Author: Kevin Berardinelli

shapes and squiggles

Armed with a pencil and paper, you can simplify about 99% of the world’s problems.

Despite a couple decades of extra-substantial technological growth, there are two things that can never be replaced: the pencil and paper. For the toughest analytical challenges, only so much can be done computationally to simply and digest such problems. For these challenges, the solutions should start with a pencil and paper.

The first step in breaking down a problem is the conversion of the problem from the brain’s three dimensional space to a the two dimensional space of paper. In mathematics, there are several examples of such similar breakdowns: matrix decompositions, polynomial factorizations, projections, transforms, etc. The breakdown is necessary to see things in a new light, a simplified light, and a light that otherwise may not have been turned on.

Step 1. Grab a pad of paper. Do not put boundaries on where you can write and draw.
Step 2. Grab a pencil. Sharpen it and keep the pencil sharpener close.

So now that we have pencil and paper in hand, what do we draw? Well here’s my point. There is a geometric toolbox that provides a valuable framework for the problem solving environment. These are the shapes and squiggles.

1. Matrices

Two-by-two matrices are especially valuable for initial sorting of qualitative data. Assign a binary variable to each axis, name the cells, and define the relationships. Categorizing concepts and attacking each cell independently can help find hidden relationships and provide insight for subsequent analyses. See my previous post on matrix power for more on matrices.

2. Graphs

For more quantitative and scaled concepts, draw a set of axes to start. Visualize relationships between variables by drawing lines or curves and then attack each extremum and graphical sector. Plot knowns and/or hypotheticals on the graph and decipher the meaning of specific coordinates. Jessica Hagy’s blog ‘Indexed’ is a good example of translating mind to graph.

3. Lists and Mind Maps
The proper organization of information is often the most valuable visual tool in solving complex problems. Of course there are technologies to assist in the visualization and organization of information (mind maps, spreadsheets, etc.) but it’s important to use pencil and paper as the primary stepping stone to using some software/web app. Check out a mind map on different mind mapping software and a post on five great uses of mind maps.

4. Circles

Circles have shape and have a shape that is unique. They overlap well, fill space comfortably, and are easy for the human mind to spatially interpret. Eulerian circles (or Venn diagrams) are the simple example of circles put to use on paper for analytical means. There are several other adaptations of circles for comparative reasoning, such as with GL Hoffman’s “gruzzles”.

5. Doodling

The mind works in mysterious ways. Drawing without bounds can release otherwise inexpressible thought. There’s the somewhat structured doodling such as with UI mock-ups, schemas, and decision trees, and very unstructured doodling that might look like an impossible maze of dots and lines. The importance lies in the fact that your brain knows most about the problem, and the pencil is driven by the brain. Any new representation put forth on paper, by your brain, is a new representation of that problem not previously seen. In other words, “doodling allows the unconscious to render in symbolic expression”.

The shapes and squiggles live on. And the shapes and squiggles will always live on because they are the simplest yet most powerful functional tools our mind can use to express our conscious, subconscious, and unconscious thoughts.

matrix power

How much of your life can you fit into rows in columns? Well, enough of it for you to cherish the matrix as a valuable organizational and analytical tool.

Spreadsheets, tables, and matrices are used in every aspect of life. We track finances, monitor tasks, plan our future, and analyze potential relationships with rows and columns. And we are surrounded by this information as individuals, as part of small social groups, and as part of large organizations such as classes, companies, or governments.

More simply, matrices and tables give a new structure to elements of our life that are not always so two-dimensional. From the new structure, we can glean new insights and inspire new visualization of those same elements to make best-informed decisions. To me, a matrix is a valuable analytical tool that helps organize information for insight and action.

(Note that I am using the term “matrix” to represent that much more than numerical arrays of the math world. I am including categorical mappings, tables, lists, and spreadsheets too.)

The University of Cambridge Institute for Manufacturing nicely defines the matrix as an essential decision support tool:
  

“A two by two matrix is a useful tool for initial sorting of qualitative data. The axes should be chosen so that, e.g., the data with the most desirable characteristics will fall into the upper left quadrant and the least desirable in the lower right quadrant. While groups may be unable or unwilling to assign absolute values to qualitative data, they usually find it relatively easy to come to a consensus as to which quadrant something belongs in.

