http://www.toktalk.net Talking about Theory of Knowledge Sun, 31 Jul 2011 18:57:34 +0000 en hourly 1 http://wordpress.org/?v=3.2.1 Educational Podcast for Theory of Knowledge (TOK) students and teachers. Talking about Theory of Knowledge Oliver Kim http://www.toktalk.net/wordpress/wp-content/uploads/pix_graphics/iTunes_300px.jpghttp://www.toktalk.net TOK, Theory of Knowledge, IB, Epistemology, Philosophy, no Oliver Kim webmaster@toktalk.net http://www.toktalk.net/2009/09/08/what-is-the-title-of-this-episode/ http://www.toktalk.net/2009/09/08/what-is-the-title-of-this-episode/#comments Tue, 08 Sep 2009 17:28:13 +0000 ok http://www.toktalk.net/?p=1545 http://www.toktalk.net/2009/09/08/what-is-the-title-of-this-episode/feed/ 0 A paradox is a self-contradictory or self-referential statement. In this episode we’re going to have a look at several examples. If I say: “I always lie” – am I then lying, or not? If the sentence “I always lie” is true, then it should not be true, because I always lie. If the sentence is not true, this would translate into “I never lie”, But in this case I lied to you, and we again have a contradiction. This is an example of a paradox. A paradox is a statement which contradicts itself. In this episode I’d like to show you a few other examples of paradoxes. Just for the fun of it. Once there was a crocodile, which stole a child. The mother talked to the crocodile and the crocodile said that it will return the child to the mother if she answers to a question correctly. If the answer is wrong, then the crocodile would eat the child. The mother agreed. The crocodile now asked the question: “What am I going to do next?”. What should the mother answer? If she says: “You are not going to eat my child.”, then the crocodile would respond: “Wrong answer, I would have eaten the child, and now I’m really going to eat it because your answer was wrong”. What’s going to happen if the mother answered: “You are going to eat my child.”. The question is now: Should the crocodile now eat the child or not? If the answer is correct, then the crocodile promised to return the child. But this would make the answer wrong again. If the crocodile really intended to eat the child, he has to return it, but at the same time can’t do that because then the answer would be wrong again. If this one was a little difficult to understand, here is a simpler one. It’s called the Omnipotence Paradox: Assuming that God is all-powerful, is He able to create a rock which is so heavy that He can not even lift it himself? I leave it up to you to reason out this one, and I think I don’t need to mention that the paradox is theological nonsense, but this is a different issue. And this one is a classic: “I know that I know nothing.” This is also a contradiction in itself. The person does know something, namely that he/she knows nothing. Russell’s paradox is also quite famous: In a village there is a barber (a hairdresser). The barber shaves everyone who does not shave himself. If I don’t have a razor at home (in this case I don’t shave myself), then the barber will take care of it and shave my beard. The question is now: Who shaves the barber? The barber is not allowed to shave himself because he only shaves those people who do not shave themselves! But then, if he does not shave himself, then he must do so, because he shaves all those who do not shave themselves. So you see, we have another contradictory, paradoxical situation. For those of you, who read George Orwell’s novel 1984, “War is peace.”, “Freedom is slavery.”, “Ignorance is strength.”. These too are self-contradictory, paradoxical statements, which, in this case, are used for propaganda purposes. There is also a quite famous song from Simon & Garfunkel called “Sounds of Silence”. How do the sounds of silence sound like? The paradoxes that I like most are the real-world paradoxes, however. A simple one: You forgot your key in your apartment and locked yourself out. But you need the key in order to open the door and to get to the key. Another one: in some countries you need to have a fixed residential address in order to be able to work. Now, if you are homeless because you don’t have any money and need a job, you can’t get a job because you don’t have an address. In other words, you need a home to get a job, and you need a job in order to earn the money to pay for a home. Again, you have a cat biting its own tail – a paradoxical situation. How wonderful that we have met with a paradox. Now we have some hope of making progress.Niels Bohr Way of Knowing: Logics/Reason A paradox is a self-contradictory or self-referential statement. In this episode we're going to have a look at several examples. http://www.toktalk.net/2009/08/23/how-can-math-be-right-and-wrong-at-the-same-time/ http://www.toktalk.net/2009/08/23/how-can-math-be-right-and-wrong-at-the-same-time/#comments Sun, 23 Aug 2009 07:38:10 +0000 ok http://www.toktalk.net/?p=1544 http://www.toktalk.net/2009/08/23/how-can-math-be-right-and-wrong-at-the-same-time/feed/ 0 To what extent does math reflect the real world? Some mathematical equations deliver results that have no connection to reality. This episode applies the correspondence and coherence theory of truth to the area of mathematics. Originally I wanted to call this episode “Does Math Reflect Reality?” or “The Limits of Math” but then I decided on the title “How Math can be Right and Wrong at the Same Time” – it sounds more, how shall I say… captivating. And yes, I’m going to start off with a little mathematical task to illustrate that mathematical solutions do not always correspond to reality. Let’s start off simple. Certainly you remember the Pythagorean Theorem. If the length of two sides of a right triangle are known, then it’s easy to calculate the third side: a²+b²=c². I’m going to show you now an example using this formula. Lets use some simple values to make calculation easy. If the lengths of the two legs of the right triangle a and b have the values 3 and 4 (a=3 and b=4), what is the length of the hypotenuse c? 3²+4²=c² 9+16=c² 25=c² Pythagorean Theorem: We have 2 possible solutions for c. Well, what is c then? We have to calculate the square root of each side. If you say c=5, then I have to say, only half correct! There are of course two answers for c, namely 5 and -5. So there are two answers for the length of the hypotenuse of the triangle. Mathematically, the length of the hypotenuse could also be less than 0, it could also be negative. You are going to say, that the length can not be a negative value. And you are, of course, right. But the question goes much deeper. It is you, the person, who has to actively evaluate the results of a calculation to check if the result corresponds to reality. The result of a mathematical calculation may be mathematically correct but still “wrong” when we try to apply it to the “real world”. There is also a second example, but here I’m not going to use any formulas. This example is from physics, from Albert Einstein’s Theory of Relativity. You already heard that the fastest maximum speed is the speed of light. I know, I know, some of you are going to complain now and say, this is not true, because the universe itself is able to expand faster than the speed of light. Still, inside space, inside the universe, the maximum speed is the speed of light. This limit does not apply to the forming of space by an expanding universe, but actually this is not the main issue I want to talk about. Just like the triangle example, the equations of Einstein’s Special Theory of Relativity offer several possible solutions. One of these solutions corresponds to the physical world that we all know. This is the “correct” one. There is, however, another solution as well, and this one is really kind of strange. The theory also predicts the existence of so-called Tachyons. Now, what are they? Tachyons are hypothetical particles which are able to travel faster than the speed of light, as a matter of fact, you are not even able to slow them down below the speed of light. Tachyons also possess some other strange characteristics. One of these characteristics is that they lose energy the faster they go. Normally we have to invest energy to make something go faster. You need more fuel to make a car go faster, for example. But tachyons are different. When their energy is 0, they have even infinite speed. The question is now, do they really exist? No. They are a merely a product of a mathematical calculation, without any connection to reality. Researchers tried to identify Tachyons, but so far were not successful. They are purely hypothetical particles. Just like the negative length in the triangle example, tachyons only exist in the world of math. Of course you can always say that maybe there are parallel universes in which these particles can exist. But this is pure speculation and not even scientifically verifiable or [...] To what extent does math reflect the real world? Some mathematical equations deliver results that have no connection to reality. This episode applies the correspondence and coherence theory of truth to the area of mathematics. http://www.toktalk.net/2009/08/20/of-justified-true-belief-and-the-snouters/ http://www.toktalk.net/2009/08/20/of-justified-true-belief-and-the-snouters/#comments Thu, 20 Aug 2009 20:36:32 +0000 ok http://www.toktalk.net/?p=1524 Rhinogradentia. Can you know that they existed?]]> http://www.toktalk.net/2009/08/20/of-justified-true-belief-and-the-snouters/feed/ 0 In this episode, I’m going to apply Plato’s definition of knowledge (justified true belief) to the recently discovered mammals, the Rhinogradentia. Can you know that they existed? Have you ever heard of the strange looking group of mammals, the Rhinogradentia? If you don’t know what they are, then maybe the name Snouter rings a bell? No? Don’t worry, I’m going to explain what they are. In this episode I’m going to use the names Rhinogradentia and Snouters interchangeably, they refer to the same animals. And, yes, I’m also not forgetting about some Theory of Knowledge aspects. In particular I’m going to address the concept of “justified true belief” as a definition of knowledge. So in that sense this episode is somewhat introductory in nature. But first, let’s talk about the Rhinogradentia, the Snouters. The Rhinogradentia are a group of mammals and were first discovered by the Swedish explorer Einar Pettersson-Skämtkvist in the year 1941. They are a fairly recent discovery, even if this was over 60 years ago. He discovered them on the Polynesian Hi-yi-yi islands in the Pacific ocean, while escaping captivity as a prisoner of war. This was during the second world war. Unfortunately only a few years later, in 1945, the island was destroyed by an earthquake. Nasobema lyricum: this one has four noses to walk on. Others only have one nose. The large ears work like wings. A nuclear bomb explosion 200 km away caused a destabilization of the tectonic plates causing the islands to sink. And this, of course, caused the extinction of the Snouters. Equally dramatic is, of course, the loss of human life. At the same time they had a scientific congress on the islands and the earthquake also resulted in a destruction of scientific records and researchers that gathered there to discuss the discovery of the animals. Now a few words about the animals. The Rhinogradentia differ from other mammals by their unique morphology and method of movement. All Snouters have one characteristic in common. They do not use their legs for movement, but rather their long extended nose or noses. This is the reason why they are called Rhinogradentia, with “Rhino” meaning “nose”. Some of them have one nose, and some of them several noses. The noses can be extremely long, nearly as long (or longer) than the rest of the body. For those of you who are more biologically interested: The biological order Rhinogradentia can be further subdivided into two families the Monorrhina (they have only one nose) and the Polyrrhina (multiple noses). In his book The Snouters: Form and Life of the Rhinogrades the author Prof. Harald Stümpke described 26 different genera of these animals. Since the publication of this book in 1957, several new genera could be identified. The two pictures that I included show two representatives of the Snouters. The top picture shows Nasobema lyricum. You can see that it has four noses. It belongs to the family Polyrrhina. “Poly” means many, and “rhina” means nose. The bottom picture shows a member of the Monorrhina, it only has one nose. If you want to read more about these interesting animals, then I’d recommend Mr. Stümpke’s book, which can be ordered online. It contains many wonderful drawings by the author. The fact that it is printed even more than half a century after it’s first publication in 1957, illustrates what a remarkable milestone the discovery of the Rhinogradentia was. The most interesting fact about the Snouters, I have not even told you yet. And I’m not going to tell you yet, because I want to build up some tension. I’m going to tell you later, I promise. But first let’s talk a little about about some TOK issues. It’ll become clear later why I’m jumping around with the topics like that. And now it’s getting a bit “TOK-ish”. I would like to answer the question “What is Knowledge?”. So, what is knowledge? Now, there are [...] In this episode, I'm going to apply Plato's definition of knowledge (justified true belief) to the recently discovered mammals, the <em>Rhinogradentia</em>. Can you know that they existed? http://www.toktalk.net/2009/08/14/the-egg-of-columbus/ http://www.toktalk.net/2009/08/14/the-egg-of-columbus/#comments Fri, 14 Aug 2009 06:59:51 +0000 ok http://www.toktalk.net/?p=1509 http://www.toktalk.net/2009/08/14/the-egg-of-columbus/feed/ 0 How do you balance an egg on its pointed side without any extra help? Many problems appear easy, once you know how to solve them. Often hidden assumptions prevent us from solving a particular problem, however.Here in front of me, I’ve got a boiled egg. And the last 10 minutes I’ve been trying to balance the egg on its corner. No. Eggs don’t have corners, of course. I’ve tried to balance the egg on its pointed end. I think I don’t have to tell you that this is an impossible feat, the egg is always rolling over to its side. It’s possible to spin the egg, but after a few seconds the egg will roll again to its side, so this is not a good solution. This egg balancing problem is not a new problem. It has been around for about 500 years now. Christoper Columbus, remember he was the one who discovered America in 1492, posed the very same problem to several Spanish nobles. And even 500 years ago they could not solve the problem. But Christoper Columbus knew a solution, one which is surprisingly simple. He took the egg and he smashed it on the table. And the egg was standing. Columbus makes an egg stand on its pointed side. I know what you are thinking. You are thinking that this is an unfair solution, because you are not allowed to break the egg. But why not? You assumed that you are not allowed to break the egg, but who says that this is not allowed? Why are we not allowed to question the basic assumptions? After all, the questioning of assumptions is essential for many types of progress, and scientific progress in particular. Unfortunately this is easier said than done. Very often we are not even aware of our own assumptions – and therefore are unable to question them. We find ourselves stuck in a problem situation that we can not solve. But once we found a solution to a problem and understand how it is solved, it becomes easy to repeat for anybody. I want to give you a second example and I’m also going to tell you the solution to it. I know that giving away the answer takes the fun out of it a little bit, so maybe you want to stop the podcast for a while to try it out yourself. To give the whole task some “TOK basis” I’m later going to talk about the assumption that you have to overcome to solve the problem. All you need is 6 matches or 6 toothpicks or 6 pens/pencils. It does not matter. They should be the same length. And now here is the task: Try to arrange the six matches (or whatever you used) into exactly four equally sized triangles, without breaking the matches. This is not a trick question. If you make 6 triangles, then it’s not right. All of The triangles should be equilateral, this means that the 3 sides should be the same length. Again: 6 matches arranged into 4 equal triangles, with no gaps. Stop the podcast now, and try to solve it. OK, I’m back again. Most people probably were