Maths and vampires

Vampires are in. Indeed, they have been all the rage for the last 200 years, appearing in books, films, comics… Vampires are a craze like aliens, dragons or superheroes --they are an icon of our society. The problem is that some people believe that they do really exist or, at least, they do not dismiss this possibility. For these cases, let’s resort to numbers.
We do not know when vampires first appeared. Some books and films hint at the time of pharaohs, but let’s be indulgent and start in more recent times: all legends accept that in the Middle Ages, castles in Central European woods were inhabited by vampires. Let’s take the year 1200 as the date of birth of the first vampire (quite late, I know, but I am being indulgent again). Then, in 1200, our first vampire flies out at night looking for a fresh neck to suck some dinner. Most legends state that vampires bite and suck the blood of their victims, who in turn become vampires themselves. However, we miss some information: when do vampires feel hungry? Every night, every week, every full moon? Let’s be indulgent again and think of a vampire who needs to be fed only once a year, far from our three meals a day, like the rest of hominids. Then, in the first year (in 1200), our immortal vampire hunts a victim, drinks his/her blood and turns him/her into another vampire, so on 1 January 1201 we have two vampires terrorizing human beings. In the following year there will be 4, because both vampires need to have a meal, and in 1204 we get 8, in 1205 we get 16 and in 1206 we get 32. Every year, the number of vampires doubles so in 1225 this exponential progression makes 16 million vampires for a total population of about 450 inhabitants on the Earth. Let’s go on with numbers. Nine years later, in 1234, vampire population would amount to 8,000 millions, which is far more than the total number of inhabitants on Earth at the beginning of the 21st century. If we go on with numbers until now-a-days, we would need a computer because the total amount of vampires will be greater than the amount of sand grains of our planet. These data clearly demonstrate that the vampire species is utterly unsustainable (even more than the human species). Just imagine the final figures if we assume that vampires have dinner every evening! Last week we said that we cannot create artificial blood yet, so vampires must have a very tough existence… We are what we eat!
Now, after publishing this post against vampires, I will hang a bulb of garlic by my door, just in case my words are too hurting...

Sources:

1. One of the main classic sources on vampirism (in French):
   http://books.google.com.co/books?id=uXAAAAAAMAAJ&printsec=frontcover&hl=ca&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false
2. Exponential progression:
   http://www.coyotes.es/ajedrez/imagenes/tablaGrande.gif 
3. Blood donation: http://www.deliveringdata.com/2011/01/let-blood-flow.html 

Superstition business

Needless to say, everybody is free to believe in anything. And this is not only for transcendent issues (life after death, the existence of a superior being who is our creator and who has some expectations on us, the meaning of our existence, etc.) but also for much trivial issues. If you want to believe that the Earth is flat, that we live among aliens, that buying the lottery at one of the most famous vendors increases your chances to be awarded, that being born under the sign of Virgin or Capricorn may influence your character or that carrying a rabbit’s foot will bring you luck (to you, not to the rabbit), you have the right to believe in those things and governments and society should respect this right.
However, when superstition is used to fool people, to get money or to subjugate people, governments should get involved and set some limits. It is rather a complex issue because believes are intimate and difficult to prove to be fake. But there are some obvious cases of deception, blatant lies, which may harm people. A hundred years ago, the magazine The Lancet claimed some laws against swindlers, but we did not get our act together until now: in the United Kingdom it is banned to advertise an amulet promising angel protection because it is not proved, and in Australia it is mandatory that the website of the company Power Balance states that there is no scientific evidence proving that Power Balance wristbands are effective. 
If drugs or food should strictly go through many tests to prove that their composition and effects are true, why not applying the same laws to the rest of products?

Sources:

1. Delivering Data about astrology: http://www.deliveringdata.com/2010/08/attraction-of-heavenly-bodies-and.html
2. Issue of The Lancet one hundred years ago: http://press.thelancet.com/editorial1911.pdf
3. The case of the “seven angels’ amulet”: http://www.telegraph.co.uk/news/newstopics/howaboutthat/7950087/Amulet-advert-banned-over-claim-of-divine-protection.html
4. Power Balance website claim: http://www.powerbalance.com/australia/CA
  

 

Let blood flow!

