and have nothing to eat. I don't want to send them away fasting, or they might faint on the way."1993

          Argument by contradiction      Instead of directly trying to prove something, we start by assuming that it is false, and show that this assumption leads us to an absurd conclusion. A contradiction argument is usually helpful for proving directly that something cannot happen. ... When you begin thinking about a problem, it is always worth asking, What happens if we negate the conclusion? Will we have something that is easier to work with? If the answer is "yes", then try arguing by contradiction. pg.46, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1439

     Confronting my own outlook      1593

        Gut feeling

Gut feeling      1680

          Following what makes me feel uncomfortable      Jerry Michalski of The REXpedition: The genesis of my Relationship Economy thesis was a realization, back around 1994 when I was writing Esther Dyson's monthly tech newsletter Release 1.0, that the word "consumer" made me really uncomfortable. I followed that energy, and it proved invaluable. Ideas kept unfolding from that initial premise. I began to notice the consumerization of so many spheres of human activity, from how we educate our children to how we elect our governments and how we pray to our Gods. I paid attention to the language of marketing to consumers, to the metaphors and business models that had spun out as a result.1755

        Peace of mind

Peace of mind      A decision substitutes for the decision maker. They are conflated. Whether there is value.1078

          Noting changes over time      We took in a lady I knew from the streets, helped her quit drinking, and took her in for two years and she worked as a cleaning lady. But then I drove her out because I thought that she should move on, as she was not active in the club's activity with the youth, but just wanted them to stay away so the club would stay clean, and didn't want to do anything more with her life.1037

          Analogy with society      Luke 18:1 He also spoke a parable to them that they must always pray, and not give up, 18:2 saying, "There was a judge in a certain city who didn't fear God, and didn't respect man. 18:3 A widow was in that city, and she often came to him, saying, 'Defend me from my adversary!' 18:4 He wouldn't for a while, but afterward he said to himself, 'Though I neither fear God, nor respect man, 18:5 yet because this widow bothers me, I will defend her, or else she will wear me out by her continual coming.'" 18:6 The Lord said, "Listen to what the unrighteous judge says. 18:7 Won't God avenge his chosen ones, who are crying out to him day and night, and yet he exercises patience with them? 18:8 I tell you that he will avenge them quickly. Nevertheless, when the Son of Man comes, will he find faith on the earth?"2058

          Does the outside match the inside?      Matthew 7:15 "Beware of false prophets, who come to you in sheep's clothing, but inwardly are ravening wolves.1488

          How things appear on the inside and the outside      Matthew 23:27 "Woe to you, scribes and Pharisees, hypocrites! For you are like whitened tombs, which outwardly appear beautiful, but inwardly are full of dead men's bones, and of all uncleanness. 23:28 Even so you also outwardly appear righteous to men, but inwardly you are full of hypocrisy and iniquity. 1561

          Telling only his disciples      Matthew 16:20 Then he commanded the disciples that they should tell no one that he was Jesus the Christ. 1330

          Whose seat they sat on?      What does it mean, to sit in Moses' seat? Matthew 23:1 Then Jesus spoke to the multitudes and to his disciples, 23:2 saying, "The scribes and the Pharisees sat on Moses' seat. 23:3 All things therefore whatever they tell you to observe, observe and do, but don't do their works; for they say, and don't do.1548

     Jesus speaks so they are free to understand or not      2029

          Jesus wanted people to understand him of their own      Matthew 11:15 He who has ears to hear, let him hear. Luke 8:8 As he said these things, he called out, "He who has ears to hear, let him hear!"1370

          Speaking in parables      Jesus spoke in parables so that people would be free to understand him or not, as they themselves chose. He does not force them to understand, and thus to believe, which would be the case if he spoke clearly. Thus he speaks plainly to those who already believe. Matthew 13:10 The disciples came, and said to him, "Why do you speak to them in parables?" 13:11 He answered them, "To you it is given to know the mysteries of the Kingdom of Heaven, but it is not given to them. 13:12 For whoever has, to him will be given, and he will have abundance, but whoever doesn't have, from him will be taken away even that which he has. 13:13 Therefore I speak to them in parables, because seeing they don't see, and hearing, they don't hear, neither do they understand. 13:14 In them the prophecy of Isaiah is fulfilled, which says, 'By hearing you will hear, and will in no way understand; Seeing you will see, and will in no way perceive: 13:15 for this people's heart has grown callous, their ears are dull of hearing, they have closed their eyes; or else perhaps they might perceive with their eyes, hear with their ears, understand with their heart, and should turn again; and I would heal them.' 13:16 "But blessed are your eyes, for they see; and your ears, for they hear. 13:17 For most certainly I tell you that many prophets and righteous men desired to see the things which you see, and didn't see them; and to hear the things which you hear, and didn't hear them.1237

          Who to give peace to      Peace is invasive, apparently. It shouldn't be forced upon others. Matthew 10:13 If the household is worthy, let your peace come on it, but if it isn't worthy, let your peace return to you.1785

     Miracles allow for belief and unbelief      2033

     What distinguishes the cultures      2032

          Do people and Jesus truly know each other?      Matthew 7:22 Many will tell me in that day, 'Lord, Lord, didn't we prophesy in your name, in your name cast out demons, and in your name do many mighty works?' 7:23 Then I will tell them, 'I never knew you. Depart from me, you who work iniquity.' 1493

