Author: IMC

A surprisingly interesting structure is the extended multiplication table, shown above for the numbers seven to ten. The algorithm for drawing these is straight forward – for an n-extended table, start out as if you were writing a “regular” multiplication table, but extend each row so that it gets as close to, without exceeding, n. Another way to think about it is to write out rows of “skip counting up to n” by i for integers i from 1 to n.

This is called an extended multiplication table since it contains a “traditional” multiplication table inside it. The 12-extended table below contains a traditional 3×3 multiplication table.

It turns out that 1 appears in an extended table once, and prime numbers appear exactly twice (once in the first column, and once in the first row). In general, for a natural number n, how many times does n appear in the n-extended table?

Before looking at that question, you might want to think about finding easier ways to draw the tables. Drawing out these tables by hand can be tedious – a simple program or spreadsheet might be easier. You can use Fathom, for example, to create the table data and draw it in the collections display. Create a slider m and the attributes listed in the table below (click on the image to see a larger version).

Modify the collection display attributes to draw the tables in the collection box. By adding lots of cases and using the slider m to filter out the ones you don’t need, you can vary the size of the table easily.

“how many times does n appear in the n-extended table?”

# of occurrances of n in the n-extended table = # of nodes in the factor lattice Fn

You can also recast both of these questions (how many occurances of n in the n-extended table, and how many nodesin the Fn factor lattice) as a combinatorial “balls in urns” problem.

Consider a set of colored balls where there are m different colours, where there are ki balls of color i, where i ranges from 1 to m. This would give a total number of balls equal to k1+k2+…+km. Suppose you were to distribute these balls in two urns. How many different distributions would there be? Using some counting techniques, you will find that the answer is (k1+1)*(k2+1)*…*(km+1).

How is this connected to the other problems? Consider the prime factorization of the number. For each prime, choose a colour, and for each occurance of the prime in the factorization, add a new ball of that color. For example for 12 = 3*3*2, choose two colours – say blue=3 and red=2. Since 3 occurs twice and 2 occurs once, there should be two blue balls and one red ball. Now consider distributing these balls in two urns. It turns out that you get (2+1)*(1+1) = 6 possibilities. This is the same number of times 12 occurs in the 12-extended table, and the same number of nodes in the 12-factor lattice. The image below shows the 12-extended table, the 12-factor lattice, and the “ball and urn problem” for the numer 12.

For a number n with the prime factorization:

The answer to all three questions is given by:

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*Credit for article given to dan.mackinnon*

Using the tools of computational complexity, researchers have discovered it is impossible to figure out whether certain Super Mario Bros levels can be beaten without playing them, even if you use the world’s most powerful supercomputer.

Figuring out whether certain levels in the Super Mario Bros series of video games can be completed before you play them is mathematically impossible, even if you had several years and the world’s most powerful supercomputer to hand, researchers have found.

“We don’t know how to prove that a game is fun, we don’t know what that means mathematically, but we can prove that it’s hard and that maybe gives some insight into why it’s fun,” says Erik Demaine at the Massachusetts Institute of Technology. “I like to think of hard as a proxy for fun.”

To prove this, Demaine and his colleagues use tools from the field of computational complexity – the study of how difficult and time-consuming various problems are to solve algorithmically. They have previously proven that figuring out whether it is possible to complete certain levels in Mario games is a task that belongs to a group of problems known as NP-hard, where the complexity grows exponentially. This category is extremely difficult to compute for all but the smallest problems.

Now, Demaine and his team have gone one step further by showing that, for certain levels in Super Mario games, answering this question is not only hard, but impossible. This is the case for several titles in the series, including New Super Mario Bros and Super Mario Maker. “You can’t get any harder than this,” he says. “Can you get to the finish? There is no algorithm that can answer that question in a finite amount of time.”

While it may seem counterintuitive, problems in this undecidable category, known as RE-complete, simply cannot be solved by a computer, no matter how powerful, no matter how long you let it work.

