Archive for May, 2018

Kurtosis, Another Definition

May 31, 2018

Tonight, I came across a third definition of kurtosis. This definition begins at 25:30 in Statistics 101: Is My Data Normal. This source defines kurtosis as a distribution having higher than expected probability mass in the tails. Compare this to the typical definition, this one returned from a Google search, the sharpness of the peak of a frequency-distribution curve, which I’ve not used since I found kurtosis to be the curvature of the tails. See More On Skew and Kurtosis. I’m still lost as to how the kurtosis statistic translates into the curvatures of skewed distributions. Complicating the curvature issues is that in an n-dimensional normal, there are more than two tails. There does seem to be a pattern of curvatures as defining a torus for a normal without excess kurtosis or ring cyclide for a normal with excess kurtosis. The torus fits flatly on top of the tails of a normal parallel to the base plane. The ring cyclide sits on flatly on top of the tails, which is tilted in regards to the base plane.

This third definition of kurtosis is nicely quick to grasp. The typical definition seems to be confused with n, the number of data points. With little data, the normal is thin, high, and has two short tails, given the absence of skew. With a lot of data, the normal is wide, lower, and has longer tails, given the absence of skew.

I have not gotten to topological data analysis and the issues of what the torus or ring cyclide is telling us.


The Technology Adoption Lifecycle

May 24, 2018

A while back I wrote about all the so-called Chasms. These days we begin our continuous innovations in the late mainstreet. Nobody crosses the Chasm.

I was working on watching a data from a pseudorandom generator for a normal distribution converge to a normal. That is supposed to happen by the time you have 36 data points. It didn’t happen. And, it didn’t happen by the time I plotted 50 data points. It didn’t help that I had to generate more data after the first 36 data points.

I made a mistake. Each call of the generator starts the process off with a new seed, aka a new distribution, so of course, it doesn’t converge. I’m not liking this dataset mindset of statistics. I’m not p hunting. I’m trying to validate a decision made in the Agile development process. I don’t have all day, but apparently, I have a week. Claims about fast discovery turn out to be bunk. A friend of mine suggested taking a Bayesian approach instead.

Through some, now forgotten thought process, I was plotting sigmas and z-scores, et all. That brought me back to some details of the technology adoption lifecycle (TALC). So I Googled it and found a whole lot of graphs of it that were just flat out wrong. No wonder everyone is confused about the Chasm. They are using one of the revised (wrongly drawn) figures. So I’ll show you some of the figures, point out the errors, and draw an older more correct view.

The misstatements seem to be sourced from Geoffrey Moore. When he moved into the late phases when the dot bust happened, he set about making the TALC relevant to the late phases and the biz orthodoxy. He has taken back most of the claims he made in his prior version of the TALC. It’s all disappointing.

One thing Moore said back in the beginning of his TALC, not Rodger’s version, was that it was was not a clock. I always thought he meant not an asynchronous clock, aka not like email. No, what he meant was we can choose to enter any phase we want. That leaves money on the table, but it accurately reflected what businesses do. This very characteristic means that businesses can completely skip the Chasm, the bowling alley, and his first tornado. Yes, some acquiring companies skip the second tornado or just suck at it so the acquisition fails. Mostly, acquisitions don’t even try to succeed. The VCs got their exit, that being the whole point of most VC investments these days.

Once you skip over the processes that are Moore’s contribution to technology adoption, people feel free to just fall back to Rodgers, a solely sociological collection of populations. Moore took Rodgers someplace else. Yes, Rodgers didn’t see the Chasm. But, Moore didn’t see Myerson’s Poisson games. The underlying model changed over time. I’ve modified the model myself. But, Moore’s processes didn’t move.

So let’s look at the mess.

01 TALC 2018

Figures from

  4. Adoption-Lifecycle.png

I’m just citing the sources of the figures. They probably copied them from others that copied them. I’m not assigning blame. But, this very small sample demonstrates the sources of confusion about the Chasm.


