mental_floss Blog » Casey Johnston

A Few Quick Things About Little League

Casey Johnston — Wed, 26 Aug 2009 12:45:22 +0000

With the Little League World Series in full swing, now’s a good time to go over a few things you might not know about Little League.

Little League was formed with the express purpose of being cost-free to players.

Little League is a non-profit organization that was founded in Pennsylvania by Carl Stotz in 1939 with the specific provision that “at no time should payment of any fee be a prerequisite for participation in any level of the Little League program.” This is largely attributed to Stotz’s experience with poverty in during the Great Depression, and the belief that even when times are hard and everyone is poor, we should all be able to play a little ball. And to this day, to the relief of parents, children continue to be supported by sometimes-unfortunately-named sponsors.

The first no-hitter was pitched in 1942.

13-year old Edward Younken, of the Lundy Lumber team, allowed no hits in a game against Stein’s Service Station (this is different from pitching a perfect game, as players can still be walked or can reach base on errors). The win resulted in the team’s entrance to, and eventual win of, the league championship that season. Apparently the young Younken had no idea what he’d done until his father came running up after the game to congratulate him. For reference, in the recorded history of Major League Baseball, there have been only 263 no-hitters.

The Little League’s Hall of Excellence has some pretty big names.

The Hall of Excellence, where the Little League pays tribute to former players who have gone on to be successful in life, is home to quite a few recognizables. Members of the Hall of Excellence include Rudy Giuliani, George W. Bush, Kevin Costner, Dave Barry, Cal Ripken, Nolan Ryan, Tom Selleck, and Kareem Abdul-Jabbar.
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Did you play, coach or ump Little League? Any war stories you’d like to share?

Frederick Law Olmsted & His Beautiful Parks

Casey Johnston — Fri, 07 Aug 2009 18:48:40 +0000

Frederick Law Olmsted (1822 – 1903) is far from a household name these days, having died over a century ago. Despite this, his reach remains wide in the United States. Olmsted was a landscape designer and pioneer of landscape architecture, and was the genius behind many urban green spaces that still exist today, and continue to anchor their cities with a measure of respect for nature. Olmsted prided himself on his ability to place natural-looking spaces smack in the middle of cities, and took great care in making his designs feel organic. He was as prolific as a landscape architect can get, and designed spaces as far west as Berkeley, California, and as far east as Boston. Below are some of his grander and more interesting designs.

1. Central Park

First and most obvious on any list of Olmsted designs is Central Park. In 1857, a landscape design contest was held to determine who would design the huge swath of land in the center of Manhattan. Olmsted, who at the time was a writer, worked with architect Calvert Vaux to win the competition with their Greensward Plan, an innovative design that gave high priority to natural-looking landscapes and separate pathways for pedestrians and other modes of transport, like bicycles and horses. A particularly beautiful and interesting feature was the use of multidimensional pathways– Vaux designed 36 separate bridges, which were used all over the park to create interesting intersections. The design, which required the removal of ten million cartloads of dirt and rocks and the installation of more than four million trees, shrubs, and plants, was not officially completed until 1873.

2. The Emerald Necklace

The Emerald Necklace actually describes a chain of several parks that reach from Boston to Brookline, Massachusetts, including the Boston Commons, Boston Public Garden, the eponymous Olmsted park, and the Arnold Arboretum. Olmsted originally designed the project in 1878 to link the Boston Common with Franklin Park, and by doing so clean up the marshy in-between areas of Back Bay and Fens near Boston. The chain of parks, which constitute a long series of walking paths along the water is now seven miles long, with a significant portion of the water that occupied Back Bay redirected into the Charles River. The Arnold Arboretum in particular exemplifies the great care Olmsted took in designing his parks: rather than flattening the landscape and ensuring orderly pathways, he carved them around the existing plant life, making a beautiful exhibit out what was already there. Also a gifted botanist, Olmsted also helped classify and arrange some of the newer plants in the park with the new classification system created by Bentham and Hooker.