Demaine concedes that a small amount of trickery was needed to make Mario levels fit this category. Firstly, the research looks at custom-made levels that allowed the team to place hundreds or thousands of enemies on a single spot. To do this they had to remove the limits placed by the game publishers on the number of enemies that can be present in a level.

They were then able to use the placement of enemies within the level to create an abstract mathematical tool called a counter machine, essentially creating a functional computer within the game.

That trick allowed the team to invoke another conundrum known as the halting problem, which says that, in general, there is no way to determine if a given computer program will ever terminate, or simply run forever, other than running it and seeing what happens.

These layers of mathematical concepts finally allowed the team to prove that no analysis of the game level can say for sure whether or not it can ever be completed. “The idea is that you’ll be able to solve this Mario level only if this particular computation will terminate, and we know that there’s no way to determine that, and so there’s no way to determine whether you can solve the level,” says Demaine.

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*Credit for article given to Matthew Sparkes*

© Dr Tom Ings

Bumblebees use complex flying patterns to avoid predators according to new research from Queen Mary, University of London.

Writing in the journal Physical Review Letters, Dr Rainer Klages from Queen Mary’s School of Mathematical Sciences, Professor Lars Chittka from the School of Biological and Chemical Sciences, and their teams, describe how they carried out a statistical analysis of the velocities of foraging bumblebees. They found that bumblebees respond to the presence of predators in a much more intricate way than was previously thought.

Bumblebees visit flowers to collect nectar, often visiting multiple flowers in a single patch. There is an ongoing debate as to whether they employ an ‘optimal foraging strategy’, and what such a theory may look like.

Dr Klages explains: “In mathematical theory we treat a bumblebee as a randomly moving object hitting randomly distributed targets. However, bumblebees in the wild are under the constant risk of predators, such as spiders, so the question we wanted to answer is how such a threat might modify their foraging behaviour.”

The team used experiments that track real bumblebees visiting replenishing nectar sources under threat from artificial spiders, which can be simulated with a trapping mechanism that grabs the bumblebee for two seconds.

They found that, in the absence of the spiders, the bumblebees foraged more systematically and travelled directly from flower to flower. When predators were present, however, the bumblebees turned around more often highlighting a more careful approach to avoid the spiders.

PhD student Friedrich Lenz, who did the key analysis, explains: “We learned that the bumblebees display the same statistics of velocities irrespective of whether predators are present or not. Surprisingly, however, the way the velocities change with time during a flight is characteristically different under predation threat.”

The team’s analysis indicates that, when foraging in the wild, factors such as bumblebee sensory perception, memory, and even the individuality of different bumblebees should be taken into account in addition to the presence of predators. All of this may cause deviations from predictions of more simplistic foraging theories.

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Credit of the article given to Queen Mary, University of London

You thought the maze looked fun, but now you can’t find your way out. Luckily, mathematics is here to help you escape, says Katie Steckles.

Getting lost in a maze is no fun, and on that rare occasion when you find yourself stuck in one without a map or a bird’s-eye view, it can be difficult to choose which way to go. Mathematics gives us a few tools we can use – in particular, topology, which concerns shapes and how they connect.

The most devious mazes are designed to be as confusing as possible, with dead ends and identical-looking junctions. But there is a stunningly simple rule that will always get you out of a maze, no matter how complicated: always turn right.

Any standard maze can be solved with this method (or its equivalent, the “always-turn-left” method). To do it, place one hand on the wall of the maze as you go in and keep it there. Each time you come to a junction, keep following the wall – if there is an opening on the side you are touching, take it; otherwise go straight. If you hit a dead end, turn around and carry on.

The reason this works is because the walls of any solvable maze will always have at least two distinct connected pieces: one to the left of the optimal solution path (shown in red), and one to the right. The section of wall next to the entrance is part of the same connected chunk of maze as the wall by the exit, and if you keep your hand on it, you will eventually walk along the whole length of the edge of this object – no matter how many twists and turns this involves – and reach the part at the exit.

