1 / 30

Mathematics & Reason

Mathematics & Reason. How understanding maths and reason changes your view of the World. What is Mathematics?. The search for pattern. Betrand Russell. “Mathematics, rightly viewed, possesses not only truth, but supreme beauty.”. Monty Hall Problem. 1. 2. 3. Monty Hall Problem. 1.

boris-ross
Download Presentation

Mathematics & Reason

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Mathematics & Reason How understanding maths and reason changes your view of the World.

  2. What is Mathematics? The search for pattern.

  3. Betrand Russell “Mathematics, rightly viewed, possesses not only truth, but supreme beauty.”

  4. Monty Hall Problem 1 2 3

  5. Monty Hall Problem 1

  6. Simpson’s Paradox

  7. Simpson’s Paradox

  8. Bayes’s Theorem A patient goes to see a doctor. The doctor performs a test with 99 percent reliability--that is, 99 percent of people who are sick test positive and 99 percent of the healthy people test negative. The doctor knows that only 1 percent of the people in the country are sick. Now the question is: if the patient tests positive, what are the chances the patient is sick?

  9. Bayes’s Theorem 99 100 1 99 9900 9801

  10. Penney Ante Game Mathematics in Gambling

  11. Penney Ante Rules 1. You pick a 3-coin sequence (e.g. H T H) 2. I pick a 3 coin sequence (e.g. T T H) 3. We toss a coin repeatedly 4. Whoever’s sequence appears first wins. T H H H H T Hyou win

  12. H H H T T T H H T T T H H T H T H T H T T T H H

  13. Penny Ante is a scam ! Imagine you choose H H H . Eventually we get the firstappearance of H H H : . . . . . . . . . . . ? H H H

  14. Was OJ Simpson Guilty? Mathematics & Statistics in the Courtroom

  15. O.J. Simpson abused his wife and she was murdered. 1 in 1,000 abused women are killed by their husbands. But 80% of murdered abused women are killed by the husbands.

  16. 3 Dice… which one would you choose? 3 2 1 3 2 4 3 2 4 3 5 4 3 5 4 6 5 4

  17. MC Esher

  18. Are there examples of this way of thinking in mathematics?

  19. 3 2 3 2 3 2 vs 3 5 3 5 6 5 BLUE beats GREENon average

  20. 2 1 2 4 2 4 vs 5 4 5 4 5 4 GREEN beats REDon average

  21. ? 3 2 1 3 2 4 3 2 4 3 5 4 3 5 4 6 5 4

  22. 3 1 3 4 3 4 vs 3 4 3 4 6 4 RED beats BLUE!!

  23. 625 Two blues beat two reds 671

  24. Benford’s Law • Take a list of data. • Examine how many of the numbers start with a 1, 2, 3, etc

  25. Benford’s Law

  26. Understanding Mathematics

  27. Picasso’s Guernica

  28. Perelman’s Poincare

  29. Why do we study such old maths?

More Related