Lies, damned lies and statistics.

Statistics is a very powerful mathematical tool that can be used to determine and describe the likelihood of certain events occurring. Thus statisticians can determine the odds of winning the lotto or calculate the number of kangaroos in a wild population even though only a fraction of the total have been surveyed. Of course, just as with any other tool employed by humans, statistics can be abused or even simulated in order to provide a more desirable message to a particular audience. We see this commonly in advertising.

One advertisement recently for a fertility clinic proclaims that 70% of successful clients became pregnant within two months of enlisting their services. What is not clear is just how many of their clients were successful at all - and how many of those successes were due to the skills of clinic staff and how much was up to the vagaries of nature. Presumably we were meant to hear this statement simply as: "70% of clients became pregnant within two months" with the keyword successful removed. If a client later says they were misled, the clinic can honestly say it's all there in black and white. The fact that the advertisers see fit to feed us this particular figure is almost an iron clad guarantee that the percentage representing those who became pregnant at all in some reasonable time frame is somewhat less than 70% - else they would quote that figure instead.

In another advertisement, this time for a breakfast cereal which is supposedly good for one's figure, we are told that a number of women are 'challenged' to try the cereal for two weeks and see how they feel. After this time the women are presumably interviewed for we are told that eight out of ten women would be willing to take the challenge again. Given that the cereal is unlikely to do anyone any serious damage it is hardly an impressive endorsement that people are willing to say that they could cope with this challenge once more.

Perhaps the silliest example that comes to mind was an advertisement for a cosmetic cream which presented the ludicrous idea that the product on offer was 50% more effective at making the user more beautiful than the products offered by their competitors. The question that comes to mind here is: how does one create a precise mathematical formula to describe the very the effects of a cosmetic on such a subjective thing as beauty? While it is true that certain aspects of beauty can be described mathematically - such as the ideal ratio of waist to hip width - very often opinions on beauty have as much to do with culture and fashion as anything else. Waist-hip ratio gives a clue to a woman's ability to bear children and thus it may be used to measure the beauty of a woman in regard to this one particular trait, but equally we cannot apply mathematics to determine the ideal BMI for a 'beautiful' woman since a quick review of cultures throughout history tells us that there is little agreement in this area.

In recent years a rather insidious example of abused percentages comes from the food industry. A foodstuff may be described as being 98% 'fat-free'. Great! There is fat in only 2% of this product! We possibly wonder what proportion of the 2% is fat - of course the answer is: 100%. The buyer is comforted by the term 'fat-free' despite the fact that the '70% fat-free' chocolate they are eating is clearly a very fatty item. Another related point comes from observing the descriptions of fat content on the packets of chocolate from the one manufacturer. A single 'serve' of chocolate contains 8-10% of the recommended daily intake of fat. However, a 'serve' is only 25g or five small squares on plain chocolate or only two or three squares for fancier varieties. Of course any self-respective chocoholic knows that two or three squares is a laughably inadequate serving and thus it is very easy to obtain a very significant portion of ones recommended daily ration of fat during a single movie.

Whenever confronted with percentages describing the qualities of a product, these figures should be treated with suspicion. Advertisers will always do their best to display a product in its best light - that's their job afterall. If the numbers seem too good to be true they probably are. Take a moment to re-read main assertions to be sure you haven't ignored a critical modifier or given too much attention to a comforting term like 'fat-free'. Also pay attention to the fine print - assuming of course you can find the find print.* Think about whether the quality being described can objectively accept a numerical score.

*It is remarkable how often wonderful deals are associated with asterisks for which the associated footnote has taken advanced camouflage training.

Number Fun

Perhaps you remember learning this trick in school:

First, take a number, add the digits together. Let’s try it with 123.

1+2+3 = 6

Now, we know that six divides evenly into three (6 ÷ 3 = 2) and the little number trick tells us that 123 is also therefore divisible by three.

On the other hand, the digits of 124 add up to seven. Seven is not evenly divisible by three, therefore 124 isn’t either.

You may also realise that this trick works for the number nine. You can see it in the multiplication table for nine:

2x9 = 18 (1+8 = 9); 3x9 = 27 (2+7 = 9); 4x9 = 36 (3+6 = 9).

The same concept is the basis for jokes like this:

Try this. It’s AMAZING! It profiles you based on numerology principles and psychological analysis to identify your favourite food from the options in the list below.

Write down your favourite number. Multiply it by three. Multiply by three again. Subtract 2.

Now take each digit of the number and add them together. Is the number larger than 9? If so add the digits of the new number. (If you have a very large favourite number you might have to repeat this cycle.)

