The Mathematical Merits of Jeopardy’s 69 Ban?

I thought it was the premise of the upcoming third Bill and Ted movie, but is there any so-called “mathematical merits” of Jeopardy’s 69 ban?

By: Ringo Bones

I have no idea when it started, but it still surprises me that middle-school kids still giggle whenever the number 69 is uttered in an unguarded moment. But during the last week of April 2019, a new ruling on the iconic TV game-show Jeopardy has been divulged preventing contestants from betting $69 on the Final Jeopardy stage of the game citing the awkward sexual nature of the number.

It is not only the number 69 that got the axe on Jeopardy – it also includes the so-called “Number of the Beast” – i.e. 666 as in $666 Final Jeopardy bets. The betting ban also includes numbers of Neo-Nazism significance, like the number 88, the number 14, and the number 1488 – odd since before the Obama Administration era episodes of Glenn Beck’s show on Fox News, the only “Nazi significance” I know of the number 88 was the 88 millimeter shell used by Nazi era Germany. Outside of joining Richard Butler’s Aryan Nation, it was probably Glenn Beck who made Neo-Nazi numerology more or less common knowledge. Fortunately, a $420 Final Jeopardy bet is still valid.

Ernest William Brown: More Mathematician Than Astronomer?

Despite being more well-known for his astronomical work in lunar theory, Is Ernest William Brown more of a mathematician than an astronomer?

By Ringo Bones 

Born in November 29, 1 in Kingston upon Hull, UK, Earnest William Brown FRS was an English mathematician and astronomer, who spent the majority of his career working in the United States and thus became a naturalized American citizen in 1923. In 1907, he was appointed Professor of Mathematics at Yale University. 

His life’s work was the study of the Moon’s motion (lunar theory) and the compilation of extremely accurate lunar tables. Brown also studied the motion of the planets and calculated the orbits of Trojan asteroids. During the height of his professorship at Yale, Brown was also an active member of the American Mathematical Society as its president from 1915 to 1916. 

Since 1923, the Lunar Tables of Ernest William Brown have reduced the Moon’s complicated motion to a numerical theory that yielded serviceable tables, which only proves that his mathematical skills are way better than his mathematical skills. Brown’s Tables were adopted by nearly all of the national ephemerides in 1923 for their calculations of the Moon’s position and continued to be used with some modification until 1983. With the advent of programmable digital computers, Brown’s original trigonometric expressions, given in the introduction to his 1919 tables (and from which the tables had been compiled), began to be used for direct computation instead of the tables themselves. This also gained some improvement precision, since the tables had embodied some minor approximations, in a trade-off between accuracy and the amount of labor needed for computations in those days of manual calculation. 

By the middle of 20^th Century, the difference between Universal and Ephemeris Time had been recognized and evaluated and the troublesome empirical terms were removed. Further adjustments to Brown’s theory were made, arising from improved observational values of the fundamental astronomical constants used in the theory and from reworking Brown’s original analytical expansions to gain more precise versions of the coefficients used in the theory. Eventually in 1984, Brown’s work was replaced by results gained from more modern observational data – including data from lunar laser ranging - and altogether new computational methods for calculating the Moon’s ephemeris. 

A heavy smoker, Brown suffered from bronchial trouble for much of his life. He was afflicted by ill-health during most of the six years of his retirement and died in New Haven, Connecticut in 1938. 

Largest Known Prime Number Discovered in a University of Central Missouri Computer

It may be seen only as a mathematical curiosity to most of us, but did you know that very large prime numbers are indispensable in maintaining effective cyber security?

By: Ringo Bones 

Previously seen as a mere mathematical curiosity – and it still is by most of the population – but prime numbers – such as two, three, five and seven – numbers that are divisible only by themselves and one, play a vital role in computer data encryption. The latest prime number discovered so far back in January 20, 2016 is more than 22-million digits long – 22,338,618 digits long to be exact - five million digits longer than the previously discovered largest known prime number. Prime numbers this large could prove useful to computing in the future – which is sooner than you might think given the current rapidity of advances in hardware and software. 

The new prime number was found as part of the “endless mathematical quest” called the Great Internet Mersenne Prime Search or GIMPS, a global quest to find a particular type of large prime numbers. Mersenne Primes are named after a French monk, Marin Mersenne, who studied them in the 17^th Century during his spare time. Given that modern programmable digital computers processes data in binary code, they can be configured to hunt for Mersenne Prime Numbers by multiplying two by itself a large number of times, then taking away one. It is a relatively manageable calculation for today’s computers, but not every result is a prime number. This year’s newly discovered prime number is written as 2^74,207,281-1, which denotes the number two, multiplied by itself 74,207,280 times with one subtracted afterwards. Since it began 29 years ago, the GIMPS project has calculated the 15 largest Mersenne Prime Numbers and it is possible that there could still be an infinite number of them to discover.  