not able to solve it, at least not quickly. At least, this is what my experience showed me in the past, when I showed the same problem to others. If you tried to arrange the six matches on your flat table, then you already made an assumption which does not allow you to solve the problem. The only way to make the 4 triangles is to make a pyramid with 3 sides and one base. You have to think in 3 dimensions and not in two, like most people. Nobody told you that you were not allowed to use the third dimension. It was your assumption (or at least the assumption of those who could not solve the problem). Again, the solution is easy once you know it, but difficult at the beginning. Now why do many people initially try to arrange the 6 matches on a two dimensional surface? The answer is simple but at the same time disturbing: Many people are fixed on two dimensions because they are already acquainted with similar puzzles, where the solution can indeed be found in two dimensions. Their previous knowledge about such puzzles limits their view. The question that I am asking myself now is, to what extent [...] How do you balance an egg on its pointed side without any extra help? Many problems appear easy, once you know how to solve them. Often hidden assumptions prevent us from solving a particular problem, however. http://www.toktalk.net/2009/08/07/what-is-enlightenment/ http://www.toktalk.net/2009/08/07/what-is-enlightenment/#comments Fri, 07 Aug 2009 08:49:55 +0000 ok http://www.toktalk.net/?p=1147 http://www.toktalk.net/2009/08/07/what-is-enlightenment/feed/ 0 Enlightenment is the courage to use your own brain. Sapre Aude! Dare to Know!Enlightenment is the courage to use your own brain. It is the courage to think on your own. What do you do if you want to make your lifestyle healthier? You talk to a doctor. He or she will advise you on what food to eat. You have a financial issue? You talk to the bank. They will advise you how to invest your money. Or maybe you have an emotional problem? Go to a psychologist! He/she will fix it. You have problems making a moral or ethical decision? You talk to a religious authority or a philosopher. You have problems settling a disagreement with somebody? What do you do? You talk to a lawyer, of course. You don’t know what to study at university? You ask your parents or your friends. They know it better. You don’t know the answer to question on an exam? You have look at what the person sitting next to you is writing. The reason why so many people are not free to make their own decisions, the reason why so many people are dependent on others is not because of a lack of intelligence. People are not dependent on others because they lack knowledge. No. People depend on others and let others be in control and be their guardians because they are simply too lazy and to afraid to think on their own. It’s too comfortable to pay for a service and to let others do the thinking for you. As a consequence you become dependent on them and you will stay in life-long immaturity. Wow. Now these are strong words. Who said that? No, it is not I, who came up with this idea. It goes to the credit of the philosopher Immanuel Kant. For those of you who don’t know yet, Kant is a central Theory of Knowledge figure and a central figure of the Age of Enlightenment. He has shaped Western Philosophy like few others have. In any case, in the year 1784 Kant wrote an essay where he answered the question “What is Enlightenment?”. He wrote: “Enlightenment is man’s emergence from his self-incurred immaturity.” Self-incurred means that the person is responsible himself for his own immaturity. According to Kant, people themselves are responsible if they are in a state of life-long immaturity because they let other people do the thinking for them. Of course it’s also easy to misinterpret Kant’s view. I want to give you some alternative examples: What do you do if you want to make your lifestyle healthier? You swallow some vitamin tablets. You have a financial issue? You try gambling. Or maybe you have an emotional problem? You can drown it in alcohol. You have problems making a moral or ethical decision? You ignore all moral and ethical standards. You have problems settling a disagreement with somebody? You take the law into your own hand. You don’t know what to study at university? You keep changing your study over and over or keep on pushing out the decision until it’s too late. You don’t know the answer to question on an exam? You bribe the teacher. Even here you do not use your own reason, but resort to a “quick-fix solution”, which doesn’t work over the long run and ultimately causes more problems. Maybe a person is mature if he/she is aware of his/her own limitations of knowledge and then consults others for help. Maybe it’s the knowledge of your own lack of knowledge which is also characteristic of an “enlightened person”. I think that Kant would agree. The Age of Enlightenment is also known as the Age of Reason. It started to emerge in Europe and the United States during the 18th century. It was the time when people started to think critically and rationally about the world. This is the time when people started to think about human rights issues, freedom issues and individual liberty. To give you an example, the abolition of slavery in the United States was made possible due to this change in attitude towards fellow humans. It was also a time when scientific progress started to increase. At that time people started to see the [...] Enlightenment is the courage to use your own brain. Sapre Aude! Dare to Know! http://www.toktalk.net/2009/08/06/of-arts-and-ethics/ http://www.toktalk.net/2009/08/06/of-arts-and-ethics/#comments Thu, 06 Aug 2009 13:22:02 +0000 ok http://www.toktalk.net/?p=1073 http://www.toktalk.net/2009/08/06/of-arts-and-ethics/feed/ 0 I’ll be exploring the relationship between arts and ethics. Is it necessary for art to go against moral and ethical conventions in order to be considered “good” art? Where are the limits to the freedom of expression of art? In this episode I’ll be asking questions, and not give answers! In this episode, I’ll be exploring the relationship between arts and ethics. Some time ago, I read an interesting news report, one which links the two areas of knowledge Arts and Ethics. It’s about an unusual art exhibition. The artist placed 10 kitchen blenders on a long table. The blenders have sharp rotating knives and are normally used to smash vegetables or fruit. But in this case, each one of the blenders contained a live little gold fish swimming in some water. The visitors of the museum now had the choice of turning on the blenders – or not. The visitor, essentially, became the “rulers of the decision on life and death”, too use the words of the artist. According to news reports, some visitors indeed turned on the blenders, killing the fish, making fish soup. Animal rights activists complained, of course, and the police started to get involved as well. When I first read about this art exhibition, I had to ask myself several questions. Must art provoke? Is it necessary for good art to provoke emotions and a discussion? Can art be unethical? And if yes, who defines it? Is it even necessary for art to be unethical in order to provoke emotions or a discussion? Does calling something “art” automatically justify a certain action or painting or work? Does calling something “artistic” make it more moral or ethical? Here we have a connection to language as well. Killing a small fish in a blender is bad. Killing a small fish in a blender and calling it art is good (or at least acceptable). Should certain types of art be censored? Where does the freedom of expression end? I know that some people have a strong view on this topic and say that art should not be censored at all. It’s a little like the freedom of science, which should be, in some people’s view, be unlimited. Now, unlimited freedom of art is also problematic. This would mean that torturing animals like dogs and cats for the sake of art, is also acceptable. Luckily there are laws for the protection of animals that prevent this. Why do people get so excited about this particular art exhibition? Many animals get killed every day for food. If somebody catches a fish and eats it – is this type of killing animals more/less/equally ethical or unethical than killing the fish in a blender? If you say that the fish in the blender was not killed for food, does drinking the fish soup (how disgusting…) make the action more moral? Then it should be the same again, you are eating the dead animal for food. And what if the artist does not use a fish, but rather a dog or a cat? I think more people would complain in this case, but then why? Are dogs or cats “more worth” than a small fish? Is size the issue here? Or is it a question of emotional attachment to dogs and cats? What kind of art is more acceptable: Killing one single fish in a blender or 2 ants? Many people would have fewer problems killing the insects. But why? The last question is a bit controversial, I have to admit. Could it be that some people (not all of them!) oppose the art exhibition not because of legitimate animal rights reasons, but because the art exhibition makes them feel uncomfortable? Maybe people became uncomfortably aware that different people have a different view and would have no problems killing the fish. Maybe they just use an the animal-rights justification as an excuse? In other words, maybe some people want to avoid an uncomfortable ethical discussion and they use an animal-rights motive to oppose the exhibition. But in reality, they don’t care about the fish. They just don’t want to deal with the uncomfortable topic of death or issues of ethics. Maybe they want [...] I'll be exploring the relationship between arts and ethics. Is it necessary for art to go against moral and ethical conventions in order to be considered "good" art? Where are the limits to the freedom of expression of art? In this [...] http://www.toktalk.net/2009/08/05/is-the-word-scientific-overused/ http://www.toktalk.net/2009/08/05/is-the-word-scientific-overused/#comments Wed, 05 Aug 2009 17:08:41 +0000 ok http://www.toktalk.net/?p=1080 http://www.toktalk.net/2009/08/05/is-the-word-scientific-overused/feed/ 0 In this edition I want to give a little warning. Sometimes the words “science” or “scientific” are used to increase the value of certain claims, even if the use of these terms is not justified. There are many claims out there that give the appearance of being scientific but they are not. Sometimes claims are shrouded in fancy language and sophisticated vocabulary – very serious sounding stuff. “It’s gotta be true, it sounds so scientific!” The media is full with claims that sound scientific but are not. Please get me right. I’m not saying that the claims that are made are always necessarily wrong. Sometimes these claims are given a higher credibility by wrapping them in a language that people associate with science. Why do they do that? In many societies of this world natural science has a very high standing and reputation. After all, medical and technological progress can be largely attributed to the natural sciences and engineering. We consciously or sub consciously realize this of course. It is now possible to increase the credibility of certain claims by associating them with science. How many times have you seen that some products are advertised by people dressed in a white lab coat? If a scientist says that it works well, then it’s gotta be true! This is what you call reference to authority. This reference to authority in itself is not a problem, if the authority justifies the claim using reasoned arguments. It starts to become problematic if the reference to authority alone is used as a justification. If only the reference to authority is used to justify a claim, then it starts to become the so-called ad hominem fallacy. “He is a well-known scientist, therefore he must be right.” In the ad hominem fallacy the person himself/herself is used as a justification and not the argument of the person. Boris Podolsky, a co-worker of Albert Einstein, criticized the over usage of the word “scientific” especially in advertising. If you want to sell a product, just add the phrase “it’s scientifically proven”. And if you use a couple of fancy, scientific sounding words, the people really get impressed by it and start buying the product. The product becomes prestigious and its value increases. One has to be careful not to be blinded by fancy words. And this is where we have a link between science and the use of language. I want to cite from Podolsky’s article “What is Science” that he wrote in 1965: “In recent years the power of Science has received such popular recognition, that the adjective scientific attached to merchandise or statement is known to give to such merchandise or to a statement prestige having definite advertising value. As a consequence the words Science and scientific are frequently abused by those who find it profitable to borrow reputation instead of earning it.” Boris Podolsky (1965), The Physics Teacher, Vol 3, Issue 2 pp. 71-73 In this edition I want to give a little warning. Sometimes the words "science" or "scientific" are used to increase the value of certain claims, even if the use of these terms is not justified. http://www.toktalk.net/2009/08/05/what-are-some-problems-with-conspiracy-theories/ http://www.toktalk.net/2009/08/05/what-are-some-problems-with-conspiracy-theories/#comments Wed, 05 Aug 2009 16:03:24 +0000 ok http://www.toktalk.net/?p=1031 http://www.toktalk.net/2009/08/05/what-are-some-problems-with-conspiracy-theories/feed/ 1 There are several problems with conspiracy theories, which are outlined in this episode. I want to start this episode with a little example. Imagine that you are walking in the forest and that you see a burning tree. I give you two possible explanations: Somebody dropped a burning cigarette and accidentally set the tree on fire. The government tested a secret weapon, which accidentally set the tree on fire. Which one of these two explanations is the better one, and why is it better? Many would probably say that the first explanation is the more reasonable one, but why is it more reasonable? The second explanation could be correct as well! Maybe there is a secret weapons program, and we don’t know about it! Could it be that the first explanation, with somebody dropping a burning cigarette, is too “normal” to be true? There just has to be more to it, right? Well, as a matter of fact, the first explanation is indeed the better one and is more likely to be correct. The reason is, that it is the simpler explanation, and it is based on fewer assumptions. Remember, you should always go with the simplest possible explanation. The second explanation, the secret weapons program, is a conspiracy theory and requires several assumptions. You have to assume that such a weapons programs indeed exists in the first place, you have to assume that the government was able to keep it secret, you have to assume that they tested the weapon, you have to assume that the weapon hit the tree and that it was able to set the tree on fire. There are simply too many assumptions that can not be verified. The person dropping a cigarette requires far fewer assumptions and is therefore to be preferred. This is called “Ockham’s Razor”, named after 13th century philosopher William of Ockham. To put it in easier words – don’t make the issue more complicated then necessary. Go with the simplest explanation that explains the observations. Do not look for complicated explanations, even if these explanations are more “exciting” or “interesting”. It is now July 2009, and 40 years after the first moon landing. A moon landing, which, according to some people, never took place. Yes, there are some folks out there who claim that the moon landing is a conspiracy, it never happened! All the pictures and films of the moon landing, in their view, were made inside a studio. The rocket did start, for all the world to see, but the astronauts were only placed into an orbit around the earth, and never really went to the moon. In the meantime, filming started in a studio on earth. After several days the astronauts returned from their orbit and their space capsule landed inside the ocean to be picked up. There are countless other examples of conspiracy theories, here are some examples: The Chemtrails conspiracy: This conspiracy started back in 1996. You have already noticed that high flying airplanes make condensation trails of water vapor, which are nothing more than clouds. If you remember your chemistry, the burning of fuel (or any organic substance) produces carbon dioxide gas and water. Now, conspiracy theorists claim, that these condensation trails are in reality some chemical or biological agent, which the government sprays on the population – for whatever reason. Of course the governments refuted these claims, but for conspiracy theorists, this is even more evidence that they have something to hide. The 9/11 conspiracy: This one states that the 9/11 attacks were an “inside job” and that the US government itself was responsible for it. The conspiracy theorists came up with many “proofs” all of which turned out to be wrong. Global warming conspiracy theory: Global warming is not really taking place, or CO2 is not responsible for it – it’s all a lie. Princess Diana: She died in a traffic accident in 1996. Conspiracy theorists say that she was assassinated. And there are many more, of course. What do all of these [...] There are several problems with conspiracy theories, which are outlined in this episode. http://www.toktalk.net/2009/06/14/tok-essay-faq/ http://www.toktalk.net/2009/06/14/tok-essay-faq/#comments Sun, 14 Jun 2009 07:19:45 +0000 ok http://www.toktalk.net/?p=967 http://www.toktalk.net/2009/06/14/tok-essay-faq/feed/ 1 This post addresses several Questions in relation to the TOK Essay. Disclaimer: The following advice is my personal advice to my students and not approved by the IB (or by anybody else). TOK examiners may have a different opinion on these issues. Use the information at your own risk. 1. Can I use the word “I” in the essay? Can I write the essay in first person? The TOK essay is a personal essay. Yes, you can use the word “I”, but you do not have to. As a matter of fact, this may even be useful if you give personal examples. Still, do not forget that the TOK essay is a formal essay. Do make sure that the essay uses a formal language nevertheless. 