All About The Number 100

In celebration of my 100th post coming earlier this week, I figured I would discuss the number 100!!! I know, what a way to celebrate…

Applications

The number of yards in a football field.
The minimum number of yards for a par 3 hole in golf.
The number of years in a century.
The number of cents in a dollar (or pence in a pound sterling)
The boiling temperature of water at sea level, in Celsius.
The atomic number of fermium which is made by blasting plutonium with neutrons (named after the great nuclear physicist Enrico Fermi).
The number of senators in the United States Senate.
The number of tiles in a standard Scrabble set.
The basis for percentages (100% represents wholeness, purity, and perfection).
In China, tradition holds that the naming of a newborn panda must wait until the cub is 100 years old.
Pythagoreans considered 100 as divinely divine because it is the square (10^2) of the divine decad (10).
Nostradamus’ work titled “Centuries” contains 10 chapters of 100 verses each.
There are 100 squares in the 10×10 Euler (Latin or Graeco-Roman) Square. A Latin square consists of sets of the numbers 0 to 9 arranged in such a way that no orthogonal (row or column) contains the same number twice. See the image above for an example of a colorful Gaeco-Roman Square for n=10 (the capability for which was discovered by E.T. Parker of Remington Rand in 1959, disproving earlier Eulerian conjectures that a 10×10 square was impossible).

In Language

“Cem” – Portuguese
“Cent” – French
“Cento” – Italian
“Cien” – Spanish
“Honderd” – Dutch
“Hundert” – German
“Hundra” – Swedish
“Hundre” – Norwegian
“Hundred” – English
“Hundrede” – Danish
“Hyaku” – Japanese
“Miyya” – Arabic
“Sad” – Farsi
“Sada” – Estonian
“Sata” – Finnish
“Sto” – Croatian, Czech, Polish
“Száz” – Hungarian
“Yibai” – Chinese
“Yüz” – Turkish

Note: “Cent” is the largest number in the French language that is in alphabetical order. And funny enough, when you spell out 2*5*10=100 in French, it’s all in alphabetical order too! (deux*cinq*dix=cent)

A Mathematical Investigation

100 = 2^2 * 5^2 (factorization of 100)
100 = (1 + 2 + 3 + 4)^2
100 = 1^3 + 2^3 + 3^3 + 4^3 = 1 + 8 + 27 + 64
100 = The sum of the first nine prime numbers (2+3+5+7+11+13+17+19+23)
100 = The sum of four pairs of prime numbers (47+53, 17+83, 3+97, 41+59)
100 = The sum of the first ten odd numbers (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)
100 = 2^6 + 6^2 making it a Leyland Number.
100 can be expressed as a sum of some of its divisors making it a semi-perfect number.
100 is divisible by the number of primes below it (25) making it a polygonal number.
100 is divisible by the sum of its digits (in both base 10 and base 4) making it a Harshad Number.
100 is the 854th to 856th digits of pi.
100 is the 3036th to 3038th digits of phi.

In numerology, 100 equals “I LOVE WISDOM TRUTH BEAUTY”
(9) + (3 + 6 + 4 + 5) + (2 + 5 + 1 + 3 + 2 + 7) + (5 + 9 + 1 + 4 + 6 + 4)

Sources / Links

A Visualization Of Deadliest Earthquakes Since 1900

Earlier today, The Guardian DataBlog resourcefully provided a link to USGS earthquake data. The table lists all individual earthquakes that have caused 1,000 or more deaths, since 1900. Data elements include date, location, latitude, longitude, deaths, and magnitude. Below are some summary tables and a map that visualize this data. You can also click here for some USGS maps of the Haiti earthquake.

Map of Deadliest Earthquakes, 1900-2009
Dot Size = Total Deaths,
Dot Color = Average Magnitude

Summary of Deadliest Earthquakes by Year, 1900-2009

Summary of Deadliest Earthquakes by Month, 1900-2009

Investigation of Relationship Between Earthquake Magnitude and Deaths, 1900-2009

As a note for the right-side plot, I’ve cut out the earthquakes causing more than 20,000 deaths to just look at those causing between 1,000 and 20,000 deaths. Looking at the entire data set, the correlation coefficient for earthquake magnitude and total deaths is about 0.286 which represents a weak positive relationship between the two variables. Obviously, the existence of a relationship does not imply that a higher magnitude earthquake causes more total deaths, but it is insightful to identify a relationship between the two variables to inspire more investigation. Moving forward, one might investigate the data for clusters based on geo-location, decade, or season (controlled for hemisphere).

My thoughts and prayers go out to those affected by the Haiti earthquake.