While it is guaranteed to work, this certainly won’t be the most efficient path – you might find you traverse as much as half of the maze in the process, or even more depending on the layout. But at least it is easy to remember the rule.

Some mazes have more than two pieces. In these, disconnected sections of wall (shown in yellow) inside the maze create loops. In this case, if you start following the wall somewhere in the middle of the maze, there is a chance it could be part of an isolated section, which would leave you walking around a loop forever. But if you start from a wall that is connected to the outside, wall-following will still get you out.

It is reassuring to know that even if you are lost in a maze, you can always get out by following some variation on this rule: if you notice you have reached part of the maze you have been to before, you can detect loops, and switch to the opposite wall.

This is especially useful for mazes where the goal is to get to the centre: if the centre isn’t connected to the outside, wall-following won’t work, and you will need to switch walls to get onto the centre component. But as long as there are a finite number of pieces to the maze, and you keep trying different ones, you will eventually find a piece that is connected to your goal. You might, however, miss the bus home.

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*Credit for article given to Katie Steckles*

Dipak Dey, Board of Trustees Distinguished Professor of Statistics and associate dean in the College of Liberal Arts and Sciences.

Dipak Dey, Board of Trustees Distinguished Professor of Statistics and associate dean in the College of Liberal Arts and Sciences, has been called an ambassador for the field. A prolific researcher, he is best known for his contributions in the areas of statistical decision theory and Bayesian statistics.

A Fellow of both the American Statistical Association and the Institute of Mathematical Statistics, he is also recognized for developing and maintaining collaborative research programs with other departments and organizations. He recently sat down to answer questions about his field.

We’ve all heard the saying, “Statistics don’t lie.” Yet it’s not uncommon to see statistics misused to prove a point. As a statistics expert, does this frustrate you? And how do you respond?

Statistics do not lie, but sometimes researchers do by misusing and misunderstanding. Sometimes people try to misuse statistics to get across a particular agenda. As a discipline, statistics is a sound science and is being prominently used in all disciplines. Unfortunately statisticians and scientists can’t control how others with a specific agenda may or may not misuse the sound principles and paradigms for their personal benefit.

Data can often be manipulated or ignored to come to a specific conclusion, but that in and of itself is not a reflection on the theory and modeling used in the field. The situation is similar to misusing any kind of legitimate system for one’s personal agenda. People are warned against doing such things, but every year we hear about some powerful interests misusing statistical data to prove a specific point. This is unfortunate and indeed frustrating. In case of such cases, are the principles of statistics at fault? We need to think before we answer.

Personally, I feel happy and proud to know what statistics is about, and how it helps society and life as a whole. After, all knowledge is golden. So I keep learning through the knowledge that can be acquired through the regular use of statistics.

Why should we all know more about statistics?

We all need to know more statistics because it is the science of using data in all fields and disciplines to determine and draw true conclusions about the world. The knowledge gained from statistics is used regularly in technology, business, economics, medicine, social science, and can be related as fact-based knowledge to help people’s daily lives.

What are statisticians doing to expand the public’s understanding of statistics and how they are used?

Besides teaching statistics at the educational level, statisticians have now joined various government agencies, nonprofit organizations, corporations, and other sectors in everything from technology to fashion. As I mentioned before, the discipline of statistics is used in virtually all fields. Whether it is for the analysis of polling data for politics or the analysis of air and water quality for the environment or the analysis of cancer data for smokers, statistics plays a key role in gaining fact-based knowledge. Specifically when it comes to the example of our government, where the decisions being made impact all citizens of the country, statisticians are playing determinative roles in the Food and Drug Administration, the National Institutes of Health, the Census Bureau, the Bureau of Labor Statistics, the United States Department of Agriculture, the National Center for Atmospheric Research, the National Institute for Environmental Research, the National Institute for Educational and Health Statistics, etc.

What role do statistics play in the public debate about an issue, such as what governments should do to deal with climate change?