          Do what I say and you are unshakeable      Luke 6:46 "Why do you call me, 'Lord, Lord,' and don't do the things which I say? 6:47 Everyone who comes to me, and hears my words, and does them, I will show you who he is like. 6:48 He is like a man building a house, who dug and went deep, and laid a foundation on the rock. When a flood arose, the stream broke against that house, and could not shake it, because it was founded on the rock. 6:49 But he who hears, and doesn't do, is like a man who built a house on the earth without a foundation, against which the stream broke, and immediately it fell, and the ruin of that house was great."1361

          What distinguishes the ways to life and to destruction?      The gate of "belief" leads to life; the gate of "caring" leads to destruction. We can distinguish the gates by seeing who goes through them. Matthew 7:13 "Enter in by the narrow gate; for wide is the gate and broad is the way that leads to destruction, and many are those who enter in by it. 7:14 How narrow is the gate, and restricted is the way that leads to life! Few are those who find it. 1485

          What is the difference between cultures?      Matthew 10:16 "Behold, I send you out as sheep in the midst of wolves. 1787

          Recast a problem from one domain into another domain      The powerful idea of converting a problem from words to pictures is just one aspect of the fundamental peripheral vision strategy. Open your mind to other ways of reinterpreting problems. ... what appeared to be a sequence of numbers was actually a sequence of descriptions of numbers ... Another example was the locker problem in which a combinatorial problem metamorphosed into a number theory lemma. "Combinatorics <=> Number Theory" is one of the most popular and productive such "crossovers", but there are many other possibilities. Some of the most spectacular advances in mathematics occur when someone discovers a new reformulation for the first time. pg. 60 The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1507

          Recognizing the impact of external motivation      In junior high school and high school I and my brother played actively in adult tournaments. The stronger tournaments were for money. The money seemed to suggest a very different way of playing that was foreign to me and so I put it out of my mind. It seemed to interfere with the idea of trying to go up against the best players rather than win a prize amongst the weaker players.1063

               The land of Galilee shall be exalted      Isaiah 9:1 But there shall be no more gloom for her who was in anguish. In the former time, he brought into contempt the land of Zebulun and the land of Naphtali; but in the latter time he has made it glorious, by the way of the sea, beyond the Jordan, Galilee of the nations. 9:2 The people who walked in darkness have seen a great light. Those who lived in the land of the shadow of death, on them the light has shined. 9:3 You have multiplied the nation. You have increased their joy.1956

          Correction of our self-conception      Matthew 23:12 Whoever exalts himself will be humbled, and whoever humbles himself will be exalted. 1557

          What follows from what?      Matthew 6:31 "Therefore don't be anxious, saying, 'What will we eat?', 'What will we drink?' or, 'With what will we be clothed?' 6:32 For the Gentiles seek after all these things; for your heavenly Father knows that you need all these things. 6:33 But seek first God's Kingdom, and his righteousness; and all these things will be given to you as well. 1461

          Why are you anxious?      Matthew 6:28 Why are you anxious about clothing? Consider the lilies of the field, how they grow. They don't toil, neither do they spin, 6:29 yet I tell you that even Solomon in all his glory was not dressed like one of these. 6:30 But if God so clothes the grass of the field, which today exists, and tomorrow is thrown into the oven, won't he much more clothe you, you of little faith? 1454

     What sanctifies      2037

          Who regards what is holy or valuable?      Matthew 7:6 "Don't give that which is holy to the dogs, neither throw your pearls before the pigs, lest perhaps they trample them under their feet, and turn and tear you to pieces. 1476

          Heighten the contrast of statements pulling us in opposite directions      On any abstract topic, contrasting truths of the heart and of the world arise, so that they pull in opposite directions, they suggest opposite actions. I heighten that contrast.1652

          An action that others will understand later      12:14 Jesus, having found a young donkey, sat on it. As it is written, 12:15 "Don't be afraid, daughter of Zion. Behold, your King comes, sitting on a donkey's colt." 12:16 His disciples didn't understand these things at first, but when Jesus was glorified, then they remembered that these things were written about him, and that they had done these things to him. Zechariah 9:9 Rejoice greatly, daughter of Zion! Shout, daughter of Jerusalem! Behold, your King comes to you! He is righteous, and having salvation; lowly, and riding on a donkey, even on a colt, the foal of a donkey.1966

          Foretelling      Jesus foretells several events that came to pass, and several that may still come to pass. How did he know? Did he gather that from the Scripture? Or his knowledge of God?1246

          Led by the Spirit into temptation by the devil      Matthew 4:1 Then Jesus was led up by the Spirit into the wilderness to be tempted by the devil.1317

          Remind of what he said beforehand      Luke 24:44 He said to them, "This is what I told you, while I was still with you, that all things which are written in the law of Moses, the prophets, and the psalms, concerning me must be fulfilled." 24:45 Then he opened their minds, that they might understand the Scriptures. 24:46 He said to them, "Thus it is written, and thus it was necessary for the Christ to suffer and to rise from the dead the third day, 24:47 and that repentance and remission of sins should be preached in his name to all the nations, beginning at Jerusalem. 24:48 You are witnesses of these things. 2088

          Requesting of Father, if it is possible      Jesus sees the distinction between his desires and God's desires. Matthew 26:39 He went forward a little, fell on his face, and prayed, saying, "My Father, if it is possible, let this cup pass away from me; nevertheless, not what I desire, but what you desire."1245

          What is written in the prophets      There will be a culture of the righteous. Isaiah 54:13 All your children shall be taught of Yahweh; and great shall be the peace of your children. 54:14 In righteousness you shall be established: you shall be far from oppression, for you shall not be afraid; and from terror, for it shall not come near you. John 6:45 It is written in the prophets, 'They will all be taught by God.' Therefore everyone who hears from the Father, and has learned, comes to me. 6:46 Not that anyone has seen the Father, except he who is from God. He has seen the Father. 1964

