Monday, December 12, 2011

Star of India - Srinivasa Ramanujan

One of the most remarkable individuals in the history of mathematics must surely be the Indian mathematician Srinivasa Ramanujan, (1887 – 1920) who overcame almost insurmountable difficulties to become one of the great mathematicians of history.

Srinivasa Ramanujan, circa 1915 (Image: Wikipedia Commons – Click to enlarge)

Born into very poor circumstances, Ramanujan was a Brahmin, the highest caste of Indian society, traditionally associated with high academic knowledge and intellectual achievement. 

But lack of available money made it difficult for him to progress to higher education and, as a result, he conducted research into mathematics, his favourite subject, virtually on his own. Using old textbooks, he developed his own style and notation and commenced research into several diverse areas of number theory.

He received a little encouragement when some of his early work was published in the Journal of the Indian Mathematical Society. He also sent several of his papers to prominent mathematicians around the world but with little result. His style of non-standard notation and presentation of results without proof probably counted against him.

But then, in January 1913, he wrote to the prominent English mathematician, G. H. Hardy, who was then resident at Trinity College, Cambridge University. 

G. H. Hardy – prominent English mathematician (Image: Wikipedia Commons – Click to enlarge)

Hardy later recalled that one night after dinner, he and his colleague J. E. Littlewood, sat down to study and try to unravel the jumble of strange formulae that Ramanujan had mailed them.

As Hardy read through the document he became increasingly astounded. He recognised that Ramanujan had derived several results in pure mathematics already known, but using hitherto unheard of techniques. But of even more significance was the fact that there were several results quoted without proof, that were, to Hardy's knowledge, entirely new to mathematics.

Hardy immediately invited Ramanujan to Trinity College, but this created some problems. Brahmins were not supposed to travel across the ocean, but somehow Ramanujan was able to attain a dispensation. He was also a strict vegetarian and this was due to create problems with the typical meat- rich English diet.

Trinity College, Cambridge (Image: Wikipedia Commons – Click to enlarge)

Nevertheless Ramanujan arrived at Cambridge in April 1914, and began a collaboration with Hardy that was to produce some of the great advances in number theory. Hardy’s careful orthodox approach, using rigorous methodology, when combined with the sheer brilliance of Ramanujan, produced a cascade of important results. These included the Ramanujan Prime and the Ramanujan Theta functions, both of which led to major areas of further research by other mathematicians. The Hardy-Ramanujan asymptotic formula was used widely in thermodynamics and atomic physics more than a quarter of a century later. 

Ramanujan was in poor health for much of his life, made worse by the fact that a vegetarian diet was difficult to maintain in early 20th century England. He spent considerable periods in hospital and it was in one such stay he was visited by Hardy, who later recalled 

“I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

Ramanujan had instantly seen that 
1729 = (1x1x1) + (12x12x12) and that also
1729 = (9x9x9) + (10x10x10)

The number 1729 is now known as the Hardy-Ramanujan number.

Recognition of number patterns such as this was Ramanujan's specialty and his skill in this domain has never been surpassed.

Ramanujan went on to produce nearly 4000 important results in number theory, was made a Fellow of the Royal Society and became the first Indian to be elected a Fellow of Trinity College at Cambridge University. Tragically he died at the young age of 34 at Kumbakonam, back in his native India. There is little doubt that he would have contributed even more to mathematics, given an average life span.

Ramanujan's home on Sarangapani Street, Kumbakonam. (image from Wikipedia Commons – click to enlarge)

Hardy, his mentor, later rated him as one of the great mathematicians of history, comparing him to Gauss, Newton and Archimedes. This was made all the more remarkable by the difficult nature of the journey he had to take along the way.

Late in 2011, the Prime Minister of India, Dr. Manmohan Singh, announced that December 22, the anniversary of Ramanujans birthday, would be declared "National Mathematicians Day", and that 2012, the 125th year since Ramanujan's birth, would be known in India as the "National Mathematical Year".

This is a fitting tribute to one of the great mathematicians of both India and human history.

Sunday, December 4, 2011

Famous Weather Quotes

Weather is supposedly humanity’s most discussed topic and when we look at the effect it has across a wide variety of human affairs, this is hardly surprising. And up until the emergence of climate change as a public issue, weather was also one of the few “neutral” topics available for general discussion.

A summer thunderstorm produces shafts of rain across the countryside
(Image from Wikipedia Commons – click to enlarge)

If you meet a stranger it’s usually poor form to attempt a discussion on religion or politics, but the weather is normally a safe area; people often have definite ideas on the topic but without being offended by a differing view. 