Statistics play a major role in the public debate about various issues, often controversial issues. Fact-based data gathered through surveys and opinion polls often determine how much support the government has toward a specific point of view or agenda. Statistics can be used to model and track climate change through scientific data. Similarly, statistics can be used to determine how people feel about certain scientific conclusions. Statistics can be used to both refute and support specific claims. Many debates are resolved by using appropriately designed models to demonstrate a point. Many agencies, e.g. Gallup and Westat, are taking polls on major issues from the public. The Roper Center at UConn is a major archive that maintains a huge database of public opinion about science, economics, and government matters. The government constantly turns to statistics to gauge the way to make policy.

What the government should or wants to do in regards to climate change is based both on public opinion statistics as well as various fact-based expert opinions from scientists. Climatologists, for example, often extensively use statistics in risk analysis and extreme event modeling to factually measure climate change. They draw conclusions based on the detailed statistical analysis.

Why should students who are considering a major pick statistics?

The two primary reasons would be a love for science and, arguably more important, the need for a fruitful career. The job market in statistics is flourishing at a rapid pace. One North American job website recently published its 2011 job ratings where they ranked “statistician” as the fourth best job of 2011. Statistics as a field is extremely popular in all sectors, and its popularity and the need for statisticians will only grow. A statistician’s talent is needed virtually everywhere, and most students should have no problem finding a job post-college. A statistics major has the choice to join various sectors, as I mentioned before, ranging from sports to the government. With a BS or BA in statistics, students can also choose to pursue higher education in a specialty fields such as biostatistics, bioinformatics, computational statistics, actuarial science, financial statistics, etc.

What are some of the career paths for statisticians now that didn’t exist a few years ago? And what types of jobs do your graduates get?

There are many career paths for today’s statisticians. Many of them evolved due to the cutting-edge development of computers that didn’t exist in the past. These include but are certainly not limited to opportunities in pharmaceutical companies, market research firms, biotech companies, insurance industries, and the government. The job prospects are endless and yet to be fully determined.

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Credit of the article given to Cindy Weiss, University of Connecticut

Alexei Borodin

For anyone who has ever taken a commercial flight, it’s an all-too-familiar scene: Hundreds of passengers sit around waiting for boarding to begin, then rush to be at the front of the line as soon as it does.

Boarding an aircraft can be a frustrating experience, with passengers often wondering if they will ever make it to their seats. But Alexei Borodin, a professor of mathematics at MIT, can predict how long it will take for you to board an airplane, no matter how long the line. That’s because Borodin studies difficult probability problems, using sophisticated mathematical tools to extract precise information from seemingly random groups.

“Imagine an airplane in which each row has one seat, and there are 100 seats,” Borodin says. “People line up in random order to fill the plane, and each person has a carry-on suitcase in their hand, which it takes them one minute to put into the overhead compartment.”

If the passengers all board the plane in an orderly fashion, starting from the rear seats and working their way forwards, it would be a very quick process, Borodin says. But in reality, people queue up in a random order, significantly slowing things down.

So how long would it take to board the aircraft? “It’s not an easy problem to solve, but it is possible,” Borodin says. “It turns out that it is approximately equal to twice the square root of the number of people in the queue.” So with a 100-seat airplane, boarding would take 20 minutes, he says.

Borodin says he has enjoyed solving these kinds of tricky problems since he was a child growing up in the former Soviet Union. Born in the industrial city of Donetsk in eastern Ukraine, Borodin regularly took part in mathematical Olympiads in his home state. Held all over the world, these Olympiads set unusual problems for children to solve, requiring them to come up with imaginative solutions while working against the clock.

It is perhaps no surprise that Borodin had an interest in math from an early age: His father, Mikhail Borodin, is a professor of mathematics at Donetsk State University. “He was heavily involved in research while I was growing up,” Borodin says. “I guess children always look up to their parents, and it gave me an understanding that mathematics could be an occupation.”

In 1992, Borodin moved to Russia to study at Moscow State University. The dissolution of the USSR meant that, arriving in Moscow, Borodin found himself faced with a choice of whether to take Ukrainian citizenship, like his parents back in Donetsk, or Russian. It was a difficult decision, but for practical reasons Borodin opted for Russian citizenship.