2. Do I have to do research? Do I need a bibliography? No, research is not required according to the criteria, but it may be helpful. The TOK Essay is not a research essay, it is an argumentative essay. You will not get points for only summarizing other people’s ideas. You get points for analysis and for understanding of these ideas. If you do use quotes or other people’s ideas, then you must give a proper bibliography, of course (as a matter of fact, points will be taken off otherwise). 3. How important is the introduction? The introduction is one of the most important paragraphs of the essay. It lays the foundation of the essay and guides the reader. If the intro is not clear, then the reader may have problems following your thoughts. An unclear introduction may also be a sign that you, the author, are not fully clear of the ideas yourself. 4. What should be included in the introduction? For students who have no idea on how to start the introduction, I would recommend to do the following (this is not written in the assessment criteria, it is a personal advice, read the disclaimer at the top of the page!): First, explain the prescribed title. What is the problem implied by the title? If you have difficulties with this (or if you simply repeat the title) then this may be an indication that the problem of knowledge is not clear to you. Explain key terms of the prescribed title, but do not give me dictionary definitions and do not simply summarize TOK theory. Second, answer the prescribed title question. Force yourself to do this. If you can not do this, it can be a warning sign that you are not clear of what you are going to say in the essay. Answer the question in a differentiated way, a clear answer may not simply be a yes/no answer. It can also be a “yes, but…” or “no, but…” answer. Try to complete the following line: “In this essay I will show that…”. If you do not want to use the “I” word, then you can reformulate the sentence: “In this essay it will be shown that…”. The answer to the title question is your thesis. It should tie the essay together and make it easier for the reader to follow the essay. The thesis should also help the author to answer the title question. Third, tell the reader which areas of knowledge and which ways of knowing you will use in the essay. Do not use too many areas (there is the danger that you can not cover everything in depth) and do not use too few. 5. Should I define important terms in the introduction? Clarify the terminology, explain the prescribed title question, but do not give me a dictionary definition. All too many students simply quote from the dictionary or from the TOK book without being clear what the term means in relation to the prescribed title. Again, you do not get points for quoting ideas, you get points for analyzing the ideas. 6. Should I use TOK theory? Yes, do use TOK theory but make sure that you use it to answer the prescribed title question. Analyze and reflect on the theory. In the past I have read too many essays which simply summarize TOK theory without any connection to the title. You do not get points for the summary, you get points for analysis, reflection and application of the TOK theory. If you write a whole paragraph explaining the different approaches to ethics, [...] This post addresses several Questions in relation to the TOK Essay. http://www.toktalk.net/2009/06/14/on-the-purpose-of-life/ http://www.toktalk.net/2009/06/14/on-the-purpose-of-life/#comments Sun, 14 Jun 2009 06:44:23 +0000 ok http://www.toktalk.net/?p=995 http://www.toktalk.net/2009/06/14/on-the-purpose-of-life/feed/ 0 Viktor Frankl (1905-1997) and the purpose of life. After a few months of idleness, I think it’s about time to add another short episode. Well, what am I going to talk about today? Today I’d like to talk about the purpose of life. Now, I know that this does not sound like one of the classical Theory of Knowledge topics, but who cares….. Why not do something different for a change. Why this topic? A few weeks before the end of the school year a student came up to me and asked me, seriously, “What is the purpose of life”? We had a short conversation on the issue and I decided to pick this topic up during the last TOK lesson of the school year. I passed on this question to the rest of the class. Some of them looked back at me with surprised big eyes. In my view, one of the purposes of TOK is to make students ask questions that they normally would not ask, and by the response that I got many of my students really never asked themselves this question before, in that sense I reached my objective. A discussion started. And it slowly started to crystallize out that there were two different approaches to the question. I like to call this the “absolutist” and the “relativist” approach. You see, I do feel inclined to throw in some TOK terminology here. One group of students, the absolutists, maintained that there must be some kind of external purpose of life. The purpose of life, in their view, does not depend on the individual. The purpose of life is absolute, is ultimate. I can imagine that a purpose of life which is defined over religion or spirituality goes into this direction. The relativists, on the other hand, claimed that each individual has to define his/her own purpose of existance. There is no usiversally acceptable purpose which applies to all people, in their view. One of the students had a particularely interesting view. She stated that it would be pretty sad if life had no absolute, “external” meaning. It would be pretty sad if the only meaning of life were the meaning that the individual defines as being the meaning of life. It’s like saying: “Life’s inhearantly pointless. So let’s start looking for a point to give it at least some kind of meaning.” Now, this can’t be it – according to her view. And I understand her point. Somewhat to my surprise none of the students, yes, this is zero %, none of the students stated that the purpose of life is to earn a lot of money, to be rich. First it surprised me in a positive sense but then I had to think about it again. Because the most common response that I got, with a soft voice and a questioning look, was: “Maybe the purpose of life is – to enjoy life, maybe?”. As If they were asking me if the answer is correct. “Well, are you enjoying life?” – I asked them back. silence. Maybe we teachers kept the students studying so hard during the last couple of years that this prevented them from asking questions like this. After a lengthy conversation I wanted to conclude the lesson with the question: “Maybe the purpose of life is to look for the purpose of life.”. But somethiw they didn’t like this and I received some protest. And maybe they were not so wrong. According to psychiatrist Viktor Frankl, you have to stop looking for a meaning in life in order to find one. He addressed this issue and he came to a quite concrete conclusion. According to Frankl, the purpose of life can be found in three different ways: by creating a work or doing a deed: some people make paintings, others write poetry and still others write a blog called TOKTalk. You can also find meaning in life by helping others. by experiencing something or encountering someone: this should be pretty self-explanatory. by the attitude we take toward unavoidable suffering: According to Frankl it is possible to find meaning by changing our attitude. We may not be able to change the situation, but we are able to change ourselves. OK, now how should I conclude? I [...] Viktor Frankl (1905-1997) and the purpose of life. http://www.toktalk.net/2008/12/28/on-relativism-and-constructivism/ http://www.toktalk.net/2008/12/28/on-relativism-and-constructivism/#comments Sun, 28 Dec 2008 17:47:20 +0000 ok http://www.toktalk.net/?p=938 http://www.toktalk.net/2008/12/28/on-relativism-and-constructivism/feed/ 0 In this episode I’m going to explain the differences between the philosophical concepts of relativism and constructivism. A student recently wrote me an email and asked me about the similarities and differences between relativism and constructivism. I already started to write an email to answer this question when I reconsidered and decided to take this opportunity to make another podcast episode out of it. Now before I start off, I just want to say that we have to be a bit careful that we are not getting too theoretical about this. And if a “real” expert on this topic discovers some inaccuracies in my explanation, I kindly request some forgiveness….. I have not studied this particular aspect in much detail myself. In any case, relativism and constructivism – These are two related philosophical concepts but they are kind of broad, and there are several different aspect to each one of them. I can certainly not cover all of these aspects in a few minutes, we have to stay elementary here. The concept of Truth Relativism is a view that absolute truths do not exist, and that truth (whatever it may be) depends on something else, on some context. To give you an example – You have probably already heard of the expression “beauty is in the eye of the beholder”. Now this statement assumes that an absolute view of beauty does not exists. What is beautiful or ugly depends on the beholder (the person viewing it). Likewise, relativists would say that absolute truths do not exist, but that truth depends on culture, experience, and other external factors – a so called “frame of reference”. Absolute ethical values, in their view, do not exist, or maybe can not exist. Scientists of course, assume that an objective reality does exist, and they try to discover this objective reality. Scientific knowledge, after all, should be independent of anyone’s culture, experience, background, opinion, beliefs, religion, etc. Constructivism is a related term and it is also used in a range of different ways. And to make the issue a bit more exciting, it is even possible to subdivide constructivism into “radical constructivism” and “moderate constructivism”. A radical constructivist would say that an objective reality, an objective outside world does not exist. It is a product of one’s mind. So if you are listening to this audio file or reading the text on the screen, then this may all be a fabrication of your brain. The computer screen in front of you does not exist! Your brain makes you think that you are looking at a screen, you are just hallucinating! Essentially it is an extreme form of relativism – the things that you percieve as reality actually depend on your brain. Moderate constructivism is, in my personal view, a bit more useful. It is commonly used in connection with education and learning theory. Essentially it states that each person has to construct knowledge individually. In their view, a teacher is not able to teach a student anything at all. The teacher is only able to support or help a student to build up his or her own knowledge. Now where is the link to relativism? Moderate constrctivists assume that each person’s view of reality (of science, of math, of arts, of history etc.) is constructed in the person’s brain, the view of reality depends therefore on the individual person. Moderate constructivism therefore is a form of relativism, but not an extreme one. Moderate constructivists may not deny that an outside reality exists. But they do state that individual people percieve and interpret this reality differenty. I want to conclude with two examples. I am not only teaching Theory of Knowledge but also Biology. Every year we are doing a little drawing activity using a microscope. I ask my students to draw the onion cells that they see in the microscope. All of the students are seeing the same cells. But when I collect the drawings at the end of the class, I receive all forms of [...] In this episode I'm going to explain the differences between the philosophical concepts of relativism and constructivism. http://www.toktalk.net/2008/12/10/six-jokes-in-seven-minutes/ http://www.toktalk.net/2008/12/10/six-jokes-in-seven-minutes/#comments Wed, 10 Dec 2008 13:57:07 +0000 ok http://www.toktalk.net/?p=276 http://www.toktalk.net/2008/12/10/six-jokes-in-seven-minutes/feed/ 0 Here is a collection of six (hopefully intelligent) jokes that count to my favorites. I don’t know if you consider them funny or not, in any case they should give you something to think as well. This time, it is something different! Do you want to listen to a few jokes? Here is a collection of six (hopefully intelligent) jokes that count to my favorites. I don’t know if you consider them funny or not, in any case they should give you something to think as well. Transcript: OK, this time I’m going to try out something different, I want to tell you a few jokes. Yes, you heard correctly. Now there is a small problem to that – I think that these jokes are funny, but maybe you don’t think that they are. Well….. tough luck for me. I any case I can’t year you not laughing, so it is not embarrassing for me if you don’t laugh. There is a second hitch to it as well…. some of the jokes are a bit difficult to understand, does not matter, at least I can laugh at them myself. Here is the first one, and as a matter of fact, it’s not by me but by a philosopher called Ludwig Wittgenstein, I took the freedom to change it around a little, the original is a bit different but the idea is the same. There are two people sitting in a garden in the shadow of a tree, the sun is shining, maybe occasionally an apple is falling from the tree, and one of them keeps repeating the words “I know that this is a tree”, “I know that this is a tree”, “I know that this is a tree”, “I know that this is a tree”, “I know that this is a tree”. The second person listens and nods. “Yes, this is a tree.”, “yes, you are right, the tree exists” “this is really a tree.” A third person comes along and watches the conversation, and asks: “Are you two OK? Can I help you somehow?” Shall I call for help? They laugh and say, oh, we are both completely fine, we are not crazy. We are just having a little Theory of Knowledge conversation. End of Joke. I can’t hear you laughing. In any case here is Joke number 2, it’s a little more advanced. It’s a math joke. An infinitely large group of mathematicians visits a bar. Apparently they just came from a math congress, some kind of meeting, where they discussed some important concepts, and now it’s time relax a bit. It’s kind of tight in the bar, with the group being so large, but the real problem is a time problem. Because the group of mathematicians is infinitely large, it would take an infinite amount of time to order the drinks. And this is of course not very practical, because some of