Very large prime numbers are important in computer encryption and help make sure that online banking, shopping and private messaging services are secure, but current encryption typically use prime numbers that are only hundreds of digits long – not millions. But given our increasing reliance on computers for online commerce and private messaging, the search for very large prime numbers can be very important to maintain encryption with ever increasing processing power – although mathematicians involved in the GIMPS project admitted in a statement that this year’s newly discovered prime number is “too large to currently be of practical value”. 

However, searching for large prime numbers is intensive work for computer processors and can have unexpected benefits. “One prime project discovered that there was a problem in some computer processors that only showed up in certain circumstances.” said Dr. Steven Murdoch, cybersecurity expert at University College London. This year’s new large prime number – the 49^th known Mersenne Prime Number, was discovered by Dr. Curtis Cooper at the University of Central Missouri. Although computers do most of the hard work, very large prime numbers are said to be discovered only after when a human operator takes note of the result. 

Ancient Babylonians: First To Use Sophisticated Geometry?

Previously known for starting an order of astrologer-priests, are the Ancient Babylonians are also the first ones to use sophisticated geometry? 

By: Ringo Bones

Before the recent research findings were published back in January 29, 2016, Ancient Babylonians were more famous for establishing the first order of astrologer-priests that would later evolve into what we know as the science of astronomy. But that all changed when evidence were uncovered that Ancient Babylonians were using a branch of geometry that only got widespread use in the 14^th Century. The new study is published in the journal Science. Its author, Prof. Mathieu Ossendrijver from the Humboldt University of Berlin, Germany said: “I wasn’t expecting this. It is completely fundamental to physics and all branches of science use this method.” The study suggests that sophisticated geometry – the branch of mathematics that deals with shapes – was being used at least 1,400 years earlier than previously thought. 

The possibility that Ancient Babylonians were using geometrical calculations to track the planet Jupiter across the night sky entered the realm of plausibility after Prof. Ossendrijver examined five Babylonian tablets that were excavated in the 19^th Century and which are now held in the British Museum’s archives. The script reveals that the Babylonians were using four-sided shapes, called trapezoids, to calculate when Jupiter would appear in the night sky and also the speed and distance that it traveled. “This figure – a rectangle with a slanted top – describes how the velocity of a planet, which is Jupiter, changes with time,” he said. “We have a figure where one axis, the horizontal side, represents time, and the other axis, the vertical side, represents velocity.” “The area of the trapezoid gives you the distance traveled by Jupiter along its orbit.” “What is so special is that this type of graph is unknown from antiquity – so making figures of motion in this rather abstract space of velocity against time – this is something very, very new.” It has been previously thought that complex geometry was first used by scholars in Oxford and Paris in Medieval times.    

The Ancient Babylonians once lived in what is now Iraq and Syria. The civilization emerged in about 1,800 BC. Clay tablets engraved in their Cuneiform writing system have already shown these people were advanced in astronomy. “They wrote reports about what they saw in the sky,” Prof. Ossendrijver told the BBC World Service’s Science In Action programme. “And they did this over a very long period of time, over centuries,” he says.  

Farewell Dr. John Nash....

As the world mourns of his recent tragic car crash, will the world be a sadder place without mathematician Dr. John Nash?

By: Ringo Bones

He’s probably more famous to the world at large via the 2001 movie A Beautiful Mind as he’s portrayed by actor Russell Crowe than by his works on game theory during the height of the Cold War and his being a 1994 Nobel Economics Prize laureate, but back in Saturday, May 23, 2015, mathematician Dr. John Nash together with his wife Alicia tragically dies in a car crash in the New Jersey Turnpike. The whole world – and not just the mathematicians’ corner – will be a sadder place without him. 

His work on noncooperative games, published in 1950 and known as the Nash equilibrium is considered as his most influential work of the 20^th Century. It provided a conceptually simple but powerful mathematical tool for analyzing a wide range of competitive situations, from cooperative rivalries to legislative decision making. His theories are used in economics, computing, evolutionary biology, artificial intelligence, accounting, politics and military theory. Dr. Nash also made contributions to pure mathematics that many mathematicians view as more significant than his Nobel-winning work on game theory, including solving an intractable problem in differential geometry derived from the work of the 19^th century mathematician G.F.B. Riemann. His achievements were more remarkable, colleagues say, for being contained in a small handful of papers published before he was 30.  

Given his lifelong struggle with depression and paranoid schizophrenia, it is quite remarkable feat indeed that Dr. Nash managed to communicate his mathematical brilliance to the whole world and managed to get recognition for it. Looks like Russell Crowe’s Tweet back in Sunday, May 24, 2015 is indeed both a touching and fitting tribute of Dr. Nash’s mathematical legacy.

Homer Simpson: Mathematical Genius?

Even though the world-renowned patriarch of The Simpsons is a well-known bumbling oaf, but did you know that Homer Simpson, at one time, exhibited his “mathematical genius”?