3. The Columbian Exposition

Chicago was able to snatch the honor of hosting the 1893 World’s Fair away from the hands of many other hopeful cities, including New York. However, at the time, Chicago had a long way to go to become a city fit to do so: in just a few years, Chicago had to turn its blackened, industrial urban spaces into a celebration of enlightenment and civilization. Olmsted had a heavy hand in this transformation, and during the preparation period drastically renovated no fewer than three parks in Chicago: Washington Park, Jackson Park, and the Midway Plaisance. Olmsted took special care in developing the three, despite many setbacks like swampy areas and vegetation crushed by workers setting up other parts of the exposition. Olmsted originally conceived of a Venetian canal system that would connect “lagoons” he constructed in each of the parks, but this proved to be too much of a hassle and the plan was abandoned. Once completed, the parks saw over 26 million visitors as part of the Columbian Exposition, and remain in existence today.

4. Congress Park

Congress Park in Saratoga Springs, New York, is a relatively small operation when compared to the like of Central Park, but has very unique features. Saratoga Springs, as the name suggests, is home to several natural springs that were revered in Olmsted’s day for their ability to impart health and youth (later, everyone realized they were just water). Nonetheless, the park was designed in the 1870s around the springs, and even today has several small pavilions housing spigots that produce water from various springs that have different aromas and flavors. The park is also home to an old gambling casino, as well as an original carousel.

5. Cherokee Park

Cherokee Park is a municipal park in Louisville Kentucky, and one of 18 parks in the area designed by Olmsted. It was opened in 1892, and its design probably coincided with that of the Columbian Exposition, adding to Olmsted’s load at the time. Like his other parks, Olmsted designed the park to integrate with the natural landscape shapes found in Kentucky, with gently rollling hills and long pathways that surround Beargrass Creek, which runs through most of the park. Its features today include Baringer Spring, a stream crisscrossed by several walkways; an archery range; hiking trails; and Big Rock, an outcropping eight feet over the surface of Beargrass Creek that is popular as a picnicking and swimming area.

Lunchtime Quiz: Where’s That Landmark?

Casey Johnston — Wed, 05 Aug 2009 15:30:28 +0000

You’ve probably read about and seen pictures of all these landmarks and attractions, but could you find them on a map? Let’s find out.

Take the Quiz: Where’s That Landmark?

5 Rules of Thumb and Their Inventors

Casey Johnston — Fri, 10 Jul 2009 14:07:09 +0000

It is a popular custom among learned society to toss around the names of theories without explanation or elaboration– Murphy’s Law, Occam’s Razor, and so on. But who were Murphy and Occam, and who are they to come up with these life-governing rules? Below are five well-known rules and laws, and the stories behind their namesakes.

1. Occam’s Razor

Occam’s razor is known more formally as the law of parsimony or the law of economy, and states that “entities should not be multiplied unneccesarily.” Put simply, it is the notion that the simplest explanation is usually the right one. It is named after William of Occam, who was a scholastic philosopher and Franciscan friar that lived in England in the 14th century. His contemporaries were the likes of Thomas Aquinas and the Islamic scholar Averroes. William was the first to write down the principle in its formal wording, and it gained his name due to its frequent usage in medieval philosophy. William was also one of the first to argue that people should not attempt to derive the idea of God from reason or natural logic.

2. Moore’s Law

Moore’s Law is not actually a law, but instead an observation made in 1965 regarding transistors– specifically, that the number of transistors that can be placed inexpensively in an integrated circuit doubles about every two years. The observation was made by Gordon E. Moore, a graduate of UC-Berkeley and Caltech, in an article in the now-defunct Electronics Magazine. Three years after this observation, Moore co-founded Intel Corporation and served in various positions before becoming its chairman and CEO in 1979, and retiring to a chairman emeritus position in 1997. Nowadays, chip manufacturers treat Moore’s Law as a professional challenge, struggling to keep the pace by constantly inventing new ways to squeeze more transistors onto chip surfaces.