As a result, many of the great minds of the past and present have offered their views on the weather, often in a humorous and witty manner greatly enjoyed by meteorologists. Here are a few examples:

“Weather is a great metaphor for life - sometimes it's good, sometimes it's bad, and there's nothing much you can do about it but carry an umbrella.”  - Terri Guillemets

“The best thing one can do when it's raining is to let it rain.”  
- Henry Wadsworth Longfellow

“Don't knock the weather; nine-tenths of the people couldn't start a conversation if it didn't change once in a while.” 
- Kin Hubbard

Mark Twain in his latter years – 1907
(Image from Wikipedia Commons – click to enlarge)

“It is best to read the weather forecast before praying for rain.”  
- Mark Twain

"Everybody talks about the weather, but nobody does anything about it."  
- Mark Twain

“Climate is what we expect, weather is what we get.” 

“No matter how rich you become, how famous or powerful, when you die the size of your funeral will still pretty much depend on the weather”.
- Michael Pritchard

“The trouble with weather forecasting is that it's right too often for us to ignore it and wrong too often for us to rely on it.”   
- Patrick Young

“Conversation may be compared to a lyre with seven chords - philosophy, art, poetry, love, scandal, and the weather.” 
“Change of weather is the discourse of fools.”

Photograph of Oscar Wilde taken in 1882
(Image from Wikipedia Commons – click to enlarge)

“Conversation about the weather is the last refuge of the unimaginative.” 

“If I'm on the course and lightning starts, I get inside fast. If God
wants to play through, let him” 
– Bob Hope

Bob Hope entertains the military in 1990 – with his golf club
(Image from Wikipedia Commons – click to enlarge)

With the emergence of the somewhat more controversial issue of climate change, perhaps a similar reservoir of insight and wit on this topic will be gradually taken up by our modern day philosophers and observers.

Sunday, November 27, 2011

The Brighton Shark Attack of 1930

When I was a young boy, my father, who had been a regular swimmer around Port Phillip Bay, near Melbourne, in the days of his youth, used to tell me about the terrible incident that took place off Brighton Pier in 1930, when a swimmer had been seized by a shark. 

I recently did an online newspaper search, and sure enough found many accounts of that terrible day. Here is what happened:

In the early days of Melbourne settlement fishermen reported numerous encounters with large sharks in Port Phillip Bay but up until 1930 there had been only two reported fatalities.

On February 6th 1876 a young man named Peter Rooney was attacked off St. Kilda beach, losing his leg, and dying from loss of blood soon after.

In 1881, one of two brothers sailing in a small yacht off Frankston, was carried away by a “giant” shark and his “arm, shoulder, waistcoat and watch” were later found inside the monster when it was caught some days after.

Contemporary 19th century drawing showing fishermen battling a large shark off the Brighton Pier

Pictures Collection
State Library of Victoria (Click to enlarge)

So two fatalities in more than fifty years of human activity in the Bay was hardly a bad record but on the afternoon of Saturday 15th February 1930 this was all about to be turned on its head when a terrifying shark attack claimed a third victim.

This attack was notably different to most others in that it was closely witnessed by a large crowd of people who literally had a "birds eye" view of the terrifying spectacle. 

Norman William Clark was with a small party of friends, diving and swimming around the Middle Brighton Pier on a fine and sunny late summer afternoon.

Swimming around piers, especially those from which fishermen operate is never a good idea. There is blood in the water from hooked fish and also fishermen will often gut their catch and throw the entrails back into the water. These activities can attract the attention of large and unwelcome visitors.

The Argus described the events that followed in the Monday morning edition of 17th February 1930:




Attacked by a shark off the end of the Middle Brighton pier on Saturday afternoon, Norman William Clark, aged 19 years, of Point Nepean road, North Brighton, was mutilated and dragged to his death before assistance could be obtained. 

Between 80 and 100 persons saw Clark disappear. So sudden was the attack that few people realised what had happened until they saw the shark grip Clark in its huge jaws. It came at him again and again, and eventually it disappeared with the body 50ft. from the pier. Witnesses described the shark as being at least 16ft. long.

The shark was seen a few seconds before it attacked Clark, but there was not enough time to give him warning. Some time before the tragedy Clark had been diving from other parts of the pier. He then went to the lower platform at the end of the pier, and after sitting there with his brother and the girl he dived in. He went out about 50ft. and returned to the platform. 

