mitchellmckain

Another problem with this proceedure is the doubling of the temperature. What possible meaning could it have? In Celsius or Farenheight the answer is not much at all. However the temperature in Kelvin is proportional to the heat energy in a material. So twice the temperature in Kelvin is twice the heat. So in that sense you can say that indeed 273.15 degrees Celsius is twice as hot as 0 degrees Celsius. However this really isn't the whole picture because Temperature is not really about heat but about thermal equillibrium, that is, it is about the flow of heat from one thing to another. Poor boling water in a cup and the cup will soon be the same temperature as the water. but this does not mean that the cup has same amount of heat as the water even if the cup had the same mass or volume as the water because different materials have different abilities to store heat called heat capacity. Any way, the point is that our perception of hot and cold is not about heat content but about the flow of heat. And the flow of heat by conduction is proportional to the difference in temperature. However since 0 degrees Celsius is considerably below body temperature it represents a negative heat flow from the body. So on the basis of heat conduction alone we might think it a good idea to make our zero degree temperature the same as body temperature. Then at 20 degrees above body temperature we would see twice as much heat flowing into the body as only 10 degrees above body temperture. Ha Ha... This is funny because I am sure that everyone knows that 95 degrees F (35 Celsius) is not what we would call a comfortable temperature. This is because the human body produces a considerable amount of waste heat that it has to get rid of and so at 95 degrees (35 Celsius), since conduction no longer works the body uses the evaporation of sweat in order to expel this waste heat. Ok suppose a comfortable temperature is 70 degrees Farenheit or about 20 degrees Celsius. So maybe a meaningful way to speak about the temperature being twice as hot would be the difference in heat flow from what we have at this comfortable temperature. So at 25 degrees Celsius (77 F) we would have about a third less the conduction of heat as at 20 C and at 30 degrees Celsius (86 F) we would have two thirds less conduction. So perhaps we could say that 30 C is twice as hot as 25 C, what do you think? Like wise at 10 degrees C (50 F) we would have two thirds greater conduction and at 0 degrees C (32 F) we would have four thirds greater conduction, so we could say that 0 degrees C is twice as cold as 10 degrees C. Unfortunately there is another complication and this is the fact that conduction is not the only means of heat loss. There is also radiation, and this radiation depends on the fourth power of the temperature in Kelvin. That is the heat flow due to radiation is proportional to Thot^4 - Tcold^4 (with the two temperatures measured in Kelvin).

The polar representation of complex numbers is also very helpful in understanding thisFor z = x + iy you can calcultate r=sqrt(x^2+y^2) and t = tan^-1(y/x), just like when you are calculating the polar coordinates from the cartesian coordinates of a point. Then z = r e^(i t). Converting back to the cartesian form is easier using z = r cos t + i r sin t.Now when you look at the power functions you find something interesting.z^2 = r^2 e^(2 i t)In other words squaring a complex number squares the distance from the origin and doubles the angle.Likewisez^(1/2) = r^(1/2) e^( i t / 2)The square root gives square root the distance from the origin and half the angle.But now the problem is that the angles do not have a unique number but, for example, 0 degrees and 360 degrees are the same angle. It doesn't make much different when you are squaring because 720 degrees is the same as 360 degrees. But in the square root, half 360 degrees is 180 degrees which is not the same angle.Thus 1 = 1 e^(i 0) = 1 e^(i 360)and sqrt(1) = 1 e^(i 0) and 1 e^(i 180), that is both 1 and -1likewise since -1 = 1 e^(i 180) = 1 e^(i 540) from adding 360 to 180we get sqrt(-1) = 1 e^(i 90) and 1 e^(i 270) which is i and -iSo for a general root z^(1/n) of z = r e^(i t) we will get n answersr^(1/n) e^(i t/n), r^(1/n) e^(i (t+360)/n), r^(1/n) e^(i (t+720)/n),... r^(1/n) e^(i (t+(n-1) 360)/n).You can see that for z=1 this means r=1 and the for the root z^(1/n) you have n possibilities which are the n equally spaced points on the unit circle including 1 as someone mentioned already.But in fact you can see this is true of any complex number on the unit circle.take for example -1 for which r = 1 and t = 180 degreesThen the fourth root gives e^(i 45), e^(i 135), e^(i 225), e^(i 315)or in cartesian form (i+1)/sqrt(2), (i-1)/sqrt(2), (-i-1)/sqrt(2), (1-i)/sqrt(2)Checking the first root means squaring (i+1)/sqrt(2) twice(i+1)/sqrt(2) times (i+1)/sqrt(2) = (-1 + 2i + 1)/2 = iand clearly i squared is -1.

Since I have been using a wireless network for the last six months I have been rather surprised at the speed and incredible range of security options. Just looking at the list of things you can do which WeaponX has provided, should give you some idea. What he doesn't say is that all these thing are as easy as clicking an option in the process of setting up your network. But I think the most important thing is that the access to your network is physically limited. Someone has to be pretty close by in order to make the attempt. Furthermore I have been rather surprised at how numerous wireless networks are. And most people seem to have made no security precautions at all. Anonymity and avoiding being a target (by using nonstandard non Microsoft software for example) is one of the greatest protections on the internet. Hackers are not so common that one is likely to be in your immediate neighborhood, so the physical limitation and numerous wireless unprotected networks provides a great deal of this anonymity.

