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The Road Not Taken

The Road Not Taken. Two roads diverged in a yellow wood, And sorry I could not travel both   And be one traveller, long I stood And looked down one as far as I could To where it bent in the undergrowth; Then took the other, as just as fair, And having perhaps the better claim

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The Road Not Taken

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  1. The Road Not Taken Two roads diverged in a yellow wood, And sorry I could not travel both   And be one traveller, long I stood And looked down one as far as I could To where it bent in the undergrowth; Then took the other, as just as fair, And having perhaps the better claim Because it was grassy and wanted wear; Though as for that, the passing there Had worn them really about the same, And both that morning equally lay In leaves no step had trodden black. Oh, I marked the first for another day! Yet knowing how way leads on to way I doubted if I should ever come back. I shall be telling this with a sigh Somewhere ages and ages hence: Two roads diverged in a wood, and I, I took the one less travelled by, And that has made all the difference. Robert Frost 1875– 67

  2. Recognising Randomness

  3. The Birthday Problem • If I pick a small group of people from this Assembly at random, how likely is it that we’ll have some of them sharing the same Birthday? • How many people should I pick for it to be more than an even chance I get a match? • How many of you should I pick to be 95% sure that I get a match of Birthdays? • Assuming no twins, no 29thFebs

  4. Slightly Odd Method! Pick 2 people • Probability that that they have different birthdays is: • 0·99726 • Therefore probability I get a pair of Birthdays is • 1 - 0·99726 • Probability of 0·0027397 • Probability I get a match is 0·27%

  5. Pick 3 people • Probability that that they have different birthdays is: • 0·99180 • Therefore probability I get a match of Birthdays is • 1 - 0·99180 • Probability of 0·0082 • Probability I get a match is 0·82%

  6. Pick 5 people • Probability that that they have different birthdays is: • 0·97286 • Therefore probability I get a pair of Birthdays is • 1 - 0·97286 • Probability of 0·2714 • Probability I get a match is 2·71%

  7. Pick 50 people • Probability that that they have different birthdays is ...going to take a while! ... • Probability I get a match is ???% • Any Guesses? 97%

  8. What is Randomness?

  9. Which of these Runs of 30 flips of a coin is made up? T TTH HT H T H HT H HHHT H T T TTTH T H T H T TT T H HT TH T H T TH HT H T H HT TH H T H T TH HT TH H T TH T TTTH T TH T TH HT T TTH T H HT TH T TH

  10. Variation & Clustering • Clustering of data is very likely in almost all trials and experiments. • What happens if you throw a handful of rice on a flat surface? • 30 flips TTTHHTHTHHTHHHHTHTTTTTHTHTHTTT • Clusters of 5 are common for this data with a sample of 30. • This is often confused with the probability of 5 Tails, which is one in 32. • Data naturally clusters together.

  11. National Lottery • The probability of getting consecutive numbers drawn is slightly less than ½ . People tend not to pick consecutive numbers on their tickets. • In fact humans are very poor at artificially creating randomness (“It’s so random!”). • As animals we base every decision on what we’ve seen before and extrapolate far sooner than we should.

  12. Lottery week 9 Jackpot prize was £16,000,000 All 6 numbers were picked by 133 tickets! Each ‘only’ won £120,000. Possibly to an unusual lack of clustering that week?

  13. Philosophical implications-some questions to consider: We’ve seen that we personalise probability instinctively and have major issues with randomness. We also have big problems with Coincidence & the very unlikely. • As animals, our natural ability to process probability is skewed by our instincts and personal experiences- did we evolve this instinct? • Instead of accepting Randomness, when we look back no events, we therefore like to look for patterns, errors or key moments to learn from to give us a “Reverse Perspective”. If we can’t find them, we look towards concepts such as Luck, Fate or Destiny: “It was meant to be”, “What’s for you will no go past you!”, “Que Sera Sera!”

  14. Chaos Theories Does our instinct to try to control what is beyond our control (or assign control elsewhere) result in a search for alternatives? Are Luck, Superstition, Fate or even Faith just our way of handling life with “reverse perspective” because, ultimately we’re all just at the whim of Randomness & Chaos? Look at the famous Poem “The Road not Taken” again- it is often assumed to be about control and boldness in life.

  15. The Road Not Taken   Two roads diverged in a yellow wood, And sorry I could not travel both   And be one traveller, long I stood And looked down one as far as I could To where it bent in the undergrowth; Then took the other, as just as fair, And having perhaps the better claim Because it was grassy and wanted wear; Though as for that, the passing there Had worn them really about the same, And both that morning equally lay In leaves no step had trodden black. Oh, I marked the first for another day! Yet knowing how way leads on to way I doubted if I should ever come back. I shall be telling this with a sigh Somewhere ages and ages hence: Two roads diverged in a wood, and I, I took the one less travelled by, And that has made all the difference. Robert Frost 1875– 67

  16. Recognising Randomness

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