Descartes, the discoverer of analytical geometry, wanted to eliminate all assumptions from his thinking. So he stripped away every belief that he couldn’t prove. He was left wondering whether he truly existed. For a long time.... Finally, he discovered, "I think, therefore I am!" But philosophers since then have countered, ‘just because you’re thinking doesn’t mean you exist. You may be dreaming you are thinking!"

What does this interchange teach us? That a large part of what we accept as true, is only firmly held belief. Widespread, supported by our peers, but belief and assumption, nonetheless. Yet it’s true that in essentially every field of study, little of sense and significance can be declared without some basic assumptions.

Thomas Kuhn claimed, in The Structure of Scientific Revolutions, that scientists are influenced more by their culture’s assumptions than the facts before them. The uproar within scientific circles forced him to recant shortly before his death. In the future, Kuhn’s recanting may become as reprehensible as Galileo’s.

But his book served to popularize the term "paradigm" to explain the foundation of assumptions that is so necessary for ordering our thinking yet, in time, can become so restrictive to our progress. Often our only route into the future is blocked by our assumptions that we must blast our way through in order to progress.

Imagine that you want to climb a mountain in the fog. You can’t decide where to start, and a hundred pathways beckon. So, you climb up on a boulder to get a better view. Indeed, the fog does part somewhat, allowing you to see which boulder to climb onto next. Do you feel bad leaving behind the first boulder that helped you to see better? You shouldn’t.

Paradigms are like boulders. They help us greatly if we use them to see better and then move on. They become barriers to progress if we become attached to them.

Lorentz derived two solutions for his famous equation. One made sense, and one didn’t. So, he discarded the nonsense. Einstein looked at the "impossible" solution and asked, "What if?" The theory of relativity was the result of his musings into the impossible.

New paradigms are born when we pay attention to data that don’t fit.

But, the desire for order is so strong that when the data don’t fit our paradigm, we call it an "outlier" (bad

data), or we stretch and patch the paradigm to include the new data. Our ability to distort a paradigm to keep it alive is as creative (and foolish) as a child explaining away a stolen cookie grasped in his own little hand. As a consequence, the data that should lead us to the next paradigm are hidden, or filtered, within the existing and bulging paradigm.

People seldom seek out the new paradigm until the existing one is torn apart by the pressure of facts that don’t conveniently fit. Finally, the new paradigm rises to ascendance after long emotional conflict between the two polarized groups of defenders (one defending the old paradigm, and one the new).

Why not avoid the conflict by refusing emotional attachment to the previously successful paradigm? Better yet, why not enter into continuous search for valuable new paradigms without battle and polarization?

There are two pathways to progress: 1) slow, tedious discovery and verification of new facts, and 2) recasting the existing facts into a new paradigm. As the old paradigm ages, the facts that don’t fit are ignored or crammed into it producing little, if any, accompanying insight. So, when these ill-fitting facts are allowed freedom of expression within the new paradigm, they speak volumes. Insights flow fast and freely within a very short time. Hence, we have a quantum jump or stunning increase in progress shortly after the new paradigm is accepted.

A tiny drop of water is a universe in chaos. All the water molecules are oriented randomly, each exerting little control over its neighbors’ orientations.

However, as the water temperature drops, a strange thing begins to happen. The molecules become more orderly, each molecule exerting its influence on many molecules further and further away. Finally, under the right conditions, an intricately designed snowflake emerges, with the right half duplicating the pattern of the left half, though it is a million molecules away.

Paradigms are like snowflakes: They bring order to chaos. However, if your universe is that one snowflake, how do you create something new and different from the water in the old snowflake? You must melt the snowflake... You must introduce chaos.

Our humanness abhors chaos. We want to preserve the order and beauty of the first snowflake. Once we ~ recognize the limitations of the first snowflake, we might tolerate minor changes. We don’t realize that our ability to construct is limited by our ability to deconstruct. The more chaos we can tolerate in our thinking, the greater the potential win we can create.

The college professor enjoyed taunting his students. "Come on! You can solve the maze quicker than that!"

Each student would strain his mind and manual dexterity to move the ball more quickly through the maze.

"Even my grandson is quicker than that!"

Finally, as each student gave up, the professor would lift the ball out of the maze and place it at the destination. "See, only takes a second!"