“Is God willing to prevent evil, but not able? Then he is not omnipotent. Is he able, but not willing? Then he is malevolent. Is he both able and willing? Then whence cometh evil? Is he neither able nor willing? Then why call him God?” -Epicurus (“De Rerum Natura” Lucretius) Some common solutions: -A God which is benevolent and all powerful does not exist. -Evil is the the consequence of human free will. Free will is more important than the existence of evil. -Evil is not real but a product of our inadequate understanding of things. -Evil is real, but human logic itself is inadequate to explain the reality of both God and evil with the information that is available to us. There is actually 2 versions of this paradox - one in regards to the existence of evil and one in regards to the existence of suffering. The philosophical problem is not difficult to answer, but something does have to give way in the solution and this does contribute to the variety of Christian beliefs about God. In addition to the philosophical problem there is also the visceral experience of evil and suffering to which philosophical solutions are somewhat lame. The problem of Evil. In the problem of evil, I go with the free will solution and I think this means that God is capable of sacrifice and risk. In order to create something interesting God risked disaster by sacrificing His absolute control over everything to give all living things a measure of free will. In fact He gave an increasing amount of free will in higher life forms until Adam and Eve had such a measure that they embodied the idea of children, whose essential free will has been experienced by every human parent. Human parents have also experienced the same sort of disaster as God did in the Garden of Eden when Adam and Eve turned from the guidance of God to learn about good and evil for themselves. This is hardly the universal Christian solution to the problem of evil. For even when free will is upheld as a solution, many Christians will insist that God sacrifices none of his omniscience, omipotence or sovereignty as illogical as that seems to me. For me, a God that must preserve his own power and control at all costs and is incapable of risk or sacrifice does not inspire any love or admiration in me. How is free will compatable with the omniscience and omnipotence of God? Omniscience and omnipotence and especially total sovereignty are not three separate things as is often imagined. They are inextricably bound together. Power is impossible without knowledge and knowledge is impossible without power. Furthermore, abosolute knowledge can only mean absolute sovereignty. It is a lesson of quantum mechanics that you cannot know without interfering in what is known. To put it simply knowledge has a hand in creating reality. Therefore absolute knowledge is absolute control. For us who are limited in power and knowledge we do not see the ultimate connection between the two. It is possible for us to know something without having any control over it, and it is possible for us to have power over something without knowing what will happen. But when we are talking about complete power and knowledge the difference between the two vanishes. If you trully know everything, then you know all the consequences of your actions, which means you have control over all of those consequences. And when you are all powerful then your actions also have no limits which means the consequences of those actions are without limit as well. The lesson of quantum mechanics is that things can exist in a natural state of uncertainty. Absolute knowledge must annihilate these states of uncertainty, changing the natural state of reality to what your knowledge dictates. The future choices of human beings are quite comparable. Free will means that our choices are ours to make and therefore are in a similar state of uncertainty until we make our choices ourselves. For God to have the future knowledge of our choices would annihilate this state of uncertainty and destroy our free will. We would be no more than automatons to Him and it would be irrational for Him to hold us responsible for anything. God is capable of sacrificing His own power and knowledge. There is this idea that omnipotence and omniscience defines God and so it is impossible for God to sacrifice knowledge or power. It is almost as if rather than knowledge and power being available to the service of God, it is He/She who is bound and enslaved by knowledge and power. This is why I make the point about risk and sacrifice. All power is available to God, but God is not ruled by this. What kind of person is ruled by power? Surely God is ruled by His own will not by His power. Likewise, I say that knowledge is available to God but God is not defined or ruled by knowledge. God can know or not as He chooses, but God is motivated by love rather than power. God cherishes life and the free will of His creatures, and their ability to surprise Him. Otherwise how boring it would be. God prefers a greater challenge. God can still plan the general course of event on an historical scale without controlling the individual. People really have very little control over the general course of events on the historical scale, for these depend on so many things quite beyond their control. Furthermore even though human beings have free will, they rarely exercise it. They really are rather predictable most of the time. But is it moral for God to limit his own power in order to make free will possible? This is the question of the morality of creating life and it is indeed a real paradox of logic. By pure logic it would seem that the creation of life is inherently immoral. For to create life is to make evil possible and to make suffering inevitable. There is only one thing that can defy this logic and make it moral and that is love. The creation of life without love indeed is a great evil. But God's perfect and infinite love for all that He has created makes His act of creation a moral one. When we have a child, it is inevitable that the child will suffer (from the birth itself, falling when learning to walk, required vaccinations, etc...), but loving parents are ready to provide comfort to help the child endure throught these moments of suffering and in the end to believe that this necessary suffering is worthwhile. But a parent who brings a child into the world without this love for selfish reasons (such as to put the child up for sale), does great evil. I am not saying that doing something out of love justifies it no matter how much pain and suffering it causes. The creation of life is a special case, because pain and suffering is not a direct and automatic result. Sure the creation of life makes suffering possible but it also makes joy and happiness possible as well. The creation of life out of love is moral, because when love is offered there is every hope that what is gained will be worth the price of suffering. It is what is called in the courtroom, doing it in "good faith". Love includes empathy, so the when the one who is loved suffers then the one who loves also suffers. Your free will means you are free to be perverse in choosing death and hate over life and love. But that is your choice and thus it is only your fault. God and a lot of other people will suffer because of this choice. And so in this sensless manner you can respond to the suffering in the world by creating more suffering, making life senseless and meaningless by your own choice. The world has seen so much of this that it is terrifyingly boring and not worth our attention. It is the creators in life who deserve and get our attention with what they pour their hard work and love into: their ideas, stories, art, music, films, inventions, games, communities, and other accomplishments. Being outside time and space does not mean knowledge of the future. There is the idea that God sees the future because He exists outside of time and space, for He created it. But Just because God exists outside of time and space does not mean that the universe exist as a four (or ten) dimensional object with past and future complete. I do not think that God even created a single living thing this world with a snap of His fingers, but only in a interactive process of being involved in the life of living things moment to moment, side by side. I think that this idea of being oustide time and space simply means that God is free to move His consiousness to any point in time for He is not bound within it. Some people deny this, saying that the future does not exist to be known. But I think God is sufficiently bound by both ethics and aesthetics to participate in our world in its proper order of time. Otherwise violates aesthetics in the sense of reading the end of a story ahead of time, and violates ethics in the sense of telling the end to someone before he reads it. Furthermore I think it is an issue of privacy. He may be everywhere in our world and life knowing our every thought and action, but the future is a privacy that he allows us and therein lies our free will. So I think that as God participates in this world He does not know its future (even though He may plan some of it). Free will implies that it is human-kind which are responsible for evil, but how is this reasonable considering our limited knowledge and power? Life innately has an infinite potentiality, for the essense of what it means to be alive, is to have the ability to become more than it is. It has the ability to learn and become what it learns. This potentiality may never be realized without the aid of God, but it is there. In any case, there came a point in God's effort of cultivating life to realize its greater potentialites when God decided that a certain lifeform was ready for a more direct form of education by means of what we call communication. If this was ever just an experiment you could say that this is where he contaminated it, for in raising young humans with speech and communicating to them the essential ideas of being a person, God truly created human beings in His/Her own image in the same way that every human parent raises their own children, inheriting much of their parents' personalities. But at a key point human beings refused the guidance of God and the world we know of is the result. God created far superior beings called angels, but their free will is a poor imitation, much like the decision making capabilities of our computers (but obviously much more sophisticated), because the fact of the matter is that they (just like our computers) are still no more or less than exactly what they were designed to be. And so the angelic world has no pain, suffering, death, evil, hate or sin. But it is also boring and rather limited in the ability to love or to be loved, and that is why God tried something quite different involving the sacrifice of his abolute control and the risk of things like pain, suffering, death, evil, hate, and sin. For in creating life, God created something which would always have a hand in its own creation, and therefore unlike the angels would not simply "be no more or less than exactly what they were created to be", but would, in fact, themselves be responsible for who and what they are. THAT is what it means to be alive (in truth rather than in the poor angelic immitation). If God is such an advocate for free will, then why tell us how to behave and punish those who disobey? Free will is the power to choose, but choice is meaningless without alternatives. Free will is life and life is the infinite poteniality of being creative, able to learn new things and become more than we are. But creativity and learning do not exist in a vacuum. The whole point of creating this infinite potentiality of life was that this was something to which God could give without limit. The creation of something without free will is instantaneous. It has what you have given it already. But living things are created continuously in a partnership with the creator, just as a farmer raises crops and a teacher teaches students. We are created with nothing but with the potential for everything. So God can lead us towards our greater potentialities eternally. When you tell your children not to play with fire that does not mean that you don't want your children to have any free will. When you insist that your children eat their vegitables that doesn't mean that you don't want them to make choices in their life. The younger the child, the more you need to control their life for their own protection, but a good parent will give their children an increasing amount of freedom to make their own choices as they grow older. I can see this progression in the Bible going from the Old Testament to the New. A mother may say to her child, "If you break your neck doing that, I will kill you." Of course the threat is an empty one, but the danger is real. The truth is that no punishment is required. Real punishment when possible and offered by the parent is a blessing for it substitutes the excessive harsh consequences of reality with milder ones, so that the child may learn the lessons of life more gradually. The idea of an eternal hell for punishment is nonsense of course. The purpose of punishment is to modify behavior so it makes no sense for it to be eternal. It is only the natural consequences of our action that can be so permanent and harsh. Suffering In the version of the problem, which we can call the problem of "suffering", I believe that the solution lies largely in perspective and the perception of suffering. I compare us to the child in the grocery store acting like it is on the verge of dying because his or her parent will not buy the candy he or she wants. The child does not know what is good for it and barely understands the meaning of desire. As we grow older we learn that if we really want something then we are willing to work long and hard for it (even suffer for it). Thus in the context of eternal life our "sufferings" in this life may be just as trivial and our complaints as childish as the child in the grocery store. Some people might argue that parents do their best to prevent thier child from suffering, and so it might seem that if a parent created the world they might create a world without suffering. But it is not really true that a parent would really do anything to keep their child from suffering. Would a parent sever their child's spinal cord or keep them on a morphine drip so that they would never feel any pain? Would a parent keep a child in complete isolation so that the child would never catch any disease or experience heartache from the rejection or mistreatment by others? I read an interesting youth novel recently entitled "The Giver" by Lois Lowry, where people tried to make a world without pain. It was a rather good horror story. The only way to eliminate the possibility of suffering is to eliminate the possibility of joy and happiness as well. Life includes the possibily of both. Now the sad thing is that there are bad parents who do not give their children the freedom they should as they grow, just as there are religious people who make their religion just as controlling and without freedom. The first does not mean that all parents are bad any more than the second means that all religion is controlling and without freedom. Experience of evil and suffering But that brings us to the experience of evil and suffering as opposed to the intellectual exercise. Albert Camus' novel The Plague comes to mind in regards to this. The ultimate suffering, it seems to me, is the loss of loved one such as a child. In the face of such an experience I would not be to surpised to be rewarded by a punch in the face for the innane philosophical arguments presented above. The renunciation of faith as a result of such an experience is not an uncommon occurence. So this is a much more real and potent example of the problem of evil and suffering to my mind than any intellectual discussion. All I can say to this is that the renunciation of faith does not seem to bring any great comfort or solution to this experience of suffering and evil. People have many different ways of expressing their grief and many are far from rational and even self-destructive. In the end, after all is said, we all have to get through this experience of being human the best that we can. Even a Christian whose child dies might turn away from God, become a drug addict, and die of an overdose. It is difficult to imagine how this suffering could have been "for their own good." Such realities are where it stops being a rational exercise and is just a matter of coping. Christians have to cope with this reality as best they can, just as do we all. As a personal pragmatic philosophy I believe that the events of my life are a gift from God to help me grow in spirit. But I am well aware that this does not work as an objective rational philosophy. I do not believe that the deeds of evil men are God's gift to their victims. The personal philosophy is my choice and determination to affect my attitutde and responses to events. It is a common personal philosophy among Christians but not all have the sensitivity and discernment to realize that you cannot paint this across everyone elses life. I do not even try to imagine that such events as described above are for anyones good. In fact, I feel quite sure that they do real harm to everyone. But I am also confident that such wounds can heal under the care of a loving caretaker. The real question (putting aside all inane questions of religion and philosophy), for everyone (all the time) is whether they want to be part of the harming or the healing.

