## More on Innovation Visualization

Revisiting the exponential-polar representation, discussed in Innovation Visualization, I’ve expanded the representation, and found surprising extension to the long tail/power law version, discussed in Cognitive Models on the Efficiency Frontier.

In this figure, I drew the exponential-polar representation for a series of three successive disruptive innovations. Then, I drew a chord across the arc representing delivered functionality before and after the threshold of disruption. I was going to try to put a conceptual model along the chord, but using the long tail/power law distribution as a shorthand for the logarithmically distributed conceptual model instead.

Log scale polar representations and commoditization thresholds and the clipping of the power law distribution of the conceptual model

The chord is shorter than the length of the arc. I’ve not drawn the circles whose diameters would represent commoditizations of the underlying technology. It turns out that the chord clips the long tail/power law distribution. Where this clipping occurs varies, but it happens well before the S-curve reaches it’s ceiling, which translates to both axes of the power law distribution.

Power law or Parento distributions exhibit a 80/20 split. In the long tail interpretation, the first 20 percent represents the hits, the remaining 80 percent represents niches. Translating this to the frequencies of feature use in an interface means that the first 20 percent is whole product partners and infrastructural elements. Some of that 20 percent may be the most frequently used features that a vendor provides. In SaaS, that first 20 percent would be browser, server, and Ajax. The rest of an applications features would be distributed down the tails (x and y axes). The vendor provided features encode an underlying conceptual model, which brings us back to the context of the earlier posts.

Another feature of all statistical distributions is convergence. A Poisson distribution converges earlier than a normal distribution. A long tail/power law/parento distribution converes much later than a normal distribution. This later convergence implies that there is always room for more features or concepts under a long tail.

The S-curve for paradigm C, the third disruption in the sequence is shown at the upper right. I’ve drawn the threshold of commoditization on that S-curve. There is always more development beyond, aka above, the threshold, but it is no longer profitable. A vendor would change their vector of differentiation at this point, which brings another technology into the mix and changes the focus of the marketing messages. Commoditization occurs when the customer is no longer willing to pay for improvements in a given technology.

Since customers are no longer willing to pay for more improvements in a given technology, you can think about it in terms of customers not being willing to pay for more features related to that technology. This implies that a feature distribution along the long tail would be clipped, and that both the x and y axes would be clipped. A vendor may have already created features beyond the threshold. There is no reason to removed them, but there is every reason to stop adding features.

This could have been Rick Chapman’s argument about not having a product manager for SaaS applications, along with the notion that in late market, costs must be minimized, hence investment in continued development would be minimized. I know that I still use Web 1.0 sites where I pay a subscription. Things that were broken long ago are still broken.

The blue arrow under the clipped long tail is the vector of differentiation related to the clipped long tail.

Clipping the long tail likewise clips the application’s underling user conceptual model. The frequency of use of a given feature also implies the the frequency of use of the concepts related to that feature.

It might be rare to see an industry undergo three successive disruptions, but functional units with staff subscribing to three or more paradigms is less rare. In cost accounting, as far as I know, you have traditional, ABC, and throughput accounting paradigms. Each of these paradigms serve the purposes of providing accounting data that managers rely upon for managerial decision making, but while they serve the same purposes and same managers, they approach and originate data from very different places and perspectives. Each paradigm has its own conceptual model. ABC cost accounting is build on top of traditional cost accounting, but variablized the once fixed categories that costs are assigned to.