Times were tough while Borodin was studying in Moscow. Politically there was a great deal of unrest in the city, including a coup attempt in 1993. Many scientists began leaving Russia, in search of a more stable life elsewhere.

Financially things were not easy for Borodin either, as he had just $15 each month to spend on food and accommodation. “But I still remember the times fondly,” he says. “I didn’t pay much attention to politics at the time, I was working too hard. And I had my friends, and my $15 per month to live on.”

After Borodin graduated from Moscow State University in 1997, a former adviser who had moved to the United States invited Borodin over to join him. So he began splitting his time between Moscow and Philadelphia, where he studied for his PhD at the University of Pennsylvania.

He then spent seven years at the California Institute of Technology before moving to MIT in 2010, where he has continued his research into probabilities in large random objects.

Borodin says there are no big mathematical problems he is desperate to solve. Instead, his greatest motivation is the pursuit of what he calls the beauty of the subject. While it may seem strange to talk about finding beauty in abstract mathematical constructions, many mathematicians view their work as an artistic endeavor.

“If one asks 100 mathematicians to describe this beauty, one is likely to get 100 different answers,” he says.

And yet all mathematicians tend to agree that something is beautiful when they see it, he adds, saying, “It is this search for new instances of mathematical beauty that largely drives my research.”

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Credit of the article given to Helen Knight, Massachusetts Institute of Technology

In a project that has long been overdue, Cambridge University, thanks to a hefty gift from the Polonsky Foundation (supporter of education and arts) and a grant from Britain’s Joint Information Services Committee (JISC), has put some of Isaac Newton’s original papers online for any and all to see. Of particular interest to most will be Newton’s own annotated copy of Philosophiae Naturalis Principia Mathematica, considered by many to be one of the greatest published works by any scientist ever. For those looking for a little behind the scenes work, the University has also published Newton’s so-called “Waste Book,” a diary of sorts that Newton inherited from his step-father which he took along with him and used for jotting notes about such things as his ideas on calculus while away from school due to the Great Plague in 1665.

In viewing the material, which can be paged through in a PDF type format, by clicking arrows, it’s easy to see that the digitization of Newton’s papers have come none too soon, as many of the pages are tattered, smeared and even burned-looking in some places. Thus, not only has putting the papers online made them accessible to anyone with a computer and an Internet connection, it has also caused them to be saved for posterity in an electronic form that will ensure they will be accessible to all those who may wish to view them in the future as well.

It was in Principia Mathematica that Newton laid out his theories on the laws of motion and universal gravitation which some suggest laid the groundwork for Einstein’s theories on relativity. And if that weren’t enough, Newton is also widely credited with “inventing” calculus, a mathematical science without which the modern world would simply not exist.

In all there are more than 4,000 pages of Newton’s work displayed on the site, which took a team of photo copyists the better part of this past summer to capture, though it’s obvious in looking at the results that there were many slow-downs as pages had to have some restorative efforts made in order to present them. Those working on the project are to be commended as the results show great care and dedication to a single purpose; namely showcasing one of history’s brightest minds.

It’s intriguing to see the notes Newton himself made on the first edition of Principia Mathematica, in preparing for the second, and happily, the University has announced that they will be adding translations for all of the text and notes as early as next year.

The University has also announced plans to make the works of other famous scientists available as the future unfolds and hopefully will continue to add more of the Newton library too, as thus far only about 20% of their collection has been made available online.

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Credit of the article given to Bob Yirka , Phys.org

When oil started gushing into the Gulf of Mexico in late April 2010, friends asked George Haller whether he was tracking its movement. That’s because the McGill engineering professor has been working for years on ways to better understand patterns in the seemingly chaotic motion of oceans and air. Meanwhile, colleagues of Josefina Olascoaga in Miami were asking the geophysicist a similar question. Fortunately, she was.

