## Archive for the ‘10 Biggest mathematical Disasters in the World’ Category

October 20, 2009
The **millennium bug** or the **Y2K bug** was going to cause planes to fall from the sky, bank accounts to be wiped out, electricity grids to cease functioning, trains to crash, cars to collide as stop lights stopped functioning, life support units to malfunction and computers to crash around the globe. For years leading up to midnight on New Years eve 1999 consults were paid extraordinary amounts of money to solve the problem. When the clock ticked over to 1^{st} Jan 2000 nothing much happened. It was, indeed, a non-event, an error in logic. (Pic from, appropriately, digyourowngrave.com)** **

**The Maths Error: Guessing the Answer**.

Computer programmers represented the year in the date of many programs using two digits but claimed logical errors would arise upon “rollover” from x99 to x00.

While consultants claimed their advice saved the world from catastrophe countries that spent very little on the Y2K bug problem (eg. Italy and South Korea) experienced as few problems as those who had spent a good deal of money on the bug eradication namely USA and UK. The solution: Don’t guess. Test parts of system by plugging in x00.

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October 20, 2009
**Tulip Mania **represents all economic bubbles. This bubble began in Holland in November 1636 when the price of tulip bulbs started to rise. Tulips became fashionable with fashionable names ( eg. Alexander the Great). Bulbs were sold before they had been dug up. Like all bubbles it ‘popped’. (See *Extraordinary Popular Delusions and the Madness of Crowds*, written by British journalist Charles Mackay in 1841.)

There have been many over the years from the Railway Bubble (1840s USA) to the property bubble (2007). A stock market bubble brought about the Great Depression in the 1930s. There have also been bubbles in mining shares, computer shares (Dot Com Bubble), art and the growing or breeding of llamas, ostriches and aloe vera.

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**The Maths Error: Assuming a Graph is Linear!!!!**

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People look at graphs and assume they straight-line graphs. But many graphs are not based on a rule or formula but rather hope. And when hope crashes so does the value of the stock.

Take note mathspigs is because Sports Cards, comics, collectibles (eg. Bean Kids) and memorabilia (eg. Signed shirts etc) can also be prone to crashes in the school yard. If the price for any product is unbelievable … don’t believe it!!!! There will be kids or others out there trying to tell you ‘Don’t worry. The prices are still rising.’

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October 20, 2009
**The Millennium Bridge **a suspension footbridge across the Thames River in the heart of London costing $Aus 32 million opened on 10^{th} June 2000. It closed half an hour later as pedestrians were being knocked off their feet by the swaying bridge.

**The Maths Error****: Designing 3D Bridge in 2D**.

The three big mistakes, often catastrophic, in engineering are maths, materials or human error (ie. Hitting the pylon of a bridge with a ship. Tasman Bridge Collapse Hobart.. 1975). The Millennium Bridge was a maths problem. The bridge was designed in 2D. The engineers allowed for up and down movement but not sideways movement. Any kid running across suspension bridge in a playground knows that as you run it wobbles sideways! The bridge’s movements were caused by a ‘positive feedback’ phenomenon, known as Synchronous Lateral Excitation or wobbles. It cost $Aus 9 million to dampen the bridge wobble.

A similar maths problem with suspension bridge design involves harmonics. If the wind keeps adding an extra nudge each time the bridge sways and the bridge has not been designed to dampen this effect it can break apart. (See Galloping Gertie. 1940 Bridge Tacoma Narrows Bridge Collapse. Watch for guy who saves dog from car. )

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October 20, 2009
The unmanned**NASA Mars Climate Orbiter **reached Mars and executed a 16 minute 23 second main engine burn on 23^{rd} September 1999 to establish an orbit around Mars at 150km. It orbited behind Mars and was never heard from again.

**The Maths Error:** **Oops! Muddled Units of Length!**

The Mars Climate Orbiter, which cost $Aus 136 million, disappeared because a Lockheed Martin engineering team used Imperial measurements while the JPL (Jet Propulsion Lab) team used the more conventional metric system. The wrong navigation information was sent to the Mars Climate Orbiter. It most likely burnt up in the atmosphere.

**2**^{nd} NASA DISASTER: On 3^{rd} December 1999, the Mars Polar Lander, the sister spacecraft to the Mars Climate Orbiter, crashed on Mars. Units were not believed to be the problem. Total cost of the Mars Program: $ Aus358 million.

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After burning up almost $0.5 billion in crashed/ashed Mars probes, NASA finally hit pay dirt. Unfortunately, the final cost of landing Curiosity on Mars blew the budget $0.9 billion over the budget estimates.