Its about time! I was getting really annoyed by all these claims for a tenth planet by people who really did not know the score. Many astronomers had already stopped thinking about Pluto as a planet for quite a while, realizing that it was just one of a whole belt of similar objects. It is just a formal definition that was lacking to make a definitive ruling on many different objects. Ruling the other way was unlikely for it would likely lead to an endlessly increasing list of planets as well as reversing an earlier decision to demote Ceres from the status of planet. Ahhh.. So that's how they rule out Ceres as well, since the presence of the belt of asteroids of which it is a part disqualifies Ceres for the same reason, although most of the mass of the asteroid belt is in this one body. The definition of dwarf planet does not have this qualification meaning that Pluto and Ceres share the classification as dwarf planets. Although I suppose Pluto and Charon will now be classified as a double dwarf planet. I am in favor of making the first criterion, "has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a ... nearly round shape", a requirement for something to be a moon, which would disqualify the two so called moons of Mars, and reduce the numbers of moons for the large planets to more reasonable numbers.

Existentialism teaches us that philosophies which do not help in dealing with the human condition and thus help in the living of our lives is meaningless. The contents of human existence are the choices we make, for in them we find ourselves. It is true that we have no real control over the events which ultimately occur, making them somewhat irrelevant to our being, but the fact that our choices do have an impact on events is what gives our choices context and meaning. A denial of this impact is contrary to the reality of human existence. So philosophies of determinism and fate are alien to the human experience and as such might be appropriate philosophies for rocks but not human beings. Human life is filled with choices for which we bear the ultimate responsibility by becoming what we have chosen. Denial of that choice is a refusal to live. Trivialization of these choices or the refusal to acknowledge the responsibility diminishes human life. This was the basic criticism that Soren Kierkegaard had for the Western rationalistic phiosophies such as that of Descartes who argues from pure reason, "I think therefore I am", concluding that only thought is assuredly real. To the existentialist this is idle chatter with nothing to do with basic experience of human life. You may like the idea that "only thought is real", but no one lives as if that were true, for they would quickly die of hunger if they did. Even as simply a means of proving that things exist, this rationalistic philosophy has no value in the existentialist approach to philosophy. The idea that existence is in doubt is ridiculous and useless to the task of living. Determinism is another point on which philosophy and the science (of the nineteenth century) became meaningless to the context of human existence. Our most basic human experience is that we are free to choose and that when we choose to do something our body responds to that choice. Assuming you are a completely healthy human being, when you move your finger, is not your experience that you chose to move the finger and the finger moved as a result of your choice? So philosophies which tell us that we are not free to choose or that all events are predetermined, it contradicts our most basic experience as human beings. It is the choices we make - how we respond to the situations that life throws at us that define who we are. If we habitually respond to adversity with anger and hatred we make ourselves an angry and hateful person. If we choose to solve our problems by lying then we make ourselves a liar. If we choose to get what we want by stealing then we make ourselves a theif. It may be inevitable because of the fall that we will choose to sin in some manner and thus inevitably become the sinner, but it is still our choice and responsibility. We find what we are in what we do as a result of the choices we make. Our only freedom is to make choices, NOT to control events. For many people, events do seems to largely coincide with the choices they make, but this often leads to a false sense of security and power. Others find themselves lost in chaotic events beyond their own control (bad things happen to good people), and they may wonder if they have any freedom at all. The choices we make and the things we do have the potential to bring misery or happiness to others. That potential is what makes our choices good or bad. It is true that even when we try to bring happiness to others we sometimes bring only misery, but that does not change the nature of our choice. Because our freedom is only the choices we make and not the eventual consequences, our freedom does not depend on knowledge. Only God has the knowledge and power to control events. We never have the full and complete knowledge of the consequences of our choices. That is why we need God as a part of our life and as a partner in our choices. Such a partnership does not subtract either from our freewill or our responsibility for no choice is ever made in a vacuum, but we choose what environmental influences we will heed and we choose the reasons to embrace for the choices we make. Unfortunately existentialism is often equated with moral relativism because of Sartre. But it must be recognized that existentialism has both Christian and non-Christian developments, and moral relativism is not part Christian existentialism. Please remember that the father of existentialism was Kierkegaard not Sartre. Satre was the atheist who embraced moral relativism in his version of existentialism. Even the agnostic Albert Camus stood against the moral relativism of Nietzsche and Sartre, although he did have criticisms of Chritianity. In any case, Christian existentialism clearly does not include Sartre or his moral relativism. Kierkegaard speaks of subjective truth as an apologist for Christianity. He is seeking to legitimize Christian thought as a natural type of human thinking by showing that not all rational human thought need satisfy the academic/scientific standards of objectivity. Indeed Kierkegaard claims that objective truth as sought by the scientists and academicians is inherently flawed and that the only real truth is what he calls the subjective.

I recently wrote an introduction to Emacs lisp for the tutorial section. I use emacs lisp all the time for quick calculations and to analyze charts of data which I download from the internet. My relativity and space simulator relspace accepts many data formats but I often found it necessary to calculate estimates for missing data on all kinds astronomical objects so they could be included in my program. Nothing beats emacs for a quick and easy way of accomplishing this if you just have a little knowledge of how to program in lisp.