  • In figures 1, 2, 3, and 5, the first phase is called “Innovators.” Well, no. The inventors happened a long time before the technology adoption lifecycle began. The word innovators are indicative of management. In the earlier texts, this population was called technical enthusiasts. They are engineers, not business people. And, in the bowling alley and vertical sense, they were programmers known to the early adopter for the given vertical.
  • In figure 2, the gray graph behind the technology adoption lifecycle has an axis labeled “Market Share.” No, in no way is a technology firm allowed to capture 100% of the market share. The maximum is 74%. After that, you have a monopoly and your business is in violation of antitrust law. The EU is probably stricter than the US. That 74% is the US threshold.
  • In figures 1, 2, 3, and 5, the second phase is called the “Early Adopters.” Under Moore’s version, this phase is more accurately called the bowling alley. It is where we sell into the vertical markets by selling to one B2B early adopter in each vertical. We would enter six verticals with a product conceived by the early adopter. That product would be built on the technology we are trying to get adopted. Products are just the means of getting the underlying technology adopted. The product visualization is the early adopter’s alone. The idea is not ours. We sell to six early adopters. This takes time. There is no hurry. We have to ensure that each of these six early adopters achieves their intended business advantage.
  • The population percentages for each phase are accurate in figure 3.
  • In figure 4, the Chasm is correctly placed, but the early adopters are to the left, aka before the Chasm, and their vertical is to the right. It is not accurate to call the entire phase where the Chasm occurs the early adopters. There is a two-degrees-of-separation network between the early adopter and their vertical. Sales reps find no particular advantage in attempting to sell to a third degree of separation. Selling to that network constitutes the central issue of the Chasm.
  • Figure 4 also splits the early and late majorities in the wrong place.
  • In figure 5, the Chasm is incorrectly placed. The Early Majority is really the horizontal, usually the IT horizontal. The Tornado sits at the entrance of this phase, the horizontal, not the Chasm. The Chasm sits at the entrance of the verticals.

One of the problems that Moore encountered was the inability of managers to know where they were in the TALC. These figures do not agree with each other, so how would managers using different versions come to agree.

I’ve made my own changes to the TALC. First, the left convergence of the normal is well after the R&D, aka science and engineering research that firms no longer engage in. The left convergence is long after the research has gained bibliographic maturity. The left convergence only happens when researchers with Ph.D.’s and master’s degrees decide to innovate after having invented. They happen long before the TALC. This doesn’t look like how we innovate these days. These days we innovate in the late phases and innovate in a scientific and engineering-free idea-driven manner with design thinking innovating around the thinnest of ideas. These early phases, the phase before the late majority start with discontinuous innovation. These days in the phases after the early majority we innovate continuously. We don’t try to change the world. We are happy to fit in and replicate as directed by the advertising-driven VCs. The VCs demand exits so quickly that we couldn’t change the world if we wanted to.

The second change was in the placement of the technical enthusiasts. They are a layer below the entire TALC. They are the market in the IT horizontal. But, they work everywhere.

The third change involves integration with my software as media model. Each phase changes its role as a media. A media has a carrier and some carried content. All software involves the stuff used to model, and the content being modeled. Artists use pens, inks, paints, bushes, and paper. Developers use hardware, software, code, … Artists deliver a message. Developers deliver a message at times more obvious than at other times.

The fourth change is my labeling the laggards as the device market and the phobics as the cloud. I do this because these populations do not want their technology use to be obvious. The phobics use technology all the time, but with deniability. They use their car, not the computer that runs the car. Task sublimation and pragmatism organize the TALC. The phobics get peak task sublimation. This is where the technology disappears completely outside of the technical enthusiast population.

Here is a revised view of the TALC that incorporates my extensions and changes.

02 Revised TALC

The end is near. The underlying technologies disappear at the convergence on the right. Then, we will need new categories that we can only build from discontinuous innovation. If you don’t read the journals, you won’t see it coming. And, if you spent your life doing continuous innovation, you won’t be able to innovate discontinuously.

Another figure out on Google correlates Gartner’s Hype Cycle with the TALC. But, this Gartner Hypecycleone is absolutely wrong. Gartner has nothing to say about technologies in the vertical. Gartner starts with the IT horizontal. If the horizontal is not the IT horizontal, Gartner has nothing to do with the TALC. The Chasm happens a long time before the Trough of Disillusionment. The Hype Cycle starts at the tornado that sits at the entry into the IT horizontal.