Links

The Intersection Of Expertise

As I begin my job search (25 applications in 2 days so far!) I keep asking myself how to describe what I’m looking for in a job and in what realm do I wish to work? There is no specific job title that describes my experience and education (e.g. “doctor” or “software engineer”) and there is no one department in which I’ve worked or wish to work (e.g. “Operations” or “Logistics” ). Yes, I have an academic background in mathematics & statistics yet it’s difficult to communicate why I have that academic background. I do not necessarily want to become a statistician but rather I fully understand the quantitative nature of things and the power that numbers, math, and quantitative methods have in all aspects of business, government, and life.

So where does this leave me? Well, unemployed and confused, for one. But that’s okay with me. I’m confident that with my capabilities, no matter how hard they may be to communicate in an application or even to a recruiter, I’ll find the position that leverages my abilities and motivation.

That being said, I think I’m at least getting close to describing where I stand, and in real-world terms. It’s at an intersection of sorts – between quantitative methods, scientific and technological realms, and the human element. It’s interdisciplinary – can fit within any group or team or stand alone as an independent researcher or consultant. It’s also dynamic – parallels the speed with which modern business operates and the flexibility required to optimally support the needs and requirements of many types of personnel.

I’ve used a similar image a few times, in posts on knowledge innovation and math in 2010 and beyond. Here I’ve intersected three main topics while including some of my strengths in the middle. Now if I could only match those to a job title…

At what intersection do you operate?

Archimedes: The Father of Mathematics

Summary

  • Birth: c. 287 BC in Syracuse, Sicily (colony of Magna Graecia)
  • Death: c. 212 BC in Syracuse, Sicily (during the Second Punic War)
  • Alias(es): Archimedes of Syracuse
  • Ethnicity: Greek
  • Residence(s): Syracuse, Sicily; Alexandria, Egypt (during school)
  • Language(s): Works were written in Doric Greek (Sicilian)
  • Religion(s): Judaic Christian
  • Father: Phidias/Pheidias (astronomer and mathematician)
  • Mother: Unknown
  • Spouse(s): Unknown
  • Children: Unknown
  • Relatives: King Herion II (unconfirmed), Gelon (unconfirmed)
  • Acquaintances: Conon, Dositheus, Eratosthenes, Heracleides
  • Class/Wealth Notes: Upper
  • Institutions/Degrees: The School of Alexandria
  • Profession(s): Mathematician, engineer, astronomer, physicist, inventor
  • Field(s) of Study: Hydrostatics, Mechanics, Geometry, Calculus, Defense
  • Famous Works: The Sand Reckoner, On the Equilibrium of Planes, On Floating Bodies, On the Measurement of a Circle, On Spirals, On the Sphere and the Cylinder, On Conoids and Spheroids, The Quadrature of the Parabola, Ostomachion, The Method of Mechanical Theorems, Book of Lemmas (Liber Assumptorum), Cattle Problem
  • Legacy: “Eureka!”; known as “The Father of Mathematics”; with Newton and Gauss he is commonly referred to as one of the three greatest mathematicians who ever lived; last words were “Do not disturb my circles”;
  • Cause of Death: Killed in Syracuse, Sicily during the Second Punic War despite orders from the Roman general Marcellus to leave him unharmed. The Greek historian Plutarch reported that Roman soldiers killed Archimedes to steal his scientific instruments. Another version states he was stabbed for ignoring a Roman soldier’s orders because he was too entranced in a geometrical diagram he drew in the sand.
  • Notable Historian(s): Isidore of Miletus, Eutocius, Plutarch, Polybius, Thābit ibn Qurra (Arabic translator), Gerard of Cremona (Latin translator)


Archimedes’ Principle & The First Law of Hydrostatics

Story: Archimedes was tasked to determine if the new crown made for King Herion II was made of solid gold. While taking a bath, he observed the level of water in the tub rise as he got in… leading to his “Eureka!” moment regarding density and displacement.

Science: A body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Therefore Archimedes could immerse the crown in water, measure the amount of water displaced, divide it by the weight of the crown, and arrive at the density of the crown.

Impact: Hydrostatics, or the study of the mechanical properties of liquids at rest, was born. Archimedes’ Principle regarding buyancy and density is used throughout science today. It’s used in the building of ships, other industrial manufacturing, and really any type of engineering. Without it, well, we might be “screwed” (see Archimedes’ other works below).