This tutorial seeks to teach by example since I find this the most efficient way to learn a computer language myself. I want to introduce what has been an extremely valuable tool in my work. It was difficult to decide whether to put it under programming or software, for although the use of it that I am suggesting involves programming in lisp, it is the specific software called emacs that I am introducing as a useful tool. However this could also be considered a tutorial in emacs lisp. You can get a free copy for your pc from http://www.gnu.org/software/emacs/manual/efaq-w32.html Emacs is a text editor and lisp interpreter combined. First of all it is a powerful and useful alternative to Notepad allowing you to handle control characters in your text files more readily (for example) among many other things. Second, it is a quick and easy way to do calculations without all the preliminaries required in using other programming languages. When you combine the text manipulation commands with the lisp interpreter it becomes a powerful analytical tool. Before explaining this lets start on the basics of lisp programing. Lisp is a calculation based language, meaning that Lisp is composed of expression that are evaluted to produce some calculated result. A lisp program is such an expression and the calculated result of this expression is automatically displayed. A lisp expression is placed between two brackets (also known as parentheses), starting with an operation identifier and followed by the arguments of that operation separated by spaces. Since I am typing this in emacs (in lisp interaction mode) you will see the actual output when the progam is run, which I get by pressing control j after the program (after the last close parentheses) right in the same place where I am typing this text. Emacs just inserts the result of the program on the next line in the text. So after each lisp program I write I will use control j and you will see the output immediately following the lisp program. You can also press control x control e at the end of the program to execute the program and display the results at the bottom of the screen without inserting the result into the text. The following are some examples of simple lisp programs consisting of a single simple mathematical expression. (+ 1 2) 3 (+ pi 2) 5.141592653589793 (cos pi) -1.0 (log 2) 0.6931471805599453 For a y^x calculation you use the expt operation (expt 5 3) 125 In order to do multiple operations you nest the parentheses like this (cos (/ pi 4.0)) 0.7071067811865476 As you can see the cosine is in radians and the logarithm is the natural logarithm. However the common base 10 logarithm is also available and is called log10. But if you want a cosine in degrees, you have to program your own fuction with the "defun" operation. (defun cosd (x) (cos (* pi (/ x 180.0)))) cosd When you press the control j at the end of this program (after the last parentheses), the interpreter prints just out the name of the function like this and after this you can use this function in other lisp programs like this: (cosd 45) 0.7071067811865476 Now that you have been introduced to the lisp language, I will now show you will show you what I found this emacs system so useful for, before continuing with an introductory tutorial in emacs lisp. Emacs is very useful in manipulating and calculating with charts of data in plain text format. For example, the following are the top 10 entries of a webpage listing the 10 brightest stars, with their distance in light years, their visual magnitude, their absolute magnitude, and their spectral classification. Sun - -26.72 4.8 G2V Sirius Alpha CMa 8.6 -1.46 1.4 A1Vm Canopus Alpha Car 74 -0.72 -2.5 A9II Rigil Kentaurus Alpha Cen 4.3 -0.27 4.4 G2V + K1V Arcturus Alpha Boo 34 -0.04 0.2 K1.5IIIp Vega Alpha Lyr 25 0.03 0.6 A0Va Capella Alpha Aur 41 0.08 0.4 G6III + G2III Rigel Beta Ori ~1400 0.12 -8.1 B81ae Procyon Alpha CMi 11.4 0.38 2.6 F5IV-V Achernar Alpha Eri 69 0.46 -1.3 B3Vnp Now if I use tab-to-tab-stop (esc i) command I can line up the numbers to make this easier to read. Actually most of tabulated data like this on the internet is already aligned into collumns so you dont usually have to do this. Sun - -26.72 4.8 G2V Sirius Alpha CMa 8.6 -1.46 1.4 A1Vm Canopus Alpha Car 74 -0.72 -2.5 A9II Rigil Kentaurus Alpha Cen 4.3 -0.27 4.4 G2V + K1V Arcturus Alpha Boo 34 -0.04 0.2 K1.5IIIp Vega Alpha Lyr 25 0.03 0.6 A0Va Capella Alpha Aur 41 0.08 0.4 G6III + G2III Rigel Beta Ori ~1400 0.12 -8.1 B81ae Procyon Alpha CMi 11.4 0.38 2.6 F5IV-V Achernar Alpha Eri 69 0.46 -1.3 B3Vnp Now what makes emacs so powerful for charts like this are a set of commands that allow you to cut and paste rectangular portions of text. First we set the rectangle by moving the cursor to one corner and pressing control space then moving the cursor to an opposite corner. Next the control x control k command will cut the rectangle so that when we move the cursor and press control x control y it will paste this rectangle in the new position (after and below the cursor). We can use this on the above chart to move the column of spectral classifications like this. Sun G2V - -26.72 4.8 Sirius Alpha CMa A1Vm 8.6 -1.46 1.4 Canopus Alpha Car A9II 74 -0.72 -2.5 Rigil Kentaurus Alpha Cen G2V + K1V 4.3 -0.27 4.4 Arcturus Alpha Boo K1.5IIIp 34 -0.04 0.2 Vega Alpha Lyr A0Va 25 0.03 0.6 Capella Alpha Aur G6III + G2III 41 0.08 0.4 Rigel Beta Ori B81ae ~1400 0.12 -8.1 Procyon Alpha CMi F5IV-V 11.4 0.38 2.6 Achernar Alpha Eri B3Vnp 69 0.46 -1.3 Now supposed we wanted to check the numbers in this chart for accuracy. We can use the magnitudes to make our own distance calculation using the formula: d = 3.26 10^(.2 (a - v + 5)) and compare this with the distance listed in the chart. First we program a function in lisp to do this calculation. (defun dist (v a) (* 3.26 (expt 10.0 (* .2 (- v a -5))))) dist Next I insert "(dist " before the third column using paste (control y), and then I add an end parentheses ")" at the end of each line to get this Sun G2V - (dist -26.72 4.8 )Sirius Alpha CMa A1Vm 8.6 (dist -1.46 1.4 )Canopus Alpha Car A9II 74 (dist -0.72 -2.5 )Rigil Kentaurus Alpha Cen G2V + K1V 4.3 (dist -0.27 4.4 )Arcturus Alpha Boo K1.5IIIp 34 (dist -0.04 0.2 )Vega Alpha Lyr A0Va 25 (dist 0.03 0.6 )Capella Alpha Aur G6III + G2III 41 (dist 0.08 0.4 )Rigel Beta Ori B81ae ~1400 (dist 0.12 -8.1 )Procyon Alpha CMi F5IV-V 11.4 (dist 0.38 2.6 )Achernar Alpha Eri B3Vnp 69 (dist 0.46 -1.3 ) So now when I go the the end of each line and press control j I get Sun G2V - (dist -26.72 4.8 )1.6188909679280947e-005Sirius Alpha CMa A1Vm 8.6 (dist -1.46 1.4 )8.734088738910044Canopus Alpha Car A9II 74 (dist -0.72 -2.5 )73.9975941714126Rigil Kentaurus Alpha Cen G2V + K1V 4.3 (dist -0.27 4.4 )3.7950508558782015Arcturus Alpha Boo K1.5IIIp 34 (dist -0.04 0.2 )29.188891356916752Vega Alpha Lyr A0Va 25 (dist 0.03 0.6 )25.073652353343473Capella Alpha Aur G6III + G2III 41 (dist 0.08 0.4 )28.133100657203222Rigel Beta Ori B81ae ~1400 (dist 0.12 -8.1 )1436.208855031364Procyon Alpha CMi F5IV-V 11.4 (dist 0.38 2.6 )11.727828326077196Achernar Alpha Eri B3Vnp 69 (dist 0.46 -1.3 )73.31918015024647 If you look at the results above you will see something than I observed years ago, the data found in charts like this on the internet are not always very consistent. Capella is the worst here, comparing 28.133 light years to 41 light years we see this is off by more than 45%. Since the result for the sun has no comparison, lets multiply by the number of seconds in a year: (* 60.0 60.0 24.0 365.25) 31557600.0 to get the distance to the sun in light seconds (* 31557600.0 1.6188909679280923e-005) 510.8831360948757 which we can compare to the usual value of 499 light seconds. Now lets go back to the topic of emacs lisp and cover some of the usual programing basics for this language in a quick summary, just in case you need them. To set the value of a variable for use in a program you can use the setq operation. (setq i 0) 0 For temporary variables within a program you can use the let operation. The following sets the variables a, b, and c to values which are used in each of the operations inside the let. (let ((a 1.3) (b (log 2)) (c (log 10))) (+ a b c) (- (* a b c) (* a (* a c))) -1.819612480849552 Notice that only the result of the final calculation is displayed. To display something else during the running of a program you can use the print operation. (let ((a 1.3) (b (log 2)) (c (log 10))) (print (+ a b c )) (- (* a b c) (* a (* a c))) 4.295732273553991 -1.819612480849552 Since the let operation also lets you combine a series of calculations into a single program, you can use the let operation with an empty list of assignments just so you can take advantage of this feature. But rembember that only the result of the last calculation will be displayed unless you use the print command as follows. (let () (print (* 2 3 4)) (print (* 3 4 5)) (print (* 4 5 6)) (* 5 6 7)) 24 60 120 210 Logical testing operations like < = > <= and >= are also available. The following computes (log 2) and (log 10) and tests to see if the first is less than the second. (< (log 2) (log 10)) t Here it tests to see if log 2 is greater than log 10. (> (log 2) (log 10)) nil Notice that these testing operations display "t" for true and "nil" for false The if operation uses these testing operations like this: (if (< (log 2) (log 10)) (sin 2) (sin 10)) 0.9092974268256817 The if lisp operation takes three arguements, the first is the test, the second is the program which is run or value which is returned if the test returns true (t) and the third is the program that runs or value which is returned if the test is false (nil). So in the above example, only the first program calculating the sine of 2 is performed and displayed because the test evaluates to true. After seting a few variables we can use the while operation for a loop to calculate the first five factorials. The first argument of the while operation is also a test, but this is followed by any number of calculations all of which are performed repeatedly as long as the test evaluates to true. The variables can be set using the setq operations but since i and j are temporary variables it makes more sense to use a let operation and this will make re-running the program much easier. (let ((i 0) (j 1)) (while (< i 5) (setq i (+ i 1)) (setq j (* j i)) (print j)) (list j 'is i 'factorial)) 1 2 6 24 120 (120 is 5 factorial) But the more usual way to do a loop in the lisp programming language is with a recursion. A recursion is a function that calls itself. When you do this it is important to test the input to check whether it is time to stop calling itself or you get an infinite loop. (defun fact (x) (if (= x 1) x (* x (fact (- x 1))))) fact This defines the factorial function so we can get any factorial up to 99! when the maximum number of recursions is reached. (fact 5) 120 (fact 99.0) 9.33262154439441e+155 Notice that I used 99.0 rather than 99. This was to make lisp use floating point arithmetic to avoid exceeding the maximum sized integer allowed. Now perhaps I should mention that lisp was specifically designed to handle lists and in fact the name lisp comes from "list processing". A list is a series of space separated items inside parentheses. So for example a lisp program is itself a list. There are a number of operation in lisp used to create, combine, and extract portions of lists. The list operation combines a series of arguments into a list (list 1 2 3) (1 2 3) The cons operation appends an item to the front of a list. The single quotation mark is used in front of a list to prevent it from being evaluated like a program. (cons 1 '(2 3)) (1 2 3) car extracts the item at the beginning of a list. (car '(1 2 3)) 1 cdr extracts the list that remains when the first item is removed. (cdr '(1 2 3)) (2 3) cadr extracts the item second item of a list and it is called cadr because it is the same as the successive operations of cdr then car. (cadr '(1 2 3)) 2 (car (cdr '(1 2 3))) 2 cddr extract the the list that remains when the first two times are removed and it is called cddr because it is the same as the successive operation of cdr and cdr again. (cddr '(1 2 3)) (3) If a list is a program you can use the eval operation to run it. (eval '(+ 1 2)) 3 Here, for example, is a function that takes a list of programs and runs them to create a list of results. null tests a list to see if it is empty '() and nil is another way of representing the empty list. (defun evalist (x) (if (null x) nil (cons (eval (car x)) (evalist (cdr x))))) evalist Now lets try this function out. (evalist '((+ 1 2) (- 1 2) (* 1 2))) (3 -1 2) Now the whole emacs text editor is really a lisp interpreter and all of the text editing commands are lisp operations. So if you press control x control e at the end of the following program it will actually move the cursor to the second line of the file that is loaded into emacs. (goto-line 2) To play around with this it would be more convenient to use two seperate windows in emacs (created using the split-window operation or control x 2). One with the file to edit in one window and your lisp programs in the other. The following program will goto the begining of the file in the other window and then find every # character and ask you if you want it replaced by a % character. (let () (other-window 1) (goto-line 0) (query-replace "#" "%")) For more details on emacs lisp and a more careful explanation of the operations see http://forums.xisto.com/no_longer_exists/ There is also a detailed manual at http://forums.xisto.com/no_longer_exists/