A few minutes later he dived in again, and swam out the same distance, returning to within 12ft. of the edge of the platform. He was treading water when the shark first attacked him. A few seconds later, a man on the pier, according to statements by witness, saw the shark glide through the water as if it had just come from beneath the pier. He called out, "A shark," but Clark apparently did not hear the warning, or perhaps thought that someone was joking. 

The next second he cried out, "Oh," and, throwing up one hand, he disappeared under the water. Even then few people realised that a shark had seized him. As he came up, however, the shark could be seen holding on to his leg. Clark appeared to be sitting across its nose, and he was punching it.

Horrified by the sight, many women on the pier fainted, and they had to be given stimulants. The girl who had been with Clark also fainted, and several men carried her along the pier. It was some time before she recovered. In the meantime, other women and men tried to frighten the shark away with noise, and it suddenly disappeared, dragging Clark down through the water. It carried him round to the south side of the pier. 

Photograph of the Brighton Pier, c 1930

Pictures Collection
State Library of Victoria (Click to enlarge)

When Clark came up again, he was still trying to beat off the shark, but his strength was fast ebbing. The water for yards around was stained red.

The shark, with its fin and tail out of the water, made another rush at Clark, and almost lifted him out of the water as it seized him round the chest in its jaws.

That was the last that was seen of Clark. He went down suddenly, several witnesses said, as if the shark had carried him away.


Clark, whose father died several years ago, lived with his mother. He was a winch driver by occupation. Frequently he visited the Middle Brighton beach. Well-built and tanned by the sun, he was a splendid swimmer and diver, and it had been mentioned that he was fond of swimming in the deep water at the end of the pier.

The victim, Norman William Clark of North Brighton
(Click to enlarge)

Mr. David Clark, an elder brother of the victim, said yesterday that his brother was a Sea Scout, and he took an active interest in all kinds of sport. "Norman was a keen cricketer, and on Saturday I wanted him to play in a team of which I am a member," he added. "We were a man short in my team, and I wanted him to fill in the vacancy. He said that he had made arrangements to go swimming."

Although not mentioned in the newspaper account, from the description of the shark and its method of attack it seems likely that the monster was a white pointer.

Sunday, November 20, 2011

Sydney's Razor Gang Wars 1925 to 1935

The recent success of the Underbelly television series has focussed attention on a rather strange period in the history of Sydney, when the kingpins of crime were two women, who brutally ruled the underworld of the city, and became fabulously wealthy in the process. This is a short history of what happened during the period from around 1925 to 1935 - a particularly violent decade.

Soon after the end of the First World War, with thousands of ex servicemen returning home after years away, a period of lawlessness descended on Sydney, the like of which has not been seen before or since.

Several factors shaped the occurrences of this period. Firstly, after the end of the war, many ex servicemen, after experiencing first hand the horrors of the frontline, had become irreligious and hedonistic with little or no thought or concern of an afterlife or judgement day. Simply put, tomorrow did not exist.

Erich Remarque well described the feelings of the World War One trench soldier in his classic "All Quiet on The Western Front" : We are forlorn like children, and experienced like old men, we are crude and sorrowful and superficial - I believe we are lost.

After drunken troop riots in Sydney in 1916, the temperance movement had initiated a referendum that resulted in 6 o’clock hotel closing taking the place of the old 11 pm mark. However the demand for alcohol after 6 was as strong as ever and a booming sly grog trade followed.

The desire for quick thrills resulted in a burgeoning prostitution industry and big money was there to be earned on Sydney’s streets. Cocaine, a previously legal drug sold over the counter in chemist shops during the first two decades of the century, was declared illegal, but because the demand was well established, the underworld was only too happy to take over the purchase and distribution of the drug, called “snow” during this time. Users were called “snow droppers”.

The Pistol Licensing Act came into force in 1927, and this produced an automatic six-month gaol sentence for anyone carrying an unlicensed firearm. As a result, the weapon of choice for many criminals became the cut throat razor, and this was used to threaten, intimidate and disfigure opponents.

In addition, the Great Depression had hit hard in Sydney, and high unemployment drove many men and women to crime, just to survive.

All these circumstances were similar to the situation in America with the Prohibition wars well under way during the “Roaring Twenties”, but instead of Al Capone and Lucky Luciano, Australia had Kate Leigh and Tilly Devine, two of the roughest and toughest ladies in the history of the country.

