Maths All Around

1. What is "equality"?

• Think about the image here, and how it might connect maths to life...

• We talk about equality in life. Equal rights. Equal pay. Equal opportunities.
  Sameness and difference. A notion of "self".
  And these are all very interesting and complex topics. And important.
  
• Can maths help us to get a handle on these ideas? ... Perhaps not! But we might learn something useful about maths if we give it a try.
  
• Maths, of course, has its own versions of equality:
  2+2 = 4
  Exercise: what does this mean? Discuss!
  
• And the dictionary says two things are equal if they are the same.
  When we say that you and I should have the equal rights, we mean that we should have the same rights. And we should have the same rights because we are the same in both being human.
  Of course, both being human does not make us exactly the same.
  There are important differences and important similarities.
  
• How about me today and me tomorrow... Am I the same person? I seem to have an idea of self -- a feeling of continuity without change.
  But of course I do change from day to day. Older me might make different choices from younger me. What does it mean to say that we are the same person?
  This (sort of) brings us to the picture of the coffee mug...
  
• ...Maybe you see why, or maybe not! (Exercise: Discuss!)
  But even if you _do_, there is another question: What has the coffee mug got to do with maths!!?... (Apart from the obvious.)
• Well, maths codifies the sense in which stages in the `life' of the coffee mug are the same, and in which they are different.
• Would you like to know more?

Some Links about `mathematical' equality, sameness and difference

• calories
• balloons
• graphs
• anagrams