          Draw a picture      I imagine that drawing a picture brings out its inner logic at the level of "icon" or "what". Central to the open-minded attitude of a "creative" problem solver is an awareness that problems can and should be reformulated in different ways. Often, just translating something into pictorial form does wonders. pg.59, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1502

          Drawing the monk problem      A monk climbs a mountain. He starts at 8 am and reaches the summit at noon. He spends the night on the summit. The next morning, he leaves the summit at 8am and descends by the same route he used the day before, reaching the bottom at noon. Prove that there is a time between 8 am and noon at which the monk was at exactly the same spot on the mountain on both days One solution is to draw the paths on a distance-time graph, which makes it clear that the paths must cross and so they must meet. The pictures brings out the two conditions and shows how they come together. pg.19, 59 The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1504

          Learning what is useful or not for whom      After my freshman year my father arranged that I work the summer as an intern for his employer, Hughes Aircraft. There wasn't much for me to do there where I was assigned so I took the chance to teach myself programming, namely, Fortran. My supervisor wanted me to create a graphing program for him but I didn't have any real guidance and so I ended up focusing on what I thought was the coolest thing I could do, which was making a program for graphing derivatives of trigonometric functions, which was absolutely useless practically. So I made sure to gain from the experience, but it was a waste for my supervisor and they didn't have me back.1005

     Models of Multiplication      Six ways of thinking of multiplication: Fractal, Proportion, Tally, Box, Label, Divide out. (Andrius thinking out loud) I think that the six pairs of levels, six kinds of variables, six Zermelo-Frankel axioms of set theory can be illustrated by models of multiplication as Maria Droujkova has been studying. Question: What does it mean to cancel out units as physicists do?

  • The addition rule is at work, adding exponents. Multiplying by 10 or dividing by 10 shifts the number with regard to the decimal point, although it looks like the decimal point is moving. We may think of this as simply changing the units, the base unit.
  • I think of rescaling as a product of actions that either make bigger (numerator) or make smaller (denominator). They are all multiplying against some unknown, acting upon it. I call the actions "multiplication drops", either "magnifying drops" (say, multiplying by 10) or "shrinking drops" (dividing by 10). So these are actions x actions x (object with units). Thus magnifying and shrinking can cancel out. Also, actions can be decomposed into component actions, into primes.
  • Repeated addition is a recounting, a shift from larger units to smaller units. 3 x (23 x dollars) becomes (3 x 23) x dollars. Amount x (large unit) becomes action x (amount x small unit) becomes (action x amount) x small unit becomes amount x small unit.
  • Multiplication can give the ways of matching units, multiple units times multiple units, as in box multiplication, accounting for all possibilities. Units times units means that conditions are satisfied, thus generating all of the solutions.
  • Multiplication can be thought of as counting items that have been grouped where each group has the same number of items. For example, we can count coins by grouping together the pennies, nickels, dimes, quarter, placing them in rows or groups of 4 or 5 or 10. Number x (Value x Unit).
  • Dividing out, for example, money per person. This is like multiple units. (Number of cycles) x (Number of people x Units )
1531

        Experiencing

Experiencing      1684

               The Algebra of Copyright      An example of the 6+4 model is in my paper The Algebra of Copyright, see especially the diagram which I got to present to Joseph Goguen's class because I related it to his algebraic semiotics of user interface design. (Yes, he was brilliant! and a great shame that he passed away.) 1705

          Empathize with the fearful      Matthew 8:25 They came to him, and woke him up, saying, "Save us, Lord! We are dying!" 8:26 He said to them, "Why are you fearful, O you of little faith?"1619

          Fractal multiplication: Recopying the whole      A whole can be recopied (however many copies), then again, then again. This is like fractal multiplication, as with your five-legged starfish whose each leg holds another five-legged starfish. It is like multiplying by powers of 10. The addition rule is at work, adding exponents as in (10**2)(10**3) = 10**5. Multiplying by 10 or dividing by 10 shifts the number with regard to the decimal point, although it looks like the decimal point is moving. We may think of this as simply changing the units, the base unit, which may be unknown.1526

        Empathize - Implicitly Understand

Empathize - Implicitly Understand      171

          Become aware that a formula is at work      When I was in junior high school I used to spend my allowance on Mad magazine. It seemed at first like very intelligent, fresh, stimulating humor and I very much looked forward to it. But over time the formula became apparent. And after a few years I became disappointed and finally lost interest and stopped buying it. I went through the same cycle with Newsweek and other publications, where what originally seemed fresh turned out to be an editorial formula that grew stale with familiarity.1004

          Set a price      I sold my car. It was a practical car, well kept and I tried to get the blue book price. Somebody wanted to buy it but they were hoping I would go down and I refused to. I thought those prices were accurate. So instead I ultimately sold it for quite a bit lower than that, to a friend.1058

               All parabolas have the same shape      I've found in teaching the quadratic equations (and searching for a use for them) that the parabola is arguably an ideal curve for learning to graph. That's because all parabolas have one and the same shape, if you discount zooming in and out. Each parabola, if you zoom in, will look flat, and if you zoom out, will look narrow, in exactly the same proportions. You can see this if you substitute x -> ax and y->ay and thereby you can transform x = y**2 to xa = y**2 a**2 so x = a y**2 effectively where a can be as you like. This means that all parabolas look the same and their graphs differ only in how you move them around, up and down, left or right, negative or positive, zoom in or zoom out. Also, I teach my students to draw too graphs because most never realize how the parabola completely flattens out at the bottom where -1 < x < 1. It's a bit like filming a movie where you have to combine full length shots of people with head shots. One shot won't do it. Gospel Math.1841