One out of ten people admitted in hospital needs blood, and this is a lot of blood. As we cannot manufacture blood artificially and we have not found any replacing fluid yet, the only way to get blood for patients is from donors. Last weekend, Barcelona held the Blood Donation Marathon which aims at increasing donations and get visible in the mass media, as the situation is rather critical, not now but always: as you can see in the website of blood donors of Catalonia, the day before this blood donation marathon, the blood stock was enough for only four days.
All you need to know about blood donation:
- It is a painless procedure, there is no risk of catching any infectious illness and the whole process lasts less than fifteen minutes.
- You can give blood four times a year and you have to wait at least two months between donations.
- If you give blood in spring, summer, autumn and winter you will help save 12 lives.
- You can give blood all year round and you are very likely to have a blood donation centre nearby. Check it on the web.

Sources:

1. Blood Donation Marathon in Barcelona: http://www.quecorrilasang.org/
2. Website of blood donors of Catalonia: http://www.donarsang.gencat.cat/en_index.html
  

Draught beer or bottled beer?

Some people clearly prefer draught beer rather than bottled beer, or vice versa, but some other people do not really care, they just want beer to be cold enough. This post is for these people: maybe the following figures will turn you into staunch advocates of draught beer.
Every barrel contains 30 litres of beer. Taking into account that half-litre to one litre beer is lost from each barrel while serving draught beer, we can state that each barrel results in 88 glasses of 330 ml, that is, about 12 fl oz of beer. The lifespan of a barrel is 10 years and barrels can be refilled as often as you want, but usually each barrel is refilled 6 times per year. In short: every barrel can serve 5,280 glasses of beer.
Let’s look at beer bottles now. A beer bottle of 330 ml can be refilled up to 7 times (after being cleaned and treated at the bottling plant), but most bottles break much before, so we get an average of 5 refillings per bottle. That means that each barrel is equivalent to 1,056 beer bottles refilled 5 times.
Finally, let’s estimate how much beer we drink in our lifetime. It is quite difficult because we all have different drinking habits, but let’s image someone who loves beer without having any alcohol addiction: this person may drink a glass or bottle of beer every day (or seven glasses or bottles of beer on the weekend). This standard drinker shall take 365 beers every year, resulting in 18,250 beers in 50 years --that is 6,083 litres.
Therefore, a standard beer drinker may use 3,650 bottles in his lifetime (each bottle refilled five times), whereas it would mean only three and a half barrels (refilled sixty times). Just imagine a pile of residues made up of 3,650 glass bottles and, next to it, three and a half barrels of beer. Our conclusion is quite obvious: the ecological impact of a drinker of draught beer is less significant, so if you do not really care about draught or bottled beer, here you have a choice!

Sources:

For our calculations, we carried out a survey in a dozen beer companies. Then, we reached our conclusions sitting around a table, with a beer in our hands –needless to say, a draught beer.

How to read statistics

Statistics can be interpreted in many different ways: just notice how political parties (and allied mass media) read poll results to realise that statistics, without any context or explanation, can be easily misinterpreted. Churchill used to say that he only believed in statistics that he doctored himself. John Allen Paulos’ book Innumeracy: Mathematical Illiteracy and its Consequences is a very interesting reading material to better understand statistics. This book shows that we know absolutely nothing about mathematical culture so it is very easy to fool us if we cannot even understand a statistic.A good proof of it is the recent reporting of sexual harassment by two Swedish girls against WikiLeaks founder Julian Assange. Some mass media, in an attempt to provide some context to this piece of news, offered the following fact: Sweden is the country with the highest rape rate in Europe. But if we look up the sourcebook of this information, we realise that it should be properly interpreted: according to this survey, Sweden is the country with the highest reported rape rate (53 rapes per 100,000 population) in Europe. Therefore, these figures do not show the actual number of rape offences committed but the high level of confidence of Swedish people in their justice and their low tolerance on such abuses. At least, these 53 reported rapes per 100,000 population in Sweden contrast with the 2 cases in Turkey, 3 in Albania, 2 in Greece or 5 in Spain. Is it a problem in Sweden or in the rest of countries?

Sources:

1. Churchill's quote: http://en.wikiquote.org/Churchill
2. Innumeracy: Mathematical Illiteracy and its Consequences: http://en.wikipedia.org/wiki/Innumeracy_(book)
3. European Sourcebook of Crime and Criminal Justice Statistics 2010 (page 46): http://www.europeansourcebook.org/ob285_full.pdf