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.
Update #1: 2010 MLB Baseball Season Predictions
Well not bad I must say. The AL East is tightening up although with news that Youkilis might be out for the season, the Red Sox seem to be fortunately getting farther away from the playoffs. Here’s how my predictions have looked so far:
Current AL East Standings (08/02/2010)
New York Yankees 66-39 (62.9%)
Tampa Bay Rays 66-39 (62.9%)
Boston Red Sox 60-46 (56.6%)
Toronto Blue Jays 55-51 (51.9%)
Baltimore Orioles 32-73 (30.5%)
Predicted AL East Standings (04/10/2010)
New York Yankees 101-61 (62.3%) -0.6%
Tampa Bay Rays 94-68 (58.0%) -4.9%
Boston Red Sox 92-70 (56.8%) +0.2%
Toronto Blue Jays 78-84 (48.1%) -3.8%
Baltimore Orioles 76-86 (46.9%) +16.9%
Average difference in prediction (absolute value, all teams) = 26.4% / 5 teams = 5.3%
Average difference in prediction (absolute value, w/o Orioles) = 9.5% / 4 teams = 2.4%
Predicted Playoff Bound (04/10/2010)
AL East: New York Yankees (Very Good Possibility)
AL Central: Minnesota Twins (Good Possibility)
AL West: Seattle Mariners (Not Possible)
AL Wildcard: Tampa Bay Rays (Very Good Possibility)
NL East: Philadelphia Phillies (Good Possibility)
NL Central: St. Louis Cardinals (Good Possibility)
NL West: Colorado Rockies (Slight Possibility)
NL Wildcard: San Francisco Giants (Good Possibility)
Predicted Most Valuable Players (04/10/2010)
AL MVP: Alex Rodriguez (Possible as he’s 2nd in RBIs, although it’s probably going to Miguel Cabrera)
AL Cy Young: CC Sabathia (Possible as he’s got 13 wins and a 1.36 WHIP, although David Price might be the best candidate right now)
NL MVP: Albert Pujols (Good Possibility)
NL Cy Young: Roy Halladay (Good Possibility)
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.
String Theory, Email Threads, and Happiness
Our lives are made up of millions of threaded 
moments in numerous conscious and subconscious dimensions. Identifying these threads – from multiple emails to time volunteering to a loving relationship – and making them last, making them stronger, and weaving them through multiple life dimensions is a key to health and well-being.
String theory attempts to relate multiple disparate concepts about our universe into a more unifying framework. Specifically, it states that subatomic elements (electrons, quarks, bosons, etc) are not three-dimensional objects but rather are one-dimensional strings that vibrate to take on semi-measurable characteristics (mass, spin, flavor, charge). Additionally, string theory posits that our universe is made up of unobservable dimensions that, at the most basic level, provide some sort of logical consistency to the known laws and theories of the physical (and metaphysical) world.
Well on a more macro level, our lives are very much made up of strings and dimensions. For our purposes, let’s just call them threads. Threads are made up of several connected points spanning one to many dimensions of our lives. These threads are our conversations, our friendships, our good deeds, our actions, and our spontaneous thought streams – the basic units by which we live our life. Our life dimensions are our jobs, families, friends, teams, systems, cultures, and countries, as well as our core knowledge, ideas, and feelings – the encompassing elements by which our lives fundamentally exist. And finally, our lives have outputs too! They are our health and our well-being, our happiness, our faith, our understanding, and the meaning we extract from the world.
Think about some threads of your life:
- Email Threads – Maintain a steady stream of
conversation to build new knowledge, ignite new thought, and establish a strong connection with someone. - Volunteering – Show up when you don’t feel like it, encourage others to work harder, and continually establish yourself as a reliable and dependable contributor to society.
- Love & Relationships – Always give to, and never give up on, the ones you love most in this world.
So now to the crux of my point: these life threads are the critical inputs to ensure our happiness and well-being are properly sustained, cultivated, and shared. By identifying these basic units, making them stronger, tying them together, crossing them through multiple dimensions of our lives, and “vibrating” the heck out of them, we can collectively share happiness and good faith as a society through better relationships, systems, and mutual understandings. Seems chaotic, yes, but in chaos there is a natural simplicity. Said the great thinker and founder of analytical psychology, Carl Jung: “In all chaos there is a cosmos, in all disorder a secret order.”
