Archive for July, 2017

Notes on the Normal Distribution

July 24, 2017

Pragmatism Slices and Sales

Progress through the technology adoption lifecycle happens in terms of seats and dollars. If you use alternate monetizations, rather than sell your product or service, drop the dollars consideration. Beyond those monetizations even if you sell your product or service, dollars are flaky in terms of adoption. But the x-axis is about population, aka seats.

Sales drive the rate of adoption in the sense that a sale moves the location of the product or service, the prospect’s organization(s), and the vendor’s organization(s) under the curve. By sales, I mean the entire funnel from SEO to the point where the sales rep throws the retained customer under the bus. But, I also mean initial sales, the point where prospects become customers. That sale moves from adoption from the left to right, from the early phases towards the late phases, from category birth to category death.

But, there are two kinds of sales: the initial sale, aka the hunter sale, and the upgrade sale, aka the farmer sale. What struck me this week was how the farmer sale does absolutely nothing in regards to progress through the various entities locations under the adoption curve. So let’s look at this progress.


People in a pragmatism slice reference each other. They do not reference people in other pragmatism slices.

In the figure, the hunter sales move the adoption front across the adoption lifecycle from left to right. The hunter sales rep made four sales. The farmer sales rep made four sales as well that generated revenues, but no movement across the lifecycle.


The size of the normal representing the addressable markets in the technology adoption lifecycle is fixed. It does not grow. A single company has a market allocation that tells us how much of that normal they own. With discontinuous innovations, that allocation to the market leader maxes out at 74%. Beyond that, antitrust laws kick in. Such a market leader would be a near-monopolist. Their market leadership will be the case until they exit the category, or face a Foster disruption. Intel was the market leader until NVIDIA brought a different technology to market. With continuous innovations, we are dealing with many players in a commodity market. The allocations are small. Market leaders can change every quarter.


In this figure, I started with a standard normal distribution (dark yellow) representing 100% of a category’s market. I represented the near monopolist’s market allocation of 74% as a normal distribution (light blue) inside of the larger normal. Then, I drew the circles (orange and blue) representing the curvature of the kurtoses of these distributions. The light blue distribution cannot get any larger. It is shown centered at the mean of the category’s normal. It could be situated anywhere under the category’s normal. Once a vendor has sold more than 50% of its addressable market, that vendor starts looking for ways to grow, ways to move the convergence of the vendor’s distribution as far to the right as possible. They try to find a way to lengthen the tail on the right. They run into trouble with that.

While a normal distribution represents the technology adoption lifecycle, the probability mass gets consumed as sales are made. The probability mass to the left has been consumed. So there is very little mass to allocate to the tail. In placing those curvature circles, I looked for the inflection points and made the circles tangent to the normals there. For the proposed tail, I drew its curvature circle. The thick black line from the mean to the top most inflection point doesn’t leave enough probability mass to allocate to the tail so the tails would be lower and the curvature circle would be larger. The thick red line from the mean to the bottom most inflection point leaves enough probability mass to allocate to the tail. It’s important that the curves represented by the black and red lines be smooth.

The points of convergence for the 74% normal, the 100% normal, and the long tail appear below the x-axis of the distribution. The mass between the convergences of the 100% normal and the long tail are outside the category’s normal distribution. The normal under the normal model used a kurtosis of zero. But, with the long tail, the kurtosis is no longer zero. That growth is coming from something other than the product or service of the vendor. And, the mass in the tail would not come from the normal inside the category’s normal. The normal was deformed when the mass was allocated towards the tail. But, again, that still does not account for the mass beyond the category normal. That mass beyond the category normal is black swan like and hints towards skew risk and kurtosis risk. Look for it in the data. These distributions just show a lifecycle of the category and vendor normals. The data should reflect the behaviors shown in the model. The pragmatism slices move as well. Taking a growth action that concatenates the tail can dramatically change your phase in the technology adoption lifecycle. Each phase change requires some, possibly massive, work to get the products and services to fit the phase they find themselves addressing.