               Axiom of extensionality      Wikipedia: Two sets are equal (are the same set) if they have the same elements. Note that there are thus two levels of equality. Equality is a bidirectional relationship. And the two levels are like levels of an atlas. An atlas defines, at different levels, what can be consider the "same" point or location from far away, though may be different from close up. The "equivalence" and equivalence classes may be "turned on or off" selectively in the atlas.1164

          Graph      Just about any situation involving "relationships" and "objects" can be recast as a graph, where the vertices are the "objects" and we join vertices with edges if the corresponding objects are "related". pg.120, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc. 1752

               Sleeping mathematicians      During a certain lecture, each of five mathematicians fell asleep exactly twice. For each pair of these mathematicians, there was some moment when both were sleeping simultaneously. Prove that, at some moment, some three of them were sleeping simultaneously. pg.120, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc. 1753

          Completing a structure by comparing it to a known template      The divisions of everything help me to recognize and complete many structures. For example, Peirce's three kinds of signs (symbol, index, icon) match with three of the four levels of the foursome. I have noticed that very often, philosophers give only three of the four levels because if they are working from a materialist representation, then Why is irrelevant, and if from an idealist representation, then Whether is irrelevant. Thus Why and Whether are null perspectives for the relevant representations. They are the baselines which the others are thought in terms of.1445

               Basket for Jerry      Dave Gray reimagines Jerry Michalski's geometry of knowledge. He draws it as a basket. The idea here is about the advance of knowledge. The spines are the various disciplines which must necessarily diverge as we attempt to understand a universe where the unknown always exceeds the known. ... The horizontal weaving strands are the threads we weave as we attempt to connect the various disciplines. ... Without the weaving the spines just lay flat on the ground and radiate out. And without the spines the basket is just a coiled garden hose on the ground. ... Over time it holds more and more meaning, life, knowledge and goodness. It's a cornucopia! :)1760

        Be perfect.

Be perfect.       Matthew 5:43 "You have heard that it was said, 'You shall love your neighbor, and hate your enemy.' 5:44 But I tell you, love your enemies, bless those who curse you, do good to those who hate you, and pray for those who mistreat you and persecute you, 5:45 that you may be children of your Father who is in heaven. For he makes his sun to rise on the evil and the good, and sends rain on the just and the unjust. 5:46 For if you love those who love you, what reward do you have? Don't even the tax collectors do the same? 5:47 If you only greet your friends, what more do you do than others? Don't even the tax collectors do the same? 5:48 Therefore you shall be perfect, just as your Father in heaven is perfect. 1262

          Be merciful as your Father is merciful      Luke 6:36 Therefore be merciful, even as your Father is also merciful. 6:37 Don't judge, and you won't be judged. Don't condemn, and you won't be condemned. Set free, and you will be set free.1352

          Distinguish the living and the dead based on their priorities      Matthew 8:21 Another of his disciples said to him, "Lord, allow me first to go and bury my father." 8:22 But Jesus said to him, "Follow me, and leave the dead to bury their own dead." 1617

          What distinguishes the Gentiles and God?      Matthew 6:31 "Therefore don't be anxious, saying, 'What will we eat?', 'What will we drink?' or, 'With what will we be clothed?' 6:32 For the Gentiles seek after all these things; for your heavenly Father knows that you need all these things.1459

        Threesome: How-What

Threesome: How-What      1515

          Standard Fisher Linear Discriminant Function      Given the Regularized Linear Discriminant Analysis, when t goes to infinity, then we get the Fisher discriminant function. The standard Fisher linear discriminant function was proposed by Fisher in 1936. It is the first known classification rule. In 1951, Anderson showed that it can be obtained from optimal statistical decision function theory. We assume multivariate Gaussian classes with a common covariance matrix (GCCM). Into the model we insert maximum likelihood sample estimates instead of unknown parameters. The Fisher rule requires the inversion of a sample-based covariance matrix. This is problematic when we have a small learning set and large dimensionality. The adaline linear classifier of Widrow and Hoff is identical to the Fisher rule when we have the same number of learning vectors from both competing classes. (See: Sarunas Raudys, Evolution and generalization of a single neurone: I. Single-layer perceptron as seven statistical classifiers", Neural Networks 11 (1998) 283-296)1386

        Negotiate

Negotiate      Would it make any difference? Negotiate. The motivated Servant provides the rich Served with choices, priorities, contracts.1091

          Give priority to what is most real      My priorities are to make sure that the government has my money, to turn in my declarations, to keep a record of my receipts, and only then to go through the artifice of keeping formal books. I said also that my income comes primarily from the United States and since I had to abide by both systems, I gave priority to the United States.1017

        Compare

Compare      154

        Let your 'Yes' be Yes and your 'No' be No

Let your 'Yes' be Yes and your 'No' be No      What is more than 'yes' and 'no' are conditionals 'if', counterfactuals, as by which Satan tempted Jesus. Matthew 5:33 "Again you have heard that it was said to them of old time, 'You shall not make false vows, but shall perform to the Lord your vows,' 5:34 but I tell you, don't swear at all: neither by heaven, for it is the throne of God; 5:35 nor by the earth, for it is the footstool of his feet; nor by Jerusalem, for it is the city of the great King. 5:36 Neither shall you swear by your head, for you can't make one hair white or black. 5:37 But let your 'Yes' be 'Yes' and your 'No' be 'No.' Whatever is more than these is of the evil one. 1264