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# UPDATE: $2.5 Billion Eagle has Landed

On 6 Aug 2012 NASA landed the plutonium-powered rover the size of a small car called CURIOSITY (pic) on Mars. According to the New York Times the original cost of landing Curiosity on Mars was estimated to be $1.6 billion. But following technical delays and further costs of $0.9 Billion, the rover was finally launched successfully. You can gain an idea of the size of the Mars rover Curiosity from the pic shown from Cosmos Magazine.

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October 20, 2009
**The USA Superconducting Super Collider **was to be the forerunner to the Large Hadron Collider, which has been built near Geneva, Switzerland. The two colliders send proton beams hurtling in opposite directions at speeds approaching the speed of light to smash into one another. Physicists have a mathematical model for the atom called the **Standard Model**. It predicts the existence of such particles as the Higgs Boson. The Hadron experiments could confirm predictions made by the Standard Model.

**The Maths Error: Assuming Mathematicians Can count!**

How can we, the public, have faith in mathematical models put forward by mathematicians who cannot add up a few dollars to arrive at realistic costs? The initial cost of the US Superconducting Super Collider was $Aus 4.35 Billion in 1987. When the project was cancelled in 1993 the cost had blown out to $Aus 13.0 Billion. 22 km of tunnel had been constructed near Fort Worth Texas when the Congress cancelled the project. The end result was a big hole in the ground costing $Aus 2.2 Billion. (Expensive Hole in the Ground pic LEFT)

**COLLIDER TRAGEDY 2: **The Large Hadron Collider (Pic BELOW) started up on 10th September 2008 and was shut down on 18^{th} September 2008. It is due to restart in Nov 2009. It final cost is estimated at $Aus 20 Billion.

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# UPDATE: 4 JUL 2012

## CERN CLAIMS HIGGS BOSON PARTICLE EXISTS

On the 4 July 2012 CERN announced that they had the proof (It is a statistical likelihood) that the Higgs Boson particle exists.

Forbes magazine estimates the cost of finding the Higgs Boson particle to be $13.25 billion so far. The running costs for the Big Hadron Collider at CERN are $5.5 billion annually. The electricity costs for the Large Hadron Collider are a staggering $23.5 million a year.

But many ask is the Large Hadron Collider a luxury we can no longer afford? The Guardian 22 Sept 2009

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October 20, 2009
On 23^{rd} July 1983** ****Air Canada Flight 143, **a Boeing 767 ran out of fuel at 41,000 feet (12,000m) altitude, about halfway through its flight from Montreal to Edmonton. The crew managed to glide the aircraft safely to an emergency landing at Gimli Industrial Park Airport, a former airbase at Manitoba. This was some challenge. No fuel means no engines. No engines means no electronics, no steerage, no navigation. An emergency propellor driven dynamo ( similar to that used to produce light on bikes) dropped down on an arm under the plane to produce basic power for steerage. Navigation had to be by sight or calculation of speed etc. That involved some maths, mathspigs. There were no fatalities.

**The Maths Error: Oops again! Muddling units of volume!**

The first error was that the fuel tank gauge wasn’t working. It was to be replaced in Edmonton. The second error was a maths error. The ground crew filled the tanks according to their records. The fuel requirements were assumed to be in litres but they had been recorded in gallons.(Pic Right : Quart*er* of a Gallon)

Here it is the metric Vs Imperial problem again. This incident was shown on *Air Crash Investigation* (or *Mayday) *Season 5, Episode 6.

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October 20, 2009

On 9 November 1998 at Chester Crown Court Sally Clark, a Cheshire solicitor, was convicted, by 10-2 majority, of smothering her two baby boys.Clark’s first son died suddenly within a few weeks of his birth in 1996. In 1998, when her second son died in similar circumstances she was arrested and tried for the murder of both sons. The prosecution used paedeatrician Prof Roy Meadows as a expert witness. He had discovered Munchausen Syndrome by Proxy (MSbP) which every student will have seen in some cop show. It relates to an adult, often the mother, inflicting injury or medicating a child to make them sick and to get attention. Sally Clark was found guilty and spent 3 years in jail.

**The Maths Error: Not Understanding Statistics!**

Prof Roy Meadows testified that the chance of two children from an affluent family suffering sudden infant death syndrome was 1 in 73 million. He arrived at this number by squaring 1 in 8500 for likelihood of a cot death in similar circumstances.

Multiplying the probability of two events only works if the events are independent like flipping a coin. But a Cot Death gene, for instance, would dramatically increase the likelihood of 2 Cot Deaths in one family.