them would have to wait too long, and tomorrow the meeting continues. Now they have to find a solution to this problem and start to discuss. After a few minutes one of the mathematicians walks up to the bartender to place an order. He says: “I want to order orange juice for the whole group (here I need to comment that alcohol is a no-no because the mathematicians don’t want to damage their brain cells), that’s why they chose orange juice. He walks up to the bartender and says – I want to order juice for the whole group, but not everyone is equally thirsty. Give me one glass of juice for the first person, only half a glass of juice for the second person, one-fourth of a glass for the third person……. Stop! Interrupts the bartender. I understand what you mean. I’ll give you two glasses of orange juice. End of Joke. I won’t explain it. You do the math. Joke 3 is a short one: If there are 5 people in a room and 6 people walk out, then one person has to walk back into the room so that the room is empty. Obvious is it not? Joke 4: This is a psychology joke. Actually it is from a cartoon that I once saw. But first some background information. Do you know what a Skinner Box is? It is a cage where psychologists keep animals, usually mice, or rats or pigeons, to study their behavior. When the animal behaves correctly, usually by pushing a certain button, then the [...] Here is a collection of six (hopefully intelligent) jokes that count to my favorites. I don't know if you consider them funny or not, in any case they should give you something to think as well. http://www.toktalk.net/2008/12/10/tok-essay-checklist/ http://www.toktalk.net/2008/12/10/tok-essay-checklist/#comments Wed, 10 Dec 2008 06:19:36 +0000 ok http://www.toktalk.net/?p=895 http://www.toktalk.net/2008/12/10/tok-essay-checklist/feed/ 0 Here is a short checklist of points to watch out for when writing the TOK Essay. Here is a short checklist of points to watch out for when writing the TOK Essay. Over the years I have proof-read uncountable essays, and there are often similar issues that appear. Many of these issues are addressed below: Introduction: You must give it a clear introduction that allows the reader to understand in which direction the essay is going. The introduction must also contain your thesis statement (“knowledge issue”). What is the problem of knowledge? You must answer the essay title and not modify it. As there are several ways to answer the essay title, you must make it clear in the introduction which way you are going. Terms: You must define the terms of the essay question, but do not simply give dictionary definitions! How do you interpret these terms? If you do use dictionary definitions, then you must critically reflect on them to get points. Structure: The essay must be divided into separate paragraphs, each paragraph must relate to the point that you make. The paragraphs answer should directly answer your thesis and the title question. Paragraphs: Each paragraph must deal with one aspect. Every paragraph must include an introductory sentence a body and conclusion. There must be a proper transition between the paragraphs. Make sure that each paragraph clearly answers the prescribed title! Critical thinking: You must include counter arguments and demonstrate critical thinking. Generalizations: As a rule, don’t use generalizing words, such as “all”, “none”, “everyone”, “no one”, “since the beginning of humankind”, “it has always been known…”, “Everyone knows”….. Chances are good that your statement will not be correct. Stereotypes: Be careful that you do not use stereotypes when addressing cultural issues! Conclusion: The conclusion must not address new points. It should round off the essay. Do not squeeze new ideas into the conclusion that are best left for a separate paragraph. TOK Issues: You must include TOK theory, but you must also apply this theory to answer your title question. A summary of theory alone is not enough. Areas of Knowledge and the different Ways of Knowing: Did you include and compare them? Some prescribed titles have a strong focus on only one Area of Knowledge or Way of Knowing. In this case it is not necessary to force yourself to include other areas as well, but a short comparison, if relevant, can never hurt. In any case, the essay should reflect a broadness in ideas. Examples: Support your arguments with relevant examples. Do not include examples that are not explained. Include specific relevant examples from your personal life. Do not just summarize examples from your teacher. Word count: If you need to stretch your essay in order to meet the word count, then you have not spent enough time thinking about your topic. Sentences without content are irrelevant and a waste of time. You will not get points for them. Word count is 1200-1600 words. Do not exceed. The Assessment Criteria: Have you written the essay with the assessment criteria next to you? If not, then I do not understand why you chose to make the task of writing the essay more difficult than necessary. The criteria should help you. Check List (based on the assessment criteria) Are the problems of knowledge recognized? Do you refer to the problems of knowledge throughout the essay? Does critical reflection take place (counter arguments, etc.), or are there sweeping generalizations? Are different Ways of Knowing and different Areas of Knowledge addressed? Are they properly linked? Is the essay properly structured into paragraphs? Does each paragraph answer the title question? Are relevant examples (from different sources) given and explained? Did you also include personal examples? Are the statements and claims factually correct? Sweeping generalizations are very risky. They show a lack of [...] Here is a short checklist of points to watch out for when writing the TOK Essay. http://www.toktalk.net/2008/12/03/newspaper-articles-does-size-matter/ http://www.toktalk.net/2008/12/03/newspaper-articles-does-size-matter/#comments Wed, 03 Dec 2008 10:26:39 +0000 ok http://www.toktalk.net/?p=268 http://www.toktalk.net/2008/12/03/newspaper-articles-does-size-matter/feed/ 0 How does the optical appearance of a newspaper article, the size of the headlines, the size of the pictures, influence its perception of its content by the readers? How does the context in which a newspaper article appears influence its perception by the readers? I like to keep myself informed and I therefore like to read newspapers. Now with the internet being so widespread, I do not buy newspapers anymore, but rather visit my favorite newspapers online. Usually I start out with the computer news to keep myself updated on new products and developments, followed by science (deep in my heart I am a scientist, after all!) and politics and economics. The sports section I usually skip, I have to admit to you that I am not very competent in this particular area of knowledge. But I do read the sports section during the Olympics. You probably already know that the front page of an online newspaper generally includes the newest articles from all sorts of different areas. There are several editors working for an online newspaper and when one editor writes a new article, then this article is automatically displayed on the front page of the newspaper. Of course each article is also part of a category, such as the science category or the politics category. But when the article is first published online it usually also appears right on the front page, unsorted. This allowes the readers to see the newest information right up front. This is the purpose of it In any case, I recently clicked around in my favorite newspaper and something startled me. On the front page, on the left side, there was an article on politics. A few hundred people died somewhere because of political riots. A sad story. On the very same page on the right side, there was an equally large article, with an equally large picture, apparently equally sad – announcing that a certain soccer team lost the championships. The contrast struck me somehow – on one side of the page a few hundred dead, on the other side of the same page – a sports defeat. Of course. The newest articles are always displayed on the front page. When I saw this contrast, several thoughts and questions came into my mind: Are both events the sport defeat and the 100 victims really equally important? After all they occupy the same amount of space! Can the importance of an event really be judged by the amount of space it is given in a newspaper? The larger the pictures and the longer the article, the more important it is? And -, and this is the question that I consider most burning, – does the article on the 100 victims make the sport defeat appear more important than it is? After all, the article of the sport defeat received the same amount of space! Or does the sport defeat trivialize the 100 dead? – making it appear less important than it is? Now if you really want to hear the issue formulated in “TOK language” I would suggest the following problem of knowledge: “To what extent is the importance of a newspaper article influenced by its context” – or: “To what extent is the apparent importance of a newspaper article influenced by by other newspaper articles around it?” — Does size matter? What message does the optical arrangement of the articles, the size of the pictures, the length of the text, the size of the headlines – what message does all of this send to the readers of the newspaper? Is there a message hidden between the lines? — I wonder. I was relieved when they separated the two articles and finally moved the sports article into the sports section and the article with the 100 victims into the politics section. Out of sight – out of mind. Questions for Discussion: Try to find newspaper articles from different sources that report on the same event. How does the optical appearance of the articles differ? Does the optical appearance communicate a certain message to the readers? How does the optical appearance of a newspaper article, the size of the headlines, the size of the pictures, influence its perception by the readers? How does the context in which a newspaper article appears influence its perception of its content [...] http://www.toktalk.net/2008/12/02/how-biased-are-history-books-are-they/ http://www.toktalk.net/2008/12/02/how-biased-are-history-books-are-they/#comments Tue, 02 Dec 2008 17:16:56 +0000 ok http://www.toktalk.net/?p=204 http://www.toktalk.net/2008/12/02/how-biased-are-history-books-are-they/feed/ 2 Are history books telling us the full story of the past? Can they tell us the full story at all? Why is it that so many history books focus on the “big players”, the kings and rulers, the big events, big politics? What about the “normal” people? I recently read an interesting poem by the German poet and playwright Berthold Brecht – a poem which got me thinking. You see, this is one of the TOK illnesses, you start to see TOK everywhere, and also in poetry. In any case, I don’t want to sidetrack again, the poem has a somewhat strange title, it’s called “Questions of a Reading Worker”. The poem describes the thoughts of a worker, who is reading a history book. I imagine him as a down-to-earth type of guy with an open and a questioning mind. I just want to give you an overview of the poem, without actually translating it from Germal to English. What follows is therefore more of a commentary than a translation. The poem starts out with the worker, who is reading the history book, asking himself who actually built the city of Theben with its seven doors. That’s a city in Greece. In the book he could only find the names of kings. The kings constructed the city. And the worker wonders if the kings actually carried the bricks themselves. King so-and-so constructed the city. Yea sure. We all know that. Why does nobody mention the thousands of other people who were involved in the building process? Some of you may now say, “well that’s clear anyway that there were many people involved in the building process, you don’t need to mention this, it’s clear anyway”. Then I am going to say that it should also be clear that somebody had to pay the cash for it, usually a king, had to commission the construction of the city! What’s so special about mentioning a king? Who says that a king is actually more important than the people who do the work? The poem goes on: The city of Babylon was destroyed several times, but who was responsible for reconstructing the city? Ah, same story here. The kings reconstructed it….. No mention of the workers and the people and the families who were all involved in the reconstruction of the city. No mention in the history book. Great Wall of China, where did the workers go to in the evening? Who says that the kings who constructed the Great Wall of China are more important than the workers who spend years of their lives doing hard labor? And Alexander the Great, he conquered India. How can one person do that? How can one person conquer a whole country? In the books you can also read that Caesar beat the Gauls. But nobody mentions that he probably also needed a cook who made his food. You get the point? The history books talk about the “big guys”, the kings, queens, presidents, dictators. But who gives credit to the many smaller people that were involved in the historic events? The uncountable individual contributions, the uncountable individual suffering, where is that mentioned? Philipp of Spain apparently cried when all of his ships sank in a battle. This you can read in the history book. No body else cried? Why are his tears more important than the tears of the family members of the people who drowned? The poem concludes with the words: “So many questions”. “So many questions”. In my view the poem addresses an interesting and maybe also a bit disturbing point. After having read the poem I asked myself the question: “could it be that some history books are a bit one-sided, biased, in their account?” Or worse yet, “could it be that the books only tell us half of the truth?” They are leaving out so many things! Now I know that this is a pretty strong statement, but I think that there is no need to be pessimistic. And I think that I can comfort you by telling you that many historians nowadays and archaeologists nowadays are indeed interested in uncovering the little every-day details of the so-called “normal” people. Because the big events are [...] Are history books telling us the full story of the past? Can they tell us the full story at all? Why is it that so many history books focus on the "big players", the kings and rulers, the big events, big politics? What about the [...] http://www.toktalk.net/2008/11/30/of-ghost-traps-and-wrist-watches/ http://www.toktalk.net/2008/11/30/of-ghost-traps-and-wrist-watches/#comments Sun, 30 Nov 2008 20:37:09 +0000 ok http://www.toktalk.net/?p=81 http://www.toktalk.net/2008/11/30/of-ghost-traps-and-wrist-watches/feed/ 0 Ghost traps are very useful devices – they can be used to catch evil spirits. What? You say that this does not make sense because ghosts do not exist? You say that ghosts are a product of our imagination? Well… do you believe in time? Could it not be that time is a product of our imagination as well? A few years ago I had the opportunity to visit a cultural exhibition. There were all sorts of interesting exhibits, ranging from art work to the local food… and of course there were also rooms filled with religious objects, handicrafts, clothing etc. I also remember the nice photographs of the landscape that were on display. For the purpose of this episode, the country is of no importance. We were a small group of approximately 10 visitors and we had one tour guide for the museum. One of the exhibits was particularely intresting: Carefully protected by a glass box, so that none of the visitors are able to touch it. It was a very strange and curious looking contraption made of wood and colorful string and cloth, about 1 meter tall. It’s a bit difficult to describe its appearance, in any case, it looked kind of delicate, with all the string and wood sticks, no wonder they put it behind protective glass. In any case, the function of this device was really not clear to me at all. I mean, if you look at a pot, then you know that it was used to store food, or a statue would probably serve a decorative or religious function. But this device was really a bit different than the other exhibits. It did not look praticularely beautiful either, but it was certainly made with great skill and delicacy. I bent over it and carefully inspected it. I am quite certain that who ever made this in my eyes strange looking “thing” had no idea that it would one time end up inside a museum, but this is a different story. In any case, our museum guide directed our attention to this exhibit and resolved the mystery. She explained us that we are actually looking at an original “ghost trap”. When I heard the word “ghost trap” I said to myself, “a what?” I have heard of all sorts of objects that were designed to chase evil spirits away, but for me it was the first time that I heard that evidently there are even traps for them. The museum guide explained us, that the natives used to place these ghost traps in the landscape. When a spirit would float by and accidentally touch one of these traps, then it would entangle itself in the string and the wood sticks and it would not get loose. The people would then collect the traps after some time and burn them. In their view, this was a very effective method of removing evil spirits and preventing them from doing harm to the people. And now the story started to become interesting. I realized that a few other people of the group tarted to smile, but it was not a friendly type of smile. Rather, it was an arrogant, condescending smile. It was a “What a stupid idea, trying to catch ghosts” type of smile. Maybe I could even identify a bit of a cultural arrogance in the smile – And I have to admit to you that this made me a bit angry. Well, I was not the only one who recognized this – also our tour guide realized that some of the group members were making fun of the ghost trap and were mocking it. She immediately picked up the issue and explained us the “deeper meaning” of it all. And this is where the TOK part, the Theory of Knowledge part starts. She told us that the ghost traps were used by the people because, quote “the system of ghost traps worked.