3. Murphy’s Law

Murphy’s Law is also less of a law and more of an old saying: “anything that can go wrong, will go wrong.” It is named after Edward Murphy, who was an American aerospace engineer who, funnily enough, worked primarily on safety-critical systems. Most of his efforts went into developing escape systems for experimental aircrafts, such a the F-4 Phantom II and the SR-71 Blackbird. Murphy thought that people in his profession should always consider the worst-case scenario, and so he often cited his old adage as a central tenet of defensive design. However, his efforts to have the law taken seriously were unsuccessful. There also exists a “corollary” to Murphy’s Law, called Finagle’s Law of Dynamic Negatives, which states “anything that can go wrong, will, at the worst possible moment.”

4. Pareto Principle

The Pareto Principle, also known as the “80-20 rule,” is the observation that for many events and sets of data, 80% of the effects come from 20% of the causes. It is named after Vilfredo Pareto, an Italian economist who lived and worked around the turn of the 20th century. In 1906, he noted in his research that 20 percent of the population in Italy owned 80 percent of the the land. He extrapolated this relationship to the general distribution of wealth, noting in a book published in 1909 that this proportion applied roughly across time and location. It wasn’t until much later that the rule was named after Pareto, by business management consultant Joseph Juran. The rule is now applied very widely, not just to wealth but to quality assurance– Microsoft has noted that fixing the most-reported 20% of bugs fixes 80% of errors and crashes– and time management by gurus like Tim Ferriss, author of The 4-Hour Workweek, who encourages people to focus their energies on the 20% of activities that generate 80% of the results. Would-be applicants should use the rule with caution, though– it is meant to illustrate a general majority-minority relationship, and is not a hard-and-fast law applicable to all cases.

5. Parkinson’s Law

Parkinson’s Law states, “work expands so as to fill the time available for its completion.” Despite the fact that it is quoted quite soberly today among efficiency experts, Parkinson’s Law began as a joke. It was the first sentence of a satire piece published in 1955 in The Economist by Cyril Northcote Parkinson. Parkinson was no economist or scientist, but rather a naval historian and professor, first in Liverpool and then in Singapore. After the success of the article, Parkinson expanded upon his piece in a book called Parkinson’s Law. Though the book was only a hundred pages long, it became an instant best seller in the United States.

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3 Solved Math Mysteries (and 2 That Still Plague Us)

Casey Johnston — Wed, 01 Jul 2009 14:49:58 +0000

Mathematics has fascinated the human race nearly as long as our existence. Some of the coincidences between numbers and their applications are incredibly neat, and some of the most deceptively simple ones continue to stump us and even our modern computers. Here are three famous math problems that people struggled with for a long time but were finally resolved, followed by two simple concepts that continue to boggle mankind’s best minds.

1. Fermat’s Last Theorem
In 1637, Pierre de Fermat scribbled a note in the margin of his copy of the book Arithmetica. He wrote (conjectured, in math terms) that for an integer n greater that two, the equation aⁿ + bⁿ = cⁿ had no whole number solutions. He wrote a proof for the special case n = 4, and claimed to have a simple, “marvellous” proof that would make this statement true for all integers. However, Fermat was fairly secretive about his mathematic endeavors, and no one discovered his conjecture until his death in 1665. No trace was found of the proof Fermat claimed to have for all numbers, and so the race to prove his conjecture was on. For the next 330 years, many great mathematicians, such as Euler, Legendre, and Hilbert, stood and fell at the foot of what came to be known as Fermat’s Last Theorem. Some mathematicians were able to prove the theorem for more special cases, such as n = 3, 5, 10, and 14. Proving special cases gave a false sense of satisfaction; the theorem had to be proved for all numbers. Mathematicians began to doubt that there were sufficient techniques in existence to prove theorem. Eventually, in 1984, a mathematician named Gerhard Frey noted the similarity between the theorem and a geometrical identity, called an elliptical curve. Taking into account this new relationship, another mathematician, Andrew Wiles, set to work on the proof in secrecy in 1986. Nine years later, in 1995, with help from a former student Richard Taylor, Wiles successfully published a paper proving Fermat’s Last Theorem, using a recent concept called the Taniyama-Shimura conjecture. 358 years later, Fermat’s Last Theorem had finally been laid to rest.