Generally, the two by two matrix is a useful tool for categorising things that can be reduced to two simple variables, particularly when quantitative information is unavailable and qualitative judgments must be made.

It enables a rapid clustering (or separating) of information into four categories, which can be defined to suit the purpose of the exercise. It is particularly useful with groups as a way of visibly plotting out a common understanding or agreement of a subject.”

Authors Alex Lowy and Phil Hood describe the matrix as “the most flexible and portable weapon in the knowledge worker’s intellectual arsenal”.

What’s best about the matrix is that flexibility. Depending on need, you can get as much power out of a 2×2 matrix as you can from a 5×5 matrix. Increased dimension does not translate to increased power. The matrix is flexible and dynamic to the needs of your analysis. You control the path to discovery.

And although matrices do a nice job of pairing categorical relationships, you can also translate these pairs to numerous other visualizations to better contextualize the information at hand. Turn your row and column headers into scaled concepts, map them to some x- and y- axes, and try and fit your qualitative information to a line that describes the relationship between x and y. Is the relationship directly proportional, inversely proportional, linear, parabolic, or along some other path? What do each of these types of relationships mean for your categorical variables?

It’s important to note that there can be fuzzy lines too. Not all cells need to have values and not all relationships need any sort of defined continuity. Empty cells and undefined relationships provide insights that are just as valuable as the populated and defined ones. Lack of data is data in itself, and that’s a great thing.

In the end, the matrix is just one part of the analytical toolbox and can provide a wide range of insight for your personal and professional life. Box up your data, organize it, visualize it, and use new structure to optimize your life.

Examples

Business/Leadership: Gartner, an IT research and advisory company, has created the “Magic Quadrant” to analyze types of entities in the business world. By plotting the ability (or inability) to execute against the completeness (or incompleteness) of vision, businesses can be categorized with those sharing similar characteristics, as Leaders, Challengers, Visionaries and Niche Players. This is a useful example of turning abstract qualities into groups for targeted strategy and decision making.

Product Development/Management: For analyzing how to grow a business from the product side, one matrix shows how plotting types of markets vs types of products can help guide that growth strategy.

Math/Statistics: Type I and Type II error tables are used to describe possible errors made in a statistical decision process. This is a great example of mapping relationships between categories, naming the cells, and using the matrix to understand what each cell represents.

update #3: this year in baseball

This post is related to the following previous posts:
Update #2: This Year in Baseball (October 5, 2009)
Update #1: This Year in Baseball (July 24, 2009) 
This Year in Baseball (February 22, 2009)

Well, here we are. Two days away from game 1 of the World Series. It’s about time I wrap up my predictions for the year and let you in on what to expect over the next week and a half.

My playoff predictions were filled with rights and wrongs. In the AL, although I predicted the Red Sox would have taken the Angels deeper than three games, I had the ALCS match up and result correct (Yankees in 6). In the NL, I was way off. I missed the NLCS match-up entirely. Part of that must have been my desire for the Yankees to avoid the Phillies. Silly me.

But here we are, Yankees vs Phillies. The first known is that the series will conclude in New York (Game 6 or 7). Neither team will let this be a short series. Therefore our options are now narrowed to four possibilities: Phillies in 6, Phillies in 7, Yankees in 6, Yankees in 7. The second known is that my love for the Yankees means more than any statistical analysis at this point. And so, my predictions:

Result: Yankees in 7
MVP: A-Rod (two game-winning hits)
Runner-Up: Cano (he’ll bat 0.450 with 5 RBIs)
Total Runs: Yankees 27 – Phillies 22
Other: Mattingly pinch hits in game 7 for a nice sac bunt.

Go Yanks!

life’s keys

life’s keys
by kevin berardinelli
october 20, 2009

There’s a key to being happy
etched deep within your soul
to find this key and use it
should be your lifelong goal

It’ll open doors to friendship
and show the world you care
life is only as pleasant
as the smiles that you share

There’s a key to finding love
found deep within your heart
the thump and beat will echo
when shot with Cupid’s dart

Although the road’s not easy
and the signs are never clear
embrace the path to get there
and the key will soon appear

There’s a key to growing old
found deep within your mind
a key to understanding
that starts with being kind

A simple thought or question
or lending a helping hand
reminds us that we’re all
a part of something grand