I was talking to my father the other day when he tried to tell me that the first heresy called gnosticism taught (in the Gospel of Thomas) that it is what you do rather than what you know that counts. I was rather surprised since I thought gnosticism was about a belief in being saved by a secret knowledge. The word "gnosis", in fact, means knowledge. Anyway I decided that I should study the matter and find out the whole story, and here is what I found out.Gnosticism was a label for a whole group of new syncretistic religions that came into being around the same time that Christianity began. Syncretistic means that these religions drew their ideas from many sources combining ideas from Greek philosophy, Roman paganism, Judaism, Christianity, Zoastrianism and even Buddhism. To the tell the truth, Christianity can be considered one of these new syncretistic religions for you can see many shared elements between these other syncretistic religions and Christianity. Now in condemning these other groups as a heresy called gnosticism, certain common beliefs among these groups were pointed out as incompatable with Christian belief. Unfortunately, however, it seems quite possible that some of the groups that were condemned as Gnostic shared none of these condemned beliefs but were variations of Christianity not much different than the differences between denominations today.The condemned Gnostic beliefs include the belief in a supreme deity called the One (or Monad) from whom emanated progressively different aspects of his being (called Aeons). There is the idea that this progression of emanations produced things less perfect than the monad. There is the belief that one of the emanations, called the demiurge (from Plato), created the universe from pre-existing matter, and that the imperfections of this world are a result of the imperfections of this creator. The demiurge also created helpers or companions called Archons to rule over the material world. There is the idea that a divine element or emanation of the monad have become trapped and imprisoned in the material world within certain human beings, with the Archons of the demiurge as the jailors. But with the proper knowledge from a redeemer (Christ, Seth, or Sophia) these divine elements can escape their material prison to return to the divine realm.However these beliefs really only describe the ideas of only a portion of the groups condemned as Gnostic, called the Syrian-Egyptian school who drew much of their ideas from the Greek philosophers of Plato and Pythagoras. In Persia, there were other groups including the Mandaeans and Manichaeins who drew some of their ideas from the religions of the east. The Mandaeans revered John the Baptist rather than Jesus. The Mandaeans naturally practice frequent baptisms and public worship on Sundays. There seems to be some influence of Zoastrianism in their ideas of a Cosmic Dualism between father and mother and between light and darkness. There also seems to be some influence of the ideas of astrology, that the planets and stars influence the fate of human beings.Manichaeism was founded by the prophet Mani, who wrote seven holy writings and who claimed to be the Paraclete (Holy Spirit) promised in the New Testament. (Some people in Islam make the same claim for Mohammed). The teachings of Mani seem to be heavily influenced by Zoastrianism, speaking of a realm of light and peace and a realm of darkness and conflict which existed from the beginning, ruled by two equal and opposite powers. They believe that the physical universe came into being as a mixture of light and darkness resulting from a conflict between these two realms. The idea of the the transmigration of souls (reincarnation) was adopted from Buddhism. And Mani was even called a Buddha, claiming him to have achieve the a state of enlightenment (Parinirvana). Perhaps, Manichaeism has had some impact on the later theological developments of Christianity through Saint Augustine who converted from Manichaeism, for although he condemned the teachings of Manichaeism, others have found some influence of it in his writings.But included in the writings that are condemned as Gnostic is at least one which seems out of place, the Gospel of Thomas. This is a collection of sayings of Jesus, most of which are easily recognized from the four gospels in the canon. Others are difficult to understand, what Jesus could have meant by them if He truly said them. Reading through them I experience puzzlement more than anything else. However scholars have found a philosophy represented in the Gospel of Thomas which emphasizes the need for us to seek the truth ourselves and make our own decisions rather than simply following orders. The appeal of this message to those find fault with the authoritarian dictatorship of the church is obvious. Therefore it is possible that this gospel of Thomas represents a Christian group with a less authoritarian approach to the truth. However, I certainly do not see anything in it like the message which my father claimed.In my opinion the gospel of Thomas is simply one of the apocryphal texts that never made it into any cannon or even into the apocrypha books included in some Bibles. This may be partially because some of the church fathers found objectionable ideas (like gnosticism) in it, but I believe that others went along with this judgement only because they found the book as a whole to be too confusing to be particularly helpful in understanding anything about the Christian faith.

Sure we need to make judgements, but I try to restrict myself to my own life. I pretty much stick to judgements like, "this is what works for me and I couldn't live my life that way". When I see the sin out there it is a warning for myself, that if I am not careful I could find myself doing the same, so if I don't like what I see I know what to fight against in myself to avoid becoming what I dislike. Indeed it is the swing to extremes like this that I fear more than anything. We need to find the kind of compromises upon which this country was built, on some issues, before we shake ourselves apart.

But I do not see this as any kind of recent trend but something that goes to the beginnings of the church. Long before Constantine, when Christianity became the thing to do, Paul struggled with this same tendency within the early churches. There were, for example, the husband and wife whom God struck down because they lied about what they donated to the church. Even before the coming of Jesus there were evil people who used religion as a smokescreen to hide themselves. I am not even sure you can make a real distinction between those merely struggling with sin and those just pretending. Only God can seperate the tares from the wheat. How can I answer such questions? Do I do enough? Do you? What shall we do? Be proud of the 10 minutes spent before bed time or some other goal we set and meet for ourselves? I know a lot of people who do everything you ask about, and yet they have their limitations. Where do you draw the line? The religion of wealth is not out there somewhere across an imaginary line. It is right there inside you. It is sinful human nature. Many fight this to varying degrees and some with the grace of God have their small victories. But the kingdom of God belongs to the weak in spirit, to those who have lost the battle and know it, begging God for help. God does help us, but we have no reason to be proud of ourselves or to judge others. The religions of both Christianity and wealth has been in North America since its first settlements, which included both Plymouth and Jamestown. This two sided nature of America is no secret. The whole world can see it plain as day. With one hand we give and with the other hand we take. I am well aware of the this idea of aquiring weath for good which you speak. And it is both true and false. The aquisition of weath (like the aquistion of power) does not in of itself condemn you but it is spiritually perilous, because of its temptations, responsibilities, and because the means to something, almost invariably in time, becomes the end. Yet I believe there is something even more perilous and that is passing judgment upon others. Let God judge the wealthy and the powerful. Only He has the ability and the right. All true. And yet maybe not. I can easily envision meeting Christ and having him ask me, "why do struggle so and make it complicated? Be at peace and rejoice, for you are mine." Need we all be intellectuals or religious solicitors? Cannot the simple mind accept the love of Christ with a simple heart and how shall we gainsay such a thing? Only God knows. He is the author of salvation and the only judge. Christianity (whether religious or spiritual in your judgement) is not the only group that seeks to dictate morality. I think liberal groups can even be more intolerant, self-righteous and dictatorial, pushing what amounts to a liberal humanistic theocracy to force their morality upon us all.