BBQ Boston Butt (Pork Shoulder) with Peppers and Onions
Difficulty: VERY Easy
Prep Time: 15 Minutes
Cook Time: 8 Hours
Description
First of all, read up on Boston Butt. It’s essentially a specially-named cut from the upper part of the front shoulder, and it’s the perfect cut for slow cooking. Best bet is to talk to the butcher. Don’t be embarrassed to ask for the best Boston butt he’s got. Virtually no prep here, flavorful as hell.
Ingredients
Pork Shoulder (4-6 lbs)
2 Green Bell Peppers
1-2 Medium Onions
Barbecue Sauce (2 bottles) – I used Sweet Baby Rays Honey Chipotle…
Other Flavors (Bourbon, Hot Sauce, Black Pepper, Mustard, etc.)
Directions
1. Slice the onions and peppers. Put half of them at the bottom of the crock pot, then put the pork on top of them, then put the other half of the peppers and onions on top/around the pork.
2. Throw a full bottle of barbecue sauce all over the pork. I used Sweet Baby Rays Honey Chipotle, but you can use whatever flavor you like best! I added other flavors too such as a little bourbon (or beer is good), fresh ground black pepper, mustard seed, worchestire sauce, and hot sauce. Cover and cook on low in the crock pot for 6-8 hours or until very tender.
3. Drain all the juice from the crock pot (I used a colander to do this) and remove the peppers and onions to whatever extent possible. Shred the pork in the crock pot by pressing a fork against it. I like mine pretty chunky but you can completely shred it if you want.
4. Douse the shredded pork with another half bottle of barbecue sauce and continue to cook on low in the crock pot for at least another hour.
5. Serve on potato rolls with the peppers and onions (and chesse too!) on top, with your favorite hot sauce. Eat as much as possible!
With regards to futurology and future studies, I’ve recently 
posted on the principles of forecasting as well as the origins of opportunity – two distant yet related topics that exemplify the breadth and depth of the field.
As my own futures research has progressed, I’ve found various sources that have proven to be quite valuable in guiding my curiosity and conjecturing. I think some of these are worth passing along:
- Acceleration Studies Foundation (ASF) – ASF is an educational 501(c)(3) nonprofit engaged in outreach, education, research, and selective advocacy with respect to issues of accelerating change.
- Futurology (Wikipedia)
- Institute for Alternative Futures – The Institute for Alternative Futures (IAF) is a nonprofit research and educational organization founded in 1977. IAF and its for-profit subsidiary, Alternative Futures Associates (AFA), specialize in aiding organizations and individuals to more wisely choose and create their preferred futures. IAF works with clients to create forecasts, scenarios, goals and strategies that are the essential tools for transforming organizations to succeed in times of rapid change.
- Institute For The Future (IFTF)
- Principles of Forecasting (ForPrin)
- Shaping Tomorrow – Online community of futurists and futures research
- Shaping Tomorrow (Ning Network)
- “The Time Lords” (Financial Times, 1/30/2007)
- World Future Society (WFS) – The World Future Society is a nonprofit, nonpartisan scientific and educational association of people interested in how social and technological developments are shaping the future. The Society was founded in 1966 and is chartered as a nonprofit educational and scientific organization in Washington, D.C.
- World Futures Studies Federation (WFSF) – The World Futures Studies Federation (WFSF) is a global NGO that was founded in the 1960s to encourage and promote the development of futures studies as a transdisciplinary academic and professional field in all parts of the world. WFSF operates as a global network of practicing futurists – researchers, teachers, scholars, policy analysts, activists and others from approximately 60 countries.
In a nutshell, futures studies is exactly that – studies 
of the future. It’s about the determining the total set of possibilities for tomorrow, finding the most probable of outcomes for tomorrow, and leveraging advanced knowledge to even shape the future.
Wikipedia, as spread across the spectrum of credibility as it may be, provides a pretty decent explanation of the mindset needed to be truly forward-looking. What qualities are required of a futurist, within any organization or for any requirement or need, to fully anticipate the unknown using the set of resources at his/her disposal (data, intuition, logic, technology, vision, science, etc.)?
