natural log

the ln of x is no more complex, than cooking or tying a shoe
just find the power to which e should be raised, to equal the x in your queue
now e may seem quirky, this two point seven one thing
but it’s just another constant, with an infinite decimal string

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Some Statistics on Civil Wars

The Economist: “How to Stop the Fighting, Sometimes” (11/09/2013)

File:Ongoing military conflicts.png

I’m always very impressed with how The Economist weaves statistics (seemingly very credible ones) into its articles. In some cases they are the baseline from which the writer provides opinion, context, and insight. In other cases, they are the context – supporting a strong central theory with some quantitative love.

The recent article on civil wars was both informative on the subject of civil wars as well as a prime example of how powerful statistics can provide essential context to a central theory. Some of the most interesting statistics extracted from the article include:

  • Of the 150 large intrastate wars since 1945, fewer than 10 are ongoing.
  • The rate at which civil wars start is the same today as it has been for 60 years; they kick off every year in 1-2% of countries.
  • The average length of civil wars dropped from 4.6 to 3.7 years after 1991.
  • From 1945-1989, civil war afflicted 18% of the world’s nations.
  • Since 1989, victory for one side has only occurred in 13% of cases (compared to 58% before 1989).
  • Since 1989, negotiated endings have occurred in almost 40% of cases (compared to 10% before 1989).
  • Leadership changes are a factor in the termination of between 25-40% of civil wars.
  • Since its founding, the UN has completed 53 peacekeeping missions. The 15 ongoing ones employ almost 100,000 in uniform.

It seems a good chunk of data came from the Centre for the Study of Civil War at the Peace Research Institute Oslo (PRIO). Very cool. Image is from Wikipedia and shows ongoing military conflicts around the world (major in red, minor in orange).

A Universal Concept Classification Framework (UCCF)

Background

Whether it’s for building the perfect chapter title, analyzing existing literature, or maybe just a personal etymological adventure,  there is usefulness in providing quantitative context to words and concepts. Should such a framework exist, it should be easy-to-understand and broadly applicable for authors, students, and other individuals alike.

The Universal Concept Classification Framework (UCCF) proposed below involves five categories in which any word/concept can be scored. Each category’s score has range [0,20], spanning the full spectrum of possible values across each category. Where possible, the highest possible score for each category (20) should represent the more complex end of the spectrum (see below). The individual scores can then be summed to give a combined UCCF Score with range [0,100].

The individual category scores as well as the combined UCCF Score provide an easy way for readers and writers to understand and analyze the relative impact of certain words/concepts on readers, among other applications.

Universal Concept Classification Framework (UCCF)

  • Get (Concrete=0, Abstract=20): Low scores represent words/concepts that are concrete, tangible, well-defined, and easy to understand. High scores represent words/concepts that are abstract and open to interpretation.
  • Act (Controllable=0, Uncontrollable=20): Low scores represent words/concepts that are controllable, created, and/or driven by an individual, group, or machine. High scores represent words/concepts that are by nature uncontrollable.
  • Dim (Independent=0, Dependent=20): Low scores represent words/concepts that are independent of other words/concepts and can stand alone for meaning and interpretation. High scores represent words/concepts that are complex, very dependent upon other words/concepts, and are often very interconnected to support interpretation.
  • Set (Known=0, Changing/Unknown=20): Low scores represent words/concepts that are very well known and not subject to change in meaning or interpretation across time, language, and society. High scores represent words/concepts that change rapidly or may be universally undefined across time, language, and society.
  • Rad (Plain=0, Intriguing=20): Low scores represent words/concepts that are plain and without dimension. High scores represent words/concepts that are multidimensional, mysterious, and full of intrigue.

Limitations/Applications

No framework is without fault, and especially in the measurement of unstructured information, the UCCF certainly has limitations. However, it’s a quick and easy way to begin to better understand words/concepts, and I believe this type of methodology has broad applications.

One example is in the building of book titles and chapters, where authors may want to represent a broad spectrum of word types. One type of chapter may want to maximize combined UCCF Scores, others may want to keep combined UCCF Scores to a minimum, and a third type may want to have words that cover the widest range of combined UCCF Scores.

Another application may be in the analysis of certain authors, languages, or successful books in general. Do authors write about similar concepts according to the UCCF? Is there a correlation between successful books and the UCCF Scores represented by certain titles? These types of questions could be investigated using a new quantitative approach.

In general, applying simple quantitative methods to abstract ideas can provide a new way for thinking and contextualizing decisions, such as choosing book titles, and analyzing content and content creators, such as popular authors/bloggers.