Can you explain a little more about what you are talking about. Maybe with examples? Why do you use the term "anti-spiritual"? What is this "push for hierarchy"? Do you mean "authoritarianism" or the right to dictate morality to other people?

I have found it interesting to be faced with the paradox of defending the role of religion in modern society to atheists and agnostics while the pastor of my church often ridicules the idea of religion. You might be tempted to think that this anti-religious sentiment expressed in modern Christianity makes Christianity unique, but the truth is that Bhuddism also started out with a strongly anti-religious message as well. Of-course since these are technically religions themselves, from an objective viewpoint, these anti-religious sentiments could easily be interpreted as merely reformative rather than truly anti-religious. Bhuddism, for example, was founded by Sidharta Gautama who spoke strongly against the idea of deity and appeasement in reaction against Hinduism in particular, and therefore laid out quite a different path (than appeasing the Gods) toward the understood goals of religion (Hinduism) which was enlightenment and the escape from the endless cycle of rebirth in a world of illusion and suffering. Likewise, in modern born-again style Christianity, the word "religion" has attained considerable negative connotations refering to the same idea of appeasing God. Certainly no form of Christianity could be anti-religious in the same sense of Bhuddism because the belief in a single deity is vigorously upheld. But according to this modern born-again style Christianity, all the religions, which tell you what you have to do in order to please God so that you can make it into heaven, are a cheat and a deception (in fact no more than human manipulation). For this type of Christianity emphatically declares that there is NOTHING that you can do to restore your relationship to God or to qualify for redemption. So in modern Christianity the word religion is usually associated with organizations with some idea of working your way into heaven. This is part of the Protestant trend away from an organization like the Catholic church which (in the past at least) has thought it holds the keys to heaven and controls access to God. Thus, accordingly, this "new Christianity" recognizes that no denomination, church, or organization of men have any ultimate authority, but that all the authority rests in the written word and the living Jesus with whom anyone can have a personal relationship without any human mediator. In this brand of Christianity, the real Church refered to in the Bible as the bride of Christ is no human organization but a spiritual one administered by Christ himself uniting all people with a personal relationship with Christ. Now certainly from an objective non-Christian point of view this can be seen as merely making the Christian church an "organization" based on shared ideas and language rather than money and human administration. But even from this objective perspective it is easy to see the advantages (not claiming it is foolproof) in forstalling the human tendency to abuse power. This does not mean that it is not susceptible to any sort of manipulation for if someone (like Bush) sings the right tune he is still quite able to gain considerable support from them.

I am a protestant and I embrace the protestant program to liberate access to God, salvation and the church from the hands of men who could misuse it as a tool of manipulation and control. Obviously I reject the common but far from universal Catholic notion of the infallability of thier leadership as foolish in the light of history. But I do have a soft spot in my heart for the Catholic church and I see much to admire in it. The Catholic church is one of oldest and largest Christian churches. It has a long history from which it has had ample opportunity to make nearly every mistake that a church can make and then learn from those mistakes. Therefore, in the Catholic church you are safe from some the dangerous excesses you can find in smaller younger churches. Furthermore since the Catholic church has always seen itself as the church for everybody, it has learned to embrace some degree of diversity of practice and in the emphasis of belief. In this manner it has become something of an umbrella church and provide quite diverse opportunities especially if you seek to devote your completely to the service of God in a vocation. Against the Catholic church is the fact that it teeters close edge of what I call the "Pauline consensus" which is a group of churches who agree what they consider the most important doctrines that define what is Christian. I think this is largely based on the importance that those within this consensus place on the epistles of Paul in understanding the Bible. By contrast the Mormons (or Latter Day Saints) and the Jehova Witnesses, do not belong to this consensus at all, and they consequently have difficulty with the epistles of Paul. The Catholic church lies on the outskirts of this group because, although they affirm most of these key doctrinal beliefs of this consensus they also, like the LDS and JWs, often claim to be the only true church. Also against the Catholic church is the sharp division between the lay members and the clergy. Historically they have not encourged the lay membership to study the word of God. Hopefully this has changed throughout much of the church but I think they still have a long way to go in this. At least I think some of the protestant churches are much more focused and effective in getting the lay members to study the Bible. Furthermore the size of the church also has it problems too. The "beaurocracy" is large and can be quite burdensome. The individual member can feel quite insignificant and powerless and the church can seem unresponsive to the needs of its members and slow to respond to problems. However the sense of mystery and reverence of things holy is quite powerful in the Catholic church, and this is of no small account. The dedication of its clergy and the weight of their prayers is another thing to consider carefully. All in all I think the Catholic church is a valuable member of the world Christian community, especially when they bother to acknowledge that community and make the effort to participate.

Well of course. It is science fiction after all. But think about the science fiction films when motion pictures first began. If we watch them now they seem just silly, because what they showed was more about the imaginations of the special effects people than the real future. But on the other hand the future that it was attempting to predict really has those movies largely blown out of the water. Truth is far far more fantastic than fiction. As a result, I say, yes, the X-men is hollywood special effects and in the future it will just seem silly, but on the other hand we really cannot even imagine..... If we take clues from the last time that evolution entered this stage on this planet (in the transition to multicelular organisms), we see that the "technology" (communication, material transport, cooperative efforts, material production) played an enormous part in the development of specialized cells. Try to imagine what will happen when you take the idea of technology compensating the handicapped, a step further to augmentation. As the handicap flourish in productive roles in the community individual survival driven evolution will reverse itself and the handicapped will rapidly increase in numbers. We will have to learn to accept greater diversity in the human community. Anne McCaffrey started exploring the possibilities a little in "The Ship who Sang" and its sequels. Other authors have looked a little bit at technological augmentation (like C.S. Friedman's "This Alien Shore"). I think it is likely that these do not even come close to the real future where biological limitations become utterly irrelevant because we routinely design our own bodies (and brains) as an integration of biology and technology. They may not be much like the X-men, but then the human beings of the future may laugh at the X-men as just plain silly because it will be clear the people of this time actually had no idea what would really be possible in the future.

According to what you are suggesting, you have got the wrong movie. Xmen was about naturally occuring mutation not genetic manipulation. The proper movie example would be more like "Soldier", which made the unavoidable ethical question in such manipulation more obvious. "Soldier" also puts much more reasonable limits on what can be expected as a result of genetic engineering. Going back to X-men and naturally occuring genetic change. I think we are indeed in the middle of a radical leap forward in human evolution, but in an entirely different direction than that indicated by the movie. The real X-men of today are the handicapped, who with the aid of technology and the support of the community now survive and are finding productive roles in todays society. These are the radically new types of human beings which represent the next leap forward in human evolution. This is actually a natural part of the process of evolution, for such a leap forward has occured before in the development of multicelular organisms. As groups of cells began working together and started protecting the weaker members of the community, this allowed a greater variety of cells to survive in the community, which stimulated the development of special cells like nerve cells and muscle cells which eventually allowed the multicelular organisms to develop capabilities that far outstripped those of single celled organisms.