The professor, and his grandson, were using 3-dimensional thinking in a 2-dimensional universe. In a 1-dimensional universe with 1000 pieces, it can take up to 1000 moves to locate a particular piece. In a 3-dimensional universe, any one piece is no more than 10 moves away from any other. (Think of a cube with ten pieces to a side for all three dimensions.)

Ways to add a dimension to your universe are: acquiring a fresh perspective, stepping away from the problem, changing the problem, or moving outside the constraints you’ve unnecessarily imposed upon yourself (as the college students did with the maze).

Einstein said, "Pick what you would like to be true, and prove it."

A fellow scientist challenged me, saying, "But, that’s not objective!" I responded, "If you remain objective, you’ll support the current paradigm, because that’s what all your peers and all the (filtered) data support." Unless you’re willing to attack thc existing paradigm with all the strength of unfounded conviction (and no data yet), you won’t even call it into question, much less, change it.

What does the boulder teach us? Today’s solution may be tomorrow’s hindrance. After five years, half of Tom Peters’ "excellent companies" had failed, using their succes4ul but dated, solutions. Many high-yield mutual funds become next year’s loss leaders, tied to past successes.

Get a pen or computer and note your past successes. Keep in mind that you see only one implementation of these successes. A small change in parameters may have given you even greater success. The road untraveled might have been better. Now treat each success as a roadblock to a better way. And, find the better way.

Snowflakes teach us that beauty and success should not be barriers to progress. And, a little bit of chaos is good. A lot of chaos is better.

Take a moment to write down the absolute truths of your universe.., your business.., the arena of your problem. What would your universe be like if that truth were not true? For a moment, embrace chaos.

How does the right side of the snowflake know how to duplicate the left? It just lets nature take its course. So too, in creative companies, less control is better. In creative individuals, allowance for intuition, gut instinct, and other "non-logical" mechanisms must be respected.

We can all produce arguments for why full-time chaos is bad. However, creative success is a delicate and delicious balance of chaos, insight and analytical persistence bringing new order into existence.

What does "N+ 1" dimensional thinking mean? Look for the edge, the key; the advantage. Look for the different perspective. Don’t be afraid to explore uncharted nonsense (for it will seem nonsense until you explore it).

Does this mean we must value change for the sake of change? No more than we would value the status quo for the sake of stability. But, we must explore and test, implementing tomorrow’s solutions before we have proof of their value.

At this point, you might be thinking I’m advocating the absence of all boundaries and a new anarchy. Actually, I’m trying to stress the point that many of our "facts" are merely beliefs and assumptions.

But, we all must have assumptions, or values, that we refuse to challenge. Otherwise, we would be on the same level of Descartes, arguing whether we existed or were only dreaming.

These assumptions give us the foundation upon which we can construct our higher logic. Look around you. Many very intelligent people have disparate logical structures that can never be reconciled with your own, based upon driving foundation assumptions (e.g., "God is" or "The mind is an accurate determiner of truth"). Permit me to use my own "values" as an illustration. In my mid-20s, I switched from agnosticism to fundamentalist Christianity. Since I was already committed to a scientific career by then, this put me at odds with much of the "truth" in science. However, even in my pre-Christian days, getting my Masters in Nuclear Engineering at the University of California, Berkeley, I noticed the fragility of scientific "truth."

My willingness to question the "absolutes" over the years has allowed me to make many contributions to my field that I otherwise wouldn’t have had the courage to undertake. For over 20 years, I’ve been predicting the future for the US government. During that time, I have encountered many intolerant people who treated their every belief as a universal truth. I found that this insight—that we often have a flawless logic structure resting upon unprovable assumptions—is useful in routing out faulty paradigms.

Test the following to see if they are "true" and consistent with your logic structure:

1. Our inability to distinguish between truth and belief keeps us locked within faulty paradigms or foundation assumptions.
2. The usefulness or success of a paradigm isn’t a proof of its truth or future value.
3. Cultivate the ability to question, introduce chaos constructively, and treat "truth" objectively and unemotionally.
4. We all must select, without guilt or question, those assumptions we value as our life’s basis. Give careful thought to these "unquestionables," for they structure the course of your life.
5. Handle the truths of others with care, especially when they’re different from your own. After all, they might be right.