## How can Math be Right and Wrong at the Same Time?

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? Continue reading »

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## Of Justified True Belief and the Snouters

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. Continue reading »

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## TOK Essay Prescribed Titles – May 2010

Here are some (possible) guiding questions to help you deal with the TOK Essay titles.

I have compiled a list of questions which should help students analyze their chosen prescribed title question (Nov 2009, and May 2010 session). The presented questions are meant as a source of inspiration. Some of you may think that simply answering these questions is enough for passing the TOK essay. Trust me, it’s not enough. And don’t say that you didn’t know. The purpose of these questions is to get you thinking about the prescribed title. I’m not saying that the questions are directly relevant for your particular approach to your chosen title question. I have to be honest with you: For many of these questions I myself do not even know an answer and maybe some questions do not even have a single, clear answer. Some of the questions may not even be relevant for your approach to the prescribed title! If you already have an approach to your prescribed title, then do not let these questions distract you. You must read these questions critically and reflect on them.

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## The Egg of Columbus

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.

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## What is the Age of Enlightenment?

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.
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## Of Arts and Ethics

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.

• Must art provoke? Is it necessary for good art to provoke emotions and a discussion?
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## Is the Word “scientific” Overused?

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.

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## What are Some Problems with Conspiracy Theories?

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?

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