The Royal Statistical Society later issued a public statement concerning the “misuse of statistics in the courts” and arguing that there was “no statistical basis” for Meadow’s claim. The journalist Geoffrey Wansell called Clark’s experience “one of the great miscarriages of justice in modern British legal history”. Prof Meadows was struck off the medical registrar in 2005. Sally Clark died of acute alcohol poisoning in her home in 2007. (Ref: BMJ )

Article Left: The Observer UK

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October 20, 2009
While the debate about the effectiveness of the Patriot Missile in the 1991 Gulf War continues, most observers believe its hit rate was closer to 10 percent than to 90 percent. The failure to stop Scud missiles in one Iraqi missile attack resulted in the death of 28 American soldiers in their barracks in Dhahran, Saudi Arabia.

**The Maths Error: Numbers too Big for the Software Program**

In late March 1992, the U.S. General Accounting Office’s report to Congress on the Patriot’s problems was identified as an error in the software, which used the target missile’s velocity and time elapsed to calculate the target position. As the report explained the program was not designed to fit the size of the numbers involved:

*‘Time is kept continuously by the system’s internal clock in tenths of seconds but is expressed as an integer or whole number (e.g., 32, 33, 34 . . .). The longer the system has been running, the larger the number representing time. To predict where the Scud will next appear, both time and velocity must be expressed as real numbers. Because of the way the Patriot computer performs its calculations and the fact that its registers are only 24 bits long, the conversion of time from an integer to a real number cannot be any more precise than 24 bits. This conversion results in a loss of precision causing a less accurate time calculation. ***The effect of this inaccuracy on the [system’s] calculation is directly proportional to the target’s velocity and the length that the system has been running.’ Consequently, performing the conversion after the Patriot computer system has been running continuously for extended periods causes the [system’s estimated Scud position] to shift away from the center of the target, making it less likely that the target will be successfully intercepted’.**

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October 20, 2009
At five-thirty on the afternoon of August 29, 1907, workers heard a loud retort like a canon shot. Two compression chords in the south anchor arm of the Quebec bridge had failed. The bridge was to have a span of eighteen hundred feet when completed — the longest in the world. It took 15 seconds for the bridge to collapse into the St Lawrence River. 75 workers lost their lives.

**The Maths Error: Not Doing the Maths**

The span of the bridge was lengthened from sixteen hundred feet to eighteen hundred feet so that bridge pillars could be built for a lower cost closer to the riverbank. In 1903 the Canadian Government provided funding and in the rush to produce drawings so that the steel for the bridge could be fabricated, there was no recomputation of assumed weights for the bridge under the revised specifications. The hierarchy ignored young engineers who expressed concern.

Failure top do the maths also caused the collapse of the **West Gate Bridge in Melbourne, Australia,** in 1970 killing 35 workers. In trying to connect the main lengthwise splice of the bridge, engineers started removing bolts from the main transverse splice at midspan to correct for misalignment without making appropriate calculations. They removed so many that the bridge suddenly collapsed. To this day travel speeds are controlled on the bridge to reduce the stress load and motorists believe speed limits are for road safety and not because the bridge might collapse!!!!!!!

Footnote: A new design for the Quebec bridge was with a single long cantilever span was produced. It was even heavier than the previous design. On September 11, 1916, when the central span was being raised into position, it fell into the river, killing 13 workers. (Pictured Left.)

Westgate Bridge Picture Left: http://www.jbrown.com.au

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October 20, 2009
** **On the morning of Monday, August 29 2005 hurricane Katrina hit the Gulf coast of USA from Florida to Texas. New Orleans, Louisiana suffered the main brunt of the hurricane but the major damage and loss of life occurred when the levee system catastrophically failed. Floodwaters surged into 80% of the city and lingered for weeks. At least 1,836 people lost their lives in the hurricane and resulting floods making it the largest natural disaster in the history of the United States.

**The Maths Error: The 100-Year Flood Won’t Happen for 100 Years**

On July 31, 2006 the Independent Levee Investigation Team released a report on the Greater New Orleans area levee failures.

Their report *“identified flaws in design, construction and maintenance of the levees. But underlying it all, the report stated, were the problems with the initial model used to determine how strong the system should be.”* The hypothetical model storm upon which storm protection plans were based is called the Standard Project Hurricane or SPH. The model storm was simplistic, and led to an inadequate network of levees, flood walls, storm gates and pumps. The report also found that “t*he creators of the standard project hurricane, in an attempt to find a representative storm, actually excluded the fiercest storms from the database.”*

Remember, mathspig, the 100 year storm can happen tomorrow!!!!!

And levees are cheap. Dirt cheap!!!!!

Street scene photostream: people.com

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