Though these keys may seem absurd
and taxing to obtain
the lesson here is crucial
and actually very plain

Look deep within your self
for guidance every day
your heart and mind and soul
will ne’er lead you astray

official st. calzone’s day 2010 announcement

And here we are, only five months away from another spectacular spring celebration of friends, food, and fun! I would now like to officially announce the date for the Seventh Annual St. Calzone’s Day celebration:

Saturday, March 20th, 2010
The venue is TBD, although, due to the great success of last year, there is currently a high probability that it will take place in Arlington, Virginia once again. The menu is by no means set, but I can promise there will be food and it will be good. I don’t think we’ll make another 15 pans of food, but will probably get some catered dishes supplemented by some homemade St. Calzone’s Day favorites: Spider Potatoes, Sausage, Peppers, and Onions, Beef Cutlets, Stuffed Shells,…
Anyways, mark your calendars for 3/20/2010 and I hope to see everyone for another great celebration!
With Sauce and Cheese,

life optimization through estimation

The ability to accurately estimate a target value is an asset to any brain. Learn to hone this ability, embrace it, and use it to optimize your life.

Our lives are surrounded by invisible data – most of it in units of time, energy, space, and money. Essentially, our brains are huge folded databases that store this data, and use it to make decisions, plan ahead, and live each day. But as with many types of data, there exists some uncertainty about that data. Unknowns about how long, how big, how much, from where, until when, should i, almost enough, maybe tomorrow… well you get the picture. Our life data is filled with unknowns.

That’s why estimation is essential. Without it we’d get lost, fall behind, and lose our sense of security and awareness. Whether we know it or not, our brains constantly work to estimate and approximate values, given set of life data at that moment in time. And whether we know it or not, our brains run predictive models to assess hypothetical scenarios, basically using present life data to predict future life outcomes.

These are important realizations, and strong connections of human nature to an innate mathematical realm. Estimation is both an art and a science, as it takes creativity and thought supported by various numerical methods. Having the mathematical ability to estimate proves useful in most situations, but without the artistic component, you lose the ability to understand and contextualize your estimation.

The main point here is that estimation should be embraced as part of human nature, supported by numerical methods. This is how we can optimize our life – by recognizing the units with which our lives are measured each day, and reducing as much uncertainty in those values as humanly possible. It will not make you completely successful and happy and secure, but it will get you close.

Examples

Here are some random examples of estimation from my life. The methods of estimation vary, but the fundamental questions being asked all have outcomes of an unknown nature.

1. Shopping: Budgeting $150 for a dinner party, break budget down to categories of purchases then allocate funds accordingly. Estimate totals and percent of total budget category to make decisions on necessity.
Outcome: Go bigger on the dinner and ask a couple guests to bring desserts.

2. Sports: Ten minutes left in the game, down by 2 goals. Have two full lines of players so will sub soon and again with 4 min left. Need at least 1 goal every 4 minutes leaving a 2 min buffer to protect the tie and go for a win, should allocate 60% of strategy to offense and 40% to defense for next 8 minutes. If I’m in for 6 min and need 60% offensive mindset, how inclined should I be to make a run towards the goal, leaving my defensive position?
Outcome: Win

3. Personal Finance: How much to take out at the ATM? Need to estimate expenses for the week – lunch, happy hour, gas, dinner, cab to meeting, etc. How often will I use my credit card? Am I more inclined to spend if I have cash? Will I be near another ATM this week if I need more cash? How conservative should I be in my spending given the holiday season is arriving?
Outcome: Take out $60 and bring lunch.

4. Daily Planning: Got a hour-long meeting at 3:30pm, soccer game at 6:30pm. Assuming there will be traffic, it will take me 35 minutes to get home then 5 minutes to change, 10 to heat up leftovers, 10 to eat, and 15 to switch and fold laundry. Need 25 minutes to get to field and 15 min to warm up. Will I have enough time if my 3:30pm meeting goes long or do I need to put off the laundry and/or dinner?
Outcome: Always put off laundry, but never dinner 😉

Links

Estimating how much gold there is in the entire world
Estimating how much money there is in the entire world
Estimating the height of anything using geometry
A bit about estimation in statistics

happy havens

We all need something – a haven – through which we can rid ourselves of stress and pain and renew our mind and body.