Booms stack the populations in the technology adoption lifecycle. See Framing Post For Aug 12 Innochat: The Effects of Booms and Busts on Innovation for that discussion.

I drew my current version of Moore’s adoption lifecycle.

The Technology Adoption Lifecycle

Moore built his technology adoption lifecycle on top or Rodgers’ model of the diffusion of innovation. Rodgers identified the populations involved in technology adoption like the innovators, early adopters, early and late majorities, and laggards. Moore went further and teased out technical enthusiasts, and the phobics, Moore changed the early majority to vertical markets and the late majority to horizontal markets. Moore identified several structural components like the bowling alley, the chasm, and the tornado.

I’ve made my own modifications to Moore’s model. The figure is too abundant. Another incidence of my drawing to think, rather than to communicate.

TALC setup

The technology adoption lifecycle provides the basis for the figure. The technology adoption lifecycle is about the birth, life, and death of categories that arise from discontinuous innovation. This leaves aside the categories that can be created via management innovation discussed in an HBJ article over the last year. A category is competed for during the Tornado and birthed when market power selects the market leader. Immediately after the birth of a category, the competing companies consolidate, or exit. Their participation in the category ends. The category can live a long time, but eventually, the category dies. Its ghost disappears into the stack. The horse is still with us. Disruption is a means of killing a category, not about competing in the disrupted category. Disruption happens to adjacencies, not within the category sponsoring the disruptive discontinuous innovation.

The populations are labeled with red text. Most of the phase transitions are shown with red vertical lines. The transition to the early majority is shown with a black line, also labeled “Market Leader Selected.” The vertical labeled with red text consists of the early adopter (EA) and the next phase that Moore called the vertical market. Some technical enthusiasts would be included in the vertical as well, but are not shown here as such.

Notice that I’ve labeled the laggard phase device and the phobic phase cloud. The cloud is the ultimate task sublimation. The device phase is another task sublimation. These are not just form factors. They are simpler interfaces for the same carried use cases. The carrier use cases are different for every form factor. Moving from early majority to late majority phases also involved task sublimation, as described by Moore. Laggards need even simpler technology than consumers. Phobics don’t want to use computers at all. The cloud provides admin-free use. The cloud is about the disappearance of both the underlying technology in the carrier layer and the functionality in the carried layer. Notice that after the cloud the category disappears. There are no remaining prospects to sell.

The technical enthusiasts, as defined by Moore, was a small population at the beginning of the normal. But, there are technical enthusiasts in the Gladwell sense all the way across the lifecycle. They are a layer, highlighted in orange, not a vertical slice, or phase. I’ve shown both views of the technical enthusiasts. The IT horizontal people would show up as technical enthusiasts if the product or service was being sold into the IT horizontal. This distinction is made in my Software as Media Model. The technical enthusiasts are concerned with the carrier layer of the product or service.

Moore’s features are shown as brown rectangles. These features include the chasm, the tornado, and the bowling alley. Specific work, tactics, and strategies address the chasm, the tornado, and the bowling ally. These are labeled as pre-chasm, pre-tornado, and keeping the bowling alley full. They show up as blue rectangles. Another feature stems from de-adoption, the “Need (for a) New Category,” and appears as a blue rectangle. This latter feature happens, because nothing was done to create a new category before it was needed. Or, such an effort failed. The point of keeping the bowling alley full is to create new categories based on discontinuous innovation on an ongoing basis. I’ve seen a company do this. But, these days discontinuous innovation is very rare. Discontinuous innovations can, but not always, cause (Foster) disruptions. Christensen’s disruptions happen in the continuous innovation portion of the adoption lifecycle.

The lifecycle takes a discontinuous innovation to market and keeps the category on the market via continuous innovation. Plant the seed (discontinuous), harvest the yield (continuous). This division of the lifecycle is labeled in white text on a black rectangle towards the bottom of the figure. Discontinuous innovation generates economic wealth (inter-). Continuous innovation generates an accumulation of cash (intra-). A firm does not own the economic wealth it generates. that economic wealth is shared across firms. I am unaware of any accounting of such.

