TOK Journal Post #13

by Michael on February 26, 2019

  1. What is the difference between a conjecture and a theorem?

Conjectures are statements or ideas that have not been proven but are thought to be true. A theorem is a mathematical statement which has been proven through mathematical reasoning. Though one has been proven and the other hasn’t, they both are accepted as truths.

  1. In THE VIDEO  Eduardo Saenz de Cabezon uses the example of people being surprised that folding a normal piece of paper 50 times, will reach a thickness as high as the sun. He challenges us to ‘do the math’ and see that he is correct. What do you think meant when he said that Maths dominates intuition and tames creativity? Do you agree with this?

While our intuition would make us think that folding a piece of paper 50 times would not reach a thickness as high as the sun, when the numbers are crunched using mathematics, the statement holds true. When Cabezon says that mathematics dominates intuition, I think that he means mathematics will always provide clear and concrete evidence for problems that our intuition could never prove. We need mathematics to prove the behavior of things in nature, and we can’t just rely on what we feel to give us a proper conclusion.

  1. List any of the knowledge questions related to maths that came out of your discussion in class.
  • To what extent are observations from experiments a reliable method of producing knowledge in mathematics?  
  • Who approves mathematical formulas and laws?
  • To what extent can mathematics be applied to the natural sciences?

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