**Skewness Risk**

This week, I visited the Varsity Bookstore, the off-campus bookstore for Texas Tech. I looked at a statistics book, sorry no citation made, that said skewness was about how much the normal distribution leaned to one side or another. When it leans, the mean stays put, but the mode moves by some angle theta. My last blog post on kurtosis mentions theta relative to one of the figures.

The notions of skewness risk and kurtosis risk came up during the work on the earlier post. It took this long to find some details hinted at in places like Investortopia. The thick tails dive under the threshold for extreme outcomes. Even with a black swan, there isn’t that much under the threshold. The negative skewness graph shows how the large losses move the convergence with the horizontal asymptote towards the present. The same thing happens with small losses possibly with the same extent horizontally, since the longer tail magnifies the small loss.

Notice that on the left side of the normal gains happen; on the right losses. Moore’s technology adoption lifecycle similarly shows the left to be growth and the right to be decline. What saves the right tail is that an acquisition is supposed to bring a 10x multiple into play, but that requires the acquirer to play the merger tornado game. That game is not played well if it is played at all. Most acquisitions provide exits to investors tied up with interlocking directors and funds.

The skewness happens because the distribution is tending to the normal, but at the moment captured by the data underlying the distribution data is missing, and the data is not normal. Once the data is captured, the normal will stand upright and centered without skewness, and without skewness, there is no kurtosis.

**S-curves**

Since I’m on the road, I’ve left the bookstore behind that had a book by a venture capitalist or strategist, no citation, no way to find this book again. But, the author said he didn’t see the relevance of S-curves to the companies in his portfolio. Well, most of those firms are built on commodity software, so they are long past the upsides of that software. Consumer software still commoditizes and that brings a black swan, a missed quarter to the stock price. When that commoditization happens, the underlying software has to be replaced with a better technology. Replacing it is an s-curve play by the seller of that technology, not the users of that technology. Most of his portfolio would be users of, rather than makers of underlying technologies. Simple fact, in the late phases of the technology adoption lifecycle, declines in stock prices, hope for a merger upside, no premium on IPO, and nobody dealing with S-curves is the norm. Oh, and the whole thing being about cash. You get rich in a upper-middle-class way, but it’s too late to create economic wealth. Confusion between early stage financing and early phase adoption is rife. Talk of early adopters is not in the Moore sense, but the Gladwell since. And, no chasms exist to be crossed. So yeah, no S-curves.

S-curves confuse disruption in the Foster sense because they can be temporary if the innovation’s s-curve slope slips below that of the incumbents. Foster put causes before effects where Christensen focuses on effects absent cause. In the 80’s and early 90’s nobody was overserved. It just turned out that the technology left everyone overserved. The small-disk manufacturers were not competing with the large-disk manufactuers. They just served their markets and the markets got bigger on their own. Alas, the old days.

Kurtosis, defined by curvature hinted at defining s-curves in the same way. Curvature is implicit. Mathematically, the curve defines the curvature. We cheat when we claim curvature is the reciprocal of the radius. We don’t know where the center is, so we don’t know the radius, thus we don’t know the curvature. There probably is some software somewhere that can find the curvature.

The red line is the s-curve. The blue horizontal line shows where rapid improvement gives way to slower improvement. The line also shows where investment is cheap and where it become increasingly expensive. The large circle gets larger as we go and shifts its center down, so we get a slower and longer curve. At the top of the large circle, we’ve transitioned to that 10x returns if the merger was actually successful.

The s-curve tells us how much change to expect. If you had the s-curve for every contributing technology, then you would have some notion of the rates of change you could expect. We overstate change in our conversations, particularly when we talk about the s-curves and rate of change of the carried content.

**Convergence and Divergence**

In today’s reading of “Concepts and Fuzzy Logic” by Radin Balahlavek, and George J. Klir, eds. As editors, the goal of this book was to foster a return to the use of fuzzy logic within the disciplines of the psychology of concepts and mathematicians. I’ve always seen ideation as being convergent or divergent, but over the life of a conceptual model, there are several convergences and divergences. The editors here sought to foster a return to a convergent conceptual model that previously converged and later diverged.

So we start with the verbs, with the tokens with which we parse the adoption of the discontinuous innovation. The drivers at this stage are those driving bibliographic maturity. We converge or diverge. In the converge, we merge separate disciplines. The conceptual model being adopted is the platform technology, the carrier. The disciplines bring their carried content into the mix. The carrier is under adoption, and the new found applications in the discipline in the carried is under adoption as well. Those applications make the business case of those in the current and near-term pragmatism steps. Those applications and the business cases will change as we approach the mid-term and long-term pragmatism steps.