2. The Enigma Machine
The Enigma machine was developed at the end of World War I by a German engineer, named Arthur Scherbius, and was most famously used to encode messages within the German military before and during World War II.
The Enigma relied on rotors to rotate each time a keyboard key was pressed, so that every time a letter was used, a different letter was substituted for it; for example, the first time B was pressed a P was substituted, the next time a G, and so on. Importantly, a letter would never appear as itself– you would never find an unsubstituted letter. The use of the rotors created mathematically driven, extremely precise ciphers for messages, making them almost impossible to decode. The Enigma was originally developed with three substitution rotors, and a fourth was added for military use in 1942. The Allied Forces intercepted some messages, but the encoding was so complicated there seemed to be no hope of decoding.

Enter mathematician Alan Turing, who is now considered the father of modern computer science. Turing figured out that the Enigma sent its messages in a specific format: the message first listed settings for the rotors. Once the rotors were set, the message could be decoded on the receiving end. Turing developed a machine called the Bombe, which tried several different combinations of rotor settings, and could statistically eliminate a lot of legwork in decoding an Enigma message. Unlike the Enigma machines, which were roughly the size of a typewriter, the Bombe was about five feet high, six feet long, and two feet deep. It is often estimated that the development of the Bombe cut the war short by as much as two years.

3. The Four Color Theorem
The four color theorem was first proposed in 1852. A man named Francis Guthrie was coloring a map of the counties of England when he noticed that it seemed he would not need more than four ink colors in order to have no same-colored counties touching each other on the map. The conjecture was first credited in publication to a professor at University College, who taught Guthrie’s brother. While the theorem worked for the map in question, it was deceptively difficult to prove. One mathematician, Alfred Kempe, wrote a proof for the conjecture in 1879 that was regarded as correct for 11 years, only to be disproven by another mathematician in 1890.

By the 1960s a German mathematician, Heinrich Heesch, was using computers to solve various math problems. Two other mathematicians, Kenneth Appel and Wolfgang Haken at the University of Illinois, decided to apply Heesch’s methods to the problem. The four-color theorem became the first theorem to be proved with extensive computer involvement in 1976 by Appel and Haken.

…and 2 That Still Plague Us

1. Mersenne and Twin Primes
Prime numbers are a ticklish business to many mathematicians. An entire mathematic career these days can be spent playing with primes, numbers divisible only by themselves and 1, trying to divine their secrets. Prime numbers are classified based on the formula used to obtain them. One popular example is Mersenne primes, which are obtained by the formula 2ⁿ – 1 where n is a prime number; however, the formula does not always necessarily produce a prime, and there are only 47 known Mersenne primes, the most recently discovered one having 12,837,064 digits. It is well known and easily proved that there are infinitely many primes out there; however, what mathematicians struggle with is the infinity, or lack thereof, of certain types of primes, like the Mersenne prime. In 1849, a mathematician named de Polignac conjectures that there might be infinitely many primes where p is a prime, and p + 2 is also a prime. Prime numbers of this form are known as twin primes. Because of the generality if this statement, it should be provable; however, mathematicians continue to chase its certainty. Some derivative conjectures, such as the Hardy-Littlewood conjecture, have offered a bit of progress in the pursuit of a solution, but no definitive answers have arisen so far.