“ – “the system worked.” The ghost traps were useful and they did their job. If you believe in ghosts, and you want to get rid of them, then you have to set up ghost traps to catch the ghosts. The system has its logics and it makes sense. whether evil ghosts really exist or not is an entirely different issue and not the point here. The traps allowed the people to control the invisible, the supernatural. The ghost [...] Ghost traps are very useful devices - they can be used to catch evil spirits. You say ghosts do not exist? You say that they are a product of our imagination? Well... do you believe in time? Could it not be that time is a product of our imagination [...] http://www.toktalk.net/2008/11/09/three-different-types-of-truth/ http://www.toktalk.net/2008/11/09/three-different-types-of-truth/#comments Sun, 09 Nov 2008 21:31:12 +0000 ok http://www.okim.info/toktalk/?p=130 http://www.toktalk.net/2008/11/09/three-different-types-of-truth/feed/ 2 Here I will explain the differences between the Correspondence Theory of truth, the Coherence Theory and the Pragmatic Theory. What is truth? This is an interesting but also difficult question to answer. It is possible to distinguish several different definitions or approaches of truth. Here are three of them. Correspondence Theory of Truth: This theory states that a statement (a “proposition”) is true if it corresponds to (or reflects) reality. If somebody states “It is raining” (the proposition) then it is true only if it is really raining outside (reality). The interesting question is now: “What is reality”? We know that senses can deceive us. So how is reality really like? And of course we have to assume that something like reality really does exist and is not simply a product of our mind. Coherence Theory of Truth: This theory states that a statement (a proposition) is true if it is consistent with other things that are considered true (and do not contradict it). Whether the statement reflects reality or not is not of primary importance. A proposition is true if it “fits into the system”. For example, I hear a pencil falling to the ground. A second person in the room also hears it, and the pencil that I just saw on my table a moment ago is now gone. Three observations fit together: me hearing it, a second person hearing it and the missing pencil. According to the coherence theory, the proposition “the pencil hit the ground” is true. But did the pencil really fall to the ground or can something else explain these observations? This is of course a different question. The Pragmatic Theory of Truth: This theory states that something is true if it is useful. Whether or not it reflects reality is of minor importance. Somebody (person A) may, for example, believe that earning much money is the most important thing in one’s life. This belief is true for this person and it is indeed a very useful belief. The person’s actions will be guided by this belief. The statement “Earning much money is important” is true for this person. Person B has a different view. B thinks that money is of minor importance. B thinks that having many friends is the most important thing. And guess what! This belief too is very useful! It is true for person B. His or her actions will be guided by it. Questions for Discussion: Maybe you have realized that some theories assume that truth is absolute (such as the Correspondence theory), others see truth more from a relative or subjective viewpoint (Pragmatic Theory). What is your view on this issue? Are you more an “absolutist” or more a “relativist”? Does the Coherence Theory view truth more from an absolute or more from a relative viewpoint? How are the “theories” of truth similar or different from scientific theories? To give you a hint, are the “truth theories” experimentally falsifyable? Why are they called “theories”? Do you consider this an appropriate term? Could this be a language issue? “Believe those who are seeking the truth; doubt those who find it.” (Andre Gide). What’s so good about seeking truth? What’s so bad about finding it? – An Ethics question! Here I will explain the differences between the Correspondence Theory of truth, the Coherence Theory and the Pragmatic Theory. http://www.toktalk.net/2008/10/27/the-tok-presentation-possibility-2/ http://www.toktalk.net/2008/10/27/the-tok-presentation-possibility-2/#comments Mon, 27 Oct 2008 16:54:13 +0000 ok http://www.okim.info/toktalk/?p=123 http://www.toktalk.net/2008/10/27/the-tok-presentation-possibility-2/feed/ 0 The TOK Presentation: A second possible approach for planning the presentation. For some of you my previous recommendation on the TOK Presentation (“The TOK Presentation – Possibility 1″) may be a bit formal and rigid. Not all of you may find it easy to identify a (good) knowledge issue from a real life situation. I would like to therefore introduce to you an alternative approach. Step 1: Start off by trying to find a knowledge issue / problem of knowledge right from the start. Knowledge issues often start with the words: “How do we know that….” or “How can we know that…..”, but it is not limited to this. Make sure that your knowledge issue is directly TOK related. This is not a good knowledge issue: “How do we know if nuclear power is safe?” If you choose an issue like this, then many students will make a nuclear power presnetation and not a TOK presentation. Better: “How do we know where to draw the line between a short-term advantage and a possible long-term risk?” Step 2: Identify at least two real-life situations (this includes the so-called related area of Assessment Criterion D) where this knowledge issue comes into play. Step 3: Apply TOK theory and critical reflection to answer the question of the knowledge issue using the real life situation as an example. Attempt to give a clear answer to the question (this is not necessarilly a simple either/or answer). Take care that your arguments are TOK based and that you do not spend too much time explaining the background of the real-life issue and the related areas themselves. The TOK Presentation: A second possible approach for planning the presentation. http://www.toktalk.net/2008/10/26/the-tok-presentation-possibility-1/ http://www.toktalk.net/2008/10/26/the-tok-presentation-possibility-1/#comments Sun, 26 Oct 2008 21:47:21 +0000 ok http://www.okim.info/toktalk/?p=111 http://www.toktalk.net/2008/10/26/the-tok-presentation-possibility-1/feed/ 2 The TOK Presentation: A 7-step approach for planning the presentation. This approach is suitable for students who have no idea where to start. Where should you start with the TOK presentation? The following section should help you out. I recommend that you try to find the required “real life problems” with the help of newspapers, but this is not an IB requirement. The following system is only one approach of many to tackle the presentation. I admit that it is a bit rigid and formal, but maybe it helps those students who have absolutely no idea on how to start off. Step 1: Get yourself several newspapers and a few (news) magazine covering current events. Step 2: Flip through the pages and try to find articles that deal with controversial issues. A controversial issue is an issue on which different people have different opinions. For right now, I’ll use the issue on whether genetically engineered foods are risky for the environment. Step 3: Identify the people or groups of people that have different opinions. Be careful that you do not generalize! Let’s assume that the issue deals with the potential risks of genetic engineering (for example). In this case do not generalize and say “the scientists are for genetic engineering” and “the consumers are against it”. Not all scientists and not all consumers have the same opinion. Step 4: Identify a knowledge issue or the problem of knowledge. This is the tough part and you need time for this. Many students make the mistake that they think that the original real-life situation is the problem of knowledge. In many cases it is not. Ask yourself WHY the different groups have different opinions. Could it be that they have different values (ethics!)? Could it be that they have different experiences and therefore assess the risks of genetic engineering differently? Could it be that they disagree on certain definitions (a language problem)? Could it be an issue of fear (emotion)? Try to identify the underlying problem of the debate. Step 5: Once you have identified the hidden knowledge problem, try to identify the sources of knowledge for each side. If side A is for genetic engineering, try to find the sources of knowledge of side A. From where do they have the knowledge that makes them support the technology? Why do they have this opinion? Do this for each side of the debate. Step 6: Now critically reflect on the sources of the knowledge of the different parties. How reliable are these sources? What are some of the problems and pitfalls? If one side is against the use of genetically engineered foods because of emotional reasons , then try to analyze how valid emotions are in this case. If people have a certain opinion because of their experiences, then analyze how reliable experiences are. In any case, it is important to give a balanced view of the issue. Your task is to try to understand each side of the debate in an objective manner. Step 7: Try to identify a related issue. What is a related issue? A related issue is a real-life issue where a similar problem of knowledge (see step 4) appears. Maybe other controversies have a similar structure and similar reasons. The TOK Presentation: A 7-step approach for planning the presentation. This approach is suitable for students who have no idea where to start. http://www.toktalk.net/2008/07/14/different-types-of-knowledge/ http://www.toktalk.net/2008/07/14/different-types-of-knowledge/#comments Mon, 14 Jul 2008 14:14:29 +0000 ok http://www.okim.info/toktalk/archives/52 http://www.toktalk.net/2008/07/14/different-types-of-knowledge/feed/ 0 What are the differences between declarative and procedural knowledge? Declarative knowledge is the knowledge of facts, procedural knowledge is the knowledge on “how to” do something. For example: I know that 5+5=10 (declarative) and I know how to calculate (procedural). Knowledge, according to Plato, is justified true belief. But this definition does not cover all types of knowledge. You know how to read, for example. This type of knowledge is not based on belief, justification or truth. In this edition we will discuss two different types of knowledge: Declarative Knowledge: This includes the knowledge of facts. Some examples could include the knowledge that 5+5=10, the knowledge that the radius of the earth is about 6500km, the knowledge that ice is less dense than liquid water. Declarative knowledge can easily be communicated from person to person. Procedural Knowledge: This type of knowledge includes the knowledge on how to do something. Someone may know how to sing or dance or ride a bicycle. You also know how to solve certain mathematical problems, or you may know how to use a microscope. Procedural knowledge also requires practice and hands-on experience. Questions for Discussion: Try to find examples for declarative and procedural knowledge in the different areas of knowledge, such as the sciences, history and the arts. Babies know how to cry. Some forms of procedural knowledge are present from birth onward. Try to find other examples! What are the differences between declarative and procedural knowledge? Declarative knowledge is the knowledge of facts, procedural knowledge is the knowledge on "how to" do something. For example: I know that 5+5=10 (declarative) and I [...] http://www.toktalk.net/2008/07/09/tok-essay-the-first-steps-identifying-knowledge-issues/ http://www.toktalk.net/2008/07/09/tok-essay-the-first-steps-identifying-knowledge-issues/#comments Wed, 09 Jul 2008 11:20:49 +0000 ok http://www.okim.info/toktalk/?p=46 http://www.toktalk.net/2008/07/09/tok-essay-the-first-steps-identifying-knowledge-issues/feed/ 2 Some prescribed TOK essay titles may require you to find a knowledge issue or a problem of knowledge which relates to the title. Sometimes there are several hidden issues. How can you find them? This edition should motivate you to play with ideas to find a possible hidden knowledge issue. The identification of a problem of knowledge in the prescribed TOK essay title is probably one of the most important first steps. But it may also be one of the most difficult tasks. What is the problem of knowledge that is implied in the title? How can one identify it? It may not always be necessary to identify an implied problem of knowledge in the prescribed title, but it may be helpful in structuring the essay. “[Mathematics] is a creative art because mathematicians create beautiful new concepts; it is a creative art because mathematicians live, act, and think like artists; and it is a creative art because mathematicians regard it so” (Paul Richard Halmos) – To what extent can this view of art, beauty and creativity be applied to other areas of knowledge? This is a hypothetical TOK prescribed title that I invented for the purpose of this podcast. In this edition we will analyze the title and try to brainstorm some knowledge issues that could relate to this topic. There are several ways in approaching the essay. One possible approach is to play around with the prescribed title a bit and to use the title as an inspiration to find different knowledge issues. This is what I attempted to do. I brainstormed a range of different issues that came into my mind. This way you start to get a feel for the title and hopefully will understand it better. Be careful! Not all of the knowledge issues that one brainstorms are directly relevant for answering the question! Be selective! I came up with the following list of knowledge issues, some of them more relevant than others: How do we know what art is? Is beauty a necessity for something to be considered art? Is creativity necessary for something to be art? Is something art only because a person considers it art? Could it not be that school math is different to the higher math done at university? School math is not very creative, or is it? Do mathematicians really live, act and think like artists? How do artists live act and think? Do all artists live act and think the same way? Can the concpet of creativity be applied to ethics? Is a “beautiful” ethical solution to a complex ethical problem also art? A computer that draws a beautiful painting – is this art? It is beautiful but not creative, so is it art? How do we know if beauty is enough for something to be considered art? An ugly painting – is this not art? When/how do scientists work creatively? Does the word “creativity” mean something