A Spatiotemporal View

A few days ago I pulled Using Business Statistics by Terry Dickey off the shelf of the local public library thinking it would be a quick review. It’s a short book. But, it took a different road through the subject.

Distance, the metric of a geometry, is the key idea under statistics. Like the idea that the distance of a z-score from the mean is measured in standard deviations. A standard deviation is an interval, a unit measure. Variance is a square, an area. And, area is the gateway to probability.

Using the standard deviation as a unit measure, we can mark off the x-axis beyond the convergences of our distribution, and use that x-axis as the basis of our time series. I’ve used this time series idea under the technology adoption lifecycle (TALC), so looking at our past and our future as fitting under the TALC is typical for me.

That was the idea, so I tried it, but the technology adoption lifecycle is really a system of normal distributions spread out over time. The standard deviations for each of those normal distributions would be different. They would be smaller at first and larger later.  The geometries for each of those normal distributions would be different as well.

Smaller and larger are relative to the underlying geometry and our point of view. In the early phases of the TALC, the geometry is hyperbolic. Now appears to be big, and the future appears to be smaller and smaller, so projections will underestimate the future. Hyperbolic geometries also give us things like a taxicab geometry with it’s trickier metric, which brings with it much risk, and the world lines of Einstein. Things are definitely not linear in hyperbolic geometries.  Across the early phases of the TALC, the Poisson games of the early adopter phase tend to the normal, and the geometry achieves the Euclidean at the mean of the TALC. Moving into the later phase of the TALC the geometry tends to the spherical. Spherical geometries require great circles, but provide many ways to achieve any result, so analyses proliferate–none of them wrong, which makes things less risky.

All of those geometries affect that unit measure on the x-axis.

Discontinuous populations generate multiple populations over the span of the TALC, so the statistic itself changes as well. That is what drives the proliferation of standard deviations. Our customer population is small and our prospect population large. The customer population grows with each sale, with each seat, and with each dollar, and similarly the prospect population shrinks with same. It’s a zero sum game. The population under the TALC is fixed. That population is about the underlying enabling technology, not some hot off the presses implementation of a product or a reproduction. Products change as the adoption of the underlying technology moves across the populations of the TALC.

Big data with it’s machine learning will have to deal with the population discontinuities of reality. For now we will do it by assuming linearity and ignoring much. We already assume linearity and ignore much.

Across the TALC, pragmatism organizes the populations. That organization extends to organizing the customers as people and companies. Using negative and positive distances from the mean, similar to +/- standard deviations from the mean, we can place companies and their practices under the TALC. We could even go so far as to break an organization down to the individual executive and their personal locations on the TALC. Even an early adopter doesn’t hire a company full of early adopters.

Delivering functionality is an early phase phenomena on the negative standard deviation side of the TALC. Design is a late phase phenomena on the positive standard deviation side of the TALC.

B2B early adopter and crossing the chasm is early phase. But, why mention that? Well, I’m tired of hearing them show up on the opposite side of the mean out here on Twitter. The consumer facing SaaS vendor is not crossing the chasm. And, their early adopters are B2C. Confusion ensues. Place gets lost. I should ignore more.

Thanks to Jon Gatrell’s comment on The Gods Must Be Crazy post for pulling me back to this blog. Another recession has intervened in my job search, so I’m still looking, but there’s nothing to find, so there is no reason to focus on that search to the exclusion of writing this blog. Thanks for letting me know that someone still reading. WordPress stats don’t tell us much.



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