2. Odd Perfect Numbers
Perfect numbers, discovered by the Euclid of Greece and his brotherhood of mathematicians, have a certain satisfying unity. A perfect number is defined as a positive integer that is the sum of its positive divisors; that is to say, if you add up all the numbers that divide a number, you get that number back. One example would be the number28— it is divisible by 1, 2, 4, 7, and 14, and 1 + 2 + 4 + 7 + 14 = 28. In the 18th century, Euler proved that the formula 2^(n-1)(2ⁿ-1) gives all even perfect numbers. The question remains, though, whether there exist any odd perfect numbers. A couple of conclusions have been drawn about odd perfect numbers, if they do exist; for example, an odd perfect number would not be divisible by 105, its number of divisors must be odd, it would have to be of the form 12m + 1 or 36m + 9, and so on. After over two thousand years, mathematicians still struggle to pin down the odd perfect number, but seem to still be quite far from doing so.

5 Familiar Numbers and the Logic Behind Them

Casey Johnston — Mon, 22 Jun 2009 17:24:16 +0000

Given how digital the world has become, we are hardly bothered by having to deal with one string of numbers after the next: credit card numbers, social security numbers, IP addresses and so on. Do these numbers hold any meaning, or are they just random sequences in a database? Read on to find out.

1. Credit Card Numbers

The string of digits that make up credit card numbers have a distinct, if subtle, structure. The first digit signifies which system it belongs to: 3 is for travel and entertainment cards like American Express, 4 is Visa, 5 is Mastercard, and 6 is Discover. The rest of the credit card number is used differently by each company — for Visa cards, digits 2 through 6 are a bank number, 7-12 or 7-15 are the account number, and either 13 or 16 is a check digit, a number that is the result of a series of simple but generally secret computations with the other digits that helps verify the full number isn’t fake. In an AmEx card, digits three and four indicate the type of card and currency, 5-11 are the account number, 12-14 are the card number within the account and 15 is a check digit (AmEx card numbers are 15 instead of 16 digits).

2. Zip Codes

Zip codes were invented by Robert Aurand Moon and by 1963 were widely used by the United States Postal Service. The five-digit number is a code for an exact location, with each successive digit indicating a more specific place. The first digit indicates a group of states; for example, a 1 directs mail to Delaware, New York, and Pennsylvania. The next two indicate a sectional center facility — a zip code beginning with 108 directs mail to the facility New Rochelle, NY. The last two digits represent a village or town near the facility or a location within a metropolitan area. Typically in a non-metropolitan area a city gets the first area code, and surrounding villages and towns receive zip codes in alphabetical order (for example, Glenmont, NY has 12077 and Gloversville, NY has 12078). And in case you were wondering, ZIP is an acronym that stands for Zone Improvement Plan.

3. Telephone Numbers

Everyone’s a little more familiar with telephone numbers — there’s country code, necessary if dialing internationally (1 is the United States), and area codes, which indicate a broad geographic area. The next three digits indicate a smaller area, and the last four are a random permutation. The area code and first three digits of a phone number are referred to in the telephone business as NPA-NXX. These numbers convey a unit of purchase for telephone companies, as they will generally buy one NPA-NXX, or one combination. The ownership reveals why cell providers are often so tetchy about carrying a number from one to another, or vice versa: you would be stealing a phone number from one company and giving it to another.

4. IP Addresses

IP addresses, at their most basic level, identify individual computers to the Internet. They are a series of four numbers punctuated by periods that look something like 255.143.68.1. Each of these numbers (such as 255 in the example) is referred to as an octet. Each octet can have a value between 0 and 255 (so if you see an IP address with any octet higher than 255, it’s fake). Together the octets of an IP address contain information about the type of network and, to an extent, the location of a computer. The first octet, called the class, tells you the size of a network a computer is in. A Class A network has a first octet between 0 and 127 and can have over 16 million IP addresses; a Class B network has a first octet between 128 and 191 and have about 65,000 addresses; a Class C network, used for most homes, has a first octet of 192-223 and can have 254 addresses. There are also Class D and E networks with first octets of 224-255 that are used for more specialized purposes. Most IP trackers use a location database to determine where an IP address is coming from, so there is not a direct scheme for the other octets. However, due to the modern use of subnetworks within a network, IP addresses are often masked. Therefore, it is no longer directly possible to tell the type of network a computer hails from.

