Can Mathematical Modeling Be Used To Stop The Spread of COVID 19?

Can mathematical modeling help us in keeping the individual spread – or basic reproduction number - of COVID 19 to less than 1?

By: Ringo Bones

Since COVID 19 transmission started in late January 2020, the use of mathematical modeling has been at the forefront of shaping the decisions around different non-pharmaceutical interventions to confine the spread of the virus. Mathematical modeling can be used to understand how a virus spreads within a population. The essence of mathematical modeling lies in writing down a set of mathematical equations that mimic reality. These are then solved for certain values of the parameters within the equations.

 The solutions of the mathematical model can be refined when we use information that we already know about the virus spread, for example, available data on reported number of infections, the reported number of hospitalizations or the confirmed number of deaths due to the infection. This process of model refinement – or calibration – can be done a number of times until the solutions of the mathematical equations agree with what we already know about the virus spread. The calibrated model can then be used to tell us more about the future behavior of the virus spread.

One outcome of mathematical models is the predicted epidemic curve representing the number of infections caused by the virus over time. Using different parameters in the model, which may illustrate different interventions, or calibrating the model against different data, can change the predicted epidemic curve.

Mathematical modeling is a powerful tool for understanding transmission of COVID 19 and exploring different scenarios. But, instead of focusing on which model is correct, we should accept that “one model can’t answer it all” and that we need more models that answer complementary separate questions that can piece together the jigsaw and halt the COVID 19 spread.

Farewell Katherine Johnson

Could the United States have won the so-called space race against the then Soviet Union without the help of NASA's African-American mathematician Katherine Johnson?

By Ringo Bones

Fortunately, she got her due credit while still alive given that her most important mathematical works were done during Jim Crow era America. As of February 24, 2020, former NASA mathematician Katherine Johnson, also known as Katherine Goble passed away in Newport News, Virginia. Born in August 25, 1918 in White Sulphur Springs, West Virginia, USA became well known as America’s NASA mathematician whose calculations of orbital mechanics during her employment at NASA were critical to the success of the first and subsequent manned spaceflights.

Katherine Johnson was better known to the generation born after the Apollo moon missions as the NASA African-American mathematician portrayed by Taraji P. Henson in the 2016 movie Hidden Figures about a group of trailblazing African American women mathematicians employed by NASA during the start of America’s Civil Rights movement at the start of the 1960s. Although Katherine Johnson’s mathematical work began earlier in the National Advisory Committee for Aeronautics / NACA – the predecessor of NASA – back in 1953. Before being made famous by the movie Hidden Figures in 2016, Katherine Johnson was awarded with the Presidential Medal of freedom – America’s highest civilian honor – by President Barack Obama in 2015.

During the early days of programmable digital computers – whose active components of which were still largely made with subminiature vacuum tubes first manufactured during 1947 – astronauts were not exactly keen on putting their lives in the care of these early electronic calculating machines, which were prone to hiccups and blackouts according to NASA. So pioneering astronaut John Glenn asked the NASA engineers to “get the girl” – referring to Katherine Johnson to run the computer equations by hand for improved reliability. Johnson and her team of African American women mathematicians did vital work for NASA that eventually made the United States won the space race by successfully landing the first men on the moon and  taking them back safely to earth before President John F. Kennedy’s end of the 1960s deadline.

Jeffrey Epstein Was A Mathematics Professor?

While his tenure at the esteemed Manhattan prep school was only a brief one, historically speaking, Jeffrey Epstein is not the only mathematics professor with an “iffy” sexuality by today’s standards?

By: Ringo Bones

When it comes to mathematics professors who had dabbled in “paedophilia”, it seems that only the most scholarly can attest that there are already two of them – i.e. Charles Lutwidge Dodgson, also known as Lewis Carroll and the disgraced billionaire financier who had recently allegedly committed suicide in prison named Jeffrey Epstein. But is there any truth to the “alleged paedophilia” to both math professors?

Even though US President Donald Trump seems to have got off Scott-free when it comes to his “paedophile adventures” with Jeffrey Epstein, it was Prince Andrew who got a grilling by public opinion after an ill-advised interview at the BBC Panorama program. But does the “mathematical profession” really attract some “perverts”?

Dalton – the esteemed Manhattan prep school  where Jeffrey Epstein became a mathematics professor back in the 1970s has long been known for its rigorous academics, repeatedly ranking among the United States’ best private schools while drawing the sons and daughters of New York’s titans of finance, media and art. And students who are enrolled in Epstein’s class vividly remembered the then mathematics professor dressing in furs with open chest revealing chest hairs and blingy gold jewelry. Many say that the only reason Epstein got the job is that a number of New York’s upper crust acquired millions via Epstein’s financial advised backed by his mathematical acumen – although Epstein eventually quit after getting richer off the New York Stock Exchange.

Even though Victorian era mathematician Charles Dodgson – aka Lewis Carroll – who wrote Alice’s Adventures In Wonderland had an extensive collection of photos of naked girls aged 8 to 11. Though Charles Dodgson signed his real name to only his “serious” mathematical works, mathematicians for decades have been intrigued by the rich skein of symbolic logic that is woven into fantasies like in Alice’s Adventures In Wonderland and Through The Looking Glass.

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.