PC458 - Maths Comon Thinking Errors April 2009
Andrew Dilnot - Numbers in Perpective

-- On Groks - Andrew Dilnot - put numbers in perspective by quoting per head of population.
- BUT THE MEDIA DON'T DO THIS e.g. 20 % increase in Finger cancer ! Which means it's increased from 5 in 100,000 people to 6 in 100,000 the difference to 1 peron : the risk was 0.005% now it's 0.006% so don't worry.
- On Amazon, On Groks

- 1. Big numbers should be presented in terms of people they effect . Relative to the real individual

- 2. care with average and median e.g the average tax payer will be $100 better off could mean the median taxpayer is $2000 worse off and a few billionaires $5m better off.

- I say These should be included in a Legal Journalism Standard in using statistics like Hippocratic Oath.

- I think he criticized people for getting into the habit of believing every system is a linear system e.g. More of input X means more of output Y
- In reality system's are often chaotic ... Which leads me to

Can't Apply Linear Maths to Climate

- The Climate is a chaotic system, but people are so accustomed to thinking about linear systems they try to apply a linear theory to it - e.g. if we reduce CO2 by this much the temperature will fall by this much.

- interesting what Ian Plimer said on Counterpoint. Yes CO2 might effect climate, but it would get to a limit. More CO2 doesn't mean more temperature like closing the curtain, it doesn't matter if you put another curtain in front of that

- Simple systems often chaoitc
- Mathematician LORD ROBERT MAY speaking on The Forum May 2009 - simple equations usually work, but sometimes even simple equations yield completely chaotic results so no matter how much computational power we will never be able to predict the weather beyond 20 days.
- Chaos doesn't mean there is no pattern in a system it just means it can swing wildly.

- his example of a simple system X1, X2, X3 ..Xn
X1(1-X1)K=X2
- where K is a constant, if K < 1 you get a pattern falling 0, if K is between 1-3 you get a steady pattern, if K >3 you get a pattern swinging wildly and so sensitive that if you make a mistake with the 7th decimal place the pattern is completely different.

Obsure Maths is Important

How Math Explains the World - Prof. James Stein Maths in Life
- On Amazon, On Groks
- bank cryptograph is based on obscure mathematics from 50 years ago
- maths says democracy doesn't work - it's never fair ... Que ??
- quite interesting

- Probability Lecture

- Gresham College How to be a Winner: The maths of race fixing and money laundering

- Geometry is ancient yet Probability is a new science less than 500 years old. People didn't have a concept of chance or equally likely events more often they attributed it to the gods. When there was evil in the town of Jonah to pick who was the evil one the people drew lots and so Jonah lost and the people cast him out.

- The first dice had numbers corresponding to a list of gods on so you knew which to pray to.

- People were playing dice games even though they didn't have the probability. In 1700s. A mate of Pascal found he could make money on there being a 6 in 4 rolls of a dice. So Pascal got into counting the probability the chance of not a six is 5/6 x 5/6 x 5/6 x 5/6 = 48% first

- can turn a biased game into a fair game by pairing. Heads Tails is equal chance of Tails Heads, but TT maybe much more likely than HH.

- Problem with intuition - fake randoms don't have the long runs that real ones do.

- to fix a race bet stake proportional to odds.

- Similar technique used to launder money at a fixed cost.

- Monty hall. I choose A When Monty shows me box B, does it give me any extra info YES ? Out of 6 events 2 times it's cos the prize is behind C, when it's behind A 1 time he'll show me B the next time C so he is giving me extra info he's telling me C twice as likely as A.

- Intuitively when 3 events are equally likely and one is ruled out then the chances are 50/50. But that is when the events are independent. But they not always independent

- Life is more due to random events rather than skill.

- from his book called The Drunkhard's walk

- Again stop thinking everything is linear - many times random factor apply

- Probability Randomness only works for large data sets. You can't judge by small samples ,but we apply it wrongly all the time
- e.g. We judge people by their success, but it's not a large enough sample, purely by chance many people can have 3 good years in a row.
- In all fields we raise people highly when their skill is the same as other people, it's just we attribute skills to people based on past success or expectation, but this is the same as expecting $50 wine to taste better than $10.

- We say Bruce Willis is a good actor, but there are plenty of equally skilled actors who didn't have the same lucky breaks.

- Wine experts were unable to tell the difference when they were given white wine dyed red.

- Expectation drives pleasure - in Brain scanners pleasure areas lit up more when partipants were given the same wine marked at as higher price. Likewise this expectation clouds our judgement

Mistakes of Intuition.
- Fund manager had 15 winning years in a row. Wow amazing ! .. No ! Over 40 years purely by chance 25% of managers should have 15 winning years.

- Fluctuation plays an important part in small samples.

- Illusion of Control Human brain thinks it can control random things, we die younger if we don't maintain this illusion. We think we get better at guessing coin tosses with practice.

- If you want to be more successful then double your failure rate. Bill Gates had a lot of lucky breaks.

- Book On Amazon, On Groks

- Edge-Of-Science

- not great except there must be a formula for pi.

- On Groks

- Inverse Square Law voting - Penrose

- on BBC The Forum - Roger Penrose explained this works better than 1 country 1 vote or voting by population size. I can't see how. It's something to do with the chance that your vote flipped the vote from No to Yes is proportional to the inverse square of the country's population

- Trying to understand
- If the majority in 4-land vote yes it gives 2 YES votes
- If the majority in 16-land vote No it gives 4 NO votes
- Why not 8 ? It's to do with the chance an individual could flip the decision in 4-land it's half the time in 16-land it's a quarter.
-
- 4-land vote options
-
- YYYB bob makes the no difference
- YYNB bob makes the difference
- YNNB bob makes the difference
- NNNB bob makes no difference
- half time Bob makes a difference

- 16-land vote options
- Bob Only makes a difference when 7 or 8 people vote Yes ie 2 times out of 16=1/8 similarly in 32-land when 15 or 16 people vote Yes ie 2 times out of 32=1/16

- chance is 2/p so where's the inverse square ?

1- land 1 vote 4--land 2 votes 16- land 4 votes

- Quick Answers via Unperceived Info

- More or Less - My mate Gert G was explaining his application of intuition or heuristics (picking the right answer without analysing all the data).

- Which city is largest the one you've heard of or the one you haven't ?
- Which sportsman will win the known or the unknown?

- In each case just the fact that have heard of something gives you a strong indication ; that a city is big or a sportsman is good.

- Same for finance this simple analysis often beats experts.
-I think the experts are worth their money for that 1/20 time something strange happens , but Gert says experts tend to overanalyse and are often wrong.

Stat-Spotting A Field Guide to understanding Dubious Data - by Joel Best
- seems like a good book - covered in the podcast Skeptically_Speaking_015_Math.mp3 11 minutes in
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