Kate Leigh made her fortune sly grogging, buying large amounts of alcohol legally during trading hours, and then selling it after 6 pm at huge mark up prices. She became extremely wealthy and defended her interests by hiring a gang of razor wielding thugs that suppressed any opposition. Nevertheless there were several takeover attempts and in 1930 she shot dead a gunman, Snowy Prendergast, who tried to break into her terrace at 104 Riley Street.

Kate did considerable prison time because of all her activities but was also known for her generosity, in particular for the lavish Christmas parties she turned on for the impoverished children of Surry Hills all through the depression years. These were held at her main address at 2 Lansdowne Street, Surry Hills. 

Kate Leigh's Prison File in 1915.
Courtesy of State Records NSW

(Click on image to enlarge)

Matilda Devine, (nee Twiss) or Tilly as she became known, was an Englishwoman who had married an Australian soldier, “Big Jim” Devine, and followed him back to Australia at the end of the war. Tilly quickly and accurately assessed the social climate of Sydney and set up an organised group of brothels in Palmer Street Darlinghurst, taking up residence herself at number 191. 

She cunningly recruited girls from the nearby Crown Street Women’s Hospital, many of whom were down from the country, having babies “out of wedlock” and without any other means of support.

Tilly brought a hitherto unseen high state of organisation to prostitution, offering her girls board, lodging and ”snow”, as well as a range of services to clients at varying pay scales. These ranged from quick and cheap back alley encounters for barrow boys to well appointed rooms for the service of gentlemen callers at greatly increased rates. Tilly received a cut in all these transactions and, like Kate Leigh, became a very wealthy woman as a result.

Tilly Devine's Prison File in 1925.
Courtesy of State Records NSW

(Click on image to enlarge)

She also defended her interests through hiring gangs of toughs, including her husband Big Jim, a violent, evil tempered gambler who beat her badly and often. Tilly also racked up numerous convictions over the years, but was able to escape the “living off immoral earnings” charge because, strangely enough, this law applied only to men and not women.

Kate and Tilly detested each other and their gangs had frequent violent encounters, producing a series of tit for tat killings and mutilations that dominated the headlines all through the period.

These were the so called “razor wars” of Sydney, that raged well into the 1930’s and were mainly concentrated in the Darlinghurst, Surry Hills and East Sydney area. But as with Al Capone, the taxman was able to do what the law enforcement agencies could not, by eventually putting both Kate and Tilly out of business through the levying of huge back taxes and fines because of undeclared income. 

Kate was declared bankrupt and died in one of her old sly grog shops at 212 Devonshire St. Surry Hills in 1964. Tilly’s wealth was also much reduced and she finally died at the Concord Repatriation Hospital in 1970.

Some of the main characters of the period were:

Norman Bruhn: A particularly violent Melbourne criminal who had come to Sydney in 1927 and headed up a razor gang to extort money from other criminals, usually cocaine dealers or robbers. Bruhn was shot dead in Charlotte Lane, Darlinghurst late in 1927. 

Frank Green's Prison File in 1933.
Courtesy of State Records NSW

(Click on image to enlarge)

Frank Green: An undersized but homicidal alcoholic and cocaine addict who was for a time the main “muscle” in Tilly Devine’s Gang. Green murdered several people, including the rival gunman Barney Dalton, in the infamous shooting outside the Strand Hotel in 1929.

The police file gives a hint of his violent lifestyle - "Bullet wounds on right side of back and on right side of abdomen. Large scar on right cheek. "ILD" above female bust outside right upper arm". (The scar on his right cheek was from a razor slash).

For a period Sydney’s number 1 tough guy, Green met a violent end when his then girlfriend, Beatrice Haggett, plunged a large carving knife into his chest at their flat in Cooper Street, Paddington, in 1956.
At her trial it took the jury only fifteen minutes to find her not guilty, on the grounds of self defence.

Guido Calletti's Prison File 1935
Courtesy of State Records NSW

(Click on image to enlarge)

Guido Calletti: An illiterate thug, thief and mugger who specialised in beating up strangers for their wallet. He was also the leader of the notorious Darlinghurst Push, one of the most violent gangs of the era. An avowed enemy of Frank Green because both were vying for the hand of Nellie Cameron (see below). When Green was in gaol Calletti was the recognised king of the Sydney underworld. He was shot dead by a member of the Brougham Street Gang at a party in Brougham Street in 1939. 