For those involved in managing the fallout from environmental disasters like the Deepwater Horizon oil spill, it is essential to have tools that predict how the oil will move, so that they make the best possible use of resources to control the spill. Thanks to work done by Haller and Olascoaga, such tools now appear to be within reach. Olascoaga’s computational techniques and Haller’s theory for predicting the movement of oil in water are equally applicable to the spread of ash in the air, following a volcanic explosion.

“In complex systems such as oceans and the atmosphere, there are a lot of features that we can’t understand offhand,” Haller explains. “People used to attribute these to randomness or chaos. But it turns out, when you look at data sets, you can find hidden patterns in the way that the air and water move.” Over the past decade, the team has developed mathematical methods to describe these hidden structures that are now broadly called Lagrangian Coherent Structures (LCSs), after the French mathematician Joseph-Louis Lagrange.

“Everyone knows about the Gulf Stream, and about the winds that blow from the West to the East in Canada,” says Haller, “but within these larger movements of air or water, there are intriguing local patterns that guide individual particle motion.” Olascoaga adds, “Though invisible, if you can imagine standing in a lake or ocean with one foot in warm water and the other in the colder water right beside it, then you have experienced an LCS running somewhere between your feet.”

“Ocean flow is like a busy city with a network of roads,” Haller says, “except that roads in the ocean are invisible, in motion, and transient.” The method Haller and Olascoaga have developed allows them to detect the cores of LCSs. In the complex network of ocean flows, these are the equivalent of “traffic intersections” and they are crucial to understanding how the oil in a spill will move. These intersections unite incoming flow from opposite directions and eject the resulting mass of water. When such an LCS core emerges and builds momentum inside the spill, we know that oil is bound to seep out within the next four to six days. This means that the researchers are now able to forecast dramatic changes in pollution patterns that have previously been considered unpredictable.

So, although Haller wasn’t tracking the spread of oil during the Deepwater Horizon disaster, he and Olascoaga were able to join forces to develop a method that does not simply track: it actually forecasts major changes in the way that oil spills will move. The two researchers are confident that this new mathematical method will help those engaged in trying to control pollution make well-informed decisions about what to do.

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Credit of the article given to University of Miami

In a new study, researchers of the Complexity Science Hub highlight the connecting elements between traditional financial market research and econophysics. “We want to create an overview of the models that exist in financial economics and those that researchers in physics and mathematics have developed so that everybody can benefit from it,” explains Matthias Raddant from the Complexity Science Hub and the University for Continuing Education Krems.

Scientists from both fields try to classify or even predict how the market will behave. They aim to create a large-scale correlation matrix describing the correlation of one stock to all other stocks. “Progress, however, is often barely noticed, if at all, by researchers in other disciplines. Researchers in finance hardly know that physicists are researching similar topics and just call it something different. That’s why we want to build a bridge,” says Raddant.

What are the differences?

Experts in the traditional financial markets field are very concerned with accurately describing how volatile stocks are statistically. However, their fine-grained models no longer work adequately when the data set becomes too large and includes tens of thousands of stocks.

Physicists, on the other hand, can handle large amounts of data very well. Their motto is: “The more data I have, the nicer it is because then I can see certain regularities better,” explains Raddant. They also work based on correlations, but they model financial markets as evolving complex networks.

These networks describe dependencies that can reveal asset comovement, i.e., which stocks behave fundamentally similarly and therefore group together. However, physicists and mathematicians may not know what insights already exist in the finance literature and what factors need to be considered.

Different language

In their study, Raddant and his co-author, CSH external faculty member Tiziana Di Matteo of King’s College London, note that the mechanical parts that go into these models are often relatively similar, but their language is different. On the one hand, researchers in finance try to discover companies’ connecting features.

On the other hand, physicists and mathematicians are working on creating order out of many time series of stocks, where certain regularities occur. “What physicists and mathematicians call regularities, economists call properties of companies, for example,” says Raddant.