Now use your final number to identify your favourite from the list below.

1. Ice-cream
2. Chocolate
3. Beer!!!
4. Lasagne
5. Fish & chips
6. Steak
7. Brussels sprouts
8. Apple pie
9. Tim Tams

OK, Good choice!

Basically, all these tricks work because we have ten different digits in our counting system which are using in a repetitive manner to form all possible numbers (which is why it is called the decimal or base 10 system). The largest single digit number is nine and so the trick works for any factor of 9 (e.g.: 1, 3 and 9).

Factor: If A is evenly divisible by B, then B is a factor of A.

Exactly why it should always work for factors of the largest single digit number is beyond my ken, but it does. We can confirm it by shifting to other counting systems.

If we had only eight digits in our counting system (octal or base 8) then the trick works for the number seven instead, because then seven would be the largest single digit number! In octal the number ‘10’ is one more than seven. In octal fourteen is written as '16'; the digits add up to seven and therefore fourteen is divisible by seven.

Computers often make use of a hexadecimal system which has 16 digits. This is represent by using the regular digits from 0 to 9 and supplementing them with the letters A to F. Thus ‘A’ is equivalent to our ten, ‘F’ is equivalent to our fifteen and ‘10’ represents the number sixteen! Since 'F' (fifteen) is the largest single digit number, the trick works for any factor of fifteen (e.g.: 1, 3, 5 and 15) when using the hexadecimal system.

So, let’s take the hexadecimal number ‘2B2,’ which equals the decimal number ‘690’, as an example. Remembering that ‘B’ equals ‘11’ in decimal, add the digits together. 2 + B + 2 = F (‘F’ = decimal 15)

Since F (15) is divisible by 3, 5 and of course 15, then 2B2 is also divisible by those numbers.

If you selected a trinary (base 3) counting system then the trick would work for the number two.

If you selected a base 5 counting system the trick would work with the number four.

Enjoy your sprouts!

(P.S. The amount added or subtracted after multiplying by 3 and 3 determines which item is selected from the list. Two is subtracted and 9 - 2 = 7 so you were forced to pick the seventh item in the list – sprouts!)

(P.P.S It doesn't work for zero or negative numbers.)

Freedom: a Fool’s Dream?

Members of the Russian punk band Pussy Riot have been sentenced to two years in prison. Why? Michael Idov, editor-in-chief of GQ Russia summarizes the situation thus: “When you trim away everything else, three young women will spend two years in jail for dancing in a church.”¹  You can watch the video here.

Knowing what these women were singing while they danced sheds significantly more light on the situation, but this is a light the Russian authorities would undoubtedly prefer left off. The shameful words were, ''Mother of God, get rid of Putin.²''

As Russia is supposedly a democratic nation, authorities cannot admit to condemning three women for making a political statement, so they must concentrate on the fact that Pussy Riot’s gig was performed without church sanction. Pussy Riot was not just speaking out against Vladimir Putin; they are also concerned about the closeness of the Russian Orthodox Church to the state. The head of the church, Patriarch Kirill is apparently a keen follower of Putin and has described the president’s leadership as “a miracle of God”.³  It is therefore convenient to accuse the young women of religious hatred and then drag out some old biddies mortally offended by the deed to act as witnesses at the trial.

By all accounts the trial itself was a farce baring little connection to justice and at best following the letter of the law. Michael Idov is scathing of the conduct of the legal teams on either side of the ‘justice’ system itself. He says:
“The only professionals anywhere in sight are Pussy Riot. From their name, perfectly pitched to both shock and attract the media, to their instantly recognisable look; from their initial punk posturing in interviews, to their pointedly academic statements to the court; these women, and they alone in this mess, know exactly what they are doing. Minutes after the verdict, the band released a new single, Putin Lights Up the Fires, through the London-based Guardian.”

Meanwhile, Russia continues to arrest protestors as more people express frustration with Putin’s regime. Obviously this whole trial is a propaganda campaign designed to draw the public’s attention away from the real issue: free speech.

*

Free speech is the friend of long-term national stability, but it is not the friend of autocrats. Free speech helps to keep authorities honest. Of course difficulties arise when the most powerful speakers – the media – are allied to the powers that be. In Australia we can be very grateful that our national broadcaster is not required to tow the ruling party’s line. (Some will say that it is clear that the ABC in pro one side or the other, but I’ve seen enough ABC news articles hounding both sides of politics. Attacking politicians of one’s own stripe does not automatically constitute bias.) Commercial media, while likewise not bound by the state, may be still influenced by the political leanings of major shareholders – nevertheless, commercial stations do play a crucial role in disseminating information. The main sin of the media, particularly commercial channels, is presenting items in order to entertain and provoke rating boosting reactions rather than seeking first of all to inform the public.