The decimal method of representing fractions has its peculiarities such as .99999... = 1 and the need for infinite repeating threes to represent a third. Then there are the irrational numbers who are represented by an infinite sequence of digits with no pattern. I have been exploring the possibility of using continued fractions to represent fractions instead. The advantages include the fact that all rational numbers are represented by a finite sequence and that square roots are represented by repeating patterns. One of the biggest disadvantages is that not all the numbers in the sequence are less than 9, not to mention the difficulty of arithmetical operations on them and the difficulty of comparing of sizes. A continued fraction is of following form 1/[a + 1/[b + 1/[c + 1/[d + 1/[e + ..... To add this to a whole integer we write N + 1/[a + 1/[b + 1/[c + 1/[d + 1/[e + ..... and for brevity I will use the following notation N#abcde... for the infinite continued fraction above. For a finite continued fraction like 2 + 1/[1 + 1/[5 + 1/[3 + 1/[7]]]] 2#1537 if any of the numbers a,b,c,d,e are more than one digit (greater than 9) they will be in parentheses like this #12( 14)53 for the finite continued fraction 1/[1 + 1/[2 + 1/[14 + 1/[5 + 1/[3]]]]] The continued fraction can be computed from the decimal form of the number by the following proceedure (using 4.146 as an example). First take off the number in front of the decimal point (take off 4 leaving .146) and this goes in front of the #. Next invert what remains (so .146 becomes 6.849315068) then take off the number in front of the decimal point and this added after the # (so you have 4#6 with .849315068 remainder). Keep inverting the remainder and taking off the number in front of the decimal point and putting it at the end of your continued fraction. This is repeated until there is no remainder. (invert .849315068 to get 1.177419355 to give us 4#61 with .177419355 remaining) (invert to get 5.63636363.. to give us 4#615 with .63636363... remaining) (invert to get 1.571428572 to give us 4#6151 with .571428572 remaining) (invert to get 1.75 to give us 4#61511 with .75 remaining) (invert to get 1.333333... to give us 4#615111 with .333333... remaining) (invert to get 3 which gives us a final answer of 4#6151113) 4.146 = 4#6151113 For example: 2/3 = 1/[1 + 1/2] = #12 4.123 = 1/[8 + 1/[7 + 1/[1 + 1/[2 + 1/5]]]] = 4#87125 7/8 = #17 7/9 = #132 7/10 = #123 7/11 = #1113 7/12 = #1122 7/13 = #116 .9 = #19 .99 = #1(99) Now for the square roots which can be represented by infinite continued fractions with repeating patterns. A truncated continued fraction with 3 or more of the repeated pattern will produce a good approximation. suppose the square root can be represented by a repeating continued fraction like this p + 1/[a + 1/[b + 1/[a + 1/[b + 1/[a + ..... = p#abababab.... with only 2 repeating digits (or only 1 repeating digit if a = where p is the largest digit whose square is less than the number Then for the square root of q, a and b are given as follows: b = 2 p, a = b / (q - p^2) This formula will not work if (q-p^2) does not divide b In such cases you can use the previous method of converting their decimal form (calculated using a calculator) to a continued fraction but stopping when the repeating pattern is found. So for example: sqrt(2) = 1#222... if this is truncated to 1#222 this gives 1.41666... which when squared gives 2.006944.. sqrt(3) = 1#1212... if this is truncated to 1#121212 this gives 1.731707317 which when squared gives 2.9988 sqrt(5) = 2#444... if this is truncated to 2#444 this gives 2.236111... which when squared gives 5.000193 sqrt(6) = 2#4242... for the square root of 7 the above method does not work, b = 4, a = 4/3 sqrt(7) = 2#111411141114.... pattern length 4 sqrt(8) = 2#1414... sqrt(10) = 3#666... sqrt(11) = 3#6363... sqrt(12) = 3#6262... for the square root of 13 the above method does not work, b = 6, a = 6/4 sqrt(13) = 3#1111611116.... pattern length 5 for the square root of 14 the above method does not work, b = 6, a = 6/5 sqrt(14) = 3#12161216... pattern length 4 sqrt(15) = 3#1616... sqrt(17) = 4#888... sqrt(18) = 4#8484... for the square root of 19 the above method does not work, b = 8, a = 8/3 sqrt(19) = 4#213128213128... pattern length 5 sqrt(20) = 4#8282... for the square root of 21 the above method does not work, b = 8, a = 8/5 sqrt(21) = 4#112118112118... pattern length 6 for the square root of 22 the above method does not work, b = 8, a = 8/6 sqrt(22) = 4#124218124218... pattern length 6 for the square root of 23 the above method does not work, b = 8, a = 8/7 sqrt(23) = 4#13181318... patern length 4 sqrt(24) = 4#8181... sqrt(26) = 5#(10)(10)(10)... sqrt(27) = 5#5(10)5(10)... Here is some emacs lisp code for playing with this idea. (defun frac (a) (- a (floor a)))(defun cf (d n) (if (= n 0) d (if (< d .000000001) '() (let ((inv (/ 1.0 d))) (if (> (frac inv) .99999999) (list (+ 1 (floor inv))) (cons (floor inv) (cf (frac inv) (- n 1))))))))(defun cntf (d) (cf d 20))(defun evalcf2 (a r) (if (null r) (/ 1 a) (evalcf2 (+ (car r) (/ 1.0 a)) (cdr r))))(defun evalcf (c) (let ((r (reverse c))) (evalcf2 (car r) (cdr r))))(cntf (- (sqrt 1435) 37))(1 7 2 3 7 3 2 7 1 74 1 8 2 1 35 176 2 4 6 4 . 0.6934215039804723)Examples://converting the #2222222 to decimal(evalcf '(2 2 2 2 2 2 2)).41421568627450983 //add 1 to get the approximation of the square root of two// square it to check (* 1.41421568627450983 1.41421568627450983) 2.000006007304883//compute the continued fraction form of the square root of five// first subtract off the integer part(cntf (- (sqrt 5) 2))(4 4 4 4 4 4 4 4 4 4 4 4 2 1 10 2 1 7 8 1 . 0.7256998704588513)//so this gives accurate results up to 12 continued fraction digits in this case

Why do you think that? Light travels at the fastest speed possible. The speed of light is our universe's version of instantaneous. Due to time dilation for the object that is traveling at the speed of light it is instantaneous. No, but electrons can produce photons. Accelerate an electron and it radiates photons.

No. That is impossible. Either something has mass and it can never reach the speed of light or it is massless and is always at the speed of light. Something with mass that was (impossibly) accelerated to the speed of light would have infinite energy (impossible) and I have as much difficulty imagining infinite energy of light as I do supplying infinite energy to accelerate the mass to the speed of light. Very high amounts of energy is very likely to produce mass in pairs of anti-particles but an infinite amount of energy would produce an infinite amount of such mass. Now it is quite possible for mass to turn completely into light as when a proton encounters an anti-proton which competely annihilate likely producing at least two very high energy photons (light). Another impossibility. Something at the speed of light could never "slow down." That would be like subtracting numbers from infinity. My first post already explained all of this.

The quesion of human free will versus God's sovereignty or the determism of physical law cuts right across all the lines between religion, science and atheism. So even though I will start this discussion in the following paragraph under the assumptions of the Christian world view, all comments and discussion of the quesion of human free will are welcome. ------------------------------------------------------------------------ The division within Christianity between those who believe in human free will and those who do not, has a long history. One critical point were the arguments between two extremists known as Pelagius and Augustine. It had become the habit of that time to solve differences of theological opinion by declaring your opponent a heretic and ex-communicating him and more often than not putting him to death. It was part of the failure of Christianity at that time not to embrace much diversity at all. And the end result was arrogant men assuming far more authority and knowledge than they really had. Thank God the Protestant reformation finally came along and eventually put an end to this. Frankly if Pelagius was a heretic so was Augustine, many of whose beliefs were just as extreme and even outrageous. Augustine once said that salvation was just God choosing a few humans to replace some angels which He had lost. It is unlikely that all of the beliefs of Pelagius are embraced within Christianity today. He was an extremist - that is clear. But certainly many of his beliefs are embraced within Christianity today. I think it would have been more fruitful if the two could have sat down and talked out some of their differences but I guess that would have been too much to expect. Today the same extremes are represented in Christianity by the Calvinists on side and the Open Theists on the other side. The Calvinists emphasize God's sovereignty and the utter depravity of sinful man so that the existence of free will is either completely denied or considered irrelevant. The open theist may go to the extreme of even suggesting that God even waits to see what mankind chooses to do and believe before making up His own mind about what to do or even what is right. While I am probably a lot closer to the Open Theist end of the spectrum, refuting all five points of Calvinism, I reject both of the these positions as too extreme. In any case I would like to start the discussion with the following argument for the case of free will within the context of the Christian world view. Many Christians emphasize God's sovereignty and omniscience so much that they conclude that the fall of Adam and Eve must have been according to God's will and plan, knowing that He could then send His son to the earth to redeem mankind, all to the greater glory of God. But if a parent set up his child to fail so that he could look good rescuing him, what would we think of such a parent? We cannot trivialize this failure either since we are not talking about any of the childish things that fallen men desire we are talking about failure in the eyes of God and Adams fall from grace which seperated him and all of his descendents from God. If God is in absolute control and he set up Adam and Eve to fail, then it was at the cost of their eternal life so that they and all their descendents would be doomed to an eternity of hell. If God did this just so that He could come down to earth and save them, all for His own greater glory, then I would call this the behavior of an evil tyrant. I would not believe in such a God. If you do something knowing for certain that as a result of what you do, bad things will happen, then are you not responsible for those bad things? For example, murder is not just pulling the trigger of a gun but setting in motion any chain of events that you know will lead to the death of the person you want dead. Now there is a small difficulty here when other people are involved. Suppose a gunman holds a woman hostage and says he will shoot her unless everyone stands still. If a person then runs from the room is that murder by the running man? Of course not, not only because it is doubtful that the running man wants the woman dead, but also because it is still the gunman who chooses to carry out his threat. He is still the murderer not the person who ran. But this really does not reflect the kind of control that God with his absolute knowlege and power has over the situation we are talking about, so let us consider another example. Suppose a computer programmer sets a trap so that clicking a series of links on the internet causes someone to be killed. Suppose also that these links actually give clear warning of what the consequences of clicking all these links will be. But the programmer knows from trial runs that numerous people will click on these series of links anyway. So the question is, when the person is killed who is the murderer? This is only a little bit closer to kind of control over the whole situation that God has in our lives. So if the computer programmer is responsible for what he caused to happen then why not God? -------------------------------------------------------------------------- The idea of free will not only has difficulty in theology with the conflict it has with God's omniscience and sovereignty, but there are difficulties in science with the conflict it has with the deterministic nature of physical law, and there are even philosophical difficulties which have made many people declare that the idea of free will is a logical contradiction and makes no sense whatsoever. So lets hear your thoughts on this issue.