Stress is a part of life. So is pain, sadness and sorrow. There are times when we feel really small – when we don’t have an impact or don’t matter that much. There are times when we feel big – the world is closing in on us and we are at a breaking point. That’s when we all need to find a haven.

A haven is a place to go – physical, mental, or spiritual – where you come back to your own self, to your most simple and purest form. It’s a place of refuge or rest. It’s a sanctuary for your mind, body, and soul.

There’s a funny thing about life, that feelings can change in an instant. Good days can turn bad with a frown. Bad days can turn good with a smile. With that, we must know that when we are in a rut, there are places to go that can always pick us up and renew our spirits. Places where you can refresh yourself and turn you back into you. Places where you can root the weeds and plant some seeds.

A haven is…
…a place that spurs rejuvenating, creative thought.
…a person that gives you the love and joy found nowhere else.
…a feeling that, when absorbed, squeezes out the immediate stresses of life.
…a view that brings you back to the “big picture”.

A haven is not…
…somewhere to just be alone – havens can be for couples, families, and larger groups.
…one place or thing – it may be the right combination of feelings and surroundings.
…unchanged – havens can be dynamic through time.
…something you have to find – many times it will find you, at the right moment and right time.

A few havens of mine:
Seeing the stars at night or the sun at dawn.
Knowing and feeling love.
Thanksgiving dinner.
Funny dreams.
Fall foliage, cool breeze, mountains, and the serenity of nature.***

In the end, it’s important to know that these places and feelings exist, and that at many times in your life, happiness is only a haven away.

***Picture at top is from last weekend in Blue Ridge Mountains / Shenandoah Valley with Christine. The foliage and scenery were absolutely beautiful and we had a great time at Wintergreen Resort – highly recommend it!

forgetfulness is funny

i remember i was here
in this place at some time
the faces look familiar
though the memory i can’t find

i rummage through my brain
i think i’m getting near
and something sounds familiar
but the picture isn’t clear

did we exchange some words?
was i laughing at the time?
and now i stand confused,
rather chuckling at my mind

well i guess i’ll give it up
and move on to something new
forgetfulness is funny
so thank you, déjà vu

Image: “Colorful Cobwebs” (via the Kazuya Akimoto Art Museum)

cents and sensibility

The negative mentality around nickels and dimes needs to “change”.

Today at Starbucks I ordered a grande regular coffee which came out to $2.01. As I reached for my cash, the barista quickly said, “Don’t worry, I’ve got a penny. You don’t want 99 cents and I don’t want to count it.” My immediate reply was, “Well thanks, but it’s all the same.”

I laughed to myself as I left and thought about this some more. Why do people truly hate getting change? If you think about it, 99 cents is just a penny less than a dollar bill. And what do you do with the change you get? Don’t most people collect it in a secure place (jar, jug, can, pouch, piggy bank, etc.) to grow and cash it in later? It’s a nice, indirect way to save money (see Bank of America’s “Keep the Change” program).

I started to really embrace coins about five years ago when i began putting every penny from my pocket, the floor, the couch, or the street, in an empty Carlo Rossi jug. I’d save up change from the entire year and put it toward groceries used for that year’s St. Calzone’s Day celebration (it’s averaged $50-250 per year).

And to this day, I still enjoy getting change. I like not only the compact weight, circular shape, grooved edges, pressed terrain, and aging color, but also the curiosity around a coin’s travels. Dollar bills seem to always be accounted for whereas it seems as though 10% of coins are lost at any moment in time.

I think that negativity around change exists mostly due to disorganization (people feel they will forget where they put it, will lose it in a couch, or are not good at collecting it) as well as due to psychological effects (people think that collectively it’s less valuable than any dollar bill equivalents). I wonder if people, when estimating the total value of coins in a jar/bottle, commonly undershoot the actual value?

There have been some interesting economical studies that suggest (and support) a related theory – that people are more inclined to spend coins rather than dollar bills. Called “The Denomination Effect”, it supports the idea that maybe people want a dollar bill because they’ll be more inclined to save it rather than immediately spend four quarters on some Fun Dip at the gas station. Interesting studies.

Regardless, my point is that we should all learn to love change. The concept itself is a universal framework for brewing mathematical juices and collecting change can provide both a direct and indirect mechanism for saving money.