          Reimagining the monk problem       A monk climbs a mountain. He starts at 8 am and reaches the summit at noon. He spends the night on the summit. The next morning, he leaves the summit at 8am and descends by the same route he used the day before, reaching the bottom at noon. Prove that there is a time between 8 am and noon at which the monk was at exactly the same spot on the mountain on both days One solution is to allow for two monks traveling, one up and the other down, so that it is clear they must meet. In this way the solution is where the two conditions are both satisfied. pg.19, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1503

          Fisher Linear Discriminant Function With Pseudoinverse Covariance Matrix      Starting with the Standard Fisher Linear Discriminant Function, we may then allow that the covariance matrix is not invertible. This is always the case when the number of learning samples is 2N < p + 2 If we write the weight vector in a certain way, then the weights approach the Fisher linear discriminant function with pseudoinverse covariance matrix. This assumes that the inputs of the activation function vary in the linear interval. We need to have non-limit target values abs(tj)<1. (See: Sarunas Raudys, Evolution and generalization of a single neurone: I. Single-layer perceptron as seven statistical classifiers", Neural Networks 11 (1998) 283-296)1387

          Allowing demons to do as they wish      Matthew 8:31 The demons begged him, saying, "If you cast us out, permit us to go away into the herd of pigs." 8:32 He said to them, "Go!" They came out, and went into the herd of pigs: and behold, the whole herd of pigs rushed down the cliff into the sea, and died in the water. 1625

               Axiom of union      Wikipedia: For any set F there is a set A containing every set that is a member of some member of F1163

               Two points a mile away      Every point on the plane is colored either red or blue. Prove that no matter how the coloring is done, there must exist two points, exactly a mile apart, which are the same color. ... imagine the vertices of an equilateral triangle with side length one mile. There are three vertices, but only two colors available! The pigeonhole principle tells us that two vertices must be the same color! pg.93, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1636

          Factoring      Here is a simple problem with a "complete" solution, illustrating one of the most important tactics: factoring. ... Find all right triangles with integer sides such that the perimeter and area are equal. ... xy/2 = x + y + square root of (x**2 + y**2) ... xy - 4x - 4y + 8 = 0 ... Now we do something clever: add 8 to both sides to make the left-hand side factor. We now have (x-4)(y-4) = 8, and since the variables are integers, there are only finitely many possibilities ... The only tricky step was finding the factorization. But this wasn't really hard, as it was clear that the original left-hand side "almost" factored. As long as you try to factor, it usually won't be hard to find the proper algebraic steps. The factor tactic is essential for finding solutions. pg.264-265 The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc2225

          Intermediate pigeonhole      If you have p pigeons and h holes, then at least one of the holes contains at least [p/h] pigeons. pg.94, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.1638

          Number theoretic functions      Of the infinitely many functions with domain N, we will single out a few that are especially interesting. Most of these functions are multiplicative ... f(ab) = f(a)f(b) whenever a and b are relatively prime ... Define sigma_r(n)= sum over divisors d of n of d**r ... Let F(n) = sum over divisors d of n of f(d). If f is multiplicative, then F will be multiplicative as well. Define phi(n) to be the number of positive integers less than or equal to n which are relatively prime to n. ... We can use the principle of inclusion-exclusion to evaluate phi(n) ... We define [the Mobius function] mu(n) = 1 if n=1, =0 if p**2 divides n for some prime p, = (-1)**r if n = p1p2...pr, each p a distinct prime. This is a rather bizarre definition, but it turns out that the Mobius function very conveniently "encodes" PIE. ... show that sum over divisors d of n of mu(d) = 1 if n=1; =0 if n>1. The values of mu(n) alternate sign depending on the parity of the number of prime factors of n. This is what makes the Mobius function related to PIE. ... phi(n) = sum over divisors d of n of mu(d)(n/d). pg.257-261 The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc2221

               Failing to sort messages from God      Once I failed miserably with this method. Almost every morning I listen to God and write down what he has to say. After several years, I tried to see if there were any patterns I could detect. However, the answers were so rich and intense that I kept getting dozens of dozens of groups, more and more as I added more data. I wasn't able to find an angle from which I could group his thoughts to me. He didn't seem too pleased, either.1541

               Why we change our minds      Joe Damal and I asked dozens of Chicago youth, Did you ever change your mind? and Why? and grouped the reasons into eight categories, which I then helped him structure.1537

          Generalized Fisher Discriminant Function      Starting with the Fisher Linear Discriminant Function With Pseudoinverse Covariance Matrix, if the target values differ from the limiting values, then the smallest deviations are obtained for medium size weights, and the activation function becomes a non-linear function, as does the non-decreasing odd and non-constant function phi (see Sarunas paper). The minimization of the cost function yields a linear classifier very similar to generalized discriminant analysis. (See: Sarunas Raudys, Evolution and generalization of a single neurone: I. Single-layer perceptron as seven statistical classifiers", Neural Networks 11 (1998) 283-296)1388