Nellie Cameron's Prison File in 1930.
Courtesy of State Records NSW

(Click on image to enlarge)

Nellie Cameron: A total enigma, who was raised in an upper middle class North Shore family and went to an exclusive girls school. Attractive and curvaceous, when she was 16 she left home and headed straight for the bordellos of Darlinghurst where she became one of the highest priced prostitutes of the era. Despite her refined upbringing she chose to co-habit with some of the worst low life in Sydney, including Frank Green and Guido Calletti who she alternately lived with, depending who was in gaol at the time.
As her beauty faded with the years she went to live in a flat in Surry Hills where she ended her life with her head in the gas oven in 1952. Numerous bullet wounds were found on her body at the post mortem.

Newspaperman Eric Baume reported in disapproving tones of the scenes at her funeral. "Avid sensation hunters got strange thrills from following trash such as Nellie Cameron as though she had been one of the nurses who died under Japanese gunfire that awful day not so many years ago, or an Australian officer kneeling erect to be beheaded".

Jim Devine's Prison File in 1939.
Courtesy of State Records NSW

(Click on image to enlarge)

Big Jim Devine: Tilly Devine’s husband and a violent, foul tempered thug with a gambling problem. Jim killed at least two people and regularly beat up Tilly if she would not provide him enough money for the racetrack. They divorced in 1942 and Jim journeyed to Melbourne where he died in 1964.

Phil Jeffs: Perhaps the smartest crim of the era, he was one of the few to die of natural causes. His forte was illegal gambling and he operated the Fifty Fifty Club in William Street in the 1930’s. Here it was possible to gamble and drink, and as a sideline, girls were also available in private rooms, provided with the compliments of Tilly Devine. He later acquired the 400 Club, and ended his criminal career as a wealthy man. During his time as an entrepreneur he did gaol time for larceny, was accused of raping a married woman, was shot and seriously wounded and charged with selling liquor without a licence. He died in his mansion at Ettalong in 1945. For views of his spectacular house, built in the so called P&O style, see

Lillian Armfield: A pioneering police officer, one of the first female detectives on the Force. Although the then Police Commissioner Bill Mackay was initially dubious about having women as detectives, Armfield’s appointment soon paid big dividends, with many of the street prostitutes providing her with valuable information they withheld from the male detectives. She became an expert gatherer of street intelligence.
Her career was long and distinguished and she finally retired from the Force in 1949, having being awarded the Imperial Service Medal and the Kings Police and Fire Service Medal.

A book about her incredible career was assembled by author Vince Kelly: Rugged Angel: The Amazing Career of Policewoman Lillian Armfield: Angus and Robertson Publishers, Sydney: 1961.

Some of the key addresses and locations of the Razor War era:

212 Devonshire Street, Surry Hills – Kate Leigh’s main sly grog shop and later home during the 1950’s.

21A Francis Street, Darlinghurst - Norman Bruhn’s address in 1927

The section of Elizabeth Street around Central Station and the then Toohey’s Brewery in Surry Hills was known as “the Barbary Coast”. The “Blue Lion “ and “Aurora” hotels were part of this.

Ernie Goods Wine bar – 236 Elizabeth Street, Surry Hills; “Sailor the Slasher” Saidler shot dead there by Ernie Goods in 1930.

Corner of Goulburn and Riley streets, Surry Hills, March 1928, Lawrence Tracey shot and killed.

Charlotte Lane, Darlinghurst – a vice centre of Sydney in the 1920’s – site of the shotting of Norman Bruhn in 1927.

Image above: The corner of Charlotte Lane and Hargrave Street in 1927. Image courtesy of the City of Sydney Archives. (Click on image to enlarge) 

Kellett Street, Kings Cross, site of vicious brawl between the gangs of Tilly Devine and Kate Leigh on 8th August 1929.

Corner of Malabar and Torrington Roads, Maroubra – house owned by Tilly and Jim Devine. Site of two murders in the 1920’s.

The Strand Hotel in William Street, East Sydney – where Frank Green shot to death Barney Dalton and wounded Wally Tomlinson in 1929.

Image: The Strand Hotel in 1915.  Image courtesy of the City of Sydney Archives. (Click to enlarge) 

104 Riley Street Surry Hills– Kate Leigh’s home for many years. 

191 Palmer Street Darlinghurst – Tilly Devine’s home in Darlinghurst

“Tradesman’s Arms” Hotel – top of Palmer Street Darlinghurst – now “The East Village Hotel” - criminal haunt of 1920’s and 30’s. Guido Calletti, Nellie Cameron, Frank Green, Tilly Devine were regulars there.