The Future of Analytics and Operations Research (WINFORMS Panel Discussion)

Program/Title: The Future of Analytics and Operations Research
Organization: Washington, DC Chapter of the Institute for Operations Research and the Management Sciences (WINFORMS)
Date/Time: Tue February 21, 2012 1800-2030 EST
Description: The exponential explosion in the amount of data available has spawned a new field: “analytics.” This recent arriviste is forcing the operations research (OR) community to reconsider how we work, with both clear benefits and risks – not only in areas like data integrity, but the very foundations of statistical problem-solving. How do we define analytics, and how does analytics relate to OR? What is the future of analytics? We’ll ask these provocative questions and others to three of our best OR intellectuals in the Washington DC area.

General Notes / Topics of Discussion

  • The difference between having an “outcomes focus” versus a “process focus”
  • Scope of similar disciplines – analytics and operations research – are they competing or allied?
  • Communication to decision makers critical – how are these skills being developed in both disciplines?
  • Philosophy of science / having the “soft skills” – is this taught, learned, or experienced?
  • When to shy away from problems – lack of customer support, intended answer, etc.
  • The difference between problems and messes… which is worse?
  • Defining constraints/limitations and discussing assumptions (e.g. acceptable solutions under certain budget constraints)
  • The importance of defining (and redefining) the problem. Critical in today’s business climate.
  • Ideal skills: Hacker skills, subject matter expertise, communication skills, ability to listen, wargaming, organizational psychology, humility, natural curiosity
  • Other related disciplines: Data Science, Statistics, Business Analytics, Big Data, etc. – how do these affect the operations research community?

Further Reading / Related Links

World Statistics Day and the Importance of Statistics in Government

The most recent issue of Amstat News features a wonderful summary of the first ever World Statistics Day, which just occurred on October 20, 2010. The article features a series of quotes from the chief statisticians at various U.S. government agencies, all of which serve as a great overview of the critical importance, broad applicability, and growing need for statistics and statistics professionals in the U.S. and around the world. Collectively, we must embrace not only the numbers, data, methods, analyses, and reports, but also the conversations and the debate around such components. In a world heavily fueled by data, I’m very glad that statistics is gaining more international awareness and recognition so that all our lives can be bettered by more informed decisions and debates.

“Statistics produced by the federal government inform public and private decisionmakers in shaping policies, managing and monitoring programs, identifying problems and opportunities for improvement, tracking progress, and measuring change. The programs of our statistical system furnish key information to guide decisionmakers as they respond to pressing challenges, including those associated with the economy, agriculture, crime, education, energy, the environment, health, science, and transportation. In a very real sense, these statistics provide data users with a lens to focus the myriad activities of our society into a more coherent picture of the status, progress, and trends in our nation. The ability of governments, businesses, and individuals to make appropriate decisions about budgets, employment, investments, taxes, and a host of other important matters depends critically on the ready availability of relevant, accurate, and timely federal statistics. Our economy’s complexity, growth, and rapid structural changes require that public and private leaders have unbiased, relevant information on which to base their decisions.”
– Katherine Wallman, Chief Statistician, Office of Management and Budget and Past President of the ASA

A few more important (and relevant) statistics resources can be found at:

Focus, Balance, and Strength

One is for focus, two for balance, and three for strength. From the most basic sequence of integers we can understand critical characteristics and qualities that, in a sense, provide a backbone by which we can be happy, learn, and grow.

One is one. There is nothing to surround it, there is nothing to be bent. It’s the focal point of many, and the starting spot for all. Above one comes everything else and into one everything comes.

Our society puts a lot of focus on one. We like to see a single result and hear a single voice. We want to find our soul mate and discover the holy grail. We seek to structure our world by its basic individual units, the atoms and nodes. We break down our problems into individually digestible chunks. One is the basic unit of math, the center of gravity, the perfect result. One is the focus and concentration of everything else.

But one stands alone. Where one is one, one is only one. One would be none if no two came from one.

Two is the balance of ones, the pairs of nature, the couplets of science, the squares of math, the rhythm and meter of poetry. Two is evenness and congruence. Two is good and evil, hot and cold, yes and no, high and low, winners and losers, protons and electrons, male and female, life and death. From two we can find harmony and bliss and make connections not previously seen by focusing on one. Two is love. Love is two. Two is the threading of life and the creator of balance within the cosmos. Two is the secret order within disorder, through connections and relationships that make us more than one.

But two still lacks shape. Where two is two, there is only one view of two. Two would be one if no three came from two.