By: Ringo Bones

Though he is more well-known as a dunce and a bumbling oaf, Homer Simpson – a world-renown animated character often used by its creators to assess the prevailing zeitgeist – once displayed his mathematical genius and even predicted the mass of the Higgs Boson to within more than 90-percent accuracy 14 years before it was confirmed by a team of particle physicists operating CERN’s Large Hadron Collider. To the curious, this was from an episode titled “The Wizard of Evergreen Terrace” where Homer Simpson got envious of Thomas Alva Edison and tries to out-invent the “Wizard of Menlo Park”.

The episode would have been forgotten and would have languished in some obscure footnote of 20^th Century history if not for Dr. Simon Singh who wrote a book back in 2013 titled “The Simpsons And Their Mathematical Secrets” that included a spotlight on the 1998 episode “The Wizard of Evergreen Terrace” when Homer becomes “obsessed” with Thomas Alva Edison and decides to become an inventor. A scene in that particular The Simpsons episode script required a reading glasses-clad Homer to be placed in front of a chalkboard with complex mathematical equations. One of the writers on staff had a physicist friend who was researching the then-theoretical Higgs Boson particle and needed a “scientifically believable” illustration of Homer dabbling with a complex mathematical equation predicting the mass of the Higgs Boson particle – which is also known as the “God Particle”.

“That particular equation - as shown on TV on that particular 1998 The Simpsons episode – predicts the mass of the Higgs Boson” says Dr. Simon Singh. “If you work it out, you get the mass of the Higgs Boson that’s only a bit larger than the nano-mass of a Higgs Boson actually is. It is kind of amazing as Homer makes the prediction 14 years before it was discovered” (in the CERN’s Large Hadron Collider). For those super interested, the Higgs Boson particle was discovered to have a mass of 126 GeV.

The Higgs Boson particle is the “visible” that interacts with the Higgs Field – just like gravitons do with the gravitational field. The Higgs Field is an energy force that permeates across the universe that gives baryonic matter mass and allows the weak nuclear force and the electromagnetic force to co-exist in the “Standard Model” of how we think, so far, on how universal molecular physics work.

Even though Homer’s mathematical musings on the Higgs Boson somewhat reminds me of 1984 Nobel Physics Prize winner Carlo Rubbia’s mathematical musings that was pictured on a 1990 era Time magazine, the field of particle physics / quantum mechanics, mathematics can be a very useful tool in discovering and describing an “unknown particle” with better than 90-percent accuracy. Back in 1962, a then 32 year old Caltech physicist named Murray Gell-Mann proposed a search for a then theoretical particle called the Omega Minus. The particle’s existence was mathematically predicted by the Standard Model, Gell-Mann argued by a theory he formulated himself and by another physicist – a then 37 year old former Israeli Army officer named Yuval Ne’eman.

This theory which Gell-Mann called “The Eightfold Way” was based on an obscure mathematical system invented in the 19^th Century in order to manipulate numbers in groups of eight since each interacting nuclear particle had eight quantum numbers how subatomic baryons and mesons are organized into octets. Independently, Ne’eman did the same. Eventually, Gell-Mann was awarded the 1969 Nobel Physics Prize for his work on elementary particles and by 1971 began work in search for a then unknown family of particles called “quarks” using "The Eightfold Way".

Career Mathematicians: America’s Most Lucrative Profession?

Given that in a 2013 survey shows that they now earn about the same as - or slightly higher than - a typical Beverly Hills plastic surgeon, are mathematicians now America’s most lucrative profession? 

By: Ringo Bones

An overwhelming majority of the American public view career mathematicians as lone researchers into the most abstruse of matters, but frequently, America’s career mathematicians frequently work with other scientists. A survey conducted back in 2013 has shown that the median annual salary of a career mathematician in the United States was about U.S. $101,360 – comparable to that of a typical Beverly Hills plastic surgeon. Given that career tenured mathematicians in the United States could turn out to be one of the best-paid jobs, could there be any prevailing trends that lead to this rather fortunate outcome? Though, if you ask me, one should not put a cheap price on brain power.  

Since the internet boom of the latter half of the 1990s, “big data” and the analytical mathematical models describing them had become a hot commodity for the top commercial internet firms. Remember how career statistician Nate Silver (full name Nathaniel Read Silver) who used mathematics to show an uncannily accurate Obama victory prediction for the 2012 U.S. Presidential Race weeks before the November election via the use of big data is a powerful proof of the power of mathematics. Though years before, Nate Silver’s powerful analytic mathematical contribution to Major League Baseball has been immortalized in the movie Money Ball. 

Will – if favorable trends continue – career mathematicians will soon be earning more money than investment bankers? Could be, given that the leading internet firms had been inexplicably quick in commoditizing and monetizing big data and are also very keen on using analytical mathematics to describe and predict trends via big data – or to use higher mathematics to manipulate big data for commercial gain.