Other Works

  • Archimedes’ Screw – This consists of a long screw enclosed in a cylinder. With tilted so that its bottom tip is placed in the water, turning the screw pushes water up the screw and out the top. This was used to bilge water out of large ship he designed, the Syracusia.
  • Law of the Lever – Achimedes supplied the first real scientific explanation of how levers work in his work titled On The Equilibrium of Planes (although he certainly did not invent levers).
  • Method of Exhaustion and Pi – Archimedes used the “method of exhaustion” to determine approximate areas and volumes of circles. It involves drawing one polygon outside of a circle, and inscribing a similar polygon on the inside of the circle. Since the area of a polygon (at that time) could be worked out more easily than a circle, Archimedes would determine the areas of the polygons, continuously adding more sides to the polygons, computing the new areas, and estimate the area of the circle which falls between those of the inner and outer polygons. This helped him determine an approximation of pi which he set at somewhere between 3.1429 and 3.1408.
  • Spheres and Cylinders – Archimedes, through the use of several means, proved that a sphere had two-thirds the volume and surface area of a cylinder that circumscribes the sphere.
  • Engineering Feats – Archimedes engineered and built several machines, based on the physical properties and relationships he had proven, to help defend Syracuse from the Roman assault. These included giant pulleys and catapults that would lift ships out of the water and shake them up, destroying them (check out the “claw of Archimedes”). He also built a giant mirror that focused the sunlight onto a ship to burn it.


Adsideological Discussion

Archimedes’ life highlights when a needs translates to accomplishments. This is a characteristic of most inventions, because they need money to flourish and inventors need money to succeed and continue inventing. But Archimedes’ accomplishments were much more than this. It seems to me that he was driven by pure curiosity and intellect, a desire to test his mind against science and nature.

At some level, perhaps he spent too little time outside of his passion of mathematics and discovery. A passion is supposed to be a majority consumer of time and energy. However, no legacy really exists, outside of his scientific accomplishments, that tells us about Archimedes the man and Archimedes the neighbor. Perhaps this has something to do with the time frame in which he lived, but a story told is a story told. Regardless, Archimedes was a life changer and contributed an incredible balance of both an immediate impact and a long term impact on society.

Happy Planet Index vs Human Development Index

With my post on “Everything is Connected” I thought I’d investigate a bridge between happiness and the level of development in a country…

The Happy Planet Index (HPI)

“The HPI is an innovative measure that shows the ecological efficiency with which human well-being is delivered around the world. It is the first ever index to combine environmental impact with well-being to measure the environmental efficiency with which country by country, people live long and happy lives.”

The Human Development Index (HDI)

“The first Human Development Report (1990) introduced a new way of measuring development by combining indicators of life expectancy, educational attainment and income into a composite human development index, the HDI. The breakthrough for the HDI was the creation of a single statistic which was to serve as a frame of reference for both social and economic development. The HDI sets a minimum and a maximum for each dimension, called goalposts, and then shows where each country stands in relation to these goalposts, expressed as a value between 0 and 1.”

Thoughts and Hypotheses

There are two relationships we will want to consider:

  • Correlation: Is there any direct relationship (positive or negative) between the values of the HDI and HPI?
  • Clustering: By region (or other characteristic field) can we find any clusters in the data?

Since these are composite indices of several weighted variable inputs, hopefully this top-level approach can identify some possible matches and mismatches between underlying data fields too. Related to the HDI, I bet the UN’s HPI (Human Poverty Index) has a bridge to happiness… or most likely, unhappiness.

Data/Discussion

  • There seems to be a connection between deviations in the data. When there exists a large deviation, for a specific region, for the HDI, there seems to also be a large deviation of values for the HPI. Notice that Africa, Australasia, and the Middle East all have similar double-digit deviations. What does this tell us about the range of development and happiness within a specific region? Perhaps this could be tested across many country-level metrics to see if the similar deviations occur more frequently.
  • As with the above note, since we have these metrics on a same scale/range, let’s combine them to see who has the highest composite score. In alphabetical order we have: 84, 125, 138, 137, 133, 134, 126, 134, 119, 117, 119. There seem to be three groups here: High (>130), Medium (100-130), Low (<100). Depending on a user need, algorithms can be created to join metrics to provide a big picture representation of economic, political, sociological, etc metrics, and flexibility can be built to dig into the weeds on the underlying data. This would be a nice comprehensive framework for understanding how countries (and regions as a whole) change over time.


  • Looking at the scatter plot, it is clear that some clusters may exist, for example with Africa (blue). Caribbean (orange), Europe (green), and Russia and Central Asia (purple) also show some quick visual clustering, while the Middle East (red) shows the opposite. What could this mean? That regional trade, policy, weather, etc are good supplementary foundations for providing happiness and development?
  • We could add trend lines and quickly check for any linear (or logarithmic) relationships. If any relationship does exist as a whole or with a region, it is certainly not a directly proportional or inversely proportional one. This was expected as these metrics are quite different (despite the overlap in life expectancy as an input dimension).

Moving forward, the methodologies and underlying dimensions (with their sources) should be compared. Data is always good, but with good data one still must be careful. That being said, this is a good start for a much larger investigation into the connections between different country-level metrics, especially if they are to be used in international and national policy.