I’ve made the necessary adjustment in the following figure. The Hype Cycle does Gartner Hypecycle and TALC Modifiedmanifest itself in the IT Horizontal and all subsequent phases. One Hype Cycle does not cross from one TALC phase to another. Each phase has its own hype cycle. I’ve only shown the hype cycle for the IT Horizontal.

The original figure was found in a Google image search. It was sourced from

The reason I moved the Hypecycle is that in the search for clients in the vertical, IT is specifically omitted, and IT is not involved in the project. The client has to have enough pull to keep IT out. The clients would be managers of business units or functional units other than the eventual intended horizontal that you would enter in the next phase. The Chasm and the earlier adopter problems discussed relative to earlier graphics is apparent here.

The second tornado came up in Moore’s post web 1.0 work. It happens after a purchase but before integration. The VCs get their money on completion of the purchase. The acquiring company gets value from the M&A only after the integration attempt succeeds.  The AT&T acquisition of DirectTV had a very long tornado. That tornado is probably done by now. Most M&As fail. Many M&As are done solely to ensure the VCs recover their money. These are not done because the acquired company will generate a return for the acquirer. The underlying company fades into oblivion shortly after the acquisition. I’ve put both tornados in the next graphic. The timing of the M&A is independent of phase.


In most figures, the acquiring company is shown moving upwards from the M&A. That is incorrect. The acquiring company is post-peak, post early majority and is in permanent decline. The best that can happen is that the convergence on the right will be moved further to the right granting the acquirer more time before the category dies. The green area in the figure reflects the gains from a successful integration, which happens to require a successful second tornado.

What was not shown was the relation of the first tornado to an IPO that pays a premium. That only happens with discontinuous innovation, and only in the early phases of the TALC. With the innovations we do these days, we are in the late phases of the TALC, so there is no premium on the IPO.  Facebook did not get a premium on their IPO.

One aspect of today’s TALC that I have not worked out is how the stack of the IT horizontal is cannibalized by the cloud.

Back when I gave my SlideShare presentation in Seattle in 2009, a lot of people didn’t feel that the TALC was relevant. It was still relevant then. It is still relevant now. We leave much money on the table by rushing, by being where everyone else is, by quoting the leaders of the early phases while we work in the late phases. We settle for cash, instead of the economic wealth garnered by changing the world. If we set out to change the world, the TALC is the way.






Generative from Constraints, a Visualization

May 23, 2018

I came across a tweet from Antonio Gutierrez from Several constraints on a plane form a triangle. That triangle could have been a point before the constraints were loosened enough to give us some space within that triangle. More constraints would just give us a different polygon.

The loosened constraints required some room for continuous innovation. The point that became the triangle could be thought of as a “YET” opportunity of a problem that couldn’t be solved yet. But, with the triangle the opportunity awaits. So we dive in from some point of view where we can see the point at some distance. We establish a baseline from our the point of our view, the origin, to the center of the triangle. From that origin, we project three lines up to and beyond the triangle. This volume is code. At some point above the constraint plane, we take a slice through that volume of code, the blue triangle, Generative From Constraints over Time from Originand ship it. We continue to work outward. This would involve very little rework.

Alas, things change. The constraints contract (red arrows) causing us rework, or widen (green arrows) to give us space for new opportunities. The black triangle at the intersections of the constraints could widen or contract in parallel to our current boundaries (black arrows). Or, we could move our origin up or down to widen or narrow our current projection. That’s three classes of change. Each class gives us different volumes to fill.

In my game-theoretic illustrations, the release is always in a face-off with the requirements, such is the nature of design in the axiomatic sense of requirements from the carried content as assertions balanced against the enabling and disabling elements of the carrier technology. The projection doesn’t go hockey stick like into the constraints of the underlying geometry. There is always a constraint up there that’s much closer than we’d like to admit. Goldratt insists that there is always another constraint. And, in hyperbolic geometry, there is always a convergence at the nearby infinity.

In another view, the first line (red) from the origin through the center of the triangle and API - w Carrier and Carriedout into space is where we start the underlying technology. It grows outward thickening the line into a solid with the pink triangle as the base of the carrier technology. The carried content is built outward from the carrier core.

Constant change can be managed. Moving the origin down contracts the code volume. Moving G towards B contracts the code volume. Moving E towards A contracts the code volume. And, moving F towards C contracts the code. You can know before you code where rework is required and where your opportunities are to be found.