Of course you mean to ask whether it is right that teachers are forced to be politically correct? A teacher is in a public position and needs to be careful. So, I think you need to be more specific. I also want to ask what your location is because I think that this problem is worse in some areas than others.

every part of existence that we can measure But space itself is curved near a large mass. Consider this question what is a straight line on the surface of an hourglass? So in Einstein's theory the idea of the straight line is replaced with something called a geodesic. Light always follows a geodesic which is the closest you can get to a "straight line" in curved space. Oh I do not doubt it. Many people put much more faith in Star Trek than in physics these days because it is so much more fun and easier to understand, even if it is complete nonsense. Mostly it is just timing and rattling off is not an apt description of what happens. When enough people lay the groundwork in developing new mathematics, finding discrepancies with old theories in physical measurements, and looking at things in new ways. Then just at that time a smart and creative person can put it all together and make a great leap forward in our understanding of things. But even then it is not finished. Because hundreds of scientists and educators come afterwards filling in details, applying the ideas to more circumstances, and testing them in new ways. So what may seem like the work of one man is really the work of many. Relativity is not the unsubstatiated opinion of one man but the checked and double checked theory of the whole scientific community. NO, this is not correct. For the electron, it is also E = m c^2. E is energy and energy can never be negative nor can m which is the mass. Even antimatter is still posititve energy and positive mass. So the equation E = - m c^2 is impossible and cannot apply to anything. Now there are more general equation which are a part of his theory, such as E = gamma m c^2 where gamma = 1/sqrt(1-v^2/c^2) is the Lorentz contraction factor which is 1 when an object is not moving and approaches infinity when the object approaches the speed of light. Whereas E in the other equation is just the rest mass energy of an object this E is the total energy including kinetic energy of the object. At a velocity of 86.6% of the speed of light, gamma = 2, so the energy of an object is doubled. That is at 86% of the speed of light the object has a kinetic energy equal to its rest mass energy. Another more general equation is E^2 = m^2 c^4 + p^2 c^2 and like the previous equation this is the total energy including both rest mass energy and kinetic energy, but where the previous equation only applies to object with mass, this equation also works with objects which are massless. For the photon m = 0 but p = hv/c (Plank's constant times the frequency divided by the speed of light) so putting this in the above equation we get E = hv for the photon. You may know that from mathematics that you should also the solution E = - hv, but such solutions don't necessarily have any meaning and it doesn't have any meaning in this case.

Einstein proved that mass was a form of energy but he never said that photons have mass. He developed a superior theory of gravity where a stress-energy tensor (computed from the energy and momentum densities and flux in space) causes a curvature in space time. Since photons have momentum they contribute to the stress-energy tensor and thus to the curvature of space-time. The curvature of space time alters the path of objects (including photons) from that predicted by Newtonian physics which assumes that space is flat or Euclidean. That is quite correct. Or to put it more clearly, if you are racing past a standing person at half the speed of light towards a wall and if you and the standing person shine a flashbulb towards the wall exactly when you are passing the standing person (and thus when you are both the same distance from the wall) then both you and the standing person will agree that the light from both flash bulbs reach the wall at the same time. This is inspite of the fact that both you and the standing person also see the light from both flash bulbs travel exactly at the speed of light away from you toward the wall, which clearly means that it takes a shorter time for the light to reach the wall (.5775 times shorter in fact) according to you compared how long the standing person thinks it takes the light to travel towards the wall. Wrong about what? What I explained above is from Einstein's theory. Obviously my post has explained some elements of relativity that are new to you. Much of relativity is difficult for the non-physicist to understand. I hope that by clearing up those points where you feel I am "wrong" you will come to understand relativity better. excuse me? Yes they have done this experiment and it was a verification of Einstein's Special and General theories of Relativity, so you are very wrong in thinking that scientists cannot explain this. They expected it. Also you got it backwards the clock that went into space was early not late. Because more time is passed on the clock that went into space, you would acually live less long in space. Of course this really is an unwarranted conclusion because that involves more than just physics, but also studies of the effect of long exposures to the free fall environment. Furthermore, whether more time passes on the clock that goes into space or less time depends on how fast the rocket carrying the clock travels during the trip. You see there are two factors in time dilation. There is the lesser gravity which makes time "run faster" and there is moving at a velocity which is a significant portion of the speed of light will make time "run slower." So if you go away from the earth at a high enough velocity then when you return less time will have passed for you than for those left behind on earth. In fact at 86.6% of the speed of light during the whole trip will mean that the time that has passed for the passengers will be about half the time that has passed for those left on earth.

Everything in this world is one of two types: those which have mass like the electron and those which have no mass like the photon (light).Electrons have mass so they always travel less than the speed of light and have kinetic energy approaching infinity as their speed approaches the speed of light. Since velocity is relative this means that the energy of the electron also depends on how fast you are moving, but because it has mass, if you have exactly the same velocity as the electron, so that relative to you it is not moving at all, the electron has no kinetic energy but it still has energy called its rest mass energy.Photons have no mass so they always travel exactly at the speed of light. However the energy of the photon also depends on how fast you are moving. As you approach its velocity (being massive you cannot reach that velocity), its velocity relative to you does not change (the relative velocity remains the speed of light), but the energy of the photon decreases towards zero (no energy at all). This may sound a bit puzzling for if the relative velocity between you and the photon never changes as you "approach its velocity" then what does "approach its velocity" mean? Well by "approach its velocity" I basically mean accelerating in the direction of its motion. There is no effect on the relative velocity between you and the photon but only on the energy or wavelength of the photon, and is otherwise known as redshift. The wavelength increases and the energy decreases.

Well,..... the moonies claim a success rate of 90% but I have every reason to doubt their claim. They are not a particularly honest organization when it comes to such things, lying to themselves as much as they do to others. Google pulls up this interesting article http://www.religioustolerance.org/chr_diov.htm which gives a divorce rate of 17% to the Unification church, only slightly better than the 21% for Catholics, Lutherans and atheists. The statistics on this site suggest a balance of two forces to me: pressure to get married which increases the rate of divorce and increased religious significance of marriage which tends to decrease the rate of divorse. In the Unification church, their arranged marriage is their baptism and when the marriage fails membership in the church tends to fail as well. The Mormons, to which the article gives a 24% divorce rate, also give a fairly high religious significance to marriage as well as a fairly high amount of pressure to get married. The only other result of my google search is http://forums.xisto.com/no_longer_exists/, which suggests that the Unification church's success comes at a price. Of course no success rate is sufficient inducement to participate in Moon's church which is certainly towards the more tyrranical end of the religious spectrum somewhere between the LDS church and Islam. I personally know of 12 successes and 4 failures in the Unification church which is a success rate of 75% if that has any significance. Of the four failures, one never really got off the ground and another did not last very long, but two involved three or more children and were "fabulous" failures. In one of these two, the incompatabilities were extreme and obvious from the beginning and the other involved constant abuse. Well obviously people are more often like you or perhaps even less compatable, whether they think so or not. People are capable of a rather large amount of self-delusion, and often approach relationships with a less than realistic attitude or wishful thinking. Then there are those people who are so incompatable that without an arranged marriage they may never succeed in starting a relationship in the first place. Anyway this is certainly an area of life that is ruled far more by human kind's irrational tendencies than by their capabilities for reason or even honesty.