Avoiding research that gets lost

“Through this study, we wish to sensitize young scientists, in particular, who are working on an interdisciplinary basis in financial markets, to the connecting elements between the disciplines,” says Raddant. So that researchers who do not come from financial economics know what the vocabulary is and what the essential research questions are that they have to address. Otherwise, there is a risk of producing research that is of no interest to anyone in finance and financial economics.

On the other hand, scientists from the disciplines traditionally involved with financial markets must understand how to describe large data sets and statistical regularities with methods from physics and network science.

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Credit of the article given to Complexity Science Hub Vienna.

Researchers at The Johns Hopkins University have discovered a way to make time stand still — at least when it comes to the yearly calendar.

Using computer programs and mathematical formulas, Richard Conn Henry, an astrophysicist in the Krieger School of Arts and Sciences, and Steve H. Hanke, an applied economist in the Whiting School of Engineering, have created a new calendar in which each new 12-month period is identical to the one which came before, and remains that way from one year to the next in perpetuity.

Under the Hanke-Henry Permanent Calendar, for instance, if Christmas fell on a Sunday in 2012 (and it would), it would also fall on a Sunday in 2013, 2014 and beyond. In addition, under the new calendar, the rhyme “30 days hath September, April, June and November,” would no longer apply, because September would have 31 days, as would March, June and December. All the rest would have 30. (Try creating a rhyme using that.)

“Our plan offers a stable calendar that is absolutely identical from year to year and which allows the permanent, rational planning of annual activities, from school to work holidays,” says Henry, who is also director of the Maryland Space Grant Consortium. “Think about how much time and effort are expended each year in redesigning the calendar of every single organization in the world and it becomes obvious that our calendar would make life much simpler and would have noteworthy benefits.”

Among the practical advantages would be the convenience afforded by birthdays and holidays (as well as work holidays) falling on the same day of the week every year. But the economic benefits are even more profound, according to Hanke, an expert in international economics, including monetary policy.

“Our calendar would simplify financial calculations and eliminate what we call the ‘rip off’ factor,'” explains Hanke. “Determining how much interest accrues on mortgages, bonds, forward rate agreements, swaps and others, day counts are required. Our current calendar is full of anomalies that have led to the establishment of a wide range of conventions that attempt to simplify interest calculations. Our proposed permanent calendar has a predictable 91-day quarterly pattern of two months of 30 days and a third month of 31 days, which does away with the need for artificial day count conventions.”

According to Hanke and Henry, their calendar is an improvement on the dozens of rival reform calendars proffered by individuals and institutions over the last century.

“Attempts at reform have failed in the past because all of the major ones have involved breaking the seven-day cycle of the week, which is not acceptable to many people because it violates the Fourth Commandment about keeping the Sabbath Day,” Henry explains. “Our version never breaks that cycle.”

Henry posits that his team’s version is far more convenient, sensible and easier to use than the current Gregorian calendar, which has been in place for four centuries – ever since 1582, when Pope Gregory altered a calendar that was instituted in 46 BC by Julius Caesar.

In an effort to bring Caesar’s calendar in synch with the seasons, the pope’s team removed 11 days from the calendar in October, so that Oct. 4 was followed immediately by Oct. 15. This adjustment was necessary in order to deal with the same knotty problem that makes designing an effective and practical new calendar such a challenge: the fact that each Earth year is 365.2422 days long.

Hanke and Henry deal with those extra “pieces” of days by dropping leap years entirely in favour of an extra week added at the end of December every five or six years. This brings the calendar in sync with the seasonal changes as the Earth circles the sun.

In addition to advocating the adoption of this new calendar, Hanke and Henry encourage the abolition of world time zones and the adoption of “Universal Time” (formerly known as Greenwich Mean Time) in order to synchronize dates and times worldwide, streamlining international business.

“One time throughout the world, one date throughout the world,” they write in a January 2012 Global Asia article about their proposals. “Business meetings, sports schedules and school calendars would be identical every year. Today’s cacophony of time zones, daylight savings times and calendar fluctuations, year after year, would be over. The economy — that’s all of us — would receive a permanent ‘harmonization’ dividend.”

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Credit of the article given to Johns Hopkins University