different in the different areas of knowledge? Does creativity in math mean something different than creativity in arts? Does creativity in arts mean something different than creativity in the sciences? Could this not be a problem of language? Does the word creativity have different meanings? To what extent can abstract concepts be beautiful? Things that can not be seen – can they be beautiful? Can it be that beauty means something different in math compared to arts? Can theories be beautiful? What makes a beautiful theory different from a non-beautiful theory? My problem of knowledge: Could it be that the words creativity and beauty may mean different things in the different areas of knowledge? My strategy: In this essay I am going to show how the concepts art, beauty and creativity apply to science, history, ethics and how it is similar or different to beauty and creativity in arts and math. Some prescribed TOK essay titles may require you to find a knowledge issue or a problem of knowledge which relates to the title. Sometimes there are several hidden issues. How can you find them? This edition should motivate you to play with ideas [...] http://www.toktalk.net/2008/06/21/what-is-knowledge/ http://www.toktalk.net/2008/06/21/what-is-knowledge/#comments Sat, 21 Jun 2008 13:04:04 +0000 ok http://www.okim.info/toktalk/?p=43 http://www.toktalk.net/2008/06/21/what-is-knowledge/feed/ 0 Plato defined knowledge as “Justified true belief”. For a person to know something he/she has to believe it, has to be able to justify it and it has to be true. This is explained here. The tree criteria needed for a person to know something are: Lack of justification: “I know that aliens exist” – there is no way that you can provide a justification for this claim. Therefore you can not know it. Lack of belief: “I know that the world is round but I don’t believe it.” – this is a contradictory statement. For you to know something you have to believe in it. But not every belief is knowledge! Lack of truth: I know that a circle has 3 corners. – You can not know things that are evidently not true. Four possible ways to justify one’s belief are: Memory Authority Logics Empirical evidence Plato defined knowledge as "Justified true belief". For a person to know something he/she has to believe it, has to be able to justify it and it has to be true. This is explained here. http://www.toktalk.net/2008/02/08/tok-essay-marking-critieria-introduction/ http://www.toktalk.net/2008/02/08/tok-essay-marking-critieria-introduction/#comments Fri, 08 Feb 2008 17:06:31 +0000 ok http://www.okim.info/toktalk/archives/32 http://www.toktalk.net/2008/02/08/tok-essay-marking-critieria-introduction/feed/ 0 The TOK Essay is marked against 4 criteria (A-D). I will explain these criteria to sensitize you on what to look out for when you write the essay. In this edition I will give you a brief introduction into the marking criteria for the TOK essay. A. Understanding knowledge issues Depth and breadth of understanding: Are you considering different ways of knowing and areas of knowledge and do you explore them in sufficient depth? Are you comparing them? Careful: Is the knowledge issue relevant to the prescribed title? B. Knower’s perspective Are you including your own experience and relevant examples from your life? Are you aware on how your own perspective is similar/different to other perspectives? Are you able to critically reflect on your own viewpoint? Careful: The essay should not be a mere summary of TOK theory and textbook examples. C. Quality of analysis of knowledge issues Are the main points and arguments in the essay justified? Are the arguments compelling? Are there and contradictions in the essay? Did you consider counterclaims? Did you identify assumptions? Careful: You will only receive points for those ideas that are relevant to the prescribed title! D. Organization of ideas Is the world count between 1200-1600 words? Is the essay well organized? Are the facts in the essay correct? Are they properly referenced? Careful: If the essay does not relate to the prescribed title, then criterion D will receive 0 points. The TOK Essay is marked against 4 criteria (A-D). I will explain these criteria to sensitize you on what to look out for when you write the essay. http://www.toktalk.net/2008/02/08/what-is-the-4-ears-model-of-communication/ http://www.toktalk.net/2008/02/08/what-is-the-4-ears-model-of-communication/#comments Fri, 08 Feb 2008 17:03:00 +0000 ok http://www.okim.info/toktalk/archives/31 http://www.toktalk.net/2008/02/08/what-is-the-4-ears-model-of-communication/feed/ 0 According to Psychologist Friedmann Schulz von Thun, when a person talks to another person he/she is passing on four different messages. This communication model is called the “4 Ears Model” and is useful in understanding why people misunderstand each other. Alice and Bob are both sitting in the car, Alice is driving. They are waiting at an intersection, the traffic light is red and then changes to green. Bob: The traffic light is green. Alice: Don’t be so impatient! … and they start arguing. What went wrong? According to the psychologist Friedemann Schulz von Thun, a message that is passed from one person to another person carries four pieces of information: The factual content of the message: The traffic light is green. A plea to do something: Start driving! Self-revealment: The sender of a message tells something about his or her inner state. I am impatient and I am in a hurry! Information on the relationship between the people: I am the boss and you are the driver. I can tell you what to do and what not to do. I am the one who has the say here. Maybe Bob did not mean to be insulting. The disagreement between Alice and Bob is because different people are sensitive to the different pieces of information that are encoded in the message. This can be a cause for misunderstandings. According to Psychologist Friedmann Schulz von Thun, when a person talks to another person he/she is passing on four different messages. This communication model is called the "4 Ears Model" and is useful in understanding why people [...] http://www.toktalk.net/2008/01/13/tok-essay-common-problems/ http://www.toktalk.net/2008/01/13/tok-essay-common-problems/#comments Sun, 13 Jan 2008 19:59:09 +0000 ok http://www.okim.info/toktalk/archives/30 http://www.toktalk.net/2008/01/13/tok-essay-common-problems/feed/ 0 There are some common, recurring problems with the TOK Essay. The prescribed title question is not answered explicitly, the examples are not explained, the essay is not organized, the….. Here is an overview of the most common problems. The following audio files should give some basic advice for the TOK essay. Some common TOK Essay problems are: Defining terms using only dictionary definitions without interpretation of the definition. Relevant ideas are not compared Use of generalizing statements and words: all, none, few, many….. It has always been known that….. Introductions that make not explicit reference to the topic, or introductions that do not properly interpret the topic question. Not mentioned how an idea is evaluated: The evaluation is based on what criteria? Students do not indicate in the introduction how they intend to evaluate the idea. Students answer the question either with yes or no, but fail to give a differentiated argument. Topic not answered: Paragraphs with TOK theory or examples that is not brought into connection with the title. Make sure that every paragraph of the essay contributes to explicitly answering the topic question. Lack of relevant examples: cross cultural examples that are based on stereotypes. Biggest threat: Students may agree with the above points but are not aware that they actually have the same problems in their own essay. Why? Because as an author of the essay you become blind to these problems – let someone else read the essay. Disclaimer: The content of this website (and this advice in particular) is not endorsed by the IB-Organization. Following this advice can naturally not guarantee you a high TOK mark, there are many factors involved. There are some common, recurring problems with the TOK Essay. The prescribed title question is not answered explicitly, the examples are not explained, the essay is not organized, the..... Here is an overview of the most common problems. http://www.toktalk.net/2008/01/09/what-are-formal-systems/ http://www.toktalk.net/2008/01/09/what-are-formal-systems/#comments Wed, 09 Jan 2008 21:08:04 +0000 ok http://www.okim.info/toktalk/archives/29 http://www.toktalk.net/2008/01/09/what-are-formal-systems/feed/ 0 Introduced here: the MIU puzzle as an example of a formal system. A formal system is composed of axioms, to which rules of inference are applied to produce theorems to which the rules can be applied again. Confused? Try to MIU puzzle yourself – it’s fun! The MU Puzzle is an example of a formal system. The objective of the MU Puzzle is to try to reach the string MU starting from MI, using only these four rules: Rule 1: xI ? xIU. If there is an I at the end of the string of letters, then you can add a U. For example if your string is MI then you can change it into MIU. You can only add a U if the last letter is an I. Rule 2: Mx ? Mxx. You can double any string that follows the M. So if your string is MIU then you can double the IU after the M. You will then get MIUIU. We have doubled the IU. Rule 3: xIIIy ? xUy. You can replace three I in a row with one U. MUIII can be changed in to MUU. It is also possible to replace the three III if they occur in the middle somewhere. MUIIIU can also be changed to MUUU. Rule 4: xUUy ? xy. You can cancel and remove any two U that occur in a row. MUUU can be changed to MU. Is it possible to reach the string MU with these four rules? If yes, then what are the steps involved? A formal system needs axioms and rules of inference. These rules are applied to the axioms and theorems are derived. It is possible to make new theorems by applying the rules to existing theorems. The first steps in solving the the MU puzzle could be: Axiom: MI Theorem 1, using rule 2: MII Theorem 2, using rule 2: MIIII Theorem 3, using rule 3: MUI Theorem 4, using rule 1: MUIU Theorem 5, using rule 2: MUIUUIU Theorem 6, suing rule 4: MUIIU etc. until you reach MU, if possible at all. Transcript: For this edition of TOK talk, you need something to write with, a pen and paper. Why? Because I’m going to show you a little puzzle for you to try out. Actually we are going through the puzzle together, but it’s difficult for you to follow by just listening to it – you need to be able to see it as well. It’s called the MU puzzle. I want to use this puzzle as an example of a formal system. I think we’re gonna do the puzzle first and I’ll explain the theory behind formal systems later. The puzzle starts out like this: Write the letters MI at the top left of the page. This is our starting string of letters. And at the bottom left of the page I want you to write the letters MU. The goal of the puzzle is to change the string MI into MU. Of course you can not just cross out the I and replace it with a U. This is not allowed. There are four rules that you can use and I am going to tell you these four rules now. I think it is a good idea to write these rules down as well. Otherwise it’s really getting kind of difficult to remember them. So, we could use the right side of the paper for writing down these rules. Here are the four rules: Rule 1: If there is an I at the end of the string of letters, then you can add a U. For example if your string is MI then you can change it into MIU. You can only add a U if the last letter is an I. Rule 2: You can double any string that follows the M. So if your string is MIU then you can double the IU after the M. You will then get MIUIU. We have doubled the IU. Rule 3: You can replace three I in a row with one U. MUIII can be changed in to MUU. It is also possible to replace the three III if they occur in the middle somewhere. MUIIIU can also be changed to MUUU. Rule 4: You can cancel and remove any two U that occur in a row. MUUU can be changed to MU. These are the only four rules that you can use. You do not have to use all of these rules. You can use the rules in any order that you want and of course you can use one rule as often as you want. In summary the four rules are: You can add a U if there is an I at the end. You can double anything after the M You can replace III with a U You can remove UU OK, let’s start. Try to write the string of letters down as [...] Introduced here: the MIU puzzle as an example of a formal system. A formal system is composed of axioms, to which rules of inference are applied to produce theorems to which the rules can be applied again. Confused? Try to MIU puzzle yourself - [...] http://www.toktalk.net/2008/01/04/what-are-the-differences-between-facts-theories-and-opinions/ http://www.toktalk.net/2008/01/04/what-are-the-differences-between-facts-theories-and-opinions/#comments Fri, 04 Jan 2008 15:21:58 +0000 ok http://www.okim.info/toktalk/archives/27 http://www.toktalk.net/2008/01/04/what-are-the-differences-between-facts-theories-and-opinions/feed/ 0 The terms facts, theories and opinions are often confused. The objective of this edition is to clarify these terms. Facts are observations or measurements from an experiment, theories are the explanation of these facts, while opinions are assessments or evaluations. The terms facts, theories and opinions are often confused. The objective of this edition is to clarify these terms. Facts are observations or measurements from an experiment, theories are the explanation of these facts, while opinions are assessments or evaluations. Opinions are often not scientifically verifiable or falsifyable. The terms facts, theories and opinions are often confused. The objective of this edition is to clarify these terms. Facts are observations or measurements from an experiment, theories are the explanation of these facts, while opinions are [...] http://www.toktalk.net/2008/01/04/what-is-determinism/ http://www.toktalk.net/2008/01/04/what-is-determinism/#comments Fri, 04 Jan 2008 13:36:39 +0000 ok http://www.okim.info/toktalk/archives/26 http://www.toktalk.net/2008/01/04/what-is-determinism/feed/ 0 Determinism refers to the idea that the future is not up to chance, the future can be predicted. Determinists claim that if you had sufficient knowledge of the current situation, then you could in theory predict the behavior of a system into the future. Certain systems are indeed deterministic, many others are not. In this edition we will have a look at the concept of determinism. In a deterministic system the initial conditions of the system determine the future behavior of the system. The behavior of both a falling apple and a rolling die depend on the initial conditions. Even the same laws of physics apply, namely classical mechanics. Both falling apple and the rolling dice are deterministic systems. But I am able to calculate the landing position of a falling apple, but I am not able to calculate the result of a die roll. Why? How are these two examples different? Why does the die seem to behave according to chance, but not a falling apple? A rolling die is chaotic and it is unpredictable, even though it is deterministic. Even if we know all the physical laws and the starting conditions of a system, it is still not possible to predict the future behavior of chaotic systems. Transcript: In this edition of TOK-Talk we will explore if sciencific laws can predict the future behavior of some systems. What is determinism? Listen to find out! Two, five, one….. Maybe you can hear it, I am rolling a die. I can not predict the next number, it seems to be – pure chance. But is it chance? The behavior of the die depends on physical laws, so it should be possible to calculate or predict the result with the help of a computer. Probably you say that the result is different because I am not throwing the die in the same way. And you are right. The roll of the die depends on the initial conditions. It depends on the way that it is on my palm, and on the way that I throw the die. We say that the die behaves in a deterministic way. The starting conditions and the rules of physics determine the outcome of the die roll. The die follows a strict cause and effect relationship. During the 19th century determinism was commonly accepted among the scientists. If we have a full information about the current state of the world, then we can predict the future behavior of the world. The universe, according to this view, works like a clockwork, and