numeracy · Arguable Intelligencehttps://ojmason.net/tags/numeracy/Personal musings on computational linguistics, AI, sailing, and generated fiction.en-gbOliver MasonOliver MasonSun, 30 Jan 2011 00:00:00 +0000Numerical Illiteracyhttps://ojmason.net/numerical-illiteracy/https://ojmason.net/numerical-illiteracy/Sun, 30 Jan 2011 00:00:00 +0000numeracypressNote: This is an older article from the blog I ran while being an academic. Most of the posts on there are about teaching and learning, but this one is of more general relevance, see also this one. I had a look at our free local newspaper, the Birmingham Mail Extra. In this issue is an article titled “Suburb is now crime hotspot”. This article has several problems, which are indicative of the problems of representing what happens ‘out there’ in the form of a newspaper article.Note: This is an older article from the blog I ran while being an academic. Most of the posts on there are about teaching and learning, but this one is of more general relevance, see also this one.

I had a look at our free local newspaper, the Birmingham Mail Extra. In this issue is an article titled “Suburb is now crime hotspot”. This article has several problems, which are indicative of the problems of representing what happens ‘out there’ in the form of a newspaper article.

Quinton had very little burglaries, “averaging just one or two burglaries a month” over the last nine years. But now, crime has “shot up by 29%”, more than the rest of Birmingham where crime only rose by 21%.

I find this rather misleading, and I worked through an example with the kids at the dinner table, which illustrates the problem:

  • Suburb A had 10 burglaries in 2009, and 12 in 2010. That is an increase of 20%.
  • Suburb B had 4 burglaries in 2009, and 5 in 2010. Increase of 25%.
  • Suburb C had 1 burglary in 2009, and 2 in 2010. A whopping 100% increase.

First lesson: percentage increase is meaningless unless everybody started in the same place. Why do developing economies have higher growth rates than Europe and the US? Because the percentage looks bigger. If you double your output from 100 cars to 200 cars you increase by 100%, but to maintain that rate you will have to produce an additional 200 cars the year after, and then 400, 800 etc.

Second lesson: without a fixed reference point (such as burglaries per 1000 inhabitants) you have no idea whether the risk of your house being burgled is high or low. Everything is relative, but you still need a fixed point to evaluate things.

Third lesson: this is not mentioned, but is that difference between 29% and 21% statistically significant? With “one or two burglaries a month”, the variation seems rather high, given those small numbers. So if there was one extra or one fewer burglaries, how would the 29% change?

Final lesson: be careful with calling places “crime hotspot” when your statistics are that shaky.

Now I don’t expect a staff reporter at the Birmingham Mail to apply the same rigour as a scientist (or any other, non-science researcher), but the way the article is presented is simply misleading. To me this sounds like a scare story being created out of some random statistics. I don’t know whether that is the case, and maybe Quinton is really a crime-ridden area, but I cannot tell from the few facts given to me in the article. The reason for this development given in the paper is that there are now 5 fewer policemen covering Quinton. Is there really such a cast-iron correlation between policemen and crime rate? How about the influence of the recession on crime? And how many policemen were there before the cut? 50? 500? 5000?

I now have more questions and know less than I did before reading that article!

]]>The longest Chip in the Worldhttps://ojmason.net/longest-chip-in-the-world/https://ojmason.net/longest-chip-in-the-world/Sat, 18 Dec 2010 00:00:00 +0000numeracyfoodIn his Metamagical Themas: Questing for the Essence of Mind and Pattern, Douglas Hofstadter talks about numerical literacy, the ability to understand large numbers. This is especially important when state budgets are thrown around which deal with billions of pounds or euros. At some point you just lose all feeling for quantities, as they are all so unimaginably large and abstract. He then goes on to pose some rough calculation questions, such as “How many cigarettes are smoked in the US every day?” – you start with some estimates, and then work out an answer, which might be near the order of magnitude of the right answer (which we of course don’t know). Quite an interesting and useful mental exercise.In his Metamagical Themas: Questing for the Essence of Mind and Pattern, Douglas Hofstadter talks about numerical literacy, the ability to understand large numbers. This is especially important when state budgets are thrown around which deal with billions of pounds or euros. At some point you just lose all feeling for quantities, as they are all so unimaginably large and abstract. He then goes on to pose some rough calculation questions, such as “How many cigarettes are smoked in the US every day?” – you start with some estimates, and then work out an answer, which might be near the order of magnitude of the right answer (which we of course don’t know). Quite an interesting and useful mental exercise.

Yesterday we had Fish & Chips for dinner. The girls were comparing the sizes of their chips, and then we came on to the topic of the longest chip in the world. Obviously, with ‘proper’ chips this is limited by the size of the source potato. However, assuming that industrially produced chips are made of mashed potato formed into chip-shapes, there is not really any fixed limit on the length. So, thinking of Hofstadter, I asked them how many potatoes we would need to make a chip that spans around the whole world.

Rough assumptions: one potato contains enough matter to produce 10cm worth of chip (the thickness is not specified). So, how many potatoes do we need for one metre of chip? This is also useful to practice basic primary-school-level maths… – 10. How many for a kilometre? 10,000. How many kilometres do we need to span the world? Roughly 40,000 km. So how many potatoes do we need? 400 million.

The next question is whether there are enough potatoes in the world to do this. Assuming a potato weighs 100g, how much do our 400 million potatoes weigh? 40 million kilogrammes, or 40,000 (metric) tons. What is the world’s potato production? According to Wikipedia, this is 315 million metric tons, so plenty enough. Now, if we were to turn the annual potato crop into one long chip, how many times would it go round the Earth? 7,875 times.

So, with a bit of basic maths (and Wikipedia for the data) you can make maths exciting for kids, practice how to multiply and divide, teach problem-solving, and have fun at the same time. And they also get a feeling for numbers: 400 million – that’s how many potatoes you need for a chip to span the Earth.

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