          Recognize the inapplicability of an idea      When I was six years old my parents opened a bank account for my birthday and deposited 10 dollars. And the next year they deposited 10 dollars, too. When my father would go to the bank he would take my book with him and they would stamp the amount of money that I had which reflected the interest I had earned, a few cents and yet it excited me that my money could grow exponentially. However, as I grew older there was inflation, but even more significantly, I realized that the older I grew as a child, the greater amounts of money I dealt with, and so it was completely absurd to save money. Finally, my parents let me take out the money and spend it. I bought an electronics kit that I had wanted. But I realized that 10 dollars had much less significance to a 12 year old than to a 6 year old. That experience made me very skeptical about the value of saving. I felt negative and so I changed my principles.1003

          Offspring of vipers      Is the viper a reference to the serpent of Genesis who tempted Adam and Eve? Matthew 23:33 You serpents, you offspring of vipers, how will you escape the judgment of Gehenna?1574

          Who was responsible for the commandments?      Matthew 19:7 They asked him, "Why then did Moses command us to give her a bill of divorce, and divorce her?" 19:8 He said to them, "Moses, because of the hardness of your hearts, allowed you to divorce your wives, but from the beginning it has not been so. 1267

          Eulerian Path      Find the conditions on a connected graph (or multigraph) for which it is possible to travel a path that traverses every edge exactly once. Such paths are called Eulerian ... A connected graph (or multigraph) possesses an Eulerian path if and only if it has zero or exactly two odd-degree vertices. In the former case, the path is a closed path. In the latter, the path must begin and end at the odd-degree vertices. pg.123-124, The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc.2158

          Viewing a problem modulo m      Viewing a problem modulo m for a suitably chosen m is a wonderful simplification tactic because it reduces the infinite universe of integers to the finite world of Zm. You have encountered this idea before with parity ... which is just the case m=2 ... Often (but not always) we turn to prime values of m, since primes are simpler, more "fundamental" objects which are generally easier to understand. In general, When beginning a number theory investigation, assume that the variables are prime or at least relatively prime. Often the general case follows from the prime case, with just a few "technical" details. ... Fermat's Last Theorem. Let n>=3. Prove that the equation x**n + y**n = z**n has no non-zero integer solutions. ... we shall point out two simplifications ... Without loss of generality, n is prime ... we may assume that ... x, y, z have no common factor (other than 1). ... One reason that primes are so convenient is that unique "multiplicative inverses" exist. Viewing modulo m emphasizes the closed nature of a system. pg.252-253 The Art and Craft of Problem Solving, Paul Zeitz, 1999, John Wiley & Sons, Inc2219

          Minimum Empirical Error Classifier      When the limit values are the targets, then for two distant classes it is possible to obtain very high weights upon applying the minimizing cost function. Then the activation function is acting as a hard limiting threshold function. If one avoids local minima by using global minimization techniques, then one obtains a classifier similar to the minimum empirical error classifier. (See: Sarunas Raudys, Evolution and generalization of a single neurone: I. Single-layer perceptron as seven statistical classifiers", Neural Networks 11 (1998) 283-296)1389

          Recognizing justice in reciprocity      After the war in Soviet-occupied Lithuania our grandparents had very little money yet they still sent packages to their relatives back home including old suits and shoes and cloth. This made a big difference to the families' well being. Years later when my grandmother was sick in bed her nieces were very happy to take turns to come out and take care of her. So on the one hand they were illegal workers but on the other hand it was a beautiful reciprocity.1042

          Fulfill all righteousness      Matthew 3:13 Then Jesus came from Galilee to the Jordan to John, to be baptized by him. 3:14 But John would have hindered him, saying, "I need to be baptized by you, and you come to me?" 3:15 But Jesus, answering, said to him, "Allow it now, for this is the fitting way for us to fulfill all righteousness." Then he allowed him. 1210

          Heaven confirms      Matthew 3:16 Jesus, when he was baptized, went up directly from the water: and behold, the heavens were opened to him. He saw the Spirit of God descending as a dove, and coming on him. 3:17 Behold, a voice out of the heavens said, "This is my beloved Son, with whom I am well pleased."1211

          How people of good will act so that others not reject them      Jesus and John choose their ways so that people might not reject them, although they do, even so. Matthew 11:16 "But to what shall I compare this generation? It is like children sitting in the marketplaces, who call to their companions 11:17 and say, 'We played the flute for you, and you didn't dance. We mourned for you, and you didn't lament.' 11:18 For John came neither eating nor drinking, and they say, 'He has a demon.' 11:19 The Son of Man came eating and drinking, and they say, 'Behold, a gluttonous man and a drunkard, a friend of tax collectors and sinners!' But wisdom is justified by her children." 1863

          Love your neighbor as yourself      Leviticus 19:18 "'You shall not take vengeance, nor bear any grudge against the children of your people; but you shall love your neighbor as yourself. I am Yahweh. ... Leviticus 19:33 "'If a stranger lives as a foreigner with you in your land, you shall not do him wrong. 19:34 The stranger who lives as a foreigner with you shall be to you as the native-born among you, and you shall love him as yourself; for you lived as foreigners in the land of Egypt. I am Yahweh your God.2021

          What makes things possible      Matthew 19:24 Again I tell you, it is easier for a camel to go through a needle's eye, than for a rich man to enter into the Kingdom of God." 19:25 When the disciples heard it, they were exceedingly astonished, saying, "Who then can be saved?" 19:26 Looking at them, Jesus said, "With men this is impossible, but with God all things are possible."2008

          Accepting our parents' values      I remember as a child we had to weed our garden every so often. It wasn't especially fun. And we weren't rewarded for it. It was just something that we were supposed to do. But there was something nice about doing that work conscientiously and feeling like part of the team, our family.1001