In a product, care must be taken to the pragmatism steps. Like pricing bifurcations due to communications channel isolation, the business cases are specific and the reference cases that will be adopted by a population on the pragmatism step are likewise specific. The early adopter’s success will not drive laggards to buy. But, that the macro view of adoption phases where pragmatism steps present the micro view.

We start with two populations. Each adopts a conceptualization at their own rate. Each has its own reference bases. Once adoption begins, a third population emerges, the adopters. People entering either of the disciplines involved after adoption begins can adopt the idea immediately. This is more pronounced when the conceptualization under adoption is discontinuous. Do students of SEO ever get around to print, or worse focus groups?

In the case documented in the book, mathematicians (yellow) worked their way towards fuzzy logic. They took the path of the continuous innovation. The psychology of concepts researchers (red) found fuzzy logic and it solved some of their problems, so it was adopted, but they were not working with mathematicians to accelerate the use of fuzzy logic.

Publication in these populations motivates adoption. Those peer-reviewed papers constitute the touchpoints in a content marketing network. Publication is likewise and event. Adoption and de-adoption are fostered by events.

In every adoption, there are collaborators and defectors in game theory speak. At some point, a defector succeeded in publishing some claims about how fuzzy logic couldn’t do this or that. These claims were accepted uncritically among psychology of concepts researchers. That led to the de-adoption of fuzzy logic by that population. De-adoption happened only in the psychology of concepts population driven by the publication of that defector’s claims. This went unnoticed by the mathematicians working in the same space. Again, like price communications isolation providing opportunities, discipline-specific communications channels provided the isolation here.

At least in this convergence, the two disciplines were not putting each other down like the demographers and ethnographers involved in ethnographic demography were. I can’t find that post mentioning that behavior. It doesn’t help that this blog has stretched across three blogging platforms. But, the behavior is typical. Those converging will be some small portion of the contributing domains.

Mathematicians continue to develop fuzzy logic to this day.

After de-adoption, a researcher looked at the claims and found them to be false. This led the editors to realize that they needed an intervention. Their book was part of that intervention. That accelerated readoption.

Realize here that in the readoption, the base population has changed, and the concepts being adopted have changed as well. The mathematicians widened the conceptual model to be readopted while the psychology of concepts researchers were gone.

Looking at the underlying populations, the psychology of concepts population had not completely adopted fuzzy logic, nor did that population completely de-adopt. Those later in the adoption lifecycle never bothered with fuzzy logic. They didn’t go through de-adoption. They did go through readoption eventually.

One of the messy things about the normal distribution representation of the technology adoption lifecycle is that adoption happens in a time series. The population is spread out along that time series. The timeline moves left to right. Each sale, whether by seats or dollars moves one down the timeline. B2B sales moves are huge. The mean becomes the marker where fifty percent of the seats have been sold. The growth side of the curve ends with the seat sitting at the fifty percent mark. This timeline is present regardless of skewness or kurtosis.

The timeline starts with the Dirac function providing the potential energy that drives the lifecycle. After the Dirac function comes the Poisson games. Then we move on to the convergence with the normal via sample populations of less than thirty, in statistics, these are Poisson approximations of the normal, which leads us to skewness and kurtosis. Once the sample populations are over thirty, we have a normal that is not skewed. Risks become symmetric. This normal is one of a series of three normals: vertical (carried), horizontal (carrier), and post-merger (whole media, both). The standard normal hides the relative sizes of these normals.

The three normals give us a hint towards Moore’s three horizons, which turn the technology adoption lifecycle around. The horizons look at the technology adoption lifecycle in the rear-view mirror as if they are right in front of us. Maybe a backup camera view is a better perspective. The B2B early adopter is barely seen or focused on. It is inconsistent with the present horizon.

Anyway, those two populations are now a third happily solving psychology of concepts problems with fuzzy logic. The defectors lost. The price-performance or s-curves make the case for adoption. Other things make the case for de-adoption, and readoption. The editors here demonstrated the role of the intervenor, or in most cases, the near-monopolistic, market power positioned, market leader that so many programmers abhor. That market leader does much to make the category happen and thrive.

So what is a product manager to do? Start with understanding the conceptual models that comprise your product. Understand the adopting populations for each. Those populations are not on the same page and don’t adopt at the same rates. Those domains do not inject change into your product at the same rates. Those populations might be deviating away from your product due to de-adoption of the underlying conceptualization. Yes, get someone to stay on top of the changes in each of those domains even. Know when a defect and defection is happening. That defection might disrupt you. That’s classic in the sense of how the hell would you, the product manager, have known. It’s not about competition. It’s about conceptualization. They change. They oscillate. They own you and your product if you’ve taken them into your product or service. They happen in the carrier and the carried of the media we play in.

Likewise know your s-curves, aka your price-performance curves. If they touch your product, know them. Sure, you can’t deal with the fabrication plant investment issue, but it will throttle your product if you need that fab.