Friday, April 13, 2012

Completing a Panini Sticker Album

When I was a kid my main ambition was to fill out the Panini Italia 90 sticker album. I promised myself when I was old and rich I would buy all the stickers I needed to fill out a championship sticker album. Some kids aim to play for Ireland, I aimed low. Turns out I am not rich but I am nerdy so at least I can work out how much it would cost to fill out the album.

This is called the Coupon Collector Problem.
"Given n coupons, how many coupons do you expect you would need to draw with replacement before having drawn each coupon at least once?"

There are 539 stickers in an album to collect. The first sticker you buy is going to be one you need, a 539/539 chance of getting one you need. The second has a 538/539 chance of being one you do not have as there is one it can clash with. This keeps going until for the last sticker every new sticker has a 1/539 of beng the right one. The formula for the number of attempts you would need to calculate the coupon collector number is 539*Harmonic Number of 539. Which according to Wolfram Alpha is 6.867858*539=3701.77. The stickers are sold in packs of five. Which means 740 packs.

On amazon a box of 100 packs cost £43.95. This would mean (assuming you could get .4 of a box at that same price) that filling the album would be expected to cost 325.23 pounds.

Panini sell the stickers at 14p each. So to buy the stickers individually would cost 539*.14=75.46 pounds.

Is there some kind of mixture of boxes of random stickers and individual ones that means you can fill in the album for as cheap as possible. Say the individual stickers can be bought at the price of a box. So thats 0.1162 pounds for each sticker. Which is not that much of a saving. It becomes more efficient to buy individual stickers than random packs at this price after about 90 stickers.

The last sticker takes on average 539 stickers to be bought to find it. So this last sticker costs 0.1162*539=62.63 pounds if you buy it in packets not individually.

But are the tickets independent? As in are some rarer than others and is each pack random? Some people studied this in the very cool paper 'Paninimania: sticker rarity and cost-ef fective strategy'
"We consider some issues related to the famous Panini stickers devoted to the football world cup. In particular, we address the following questions: is there a planned shortage of some stickers? What is a good cost-e ffective strategy to fill in an album?"
Which proves amongst other things I am not the only nerd that still wants to fill in a Panini album.

Tuesday, April 10, 2012

The Rational Voter On Science

The myth of the rational voter is a great book by Bryan Caplan about how democracies make predictable errors because people are biased against certain beliefs. The video below gives a good synopsis of his arguments

The belief that people having incorrect beliefs will not be a problem is called "The miracle of aggregation" where people don't know much all disagree with each other and those small number of people who do know something are the ones who are left after all the noise is cancelled out. But because these beliefs are not randomly wrong but biased to one side this cancelling out doesn't happen.

He talks about the economic areas of being anti market, making work for the unemployed, anti foreigners and that people are too pessimistic and how general opinion on these issues disagrees with that of economists. You could argue that the people are right and economists wrong on these issues but generally people who are experts in a field tend to know more about it. If you disagree I am available for entirely unqualified and haphazard brain surgery if you want to put your brain where your mouth is.

But what about non economic questions? Are there scientific questions people get wrong that might result in voting based on a mistaken view of how the word works. There is a poll about scientific question that takes place across many countries called the National Science Foundation, Science and Engineering Indicators which asks what it thinks are basic science questions everyone should know the answer to.

If many people get the wrong answer about these questions, and the question is important from a policy point of view then this poll will show an area the voter is likely to be irrational about and we will get bad policy in that area.

· The center of the Earth is very hot. (True) 78.0% of Americans in 2006 got this right.
A politiician who did not believe this might have a hard problem supporting geothermal heating. But geothermal is not that big a source of energy so it would mess things up very badly.

· All radioactivity is man-made (False) 73.0% got this right.
Without realising this you might overestimate the risk man made radioactivity is going to cause. I am willing to bet the 27% of people who didn't know this might be less in favour of nuclear power stations. But I really don't know if more nuclear power is a good policy. Lovelock and Brand say it is. Unless I can prove the connection between holding the belief that all radioactivity is man made and being anti nuclear power it is a stretch to claim this false belief harms us.