even human behavior is deterministic. I once even read that some scientists were frustrated about this, because they thought that there was essentially nothing new to discover anymore. If we know the position and movement of every atom of this world, then it is possible, using Newton’s laws of motion, to predict the future development of the world. We can even predict human behavior this way, we remember that humans are also made of atoms. Well, this view has changed dramatically during the last century. I want to quote Sir Karl Popper here: Determinism means that if you have sufficient knowledge of chemistry and physics you can predict what Mozart will write tomorrow. Now this is a ridiculous hypothesis. Sir Karl Popper (1992) I want to give you two examples why it is not possible to predict the future behavior of some systems. The first example is from chaos theory and the second one is from nuclear physics, from quantum mechanics. Drawing of the lottery numbers in TV: plastic balls arranged according to number, the plastic balls fall into a container, they are mixed and then the numbers are drawn. And if you are lucky you win. Now why is it that always different numbers are drawn? Should it not be possible, using the equations of physics, and with the help of a computer, to calculate the result? I know the starting positions of the plastic balls, I know their mass, I know how the machine works and how it mixes the balls, and so on. So why is it, that we always get different results? Why can we not compute the ourcome? This is because very, very small deviations in the starting conditions [...] Determinism refers to the idea that the future is not up to chance, the future can be predicted. Determinists claim that if you had sufficient knowledge of the current situation, then you could in theory predict the behavior of a system into the [...] http://www.toktalk.net/2007/12/24/what-are-thought-experiments/ http://www.toktalk.net/2007/12/24/what-are-thought-experiments/#comments Mon, 24 Dec 2007 21:01:45 +0000 ok http://www.okim.info/toktalk/archives/20 http://www.toktalk.net/2007/12/24/what-are-thought-experiments/feed/ 0 It is not always necessary to conduct real-life experiments to reach a valid scientific conclusion. Thought experiments may in some cases also suffice. In this edition I will illustrate you a thought experiment from physics: In a vacuum, all objects accelerate the same way and they both have the same velocity. Heavy objects will not fall faster. But how can we test this? We do not have a large vacuum chamber to test this. A thought experiment can be useful in this case. In this edition of TOK-Talk I will explain you what a thought experiment is. Is it always necessary to conduct real-life experimets to reach a valid scientific conclusion? Listen to find out! Do heavy or lighter objects fall to the ground faster? Which one will hit the ground first when dropped at the same time from the same height – a bowling ball or a ball of crumpled newspaper of the same size? The answer is: “it depends”! If you drop both objects from a tower on earth, then the bowling ball will hit the ground first. If you drop both objects on the moon, then both will hit the ground at the same time. Here on earth, the air resistance has a large influence on the falling velocity of an object. In a complete vacuum all objects hit the the ground at the same time. This may be difficult to imagine, but it is indeed the case. The problem is that we can not go to the moon to test this physical law. We could construct a giant air-less vacuum chamber here on earth. But this is of course not practical – and not necessary either! I would like to introduce to you a thought experiment that demonstrates that all objects do indeed fall to the ground at the same rate. Now, it is very critical that we take the experiment step by step, otherwise it can become a bit confusing. Step 1: We start the thought experiment by making an assumption. We assume that heavy objects fall to the gound faster than light objects. I know that I just told you that in a vacuum all objects fall to the ground at the same rate, but for right now we need to take this assumption. Again: we assume that heavy objects fall to the ground faster. I take a square block of lead with a mass of 10kg into my left hand and a block of lead with a mass of only 1kg into my right hand. Actually you have to be pretty strong to carry the 10kg lead block in one hand, but as we do this only in our imagination, this is not a problem. I drop them both at the same time from the same height. The 10kg lead block will hit the ground before the 1kg block. It will accelerate faster. We hear two sounds as the two blocks hit the floor: boom – boom. The first boom is from the 10kg block and the second boom is from the 1kg block hitting the floor. This is what we assume. Close your eyes and try to imagine this situation. Just don’t drop them on your toes. Step 2: I now pick up both blocks of lead from the floor. Luckily it is only a thought experiment so no real damage has been done to the floor (or your toes). In your imagination put the larger 10kg block of lead on top of the 1kg block. The two blocks are now stacked on top of each other. You now have one chunk of lead, 11kg heavy. The large block is sitting on the small one. The next observation is crucial. Drop this chunk from the same height. What should happen? The smaller block will fall slower than the larger one. The larger block wants to fall faster, but is slowed down by the smaller block in front of it. The falling velocity of the 11kg combination block will therefore be between the velocity of the 10kg and the 1kg block when they are dropped separately. The combination block will fall slower than the 10kg block alone. This is because the small block breaks the falling of the larger block behind it. Actually the situation is similar to two people running, a fast person running behind a slow person. The fast runner bumps into the slower runner in front. The faster runner is slowed down. Step 3: Now it’s starting to become interesting. [...] It is not always necessary to conduct real-life experiments to reach a valid scientific conclusion. Thought experiments may in some cases also suffice. In this edition I will illustrate you a thought experiment from physics. In a vacuum, all [...] http://www.toktalk.net/2007/12/24/why-are-simpler-explanations-usually-better/ http://www.toktalk.net/2007/12/24/why-are-simpler-explanations-usually-better/#comments Mon, 24 Dec 2007 20:53:45 +0000 ok http://www.okim.info/toktalk/archives/19 http://www.toktalk.net/2007/12/24/why-are-simpler-explanations-usually-better/feed/ 0 The purpose of science is to make things simpler and not more complicated. Scientists strive to discover theories and explanations that simplify the view of our world and not complicate them. According to Wiliam of Ockham (c. 1288 – c. 1347), if there are competing explanations for a phenomenon, the simpler explanation is to be preferred. The simpler explanation is often the correct one. It can be summarized as “With all other things being equal the simpler solution is the better one.” Simpler explanations rely on fewer assumptions which can not be proven or disproven. In this edition of TOK-Talk I would like to explore the difference between a good and a bad explanation. Why are simpler explanations usually the better ones? Listen to find out! Sometimes I am asked the question, why science is so complicated. I remember that during my studies at university, I also asked my professor the very same question. At that time I was very intrigued by the complexity of the biochemical events that occur in living cells. He laughed, but in a well meaning way, I’d have to add, and responded that everything is complicated only if you hear it for the first time. If you hear something over and over again, then you start to become used to it. Naturally, I have to admit that many aspects of the sciences are indeed difficult to understand for the “non-initiated”. There are several reasons to it. Many scientific concepts are difficult to imagine and often we are missing suitable analogies to our real-life world. We have a difficulty in drawing parallels. If I tell you, for example, that the DNA, the genetic information in each one of our body cells is over 2m long, then this is difficult to imagine how you can fit so much DNA into one single cell. We simply do not have any real-life comparison. The DNA is just unimaginable thin. Or another example: the total surface area of our lung is about 100m². That’s the area of my apartment. And the total length of all blood vessels in the human body is nearly 100000km. This is 2 and a half times around the earth, or 1/3 of the way to the moon. This is of course difficult to imagine, because we are missing a link to our everyday experience. And let’s not talk about the dimensions in the universe or time scales of billions of years. I claim that not even scientists can imagine these dimensions, but they have learned to at least work with these numbers. These were now rather subjective perception of complexity in the sciences. But are there are also other criteria. William of Ockham lived in the 13th and 14th century. He was a scholar and an early proponent for the KISS principle: Keep it Short & Simple. The purpose of science is to make things simpler and not more complicated. Scientists strive to discover theories and explanations that simplify the view of our world and not complicate them. According to Ockham, if there are competing explanations for a phenomenon, the simpler explanation is to be preferred. The simpler explanation is often the correct one. It can be summarized as “With all other things being equal the simpler solution is the better one.” Please don’t laugh right now, but as you know, I sometimes like to give extreme examples to make my point clear. – I have got a little thermometer here. When I place the thermometer into the sun then the mercury rises. When I put it into the shadow, the mercury drops. Do you know why this happens? There is a little invisible demon inside the glass column. In the sun the demon wakes up and makes the mercury go up. When it’s dark the little critter goes to sleep and the mercury column drops. During a bright winter day the demon is asleep. It is hibernating and will only wake up in spring. Sometimes the little demon wakes up even during winter and makes the mercury go up a bit… You see, the little demon is very convenient. We are able to explain every movement of the mercury column with its help. No matter how [...] According to Wiliam of Ockham (c. 1288 - c. 1347), if there are competing explanations for a phenomenon, the simpler explanation is to be preferred. The simpler explanation is often the correct one. It can be summarized as "With all other [...] http://www.toktalk.net/2007/12/24/what-is-the-scientific-method/ http://www.toktalk.net/2007/12/24/what-is-the-scientific-method/#comments Mon, 24 Dec 2007 20:22:33 +0000 ok http://www.okim.info/toktalk/archives/18 http://www.toktalk.net/2007/12/24/what-is-the-scientific-method/feed/ 0 If we want to reach an objective description of our world, then we need to reduce these subjective influences. We need standardized procedures in gaining further knowledge of our world. The scientific method is such a standardized procedure in gaining further knowledge in the natural sciences. One of the goals of science is to explain various phenomena of the natural world in an objective and unbiased manner. Different people perceive the world differently, due to different educational and cultural backgrounds. For some people a glass of water is half full, for others it is half empty, and still for others it is just a glass of water. Different people perceive and interpret reality differently. If we want to reach an objective description of our world, then we need to reduce these subjective influences. We need standardized procedures in gaining further knowledge of our world. The scientific method is such a standardized procedure in gaining further knowledge in the natural sciences. Transcript: In this edition of TOKTalk we will have a look at the scientific method. What are the steps involved? Listen to find out! One of the goals of science is to explain the phenomena of the natural world in an objective and unbiased manner. Different people perceive the world differently because they have different educational and cultural backgrounds. For some people a glass of water is half full, for others it is half empty, and still for others it is just a glass of water. Different people perceive and interpret reality differently. If we want to reach an objective description of our world, then we need to reduce these subjective influences. We need standardized procedures for gaining further knowledge of our world. The scientific method tries to eliminate these subjective influences. It also sets a standard on how further knowledge should be gained in the natural sciences in the first place. Other disciplines, such as history or mathematics use of course different methods for gaining further knowledge. Most of us are using the scientific method in our every day life, without being consciously aware of it. In the following few minutes I would like to give you an overview of the different steps of the scientific method and I would like to base it on an every day example. Imagine that you want to start your car in the morning to drive to work, and the car refuses to start. Step 1: Observation: You turn the key and realize that the car does not start. Maybe you hear a short sound of the turning starter motor, but the sound dies off immediately and the car is quiet again. You also realize that the car radio stops to work and that the head lights dims when you turn the key. Step 2: Hypothesis: You are under time pressure and need to leave. We need to isolate the problem and find a solution. Are we out of fuel? Is the temperature to cold for the engine to start? Did a fuse break? Is the battery dead? Is there a mechanical problem with the engine? There are probably many possibilities why a car does not start, and this is not the time for wild guessing. We need to eliminate the options. The car was refueled yesterday, so the missing gasoline is not the problem. Is it a broken fuse? In this case the whole electrical system would not work and there would be no sound at all. Can we exclude a mechanical problem? Possible, but the engine did work before and there was no indication. Maybe, for whatever reason, the battery of the car is empty. Maybe we should start looking here first. A hypothesis is an educated guess and not a wild guess. There should be a good reason for choosing a particular hypothesis. Step 3: Experiment: You now test the hypothes by conducting an experiment. You think that the battery is dead, so you exchange the battery or you use the battery of another car to get the engine working. This experiment will either prove your hypothesis correct or wrong. Step 4: Conclusion: If your hypothesis was proven correct, if [...] If we want to reach an objective description of our world, then we need to reduce these subjective influences. We need standardized procedures in gaining further knowledge of our world. The scientific method is such a standardized procedure in [...] http://www.toktalk.net/2007/12/24/what-is-falsification/ http://www.toktalk.net/2007/12/24/what-is-falsification/#comments Mon, 24 Dec 2007 20:20:11 +0000 ok http://www.okim.info/toktalk/archives/17 http://www.toktalk.net/2007/12/24/what-is-falsification/feed/ 0 In this edition of TOK-TALK we will talk about Karl Poppers contributions to the philosophy of science. Sir Reimund Karl Popper is considered to be one of the most influential philosophers of the 20th century, and of course it is difficult, if not impossible to summarize his contributions in a few minutes (or a few lines). Where should you draw the line between the sciences and the pseudosciences? What characterizes scientific theories? In this edition we will have a look at the falsification principle which offers an answer to these questions. In this edition of TOKTalk I will talk about Karl Poppers contributions to the philosophy of science. What makes a theory scientific and what is the principle of falsification? Listen to find out! Transcript: Sir Reimund Karl Popper is considered to be one of the most influential philosophers of the 20th century, and of course it is difficult, if not impossible to summarize his contributions in a few minutes. Maybe I’ll start out by giving you