Chard House, 171 William St East Sydney – on the 4th floor was the infamous “Fifty-Fifty Club” owned by Phil Jeffs.

Image: The Prince Albert Hotel . Looking southeast from the corner of Riley street and William Street 1916.  Image courtesy of the City of Sydney Archives. (Click to enlarge) 

17 Denham Street, Surry Hills, home of Nellie Cameron in the 1950’s

25, 27 and 31 Kippax St. Surry Hills – houses owned by Kate Leigh and used for drugging and robbing passing victims.

2 Lansdowne St Surry Hills: Kate Leigh’s home for many years

21 Harmer Street Woolloomooloo: Frank Green’s house during the late 1920’s.

Sunday, November 13, 2011

Rock Fishing

Rock fishing is a pleasurable pastime in the right conditions, with the added bonus of bringing home a few tasty fish for the dinner table. But it can also be quite dangerous, with ocean swells sometimes ramping up unexpectedly to trap the unwary fishermen.
Above: Large waves can quickly break across rock ledges used by rock fishermen. Image from Wikipedia Commons.

Numerous tragedies have occurred along the Australian shoreline over the years, usually involving fishermen being washed off the rocks where they can be injured or drowned in the pounding waves. One such event occurred on Sunday 30th May 1937 near Victor Harbour in South Australia. It was reported in The Mail, soon after:

Stories Of Big Waves

Many stories of hairbreadth escapes from big, unexpected waves are being told among Victor Harbor anglers following the tragedy last Sunday, when H. M. Mildred, of Adelaide, was washed by a huge wave from a rocky ledge and drowned at the base of a 200-ft. headland near Waitpinga.

General opinion is that novices should not fish on the rocks and cliff faces of the South Coast without some one who knows the dangers.

Mr. Paul Cudmore tells how on a fine, hot day he and several companions lost all the fish they had caught, and some of their tackle. It was on the other side of Waitpinga beach, where three strangely shaped rocks project from the water.

The men had to wade through water up to their armpits to reach the farthest rock, where they caught three dozen 2-lb. sweep. Suddenly the water, which was comparatively smooth, rose up without warning, and rods, lines, bags, and fish were swept into the water. It was not so much a wave as a sudden movement of the sea.

As the men were clinging to the rock they saw two big sharks snapping up their fish. Within two minutes the water had subsided, and they recovered some of their tackle. But in view of the accident, and the arrival of the sharks, they decided to call it a day.

Big surf breaking across ledges favoured by rock fishermen can easily wash people into the water. Image from Wikipedia Commons.

Even today there are regular tragedies involving rock fishermen being swept from the shoreline and so safety remains of paramount importance. Important tips from the experts include:

* Know the tides and weather expected on the day
* Never fish alone
* Wear a personal flotation device, light clothing and shoes with cleats or non slip soles.
* Never turn your back to the sea.
* If you are swept in, swim away from the rocks.
* Be aware of any emergency rescue devices nearby, such as life rings and anchor points.

The golden rule of rock fishing: No fish is worth your life.

Monday, November 7, 2011

Tsunamis in Australia

A tsunami is a wave, or train of waves that have been generated by a large scale displacement the ocean. This is usually caused by an undersea earthquake, but can also be the result of landslides, volcanic activity and more rarely, the impact of meteors.

As we have seen in recent times tsunamis can be devastating and immensely lethal. The Boxing Day tsunami of 2004 was one of the great disasters of modern history with over a quarter of a million people losing their lives as giant waves crashed along the coasts of Indonesia, Thailand, Sri Lanka and India. More recently, on March 11 2011, a tsunami struck the coastline of eastern Japan, killing over 13,000 people and producing many billions of dollars worth of damage.

Devastated township in Sumatra following the Boxing day tsunami of 2004. (Image from Wikipedia Commons – click to enlarge)

As a result of these tsunamis, a question commonly asked today is “Can Australia be struck by a tsunami”? The answer is certainly yes and indeed several such events have been recorded over the last 200 years.

However, the threat posed by tsunamis to the Australian coast varies markedly according to location. The risk is low along the southern coastline of the mainland, including South Australia, but moderate along the northwest coast of Western Australia because of its exposure to the geologically active area around Indonesia.

In August 1977 a large earthquake near Indonesia produced a tsunami at Cape Leveque, on the Western Australian coast to the north of Broome, that generated rises in sea level of 6m above the norm.