· It is the father’s gene that decides whether the baby is a boy or a girl (True) 62.0% got this right
Many parents want male children and without realising this then women could get blamed as the female kids are their fault. I'm not sure what political policies would change if you did get this wrong though. Sex selective abortion seems wrong whether you understand the y chromosome or not.

If more people understood the sperms role in sex selection more sperm sorting techniques could be used. This might result in lower numbers of children in those who want to 'balance out' their families.

· Lasers work by focusing sound waves (False) 42.0%
'over 25% of the GDP of developed countries is directly based on quantum physics' someone who got this wrong would have very wrng views about something fairly fundamental to the modern economy.

· Electrons are smaller than atoms (True) 45.0%
Similar issue with understanding one of the main sources of income in a modern economy. Could someone who got this wrong really hope to decide between investing research money in on scientific field or another?

To be fair I might get this question incorrect. Electrons do not really have a size. As wikipedia says "the electron has no known substructure.[2][72] Hence, it is defined or assumed to be a point particle with a point charge and no spatial extent". This question is a bit like asking is a car smaller than hope. The question doesnt really make sense.

· Antibiotics kill viruses as well as bacteria (False) 54.0%

This one is really important. Overuse of antibiotics is making them less effective. Megan Mcardle has a great piece on the problem here.

Some people give antibiotics credit with increasing our life expectancy by about 8 years and no one thinks they have had a tiny role in our large life expectancy increase during the 20th century.

Getting antibiotics policy wrong is a really big issue and one the public get wrong. You don't hear politicians on the "If you vote for me you wont get penicillen for your earache" platform. This is an important issue probably up there with the economic ones Caplan describes in his book.

I have heard Michael Graham on Irish radio saying he doesnt care about politicians opinion on evolution because it will not effect how well they govern. The case of antibiotic resistance shows how important it might be to have politicians who accept evolution as it is in progress in this case limiting the power of one of our most important healthcare tools. I get the feeling many of these questions are actually about aligning yourself with literal interpretation of the bible rather than science knowledge.

This is one area public health campaigns are trying to explain

· The universe began with a huge explosion (True) 40.0%
This is another question I might get wrong. Calvin and Hobbes described the big bang as the 'Horrendous Space Kablooie' which might be more accurate than calling it an explosion.

I can't see this issue having a big effect on policy though. The "if i am elected I will combat the inflation of the universe" party probably won't change much.

· The continents have been moving their location for millions of years and will continue to move in the future (True) 77.0%
You might have a pretty weird view of earthquakes if you didn't believe this but again I can think of no specific policy issue you are likely to get wrong

· Human beings as we know them today, developed from earlier species of animals (True) 50.0%
What policy would someone who did not believe this get wrong? Some medical ones about the usefullness and ethics of animal testing maybe. There must be more then that though. If you can think of any specific policy people who don't know the right answer voting on would cause harm please add it in the comments.

This is a question the majority is not right on. So if there is a policy question that this deals with it could be one where those that know the correct answer are drowned out.

Not to go all Karl Popper on this but I could also argue about which of these are true/false and which are the current best theories. I think most cosmologists would put a higher probability on the big bang theory being overtaken then the heliocentric solar system one. Also there would be a higher certainty on all these theories than any of the economic ones IMHO. But that does not mean I couldn't argue with the phrasing.

Does the Earth go around the Sun or does the Sun go around the Earth? (Earth around Sun) 71.0% got this right.
I'm not sure you can say the earth goes round the sun. It move in a eliptical orbit with the sun at one foci. If a politician actually believed the sun went round the earth would it specifically result in any bad policies? As opposed to general worry about his intellect? Not any I can think of.

If you know of any other polls of the public belief about scientific questions please post them. Based on this one survey (results for other countries here) On antibiotic control policy the public is likely to support the wrong policy.

Other than economics and science are there other areas the public is probably supporting policies the vast majority of experts in the area disagree with? Public Health and Criminology experts probably disagree with policies politicians run on and people vote for. I would like to see any polls that would show this.

Wednesday, April 04, 2012

Where Is Bezos' Laser?

Jeff Bezos who set up Amazon is starting to scare me.
Last week he bought a robot army, Kiva systems.
Soon he is getting moon rocket engines from the sea.
He is building a giant base inside a mountain.
Also if I understand cloud computing he also owns the weather

This is the CV of a Bond villian.