Sunday, April 29, 2012

Delegation - A Story of Flagpoles

One of the most important functions of a manager is to facilitate the so-called process of delegation - this is defined and discussed in the online resource “Management Study Guide” at 

“A manger alone cannot perform all the tasks assigned to him. In order to meet the targets, the manager should delegate authority. Delegation of authority means division of authority and powers downwards to the subordinate. Delegation is about entrusting someone else to do parts of your job. Delegation of authority can be defined as sub division and sub allocation of powers to the subordinates in order to achieve effective results”.

Despite the simplicity of the concept of delegation, it is one of the most difficult management functions to balance effectively.

The two extremes of management style are:
  1. The micro manger – he or she does not delegate and prefers to perform all the tasks personally. This can be a sign of distrust in the ability of the subordinates. By using much of the available time in performing subordinate’s work, the micro manager does not give enough attention to the big picture that can languish as a result. 
  2. The hands-off manger – he or she is interested only in the big picture and is not greatly concerned with supervision of the subordinates work. The quality of this will often suffer as a consequence.
Most managers fall somewhere in between and it is one of the most difficult tasks to find the right balance – a balance that will vary in each type of corporation.   

I learned a very valuable lesson on delegation when I was in the military – we were performing aptitude tests for officer potential and one of the problems we were given went like this:

Task: You are to erect a flagpole 100 feet high.
Personnel: You have at your disposal a platoon– 1 sergeant, 3 corporals and 3 sections of soldiers, 10 in each section.
Equipment: There are three lengths of rope provided, each of which is 200 feet in length. The rope cannot be further subdivided. You also have 3 sledgehammers and 3 steel pegs, each two feet long.
Describe how you would erect the flagpole.

My solution was probably the most common one suggested from individuals in the group. 

“After tying the three lengths of rope to the top of the flagpole, each section of men, under supervision of the corporals, then marches outwards to form an equilateral triangle – with the flagpole at the centre. The sergeant would then supervise the hoisting of the pole and driving the pegs into the ground at the right positions.   
My solution to the flagpole problem
(Click to enlarge)

Several other methods were suggested, all containing various degrees of complexity and practicality, but none described the solution the Army was actually looking for - which was simply this. 

You issue the following order  – “Sergeant, have the men erect the flagpole”.

This is a perfect example of delegation. To attain the rank of Sergeant in the Australian Army, you have to be a very capable and practical individual, well able to solve problems of the flagpole type. The Sergeant can therefore be entrusted with the task, leaving you, as the officer, free to engage in other work.

Above: One of the world's tallest flagpoles, located in Amman Jordan. It is 126.8 m (416 feet) tall.  (Image from Wikipedia Commons - click to enlarge)

This principle can be carried across to all corporations, but if you can’t trust your subordinates, it can mean that there are problems in the recruitment or promotion system within your organisation. Or it can mean, that as a manager, you will have to learn to trust others – one of the most important assets of leadership, both in the military and in civilian life.

Monday, April 23, 2012

Rain on Your Wedding Day

Over recent years outdoor weddings have become increasingly popular, and events held by the sea or on mountain peaks for example, can provide spectacular backdrops for that very special day. However it also means that the weather becomes a major factor in the equation and this is often a difficult issue.

Outdoor wedding ceremonies are subject to the vagaries of the weather. (Image from Wikipedia Commons)

The fundamental weather problem emerges in the early stages of planning – weddings are normally organised several months ahead, but reliable forecasts for a given location ore normally only possible out to a week ahead. This mismatch of time intervals often causes substantial grief both to the wedding organisers and to the meteorologist who is called on to produce the weather forecast for the ceremony. 

Many of my numerous grey hairs have been produced from wrestling with this problem and I’ve found that one of the most dangerous life-forms in the jungle is a wet bride with her wedding dress trailing in un-forecast mud.

So are there ways around this dilemma? Well firstly, planning should take into account the long term climate averages – these can readily be obtained online and will give you some idea which are the wettest, driest, coldest and hottest months in your area of interest. However the problem with this is that on any particular day, average conditions are not always encountered. Remember Mark Twain’s observation – “Climate is what we expect, weather is what we get”.

Secondly, and most importantly, always have a plan “B” ready to go.
This simply involves organising access to a shelter nearby should rain develop on the day. This will take a lot or stress out of the decision-making and also off the meteorologist who is sweating this out with you.

Outdoor wedding ceremonies were practiced over many centuries across different cultures. This contemporary painting shows the wedding of the great Mughal Emperor Shah Jahan, circa 1630. Fireworks accompanied the ceremony throughout the night. (Image from Wikipedia Commons)

Then thirdly, start watching the weather forecasts 7 days out from the wedding – monitor these on a day to day basis and this will help you “fine tune” your arrangements. The forecasts tend to become more accurate the closer we get to the actual day.

Finally, I always fall back on my last defence which is the old belief, common to many cultures, that it is good luck if it rains on your wedding day. This relates to the association that rain has with the fertility of trees and plants, and the refreshing effect it has on the atmosphere.

In Hindu tradition rain is good fortune because a wet knot - the knot of marriage - is harder to undo than a dry knot. The Italians, have a wonderful saying “Sposa Bagnata, Sposa Fortunata,” which means “Wet Bride, Lucky Bride.” However many brides-to-be are not reassured by this knowledge.

