I’ve been thinking about geometry a lot these days. What does the sparseness of a hyperbolic geometry feel like? Does hyperbolic geometry encompass Moore’s bowling ally? Does hyperbolic geometry and Poisson games encompass the core management issues? Lots of questions. It just compels me to learn more math, but much of that math hides the geometries, or explains everything from the comfort of the Euclidean geometry. The linear assumption of management includes the Euclidean assumption. We bumped into this in my last post, Depth of Value.

So, I’ve sketched up a quick graphical comparison of the geometries. I use the geometries: hyperbolic (H), Euclidean (E), and spherical (S) to show what a triangle looks like, the triangles of the Triangle Model. These geometries are blunt instruments.

They didn’t teach us this stuff back in school. They do teach it to high school students these days. We’re on the cusp of many new understandings. Oh, don’t blame out teachers. Mathematics teaching lags mathematics by about 50 years. Some of the mathematicians that produced the ideas we are just now hearing about are still walking the halls of academia, or died in our lifetimes. I am finding math textbooks at half-price books that have moved the ball. Yes, your kids know what a Markov distribution is and what to do with one. Great!

I’ve correlated the distributions we use with the geometries. A discontinous technology starts out as a Poisson distribution. It’s hyperbolic out in the bowling ally. The lanes are straight, like Einsteins light, and all that ensuing weirdness. That discontinous technology then crosses the chasam and moves into the normal distribution (6 sigma) of the vertical, a smaller normal in terms of standard deviations, sigmas, than the normal of eventual IT horizontal. These normals live in Euclidean space. Eventually, that discontinuous technology company is M&Aed into the huge public companies with the vast sigmas (30 sigma), the vast normal. The total probablity under that vast normal is still one, so the height falls, the margins thin, and you need a scraper to get it off the floor. The vastness still reflects the decisions constituting a decision tree, a triangle, but it bulges out of the confines of the Euclidean plane. Real options, strategic choices abound in the spherical, but not so in the hyperbolic.

Notice that the figure doesn’t include all eight lanes in our bowling ally. Three were enough for purposes. There is much more to this Poisson tending to the Normal and it’s visualization across an eight lane bowling ally and time. And, more again when you start to account for the layered structure of a media.

Somehow, we build a business orthodoxy based on the likes of Sloan’s GM. We teach that orthodoxy. We use linearity to discuise the spherical geometry under the hood. The gaps don’t bother us much. It looks like a nice generic set of tools, so we preach them as universals. We teach it to everyone. Then, we wonder why we can’t innovate. We blame the innovation itself, because we never blame ourselves, and never question the generalist, generics of our orthodoxies.

I defend innovation, because it builds the businesses the orthodoy milks, the cash cows. It builds wealth, wealth as something other than piles of cash, wealth that requires collaboration beyond the firm, beyond the cash flows of our own organizations and value chain. It’s how we make a world different from what we’ve known.

Continuous innovation doesn’t do the hyperbolic geometry. But, discontinuous innvaton will happen there, because discontinuous innovation is just part of product being used to foster adoption of that technology. The transition from Euclidean to Spherical still happens with continuous innovation, so even continuous innovation can find gains in the awareness of their geometries.

Mind your geometries.

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