5. Social Security Numbers

Social Security numbers are nine-digit strings that most Americans are assigned at birth, and are generally used as an identifier as well as a qualifier for various kinds of insurance and income from the government. The first three numbers tell where the person first applied for the card; if the card was applied for at birth and the mailing address used was also the residential address, the numbers tell the rough location of birth (doesn’t apply to babies born during vacation in Panama, but in general this is true). The next two digits are called the group number, and allow SSNs of the same area number to be broken into smaller groups. They are assigned in the following order: odd numbers 01-09, evens 10-98, evens 02-08, odds 11-99. The last four digits, the serial numbers, are assigned consecutively 0001-9999.

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4 Women Who Rocked Physics

Casey Johnston — Tue, 09 Jun 2009 16:30:25 +0000

When asked to name women who have significantly contributed to science, most people shrug and say, “Marie Curie?” In fact, women have added to our scientific repertoire capabilities no less than nuclear fission and modern day alchemy, among many other discoveries.

1. Lise Meitner

Lise Meitner (1878-1968) was a quiet, self-effacing Austrian-Jewish woman who has come to be known “the mother of the atomic bomb.” After studying under Boltzmann and Planck (yes, that Boltzmann and Planck), she became the acting director of the Kaiser-Wilhelm Institute of Chemistry in Berlin. It was there that, alongside partner Otto Hahn, she noted in an experiment that uranium-238 nuclei split into barium and krypton, along with several neutrons and a pocket of energy. Meitner was the first to describe and name the process– “nuclear fission”– and noted the potential for a chain reaction (Keanu Reeves not included). However, she was exiled from Germany shortly after the Anschluss, and so Hahn and two others published the research in 1938. For this, Hahn two other men won the 1944 Nobel Prize in Chemistry.

2. Chien-Shiung Wu

Chien-Shiung Wu (1912-1997) was born in China and earned her Ph.D. from UC-Berkeley in 1940. At this time, it was considered a dependable rule in matter behavior that identical particles would always act in a way that was consistent and symmetrical. However, upon observing the beta decay of cobalt-60, Wu noticed that the weak interactions between emitted beta particles caused them to strongly prefer to travel in a certain direction – roughly equivalent to watching air rush into a balloon of its own accord. With this research, Wu proved that nature is not always naturally symmetrical, upending a formerly watertight law. The Nobel Prize for Physics in 1957 was awarded to researchers of this discovery; Wu was not among their number.

3. Maria Goeppert-Mayer

Maria Goeppert-Mayer (1906-1972) hailed from Germany and attended the University of Gottingen. After stints working with Born and Planck and teaching at Sarah Lawrence College, Goeppert-Mayer ended up in Chicago working at the Argonne National Laboratory. While there she worked with Edward Teller and Enrico Fermi, learning the ropes of nuclear physics as she went. It was at this time she developed a model of the atomic nucleus, which took the form of shells similar to the atomic shell model. She also discovered that there were certain “magic numbers” of nucleons for which the energy holding them together was less than the preceding number — for example, it took significantly less energy to hold together 20 nucleons than it did 19 — and she worked out the supporting mathematics. For this achievement, she won the Nobel Prize for physics in 1963.

4. Harriet Brooks

Harriet Brooks (1876-1933) was born in Canada, attended McGill University, and worked as a graduate student under Ernest Rutherford. Rutherford had noticed that radioactive thorium gave off a substance other than radioactive rays, and left it to Brooks to figure out what it was. Brooks identified the “emanation” from thorium as an element in gas form that was, strangely, not thorium. Brooks realized that this meant that one element could, with the right conditions, be used to produce a completely different element. It may sound uncool to discover that alchemy actually works roughly a millennium too late, but on the upside, nuclear transmutation is used today in tokamaks as well as fission power reactors.