I’ve kept this simple. You can imagine that your carrier and your carried content have their own constraints, timeframes, and rates. There would be two planes, two centerlines, two triangular solids intersecting on the place representing what we will ship. We could slip in a plane to project onto and out from. Oh, well.



Holes II

May 8, 2018

This week I revisited fractional calculus. A few months ago, someone on twitter tweeted a link to a book on fractional calculus. I didn’t get far. My computer crashed, so I lost my browser tabs. I didn’t reload them, because I had so many the browser was slowly doing its job, which apparently is collecting vast numbers of tabs of readme wannabes.

The topic came up again. I’m not sure the original link got me to the Chalkdust article, or if I had to Google it. The content was less complete, and not historical at all. But, you come away with two methods of getting the job done.

The article ended with a graphic that blew me away when I look at it from the perspective of discontinuous innovation. The discontinuity is large. It went on to hide, you might say, another discontinuity. I’m always asked what discontinuities are. I try never to make the mathematical answer to that question. The Wright brothers were not math equations.

Fractional CalculusSo here is the figure from the article. Do you see the discontinuities? The first one is glaring if you’re always looking for and needing discontinuities. Much like the discontinuities that the Mittag-Lefler Theorem, discussed in my last post, Holes,  lets us generate one or more discontinuities are essential to discontinuous innovation. There is profit in those holes. They are profit beyond the cash plays of continuous innovation, the profit of economic wealth that accumulates to the whole, the “we,” not just to the “me.” They are profit in the sense of new value chains, new careers, and revised ways to do jobs to be done.

Fractional Calculus - DiscontinuityI marked the figure up to uncover the discontinuities. We can start with the plane ABCD. The plane is outlined with a thin blue line containing the red surface from which the differentiation process departs. I drew some thick red lines to outline the hole where the process lifts the differentiation process above the plane.

There is a shadow that is visible through the front surface of the process. It was visible in the original graph. Highlighting it hides it. The thin orange lines highlight that surface.

D8 and D9 do not intersect. The third dimension lets them slide by each other without intersecting. When confronted with an intersection of constraints, look for a dimension that separates them, or look for a geometry that separates them. As product managers, we just have to look for the mathematicians and scientists that separate them. Product has always been about breaking or bending a constraint. Here we broke one. It looks like all we did was bend a constraint as of yet.

The hole is on the floor of the atrium, not on the canvas comprising the surface of the tent.  I drew a line parallel to the y-axis and put a hole on it so we could see the discontinuity. It’s not a hole that is a point. It is an area, an area on the plane. I drew a gray line across the plane to characterize the hole on that line. These scan lines don’t have to be parallel or orthogonal to the x-axis, but a polar or complex space would not simplify what we are doing here.

Everything under the surface of the graph and above the original plane is the hole. Another plane would characterize the hole differently.

That’s the first discontinuity.

Having read the article, I know that fractional derivatives involve deriving and then adding an approximation of the fractional component, or deriving past the integer power and subtracting the fractional component. In integer calculus, it’s all about functions until you get to a constant, a number. And, when you get a constant of zero, you’re done. There is a wall there. There is a hole on the other side of that wall into which no mathematics I know goes to take a swim. Yes, the differentials can be negative. We call that process integration. But, the switch between analysis and the approximation by the Gamma function is significant as is the switch between analysis and number theory.

I drew an axis above the graph in the sense of derivatives only omitting integration and projected the boundaries between equations, numbers, and zero. At zero, the zero deflects integration when zero is a number, rather than a function with the value of zero. It’s a gate. When that zero is the value of a function, integration passes unimpeded into the negative differential region.

Most of the time the “Does not exist” answer to the equation just means that we don’t know the math yet. Yes, we cannot divide by zero until calculus class, then we divide by zero all the time. The Mittag-Lefler theorem welcomes us to put holes where we need them. The mathematics is simpler without holes, so mathematicians sought to get rid of them. But, as product managers, we need our holes, if as product managers you are commercializing discontinuous innovation.

On our plane, point D at the far left where we’ve gone to number. The second hole is to the left of the orange line I projected up to our function-number axis. I don’t yet know what’s on the other side of line. Now, I’ll have to go there.