          Appreciate that the situation may change      Also, it's my position that laws are in flux and they may well change in my favor as I get to them.1055

        Engage God

Engage God      139

                    Creative constraint      Sometimes, as my debts grew, I would wonder if I should have foresworn from ever going into debt. But time and again I realized that the pressure of my debts kept me from sitting still, from stagnating, and forced me to be enormously creative in ways that I probably would not have been otherwise. I thought of it as a creative constraint that opened up my thinking, just as such constraints can in the creative arts.1107

     What is the nature of good?      I did a study of the Gospel of Matthew to see how Jesus variously uses the concept "good". He talks of: good heart, good God, good gift, good quality, good person, good deed, good word, good news.1240

               An angel told Joseph to flee to Egypt      Matthew 2:13 Now when they had departed, behold, an angel of the Lord appeared to Joseph in a dream, saying, "Arise and take the young child and his mother, and flee into Egypt, and stay there until I tell you, for Herod will seek the young child to destroy him."1179

               Fulfilled: Out of Egypt I called my son      Matthew 2:14 He arose and took the young child and his mother by night, and departed into Egypt, 2:15 and was there until the death of Herod; that it might be fulfilled which was spoken by the Lord through the prophet, saying, "Out of Egypt I called my son."1192

               God created the sky between the waters above and below      1:6 God said, "Let there be an expanse in the middle of the waters, and let it divide the waters from the waters."1120

               Jeremiah's prophecy fulfilled      Matthew 2:17 Then that which was spoken by Jeremiah the prophet was fulfilled, saying, 2:18 "A voice was heard in Ramah, lamentation, weeping and great mourning, Rachel weeping for her children; she wouldn't be comforted, because they are no more."1194

               Name the earth and seas      Genesis 1:10 God called the dry land "earth," and the gathering together of the waters he called "seas."1118

               Name the sky      Genesis 1:8 God called the expanse "sky."1117

               Plato's Cave      Plato considers an elaborate scenario where people sit in a cave and view projections which they purport to be real. (He invented movies for the purpose of this scenario!) A person ventures outside the cave and discovers the real world, then goes back to the others and tries to tell them of it, but they deride him.836

          Be warned in a dream      Matthew 2:12 Being warned in a dream that they shouldn't return to Herod, they went back to their own country another way.1189

          Confession      Matthew 3:6 They were baptized by him in the Jordan, confessing their sins.1201

          Counting the generations      Matthew 1:17 So all the generations from Abraham to David are fourteen generations; from David to the exile to Babylon fourteen generations; and from the carrying away to Babylon to the Christ, fourteen generations.1176

          Inquire      Matthew 2:7 Then Herod secretly called the wise men, and learned from them exactly what time the star appeared. 1185

          Jesus sorts out the good and the bad      Matthew 3:12 His winnowing fork is in his hand, and he will thoroughly cleanse his threshing floor. He will gather his wheat into the barn, but the chaff he will burn up with unquenchable fire."1208

          Judge the tree by the fruit      Matthew 3:7 But when he saw many of the Pharisees and Sadducees coming for his baptism, he said to them, "You offspring of vipers, who warned you to flee from the wrath to come? 3:8 Therefore bring forth fruit worthy of repentance! 1204

          Jörn Rüsen's disciplinary matrix      Jörn Rüsen's "disciplinary matrix" of historiography relates five factors: the cognitive interest of human beings in having an orientation in time; theories or "leading views" concerning the experiences of the past; empirical research methods; forms of representation; the function of offering orientation to society. See: "Jörn Rüsen's Theory of Historiography between Modernism and Rhetoric of Inquiry" by Alan Megill, Vol. 33, No. 1, Feb., 1994, History and Theory. Also: Istorika. Istorikos darbų rinktinė compiled by Zenonas Norkus.1307

          National psyche      When I think of the behavior of the Russian nation, especially its brutally domineering attitude towards Lithuania and other neighboring countries, then I wonder, where did that come from? And so I trace it back to the Mongol occupation of the Russian principalities, which was remembered as very brutal. I imagine that the subsequent history of the Russian nation as a whole is a reaction to that traumatic experience, much as an adult's behavior can sometimes be explained as a reaction to childhood experiences. It seems that feelings of national solidarity can carry down attitudes for centuries, long beyond the source of those attitudes is relevant. I think the Serbian nation similarly experienced were traumatized by the Turks. I think the Spanish nation was traumatized by the Moors, and attributed its victory to Catholicism, and thus pursued with zeal the Inquisition and missionary work in the New World. The American South, Black American and even the urban North of the United States deal with trauma of slavery and the end of the plantation culture. National psyche is the mindset that is attributed to a nation rather than to the individuals of the nation. The latter would be the ethnic character or cultural influences on people. The Wikipedia article on National Psychology confuses these.1313

          Not having sex      Matthew 1:24 Joseph arose from his sleep, and did as the angel of the Lord commanded him, and took his wife to himself; 1:25 and didn't know her sexually until she had brought forth her firstborn son.1182

          Removing himself      God thinks as he creates, and he creates by removing himself, thereby considering whether he would be even if he was not.1216

          See everything      Genesis 1:31 God saw everything that he had made, and, behold, it was very good. 1132

          Self-collaborate      Note the use of the plural "us". Genesis 1:26 God said, "Let us make man in our image, after our likeness: and let them have dominion... 1127

          Semiotic algebra of symbols      Semiotics is the study of symbols and can be used to study history, for example, who reacted to whom, who chose to use who's symbols, and who chose to use different or opposed symbols, and who chose to join symbols of various origins.1315