The Boxing Day Tsunami of 2004 was detected right along the Australian coastline as was another tsunami in May 1960, when a massive earthquake occurred in Chile. This latter event also produced a surge of water along the NSW coast, and boats were torn from their moorings in Sydney Harbour, Newcastle and Evans Head.

Going back further, another massive Chilean earthquake on 14th August 1868 was also detected in South Australia but produced a far greater effect in Newcastle Harbour on the NSW coast, as the tsunami finally reached the area. A contemporary newspaper report described the scene:

"An extraordinary tidal disturbance has been experienced here this morning since half past 6 o'clock, - the vessels at the coal shoots broke from their moorings, one nearly losing her masts; the ship “Lucibelle”, 1000 tons, was swung round four times, although a strong ebb tide was running; and the vessels in harbour swung round in all directions".

Newcastle Harbour – hit by the tsunami of 1868 (Image from Wikipedia Commons – click to enlarge)

In order to alert the Australian public about any tsunami activity approaching the Australian shoreline, the Joint Australian Tsunami Warning Centre was established in 2007, operated by the Bureau of Meteorology and Geoscience Australia.

Thursday, October 13, 2011

The Ultimate High Jump

In any top-notch athletics meeting, one of the blue riband events has always been the high jump and the world record for this event has been of great and constant interest to the general public.

In 1912 the record was 2.00 m and this progressed steadily over the following decades, finishing up with 2.45 m in 1993, a progress of nearly half a metre in 100 years. The fact that the 1993 record still stands may well be an indication that we are approaching the height limit that a human being can jump and it's an interesting problem to try and estimate this limit.

And a limit seems to be intuitively likely – we cannot jump 5 m so therefore a limit exists somewhere between the current world record of 2.45 m and 5 m that places a ceiling on how high a human can jump.

Since 1920 several areas of progress have emerged in this event. The type of jump itself has evolved into more efficient styles that have enabled greater heights to be reached.

The old scissor jump was replaced by the so-called "western roll" in around 1912 and this was followed by the "straddle" jump over the following two decades. In his jump the athlete rotated over the bar whilst in a horizontal position and the US athlete Charles Dumas became the first human to jump 7 feet (2.13 m) in 1956 using this technique.

Above: A jumper clears the bar using the straddle technique (Image from Wikipedia Commons (Click to enlarge)

The Soviet jumper Valery Brumel was the great straddle expert of history and he took the record up to 2.28 m in 1964. Some great footage of Brumel in action can be seen at

Brumel was an extraordinary athlete in every way, and he regularly preformed a “party trick” that was truly amazing. He could leap upwards and touch the ring of a basketball hoop 10 feet off the floor with his foot! (I wonder how many could do this today?)

For an image showing this incredible feat see

The next style breakthrough came through a young American, Dick Fosbury, who in the late 1960’s pioneered a technique in which the jumper cleared the bar backwards and looking upwards – a sort of half back somersault. This style was made possible by improvements in the landing pit that was softer and raised so that an athlete could land on his back without risking serious injury. This jump became known as the “Fosbury Flop” and enabled jumpers to reach significantly greater heights.

Above - The Fosbury Flop
(Image from Wikipedia Commons - click to enlarge)

Dick Fosbury used his technique to win the high jump gold medal at the 1968 Olympic Games in Mexico City. His winning leap was 2.24 metres (7 feet 4.25 inches) which was also a new Olympic record. This turning point in high jump history can be seen here:

It was used with great effect by jumpers over the following four decades, with the present record holder Javier Sotomayor using it to establish the present world record of 2.45 m in 1993.

A complete list of the high jump world records can be found at

but for the sake of our discussion here we will consider only the following four:

2.03 m in 1924 by Harold Osborn (USA)
2.28 m in 1963 by Valery Brumel (URS)
2.41 m in 1985 by Rudolf Povarnitsyn (URS)
2.45 m in 1993 by Javier Sotomayor (CUB)

We can try and simulate this record progression with mathematics and it turns out that by using a device called the geometric series, we can come up with a reasonable simulation. In doing so I remark that there is no physical reason whatsoever for adopting this method but what I set out to do was

(a) Use a mathematical process that reproduced the past
(b) Had an accuracy of greater than 95% in doing this
(c) Tended to a limit that was realistic

It works like this:

The world record in 1925 was 2.03 metres and we write this as

0.53+1+0.5 = 2.03

40 years later, in 1965, the record was 2.28 m, which is

0.53+1+0.5 + 0.25 = 2.28, or

0.53+1+(1/2)+(1/4) = 2.28

20 years later, in 1985, it was 2.41 m, which is close to

0.53+1+0.5 + 0.25 + 0.125 = 2.405, or

0.53+1+(1/2)+(1/4)+(1/8) = 2.405

10 years later, in 1995, it was 2.45 m, which is close to

0.53+1+0.5 + 0.25 + 0.125 + 0.0625 = 2.4675, or

0.53+1+(1/2)+(1/4)+(1/8)+(1/16) = 2.4675

Our prediction therefore produces an error of less than 2%.

