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The following episodes relate to the 'Mathematics' Category



Linking Arts, Math, Perception and Emotions


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Here are 2 videos which link arts, math, sense perception and emotions. Watch them! They are very good, easily understndable and motivating!

Ifound two videos which illustrate the importance of emotions and perception in understanding statistics. In the first video, the speaker Hans Rosling uses animated graphs to visualize the development of different countries. It is a powerful illustration on how a visual representation (sense perception!) of numbers in the form of colorful dots greatly helps in understanding statistics. Tables with numbers alone are too difficult to perceive. Rosling’s computer program makes these numbers accessible.

The second video is quite remarkable as well. It links the areas of knowledge arts, statistics (math), with the ways of knowing sense perception and emotions. The photographer Chris Jordan wants to create impact by visualizing very large numbers and thus causing emotional involvement. We people often do not want to act to improve our environment, for example, becasue the numbers and statistics that we have available are simply to abstract and too large. What does it mean, when we say that we use millions of paper cups every day? How much is a million? Is this a lot? How much is a lot? Chris Jordan’s artwork helps us in perceiving these numbers, this way causing emotional involvement and creating an incentive to act.

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Of Science, Math and Beauty


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In this post I’m pondering on the relationship between math and beauty. Can math be beautiful as well? And what is beauty in the first place?

I recently read an article about the mathematics of beauty. Researchers found out that beauty is not in the eye of the beholder, and that beauty can indeed be quantified. If you want to read the article, here is a link.

Now, if it is possible to describe what beauty is using mathematical formulas, maybe it is also possible to look at the issue the other way around. Can math itself be considered beautiful or ugly? I did find an answer to this question by the English mathematician G. H. Hardy (1877-1947):
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How can Math be Right and Wrong at the Same Time?


 

A hot air balloon
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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Six Jokes in Seven Minutes


 

Pumpkins
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.
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What are Formal Systems?


 
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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.
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What are Thought Experiments?


 

Truck
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!
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