Politicians who are in power for the right reasons should not fear honest appraisals of their performance in the public arena. By the same token, the media needs to be accountable when it fails to provide honesty.

It is not just in a democracy that free speech can serve stability. A monarchy is as far as one can get from true democracy. If the monarch serves his or her nation as a monarch should then fair appraisals in the media are nothing for them to fear The European royal families that survive today have recognised the need to stay on the good side of their subjects. Indeed, seeing the writing on the wall, they have adapted to changing expectations and relinquished much of their power.

Though little more than a figurehead today, the House of Windsor retains much wealth as well as the love and respect of many whereas the royals of France are long extinct. In the Britain parliaments have given at least some privileged persons the ability to speak up and influence the nation since the thirteenth century. In other words, the monarch could be pretty sure that he/she would be supported in his/her actions because he/she had bothered to ask his ‘important’ subjects (i.e.: the lords and the church hierarchy) for their input before laying down the law. The French did not have a regular, national parliament until after the revolution in 1848 – which was a little too late for the newly dead French royals.

*

Of course President Putin in Russia might argue (privately) that he did have the support of the important people – just like those old English kings, or the Russian Tsars; the trouble is it is a different world now. For all the conservativeness of many Russian citizens, the proportion of well-educated Russians with modern expectations and the means to put pressure on the ruling elite is much higher than it was.

The potential for intellectuals spoiling a good tyranny is something Russia’s rulers know how to deal with. Stalin was the master.

In 1940, after the Russians pushed the Germans out of Eastern Poland, Stalin arranged a massacre of about 22,000 Poles at Katyn Forest. Like Hilter, Stalin wanted the Poles docile so he arranged for the removal of the most effective opposition – both military and intellectual. Those murdered included 8,000 military officers, 6,000 police officers and members of the intelligentsia arrested for being “intelligence agents, gendarmes, landowners, saboteurs, factory owners, lawyers, officials and priests”.⁴

Trofim Lysenko held some ideas about evolution that were unpopular with mainstream scientists - who favoured the views of Darwin, Wallace and Mendel. Lysenko, however, was Stalin’s pet and, as the head of the Academy of Agricultural Sciences of the Soviet Union, he had the influence necessary to cause the ‘expulsion, imprisonment and death of hundreds of scientists’.⁵

*

Pussy Riot may look like a bunch of silly girls playing a dangerous game, but they are both smart and brave. They continue the noble tradition of Dylan, Orwell and Voltaire who have used the power of words to fight or illuminate the wrongs they observe in society and in the institutions of government and church which should be leading society in the fight against wrong-doing.

Dressing up in outrageous costumes and poking fun at the ruling elite also brings to mind the honourable tradition of the court jester. Honourable? The jester or fool was in many cases not present at court merely to entertain.
A licenced Fool in a medieval European court held a position of importance was often a person of some wisdom. The Fool was licenced to speak his mind – when and how he pleased. When a monarch did or said something unwise or a discussion between nobles became overly heated, a witticism from the Fool could ease tension or even put a monarch back in his/her place without loss of face. Queen Elizabeth I is said to have rebuked one of her fools for being insufficiently severe with her.⁶

Stańczyk (1480-1560) is the most famous Polish jester. He was praised by contemporary writers and historians as a guardian of truth against hypocrisy. Later when Poland was partitioned between Austria, Germany and Russia his memory became a symbol of Poland’s struggle for freedom and as such was a favoured subject of the artist Matejko.^7,8,9

“Stańczyk” by Matejko. (Here he is depicted as the only person at a ball who is concerned about the Russian capture of Smolensk in 1514.)

*

Silencing one’s critics by force only gives them credibility. A wiser move is to ignore them. Even wiser is to minimize the need to be criticized. If a ruler would be a successful leader he/she should remember that that, in the long run, the carrot is mightier than the stick. Mr Putin, laugh at the antics of the girls and quietly amend the freedoms of your people; there will be no loss of face and you will still be living in luxury.

Russia has given the world brilliant minds such as Dostoyevsky, Mendeleev, Tchaikovsky, Tolstoy and Pavlov. The illustrious list of Russian thinkers indicates that Russia has much potential to shine as a bright beacon in the world. If only the ones carrying the flame would not snuff out the light every time they carelessly burnt their fingers.