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26 January 2013

Common mistakes #9: “220% times less” – the American academic who speaks Russian and English, but who cannot speak Arithmetic

It is often as important to be numerate as literate, especially in a digital world.
     One of the most infuriating aspects of innumeracy is the habit of saying things like “The total is two times less than last year.” It is meaningless. “Two times as much as last year” is fine, as it means that the total has been multiplied by two. It would perhaps be clearer to say, “The total is double last year’s”, or “It is twice as much as last year’s”, but if a fraction or percentage is involved, it is fine to say, “The total is 220% of last year’s”. That means, to take a specific example, that if last year’s total was 66,000 then this year’s was 144,000, or thereabouts.
     But this cannot be done the other way round without violating every rule of sense.
     This morning, while lounging in bed with my tea, I read, in the Georgia Journal of International and Comparative Law (2008), a long paper entitled “Vladimir Putin and the Rule of Law in Russia” by Professor Jeffrey Kahn. In the course of it, Prof. Kahn says of the beneficial effects of the new procedure officially operating in criminal cases in Russia:
“In addition to stripping prosecutors of the power to order pre-trial detention, amendments to the Criminal Procedure Code and the Criminal Code, in March 2001 and October 2002, respectively, limited the types of crimes for which someone could be detained. Cases in which investigators requested pre-trial detention decreased from 144,000 in the first half of 2000 to 66,000 in the first half of 2003 - an almost 220% decrease.”
     That last sentence is nonsense.
     How can one figure be 2.2 times less than another if it not to be a negative number? The absolute minimum quantity of people held in pre-trial detention is 0. There cannot be a minus person,  as it were, unlike with temperature, say, which is -16C today in Khimki.
     What Professor Kahn ought to have said was that the number of pre-trial detention cases decreased between 2000 and 2003 by 54%. The decrease was 78,000 (i.e. 144,000 – 66,000), which is 54% of 144,000. It is not, and never can or could be on basic logical grounds, a decrease of 220%. To repeat: you cannot have a negative number of people, even—or perhaps especially—in a Russian pre-trial detention centre, which is another name for jail.
     The general rule should be: increases can be described as either fractions or multiples, but decreases can only be described correctly as fractions. 
     This is part of Arithmetic Etiquette for Americans, Russians, Britons, Brazilians, Burundians, Falkland Islanders, people in space, old Uncle Tom Cobleigh and All.


  1. Thank you! Very interesting theme – I have never thought that “…times less than” could be misunderstood. At least in scientific English "...times less than" is used more then often.

    I know for sure that this "Arithmetic Etiquette" you mentioned here is absolutely false for the Russian language (we can say either "в два раза меньше" or "на 50% меньше").

    As for the English language - it was a mystery for my why they can't understands meaning of "...times less". When I translate from English, “…times less” means “в… раз меньше” – what’s a problem? And the problem is that many English-speaking people believe that “times” means multiplication and “less” means “minus”:

    Rather strange for me, but any way – famous English mathematicians are on my side :)

  2. You make a very interesting point, Tatyana, and I entirely accept your Russian analogy. However I suspect mathematical confusion in one language is the same as mathematical confusion in another.

    What I would say is that the first rule of good writing is clarity. Irrespective of what Isaac Newton may have felt to be clear writing in the seventeenth century (having read the blog reference you gave), today we are not very numerate.

    But that is still not a full answer, I accept. My feeling is that to say “five times less than” sounds ugly and inappropriate, but is not likely to be misunderstood, whereas to say “220% less” is. Somehow a percentage implies a relationship with the integer, which is 100%, and that is violated by having a negative (as it were) multiple of greater than 100 when something like numbers of people is being talked about that can never be less than one—unlike something conceptual, like temperature readings on non-Kelvin scales. Ладно!

    But all that probably just makes the whole thing even less clear!

    And what are we to think about the Einstein enthusiast who decided to learn German in order to understand E=mc2?