- Trend Assessment – The competency to
understand trend directions, weak signals and wildcards, assess their likely impact and effect on one another and respond in a timely and appropriate manner - Pattern Recognition – The ability to see patterns rather than individual factors
- System Perspective: The capability to envision the entire system rather than the isolated components
- Anticipation: To anticipate short and long term consequences over time, novel situations and geography
- Instinct & Logic: To rely on a combination of instincts and logic rather than purely rational analysis
Yes, there is a plethora of philosophical, political, religious, scientific, and even incomprehensible factors that may give shape to the future (or take that shape away). But that should not deter us from facing it head on. We all need to work smarter not harder, avoid surprises, exploit new opportunities, plug weaknesses, and (where possible) influence the future.
As the World Cup approaches, countries begin to solidify their rosters, trying to optimize their squad to give the best chance of taking home the FIFA trophy. As the Bob Bradley recently announced the United States’ 30-man roster, we wonder where these players come from and how can their stats be visualized?
Obviously, it would be most valuable to visualize comprehensive stat sheets of the U.S. team players against all other teams and their players, especially the others in Group C (England, Algeria, Slovenia). Unfortunately, I don’t have that much time! So, elementary as these may be, here are some quick visualizations, given the data provided on the US Men’s National Team (USMNT) website.
1. Full 30-Man Roster, with Hometowns, Club Teams, and Total USMNT Goals (by Position)
2. Player Experience (Age vs Total Caps, by Position)
3. Player Size (Height vs Weight, by Position)
Some things to note, although I have not determined an international baseline from which these conclusions can be definitively made, is that our goalkeepers are old and our midfielders are relatively small, young and inexperienced. But I bet you didn’t need me to tell you that!
Regardless, the World Cup is surely a global spectacle and I’m very much looking forward to it. Hopefully the US squad can take Group C and show some true grit and determination on the international stage. Four weeks to go…
The Origins of Opportunity
I’ve been deep into future studies / futurology over 
the past few weeks. It’s an intriguing field for me at both a professional/academic level and a personal level. How can we better understand the future? Are there core methodologies that we can employ to optimize our current positioning and decision-making? How can we be better prepared for the future? What’s inevitable and what’s not? Where lies the line between info-driven forecasting and innate intuition?
Although the netweb has helped to grow and organize both the futurological information and the community through which that information is developed and shared, it seems as though the field itself remains cloudy. I must hope that at some level I can build upon the existing thoughts of others and contribute new thoughts of my own so that at least the window to the future becomes more clear.
One cornerstone of future studies is in how to evaluate, filter though, and create opportunity from statements about the future. And so I wonder: from where does opportunity arise, and how can this recognition be leveraged to inform (and in some cases, influence) the future? In general, how can we characterize the origins of opportunity?
- Is it through early recognition? This is not beating others to the finish line, but rather beating others to the starting line. Can we identify gaps sooner than others?
- Is it through resourceful timing? Often opportunity arises in not being first, not being last, but somewhere in between. The earliest adopter may have his/her vision obscured through too many details, the latest adopter may be left with the crumbs. And often we find much opportunity in the failure of others – developing the right trials from the errors of others.
- Is it through pure knowledge and intelligence? Can brute force brainpower create the most opportunity? Or is it more dependent on the ability to apply one’s knowledge, no matter how limited it may be? Is it about having the right skill sets and tools, tactics and strategies?
- Is it though pure luck? Can being in the right place at the right time govern our ability to find and harness opportunity? Is pure luck within our beyond our control?
It’s simplest to think that opportunity may arise as a result of any combination of these factors. Therefore, to maximize our opportunities, we should focus on being in the right places, having the right tools, being with the right people, understanding timing as an approach, building the right knowledge base, and building an overall recognition for the many faces of opportunity.
If we can learn to recognize opportunity and better understand where it may arise, we can begin to gain a better picture of the future. Then, we can work to inform that picture with data and models to ensure that we take full advantage of those opportunities to better our self, our communities, our world, and that of tomorrow.
What’s The Difference?
Okay my baseball-ish golf swing could use some work! My pic was from East Potomac Golf Course (Blue) on 4/11/2010 (thanks to Benny T for the pic). Round 2 of the 2010 season is in two days so we’ll see if I can improve on my +16 round (88 total). This time it’ll be at Penderbrook Golf Club in Fairfax, VA.
