In this blog, I’ve wondered why discontinuous innovation is abandoned by orthodox financial analysis. Some of that behavior is due to economies of scale. Discontinuous innovation creates it’s own category on it’s own market populations. Discontinuous innovation doesn’t work when forced into an existing population by economies of scale, or economies of an already serviced population.

But, there is more beyond that. In “The Inventor’s Dilemma,” Christensen proposed separation as the means to overcome those economy of scale problem. Accountants asserted that it cost too much, so in the end his best idea did not get adopted. Did he use the bowling ally to build his own category and market population? No. Still, his idea was dead on, but not in the familiar way of separation as a spin out.

Further into the math, however, we find other issues like the underlying geometry of the firm evolves from a Dirac function, to a set of  Poisson games, to an approach to the normal, to the normal, and the departure from that normal. The firm’s environment starts in a taxi cab geometry (hyperbolic) where linearity is fragmented, becomes Euclidean where linearity is continuous, and moves on to spherical where multiple linarites, multiple orthodox business analyses, work simultaneously.

With all these nagging questions, we come to question of coordinate systems. Tensors were the answer to observing phenomena in different frames of reference. Tensors make transforms between systems with different coordinate systems simple. Remember that mathematicians always seek simpler. For a quick tutorial on tensors, watch Dan Fleisch explain tensors in “What’s a Tensor.”

In seeking the simpler mathematicians start off hard. In the next video, the presenter talks about some complicated stuff, see “Tensor Calculus 0: Introduction.” Around 48:00/101:38 into the video,  the presenter claims that the difficulties in the examples were caused by the premature selection of the coordinate systems. Cylindrical coordinates involve cylindrical math, and thus cylindrical solutions; polar, similarly; linear, similarly. Tensors simplified all of that. The solutions were analytical, thus far removed from the geometric intuition. Tensors returned us to our geometric intuitions.

The presenter says that when you pick a coordinate system, “… you’re doomed.” “You can’t tell. Am I looking at  a property of the coordinate system or a property of the problem?” The presenter confronts the issue of carried and carrier, or mathematics as media. I’ve blogged about this same problem in terms of software or software as media. What is carried? And, what is the carrier presenting us with the carried?

Recently, there was a tweet linking to a report on UX developer hiring vs infrastructure developer hiring. These days the former is up and the latter is down. Yes, a bias towards stasis, and definitely away from discontinuous innovation in a time when the economy needs the discontinuous more than the continuous. The economy needs some wealth creation, some value chain creation, some new career creation. Continuous innovation does none of that. Continuous innovation captures some cash. But, all we get from Lean and Open and fictional software is continuous innovation, replication, mismanaged outside monetizations and hype, so we lose to globalism and automation.

I can change the world significantly, or serve ads. We choosing to serve ads.

Back to the mathematics.

I’m left wondering about kernels and how they linearize systems of equations. What does a kernel that linearizes a hyperbolic geometry look like? Spherical kernels likewise? We linearize everything regardless of whether it’s linear or not. We’ve selected an outcome before we do the analysis just like going forward with an analysis embedding a particular coordinate system. We’ve assumed.  Sure, we can claim that the mathematics, the kernel makes us insensitive or enable us be insensitive to the particular geometry. We assume without engaging in WIFs.

Kernels like coordinate systems have let us lose our geometric intuition.

There should be a way to do an analysis of discontinuous innovation without the assumptions of linearity, linearizing kernels, a Euclidean geometry, and a time sheared temporality.

Time sheared temporality was readily apparent when we drove Route 66. That tiny building right there was a gas station. Several people waited there for the next model-T to pull in. The building next to it is more modern by decades.

This is the stuff we run into when we talk about design or brand, or use words like early-stage–a mess that misses the point of the technology adoption lifecycle, only the late main street and later stages involve orthodox business practices typical of F2000 firms. That stuff didn’t work in the earlier phases. It doesn’t work when evaluating discontinuous innovation.


Is the underlying technology yet to be adopted? Does it already fit into your firm’s economies of scale? Wonder about those orthodox practices and how they fail your discontinuous efforts?





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