From this we would predict that 5 years later, in 2000, the record would be

0.53+1+(1/2)+(1/4)+(1/8)+(1/16)+(1/32) = 2.49875,

but in fact it remained at 2.45m, as the record set in 1993 still stood.

This represents an error of 4.9%.

Mathematicians will recognise what is called a geometric series emerging here, which is

1+(1/2)+(1/4)+(1/8)+(1/16)+(1/32)+(1/64)+(1/128) + …..,

and the interesting fact about this series is that it converges to a limit, which is 2. When we add our 0.53 that we started with to set our figure at the 1925 record, this predicts that the theoretical height limit to which a human being can jump is 2.53 metres.

If we assume an error of 5% on top of this, it means that its likely the world high jump record will peak somewhere between 2.53 and 2.66 metres.

However humans can seldom be described by mathematics. Perhaps somewhere, sometime out there, a boy will be born with special genetic gifts. As he reaches manhood he will have the spring of a Brumel, the finesse of a Fosbury and the strength of a Sotomayor. He will defy the geometric series and astound the world. It is only a question of when.

Stop press: Since writing this article I discovered an interview with Dick Fosbury located at

A quote from this says: "I have predicted in the past (1978) that I believe the peak in my lifetime would be about 2.50 m based on my experience and observations. I'm still watching".

This figure agrees well with our 2.53 m prediction through the geometric series.

Thursday, September 29, 2011

Grand Final Weather

The Australian Football League Grand Final:
Weather has played a big part in some of the great finals matches of the past.

In the amazing Preliminary final of 1921 between Carlton and Richmond the match was delayed after a massive hailstorm carpeted the MCG in ice. For the record, Richmond won that one.

The 1927 Grand Final was more of a regatta than a footy match with torrential rain falling throughout the game turning the field into a quagmire. Jock McHale’s Collingwood side beat Richmond in a very low scoring match.

Above: Umbrellas were all the go in the 1927 Grand Final, when Collingwood defeated Richmond by 12 points. (Click on image to enlarge)

One of the most famous weather affected matches was the great 1958 Grand Final when rain during the match slowed the pacy Melbourne Demons down and the gritty Collingwood side got up for one of the biggest upsets of all time. Some tough tactics by the Magpies Murray Weideman and Hooker Harrison also helped. On this day, the 20th September 1958, the temperature only managed to reach a winter like maximum of 11.3C, making this the coldest Grand Final Day on record.

The 1960 Grand Final was also a mud-bath after two days of torrential rain leading up to the match. It was Melbourne’s turn to beat Collingwood in this one.

The highest temperature ever recorded on Grand Final Day was on 3rd October 2015, when the temperature reached  a summer like 31.3C, and Hawthorn managed a comfortable win over the West Coast Eagles in the enervating conditions.

The Rugby League Grand Final:
The weather has not only had an influence on several grand finals in the past, but it has also provided the background for the design of the famous NRL Premiership trophy, the trophy for which each team strives during the Australian Rugby league season.

On Saturday, August 24, 1963 at the Sydney Cricket Ground, a record crowd of 69,860 witnessed St. George and Western Suburbs do battle in the Grand Final. The match was played in atrocious conditions after heavy overnight rain had turned the ground into a quagmire.

August 1963 had been a wet month, with 80 mm of rain falling up until the morning of the match and 12 mm of
rain falling the day before. As a result, the ground was a bog and soon after the start of play most players were coated in mud.

The game resulted in a victory for St. George and as the players left the field, two of the mud spattered warriors, Arthur Summons and Norm Provan, shooks hands. The Herald Sun photographer John O’Grady captured the moment for the next day’s edition and in the account of the match conditions were described as “far from ideal” – a massive understatement.

That photograph became immortalised as the model for the famous NRL Premiership trophy – the design of which was heavily influenced by the weather.

Above: The NRL Premiership trophy (Image from Wikipedia Commons)