Three is the unit of strength, the shape of our space. It represents our current (most common) perception of spatial dimensions. Three is triangulation, inflection, exponentiation, and curvature. Three is the operation and its result – a combination of the whole picture. Threes provide motion and non-linearity, a dynamic quality of life. Threes make twos unique and unbounded while making stronger our threads. Three is two and one together, forging balance and focus for strength.

Three is the strongest number. Geometrically, the triangle is the only shape that cannot be deformed without changing the length of one of its sides. Spatially, three provides dimension and perception. Three is our basic unit of existence and reality, and well, most of our buildings too.

Three also represents complexity in knowledge. If two is the threads, three is the knots. Three is multiple connections – knowledge with shape. Tie two threads together and you’re building new shapes, discovering new binds, making new questions for answers worth seeking.

And triplets are an optimization of our minds. Remember two things and you could have remembered a third. Try to remember four things and you are likely to leave one out. Triplets are an innate unit of the human mind, something by which we are all naturally bound.

Focus, balance, and strength. With three we find strength, and from three we derive balance and focus. Three qualities that make us better individuals, partners, and citizens. Three qualities that, if we learn to utilize and optimize through our life, will surely better our professional, personal, and spiritual lives.

And at the end of the day, numbers are an underlying language of life. We can look to numbers to represent many aspects of life – both physical and philosophical – to help understand how we interact, how we grow, and how to succeed. Looking at a simple sequence of numbers can provide insights that are easier to understand in a world of infinite space and color. Numbers help provide shape to our thoughts and can thread our understanding across cultures and generations. Now did somebody say math is boring? 🙂

Math Tricks, Negative Space, and Simple Beauty

Once again we start with two of my favorite things: soccer and math. I’ve talked about them both at length, for example in my “geometry in soccer” post from March 2009. Both are related by a similar underlying, structured framework. Both have rules, methods, and strategies for finding success, whether that’s solving a problem or winning a game.

What most non-players don’t understand is that despite the rules that govern both math and soccer, there are tricks to the game as well. These are the visions and insights that exist not within the simple rules and methods of an operation or a play, but rather in the negative space – the non-obvious space surrounding the operations and plays. You may find, more often than not, that recognizing these tricks in all aspects of life can provide the competing advantage necessary for happiness and success.

The soccer tricks will have to wait until after some knee surgery, so for now, I’ll stick with the math. There are thousands of known tricks in math, and probably an infinitesimal amount of unknown tricks waiting for an epiphany of recognition. Here’s an example:

Squaring Any Number Ending in “5”

Although this works for any number that ends in 5, it’s probably most practical for two digit numbers when no calculator is present. Let’s use 65 as an example, where we try to quickly compute 65 squared, or 65^2.

All you have to do is look at the number to the left of the “5” in the ones place. For our example, we have a “6”. Multiply this number by the number that follows it sequentially, which is “7” for our example. We get 6*7=42. To find our final answer of 65^2, all we have to do is take the result of our multiplication and append a “25” to the end of it, recognizing that the last two digits of the square of any number ending in “5” will always be “25”.

So for our example, we have “42” + “25” which gives us 4,225. The square of 65 is 4,225. Pretty neat, huh? Try it with some others…

25^2:     2*3=6,             “6” + “25”        = 625
95^2:     9*10=90,         “90” + “25”     = 9,025
475^2:   47*48=2,256, “2256” + “25” = 225,625

For a proof, I’ve looked to Dr. Math at the MathForum.org website. Here goes:

Let’s generalize a two-digit number ending in “5” by the representation X5, where X could be 1, 2, .., 8, or 9. Essentially, X5 is really a shorthand notation for the integer represented by

10*X + 5

Let’s go ahead and square X5:

(X5)^2 = (10*X + 5)^2 = (10*X + 5)*(10*X + 5) = 100*X^2 + 100*X + 25

Now factor our the 100 and an X from the first two terms:

= 100(X^2 + X) + 25 = 100*X*(X+1) + 25

Looking at this closely, you can see that this is exactly the product of X and the next sequential integer (X+1) with “25” appended to the end. Pretty cool, huh?

Notice that this trick works for squaring any integer that ends in “5”, not just two-digit numbers. Dr. Math shows us that for the the larger proof would have to be modified a bit (since all integers that end in “5” cannot be represented by 10*X + 5).

Seemingly Complex, But Beautifully Simple

Although the rules and structure of math may at times seem complex and chaotic, in the negative space of math we can find a beautiful simplicity through which things can fall in place. The same can be true for soccer, language, love, astronomy, cooking, and all aspects of life. Sometimes we’ve defined a framework (or have had it defined for us) of rules and methods to follow. But if we take a step back, look between the numbers and think outside the box, maybe we’ll find a simpler route to happiness and success.