Interestingly, in some parts of the world, it is law that the marriage ceremony must be performed under a roof, and this makes life a lot easier for the local meteorologists. If ever I run for Parliament that will be my main policy plank and, assuming I have the numbers, I’ll institute it immediately I become Prime Minister.

Thursday, April 19, 2012

The Amazing François Viète

François Viète (1540 -1603) was one of the foremost mathematicians of the early Renaissance era.

Born into the French upper middle class, he became a lawyer by profession but his high intelligence allowed him to excel in several fields, including mathematics, astronomy and geography.

During the period when Spain and France were at war Viète broke the Spanish military code allowing the French to read secret dispatches. The Spanish King accused the French of using sorcery against him.

François Viète - great French scholar and mathematician.
(Image from Wikipedia commons)

But it was in mathematics that Viète was to leave his greatest mark. Investigating methods of generating π, the ratio between the circumference of a circle to its radius, he discovered one of the classical formulae of mathematics that today is called Viète’s equation. It was one of the very early formulae involving infinite products and nested square roots.

                      .             2               .              2                  .....   =  π//2     
             √(2)              √(2+√(2))           √(2+√(2+√(2)))                         

Inspired by Viète I've been playing around with nested square roots over the last few years, and the results I've come up with are below. The 5th result contains a generalisation for pth roots, and the 6th is a generalisation of Viète's equation

No proofs are included but I thought the results themselves may be of some interest to a mathematician out there.

1.        If  x(n+1)=√(2+xn)  ,  x0=x, n=0,1,2,3…

            then xn=2cos((cos-1(x/2)/2n)) for |x|≤2
            and lim xn = 2.

            Also, for x>2,


2.        If xn+1=√(2-xn)  ,  x0=x, |x|≤2, n=0,1,2,3…

           then xn=2cos(π//3+(-1/2)n (cos-1(x/2)- π//3))

           and lim xn = 1

3.       If  xn+1= (√2/2)(√(2+xn)+√(2-xn))  ,  x0= x, |x|≤2, n=0,1,2,3…

          then xn=2cos(π//6+(-1/2)n (cos-1(x/2)- π//6))

          and lim xn = √3

4.         1  .           1           .                1             ……….  =  √3      
           √2       √(2-√2))             √(2-√(2-√2)))                       2

5.      If xn+1 = {( xn+√ (xn2-4))/2}1/p + {(xn-√ (xn2-4))/2}1/p

         then xn=2cos((cos-1(x/2)/pn)) for |x|≤2, and

         xn=2cosh((cosh-1(x/2)/pn)) for x>2, 

6.                   .              2               .              2              ..   =  arcos(x/2)  
             √(2+x)      √(2+√(2+x))          √(2+√(2+√(2+x)))         (1-(x/2)2)
              for |x|<2

Tuesday, April 17, 2012

The 1948 London Olympic Games

Following the dark years of World War Two, when two successive Olympic Games were missed (1940 and 1944), a triumphant return was held with the London Olympic Games of 1948.  59 Nations participated but Germany and Japan, under Allied military occupation at the time, were not permitted to compete. The USSR chose not to do so.

 The official logo for the 1948 Olympics (Image from Wikipedia Commons)

That the games were held in London was a story in itself. Before the war the city had been selected to host the 1944 games but the war derailed this plan. The war had been over for nearly 3 years by 1948, but shortages of all types persisted in England, including food, petrol and accommodation and many were sceptical that London could successfully stage the Games.

However using much improvisation, the Organising Committee overcame all the problems. In marked contrast to the massive expenditure of recent Olympics, the London budget was miniscule. A special Olympic Village was deemed too expensive and instead, male athletes were housed in existing wartime RAF camps and female athletes in various London Colleges. As a result of these measures the 1948 Olympics became known as the “Austerity Games”.

On a sparkling summer day on 29th July, the Games were opened at Wembley Stadium before a crowd of 85,000 people and presided over by King George V1. The athletes paraded through the stadium, led by Greece and followed last of all by the athletes of the home country – the United Kingdom. And for the first time an Opening Ceremony was televised live and transmitted across the BBC network.

 An advertising poster for the Games (Image from Wikipedia Commons)

The Games concluded on 14th August 1948 and proved to be a resounding success. For the war weary world that participated they marked the start of an era of peace and general prosperity for the next decade.

Later this year London will become the first ever city to host the summer Olympics three times – in 1908, 1948 and 2012.

Olympic showcase:

One of the star athletes of the London Games of 1948 was the extraordinary Dutch athlete Fannie Blankers – Koen, who was then the mother of two children and competing at thirty years of age.

             Statue of Fannie Blankers – Koen in a park at Rotterdam
(Image from Wikipedia Commons)

Nick-named the “Flying Housewife” she won four athletic gold medals at London – the 100 and 200 metre sprints, the 80 metre hurdles and was also a member of the victorious Dutch team in the 4x100 metre relay.

And along the way she proved several people wrong – before the games it was said that thirty was too old for elite athletics, and that anyway she should be home looking after her family. Remarkably it was later revealed that during her London triumphs she had been pregnant with her third child, eventually born in early 1949.

Blankers-Koen had competed in the 1936 Berlin Olympics as an 18 year old, and following London also competed at the Helsinki Olympics in 1952. She also ended up winning 58 national titles in Holland and was voted the “Female Athlete of the Century” by the International Association of Athletics Federations in 1999.

Her stellar career finally ended with her death in January 2004.