          Who is God's beloved Son      Matthew 3:17 Behold, a voice out of the heavens said, "This is my beloved Son, with whom I am well pleased."1213

          Who pleases      Matthew 3:17 Behold, a voice out of the heavens said, "This is my beloved Son, with whom I am well pleased."1212

          Who watches over us      Matthew 3:9 Don't think to yourselves, 'We have Abraham for our father,' for I tell you that God is able to raise up children to Abraham from these stones.1202

          Writing      Tom Mandel: Writing is my primary tool for investigating the world.1229

     Other ways: Philosophy      1138

          Amend the truth      Wikipedia about Badiou: While such knowledge is produced in the process of being faithful to a truth event, it should be noted that, for Badiou, knowledge, in the figure of the encyclopedia, always remains fragile, subject to what may yet be produced as faithful subjects of the event produce further knowledge. 1151

          Arrange concepts to spark a new insight      Wikipedia about Badiou: His view of the link between philosophy and art is tied into the motif of pedagogy, which he claims functions so as to "arrange the forms of knowledge in a way that some truth may come to pierce a hole in them". 1156

          Consider methods as methods (or not)      Wikipedia: Truth, for Badiou, is a specifically philosophical category. While philosophy's several conditions are, on their own terms, "truth procedures" (i.e., they produce truths as they are pursued), it is only philosophy that can speak of the several truth procedures as truth procedures. (The lover, for instance, does not think of her love as a question of truth, but simply and rightly as a question of love. Only the philosopher sees in the true lover's love the unfolding of a truth.)1145

          Consider what a concept denies      Wikipedia: In Handbook of Inaesthetics Badiou coins the phrase "inaesthetic" to refer to a concept of artistic creation that denies "the reflection/object relation". Reacting against the idea of mimesis, or poetic reflection of "nature", Badiou claims that art is "immanent" and "singular". 1153

          Intersect different methods      Wikipedia: Consequently, philosophy is, according to Badiou, a thinking of the compossibility of the several truth procedures, whether this is undertaken through the investigation of the intersections between distinct truth procedures (the intersection of art and love in the novel, for instance)...1139

          Mediated by other or self?      Wikipedia: Reacting against the idea of mimesis, or poetic reflection of "nature", Badiou claims that art is "immanent" and "singular". It is immanent in the sense that its truth is given in its immediacy in a given work of art, and singular in that its truth is found in art and art alone. 1154

          Name the truth into the world      Wikipedia about Badiou: The subject who chances to witness such an event, if she is faithful to what she has glimpsed, can then introduce the truth by naming it into worldly situations.1149

          Reconcile      Wikipedia: The major propositions of Badiou's philosophy all find their basis in Being and Event, in which he continues his attempt (which he began in Théorie du sujet) to reconcile a notion of the subject with ontology, and in particular post-structuralist and constructivist ontologies.[9] A frequent criticism of post-structuralist work is that it prohibits, through its fixation on semiotics and language, any notion of a subject. Badiou's work is, by his own admission,[10] an attempt to break out of contemporary philosophy's fixation upon language, which he sees almost as a straitjacket. ... two elements mark the thesis of Being and Event: the place of ontology, or 'the science of being qua being' (being in itself), and the place of the event - which is seen as a rupture in being - through which the subject finds realization and reconciliation with truth. This situation of being and the rupture which characterizes the event are thought in terms of set theory, and specifically Zermelo-Fraenkel set theory (with the axiom of choice) ...1158

          Put forward ideas      Pamela McLean, April 11, 2011: My hunch is that any ideas I might put forward on developing educational systems would probably be 99% ignored and 1% ridiculed - but I might have got the proportions wrong.1276

          Centering around the learner      Pamela McLean, April 11, 2011: All our courses will be learner centred.1279

          Collect resources      Pamela McLean, April 11, 2011: The resources that they collect and the original work they produce will be shared using whatever is Dadamac's current system (at present that is through our standard spreadsheet structure - see Published Dadamac spreadsheets and docs - compiled 2011 for examples of the structure).1282

          Create a portfolio      Pamela McLean, April 11, 2011: Students will be based "within the Dadamac.net space". They will create a collection of work, things they have written, practical projects they have done, people they have learned from and so on. Over the years,as they study (and help others to study) they will develop evidence of work done, and a high trust network of fellow learners, teachers and collaborators.1286

          Growth      Pamela McLean, April 11, 2011: Fortunately, because we are an online and emergent organisation we don't need a big budget or a big launch - just a vision and gradual growth.1294

          How things will emerge and how I would like them to      Pamela McLean, April 11, 2011: I have some clear ideas of how educational systems could emerge during the 21st century (and how I would like them to). 1274

          My hunch      Pamela McLean, April 11, 2011: My hunch is that any ideas I might put forward on developing educational systems would probably be 99% ignored and 1% ridiculed - but I might have got the proportions wrong.1275

          Naming      Pamela McLean, April 11, 2011: In recognition of its roots in Dadamac - and because I like the sound of the word - I name it "The Dadamacadamy" (to pronounce it say "acadamy", say "macadamy" say "dada', then run those two together for "Dadamacadamy").1295

          What is fortunate      Pamela McLean, April 11, 2011: Fortunately, because we are an online and emergent organisation we don't need a big budget or a big launch - just a vision and gradual growth.1291

          What is likely based on how things currently are      Pamela McLean, April 11, 2011: Given our current areas of activity it seems likely that studies related to health, development, education, social-processes on the Internet, and ecology will come to the fore.1290