Knowns, Unknowns, and Aether Abound

Much of our lives is about problems and solutions. Faced with a barrier, we find a way to knock it down. Presented with a challenge, we work to overcome it. Our collective problems bring us together, and our collective solutions make us safer, stronger, and happier.

These problems come in many shapes and sizes: math problems, career problems, logistical problems, emotional problems, physical problems. Rather than maintain special problem solving techniques for individual problem types, we can expand our methods into a global group, and learn from one type what may be helpful for another. Sticking with math – a common language and underlying framework of nature and intellect – we can relate our methods for solving math problems to the rest of the world around (and above us).

There is an innate simplicity to many math problems: there are knowns and there are unknowns. The solutions often reside in the application of methods and operators to the knowns to determine one (or all) of the unknowns. Therefore, the first step is often determining what is known and what is unknown. Although, this notion has been most popularly  represented by set theory (a foundational system of mathematics that deals with collections of objects), this concept has been the spark for other applied methods and disciplines through which many more complex problems are tackled in today’s society.

In game theory, a player’s strategy can be represented by differentiating the sets of moves that could make positive gains versus those that could make negative gains, given the possible situations at each stage of the game. Closely related is decision theory, where we look for the pros and cons, uncertainties, and rationalities behind potential decisions to determine an optimal course of action. In chaos theory, we define initial conditions and explore how the behaviors of some dynamical systems change as those knowns vary or as unknowns are introduced into the system.

To delve deeper into the questions of known-unknown identification, set theory, and related applied methods, we can think about a problem that began on day one, has no end in sight, yet has made incredible progress over centuries in terms of approaching a solution: what’s above us? What’s with the sky, the planets, the stars, the universe – the aether that surrounds us?

Is the total set of knowns and unknowns about the universe infinite? Does a new known always present us with a new unknown? Is the same true for every problem, or just some? For which types of problems might this be true? Are we better at approaching a solution collectively or as individuals? How can this be determined at the onset of a problem? If the set of unknowns has no limit or boundary, is the solution intelligently impossible? Does a single element of randomness deny a complete solution from every being possible? Are we better off existing without a solution? Or would we be complete with a world of all knowns?

I fundamentally believe that we find meaning in life through the unknowns, not the knowns. The set of unknowns is infinite, and it is our drive to understand unknowns and, in general, the curiosity into the mysterious world that provides completeness. The knowns give safety, guidance, comfort, and pleasure.

For all problems we face, and as with the aether abound, we can continue to move forward, learn what we know, and question that which we don’t know. We can start with sets – knowns and unknowns – and move from there. Problem solving can be simple, if you start simple. As for the things we don’t know we don’t know – the unknown unknowns – well, we better stay curious with the mysterious, and just be happy for that.

Curiosity, Passion, and Quantifying Human Characteristics

“You can’t light the fire of passion in someone else if it doesn’t burn in you to begin with.” – Thomas Friedman

In his The World Is Flat, Friedman speaks to the growing need for curiosity and passion in today’s job market. Core intelligence, as historically measured by the Intelligence Quotient (IQ), is and will always be important, but in a flat world it’s the curiosity and passion that will matter most.

Friedman references a Curiosity Quotient (CQ) and a Passion Quotient (PQ) that purportedly parallel the common IQ framework for scoring a person’s intelligence. More specifically, he expresses a comparative relationship between the three variables: CQ + PQ > IQ. But can curiosity and passion be measured like intelligence? More generally, can other individual characteristics be measured?

Traditional measurement is the process of obtaining a magnitude for a quantity. Things are measured by counting, and not by observation or estimation. It’s supported by strong criteria that support that measured value, such as a universal frame or scale of reference. By traditional measurement, we cannot really find CQ, PQ, or even IQ. However, there are other types of measurement…

In representational theory, measurement is defined as a correlation of numbers with entities that are not numbers. In information theory, measurement is actually a component of estimation with the uncertainty reduced infinitesimally to zero. Measurement means estimating through support of any number of measurable or unmeasurable parameters, and reducing uncertainty through various means until reaching a high-confidence end value. By the extended definitions of measurement, we can practically quantify anything!!!

So what do we get by measuring traditionally-unmeasurable human characteristics, emotions, abilities, and qualities? What do we get by identifying any new particular Qualitative Quotient (QQ) such as the CQ or PQ? Well, Friedman is on the right track here. We become smarter by surpassing our current understanding of intelligence. And as our QQs surpass the IQ, so does our ability to flatten the world, innovate, grow and succeed as a civilization and society.

The process of trying to quantify characteristics helps us realize the underlying factors that contribute to a specific quality. What makes someone passionate? How can we tell if someone is curious? Is it genetic, demontrated by experience, and exhibited sub-consciously? Can it be determined through the collective interpretation of dreams? Examining the underpinnings of qualities makes us more intelligent as individuals, organizations, and societies. Once quantified, we can look for patterns and trends in our data across different geographies, demographics, and slices of traditionally-measurable data.

What we’ll learn then, well, I’m curious to find out.

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