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Of Science, Math and Beauty


Colorful Houses
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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TOK Essay – The First Steps: Identifying Knowledge Issues


 

Flying sparks
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? Continue reading »

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What are Formal Systems?


 
Pink Flowers
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.
  • Continue reading »

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Imagination is more important than knowledge. For while knowledge defines all we currently know and understand, imagination points to all we might yet discover and create.

- Albert Einstein -
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