a brief biographical overview over his life. Popper was born in 1902 in Vienna, Austria and with the rise of Nazism in Germany and Austria he emmigrated to New Zealand. Later he went to Great Britain where he spent most of his life teaching at the London School of Economics. Popper contributed greatly to philosophy of science and published a notable book on this issue called “The Logic of Scientific Discovery” in 1934. He was also a political philosopher. One of his most well known books on the issue is “The Open Society and Its Enemies”, which was published in 1945. Popper died at the age of 92 in 1994. Now what were his contributions for the philosophy of science? I think that I need to start at the beginning here. Popper was living at the the time when Albert Einstein formulated his theory of relativity. He was highly fascinated by this progress of science. Einstein formulated his Special Theory of Relativity in 1905 and then the General Theory of Relativity by 1915. At that time Einstein did not yet have experimental evidence for his theory. His theory made predictions, but the actual test to see if the predictions were correct was not performed yet. Einstein’s theory could be tested a few years later during the total solar eclipse of 1919. So Popper was of course excited to find out if the Einstein’s theory will be proven correct or not. If the outcome of the experiment confirms the theory, then the theory will be strengthened, if not, then Einstein’s theory will be abandoned. Well, the experiment did confirm the theory, but this is was probably not the main point. Popper knew that the scientific community would have abandoned Einstein’s theory if the outcome would not have met the predictions. This is how science works, and how it should work. If the theory fails to make the correct predictions, then you have to replace the theory. This is what you call scientific progress. You replace old theories with better ones. According to Popper scientific theories can not give you you certainty. The 1919 solar eclipse did prove Einstein’s Theory of Relativity correct, but maybe in the future another experiment will prove the theory wrong. In this case the Theory of Relativity will be falsified, and it is necessary to search for a new theory that is able to explain both the old and the new experimental results. As a matter of fact, even hundreds or thousands of proofs are not enough to ultimately prove a theory absolutely correct. You can never be certain, maybe the next experiment will prove the theory false. One single experiment is enough to falsify a theory, no matter how many times the theory has been proven correct before. Naturally one has to be a bit careful here. Some theories are very well established already. And it is quite possible that experimental errors give the appearance that a theory is wrong. So it is not wise to jump to too early conclusions and to throw an established theory overboard to quickly. [...] In this edition of TOK-TALK we will talk about Karl Poppers contributions to the philosophy of science. Sir Reimund Karl Popper is considered to be one of the most influential philosophers of the 20th century, and of course it is difficult, if not [...] http://www.toktalk.net/2007/12/24/what-is-the-observer-effect/ http://www.toktalk.net/2007/12/24/what-is-the-observer-effect/#comments Mon, 24 Dec 2007 20:16:01 +0000 ok http://www.okim.info/toktalk/archives/16 http://www.toktalk.net/2007/12/24/what-is-the-observer-effect/feed/ 0 Every measurement changes the object that we want to measure. This is called the Observer Effect. When we stick a thermometer into a glass of water to measure its temperature, then the thermometer will change the temperature of the water as well. Similar effects can be observed when measuring voltage or current in electrical circuits. Also in the social sciences we have a similar problem: people will not behave naturally when they feel that they are observed. In this edition of TOK-TALK we will explore if it is in principle possible to measure anything accurately. How does a measurement change the value of that what you want to measure? Listen to find out! Here in front of me, I have a cup of hot water, and over here we have a thermometer. Let’s put the thermometer into the glass, we have to wait a bit for the temperature reading to adjust. For our listeners, it’s a digital thermometer with a metallic probe. You use similar thermometers to measure the inside temperature of a cake to check if it is finished baking. Now the temperature is slowly climbing and leveling off. We have a reading of 76.2C. We can see that it is fluctuating a bit, now we can see 76.1C. Of course we have to be careful here, because this is the temperature reading of the side of the glass. The center is much warmer. Let’s stir the water a bit. OK, we are up to 82.5C. We could agree that we want to measure the average temperature of the water, so we have to stir the water. But this would of course increase the cooling rate. But then there is the problem that we are measuring a value that is continually changing. The water is cooling down. We could try to completely isolate the water from its colder environment. But we first have to bring up the temperature of the container to the same temperature as the water. Otherwise the container will cool down the water. The isolating container will prevent the cooling of the water, but first the container has to assume the same temperature as the water. So we have to determine the temperature of the container as well. And the situation becomes even worse. Of course the thermometer itself also has a certain temperature. By sticking the thermometer into the water, we are already changing the temperature of the water. Every measurement changes the thing that we want to measure. We could of course try to compensate this error mathematically, but for that we have to know the exact temperature of the thermometer that we are using. So we need another thermometer to measure the temperature of the first thermometer. But then this measurement would of course change the temperature of the first thermometer just like the thermometer would change the temperature of the water. We are pushing the problem out. We could make the mass of the water very large compared to the mass of the thermometer. If we use a large amount of water and also a large thermometer, then we do not gain anything. And can you imagine it if we attempt to use a very large thermometer to measure the temperature of a drop of water? The thermometer would influence the temperature of the drop more than the drop the thermometer. This is what we call the „Observer effect“. When we observe something, we end up changing the thing that we observe. Besides temperature measurement, there are other examples as well. In my younger days I used to play around with electronics a lot. I liked to assemble radios and other electronic gadgets. I bought myself a nice voltmeter to measure volage, resistance and current of electrical circuits. The only problem was that the device, being electronic itself, actually influenced the object that I wanted to measure. The ammeter measured the current flowing through a cable, but the device of course consumed some of this current itself. So it changed the current that I wanted to measure. Of course manufacturers try to keep this effect small, but the effect does exist. The current measured must be substantially [...] Every measurement changes the object that we want to measure. This is called the Observer Effect. When we stick a thermometer into a glass of water to measure its temperature, then the thermometer will change the temperature of the water as well. [...] http://www.toktalk.net/2007/12/24/what-are-ethical-dilemmas/ http://www.toktalk.net/2007/12/24/what-are-ethical-dilemmas/#comments Mon, 24 Dec 2007 20:04:26 +0000 ok http://www.okim.info/toktalk/archives/15 http://www.toktalk.net/2007/12/24/what-are-ethical-dilemmas/feed/ 0 In this edition we will have a look at ethical dilemmas. What are they? What are some different opinions in making an ethical choice? There are several schools of thought in finding a solution to an ethical dilemma. The consequentialist school maintains that actions are either moral or immoral depending on the outcome (the consequence) of the action. An action is morally right, if it results in an increase in the overall happiness for the people. The deontological school states that the outcome of an action is irrelevant. It is the action itself that is moral or immoral. Lying, according to this school, is always wrong, regardless of the outcome. There are arguments for and against each one of these schools of thought. In this edition we will have a look at ethical dilemmas. What are they? What are some different opinions in making an ethical choice? Listen to find out! I would like to start off with a little example, a classic. A man has a wife and 3 kids at home, but he is jobless and his family is starving. Is it morally right for the man to steal money to support his family? If he steals money, then he does something wrong, but the outcome is good. If he does not steal, then the family will starve. Whatever his choice, there is a moral problem and a moral rule is transgressed. Now if you think that this is a rather extreme example and not very realistic, then I would like to inform you that ethical dilemmas are often formulated in a simplified, idealized manner to get the point across and to make them more accessible to systematic study. Some of you may now say that he should go out and find a job or that it is the responsibility of government agencies to support the family. Others may give the recommendation that the father should stay at home and the mother should find a job. Maybe she has a better chance. But for right now, we ignore these possibilities. Now how do you go about solving ethical dilemmas? What should the man do, based on the given information? First of all, it must be made clear that dilemmas can not be “solved” like a mathematical problem. There are of course different ethical approaches and there are rational methods. But a universally acceptable “correct” solution does probably not exist. I would recommend a 4-step guideline in approaching problems like these. Step 1: First of all you have to know that you will have to break a moral value. It is in the nature of dilemmas that you will, ultimately, break one ethical or moral rule when you do make your choice. If you do not decide and lean back, then you have also have chosen not to act, and yes, there will be an unfavorable outcome as well. You have to be prepared to accept criticism for your decision. And you have to understand that ethical dilemmas can not be solved like a puzzle. Step 2: Next, you should analyze the actions that you have to take. In the example of the starving family, the man has two choices: either not to act, or to steal. Not stealing is morally acceptable. Stealing is not. You should not consider the consequences of your actions yet! Just analyze the actions independently from the possible outcomes. This may be difficult to do, but you should try. Step 3: We are not finished yet, and the next step is quite crucial. You should now analyze the outcomes of each action. In one case the family will starve, in the other case the family will survive. Again consider the outcomes independently of the previous actions that were taken. In this particular example the outcomes seem to be quite clear, but in real life there may be many unexpected side-effects. Step 4: Only now one should compare the negative action with the negative outcome. As a last step we weigh the negative outcome of the action (the starvation) against the negative action (the stealing). Which one is a morally worse? Which one is more acceptable? Death of the family or stealing? Form a decision by weighing these two outcomes against each other. Most [...] In this edition we will have a look at ethical dilemmas. What are they? What are some different opinions in making an ethical choice? There are several schools of thought in finding a solution to an ethical dilemma. The consequentialist school [...] http://www.toktalk.net/2007/12/24/what-is-the-mpemba-effect/ http://www.toktalk.net/2007/12/24/what-is-the-mpemba-effect/#comments Mon, 24 Dec 2007 19:35:44 +0000 ok http://www.okim.info/toktalk/archives/13 http://www.toktalk.net/2007/12/24/what-is-the-mpemba-effect/feed/ 0 In this edition I would like to explain why hot water freezes faster than cold water, when put into the freezer. It is a very counter-intuitive observation, it’s a paradox. This is called the Mpemba Effect. The effect is named according to Tanzanian high-school student Erasto B. Mpemba who re-discovered the effect while making ice-cream, back in 1963. The Mpemba Effect is a nice example how the change of one variable, the temperature, can have unexpected side effects. Most people assume that the difference between a hot glass of water and a cold glass of water is only the temperature. But this is not the case. Just by heating the water we are introducing a range of other variables that have an unexpected effect on the outcome. In this edition of TOK-Talk I would like to explain why hot water freezes faster than cold water, when put into the freezer. How is this possible? Listen to find out! The Mpemba Effect is a very, how shall I say, counter-intuitive observation, it’s a paradox. It is the observation that under certain circumstances hot water freezes faster than cold water. The effect is named according to Tanzanian high-school student Erasto B. Mpemba who re-discovered the effect while making ice-cream, back in 1963. Aristoteles already described the effect 300BC. So it really is not a new discovery. The effect occurs only under certain circumstances. You put a glass of hot water into the freezer, next to a glass of cold water. If the conditions are right the hot water will have turned to ice before the cold water. The actual causes of this effect are not fully understood. There seem to be a number of factors responsible, however. This effect will only work for certain temperatures. If you place water with 99C next to a glass of water with 1C then the 1C water will of course freeze faster. But at other temperatures the issues are different. Let’s assume that 30C water takes, lets say, 30 minutes to freeze. And let’s also assume that a glass containing 70C water takes 20 minutes to cool to 30C, which is the starting temperature of the fist glass. We would conclude that it takes the 70C a total of 50 minutes (20min+30min) to freeze. This is not what we observe, however. And yes, the volume of the water is initially the same for both. The shape and material of the container are also the same. So why does the hot water freeze faster? We may not even need experiments to determine possible causes for this observation. Most people assume that the difference in temperature of the water is the only variable. But if the observations don’t fit and there was no error in the method, then we may need to question our assumptions. And in out case we have to question the assumption that the only difference in the two water containers is the temperature. We have to look for other differences that may be responsible for the faster cooling of the initially hot water. Now close your eyes and imagine two glasses of water standing in front of you – one hot and one cold. The hot water is steaming. The hot water loses volume due to faster evaporation. Water with less volume will cool down faster. And as the water starts to freeze, the volume will increase again. Ice is less dense than liquid water. We would actually see a volume increase in the glass, and would not notice the loss. There are, however, several other reasons involved as well. The loss of volume of the water actually changes the concentration of minerals in the water. The glass with some evaporated water will have a slightly higher mineral concentration than the glass with the original volume. The salts in the water will not evaporate out. Now, I know that a higher concentration of salt actually lowers the freezing temperature, that’s why we put salt on the roads during winter to prevent ice. So in my view the higher mineral concentration would actually have the opposite effect. But maybe the cooling due to the loss of volume overcompensates the higher [...] In this edition I would like to explain why hot water freezes faster than cold water, when put into the freezer. It is a very counter-intuitive observation, it's a paradox. This is called the Mpemba Effect.