At the very top of the lifecycle, the early and late phases are annotated. The early phases constitute the growth phase of the startup. The late phases constitute the decline phase. The decline phase can be stretched out, as discussed in the previous section. When the IPO happens in the early phases, but not before the Tornado, the stock price sells at a premium. When the IPO happens in the late phases, the stock price does not include such a premium. The Facebook IPO bore this out. It’s typical these days, these days of continuous innovation, that no premium is involved.

Founders, at least in carrier business, with discontinuous innovation are engineers, not businessmen, so at some point, they have to hire them to put the biz orthodoxy in place. VCs these days require a team that is already orthodox. The hype before the Shake Shack IPO demonstrates that innovation has moved on from software. Orthodox businesses are now seen as innovative, but only in the business model, continuous innovation sense. Shark Tank and VCs don’t distinguish the technology startup from other startups. The innovation press confuses us as well. It used to be that the CFO and one other person had an MBA, now everyone has one. But, in an M&A, the buyer doesn’t want to spend a year integrating the business they just bought. The merger won’t succeed unless the buyer can launch their own tornado and bring in new customers in the numbers they need. The Orthodoxy needs to be in place at least a year before the IPO, or the stock price will underperform the IPO a year after the IPO.

From a statistical point of view, the process of finding a new technology involves doing Levy flights, aka a particular kind of random walk, until that new technology is found. It should not be related to what you are doing now, aka to your install base. You are building a brand new company for your brand new category. Google’s Alphabet does this. Your company would become a holding company. Managing the diversity inherent in the technology adoption lifecycle becomes the problem. “No, that company is in a different phase, so it can’t do what our earlier company does now.” Contact me to find out more.

After the Levy flights, we search for early adopters. Use Poisson games to look at that. The Poisson distributions tend to the normal. Those normals become higher dimensional normals. The standard normal has six sigma, the later normals in later phases of the lifecycle have more than six sigma. These divisions translate into geometries. The nascent stages of the lifecycle occur in a hyperbolic geometry where the distant is small from a Euclidean perspective generated by the inherent L2 geometry of linear algebra. Artists see the distant as small reality in perspective drawings. They call that foreshortening. We foreshorten our financial forecasts and small is bad. But, as the Poisson become a normal, those financial forecasts stop foreshortening. The idea we threw away becomes obviously invaluable after the founder builds a market, a technology, a product or service, a company, value chains,… The distributions change, and the geometries change. Once you move beyond six sigma, the geometry becomes spherical. In such geometry, there are many ways for followers with different strategies to win. We start with a very narrow way to win in the hyperbolic, arrive at the one way to win in the Euclidean, and find ourselves in the many ways to win in the Spherical. Or, damn, so many fast followers, geez.

Last but not least, we come to the Software as Media model. Media is comprised of carrier layers and carried content layers. The phases of the adoption lifecycle change layers when they change phases. The technical enthusiast is about the carrier layer; the early adopter, the content layer; the vertical, the content layer; the horizontal, the carrier layer; the device, both; and the cloud, carrier. At the point where you need another category, it could be either. But, these oscillations involve the market and the way the vendor does business. Each phase is vastly different. The past has nothing to do with the present. Yes, the practices were different, but they fit their market. They were not better or worse unless they did not fit their market.

Designers whining about the 80’s were not around then. They take today’s easiness for a given and think the past should have been done their way. The past taught. We learned. And, as we cross the technology adoption lifecycle, the Ito process that crossing, the memories are deep. We learned our way here. And, when we repeat the cycle, our organizations are not going to start over. They don’t have to if properly structured. Call me on that as well. But, usually they don’t start over from scratch, but should, because they forgot the prior phase, as they moved to the next.


The Curvature Donut

July 23, 2017

In last month’s The Cones of Normal Cores, I was visualizing the cones from the curvatures of a skewed normal to the eventual curvatures of a standard normal distribution. The curvatures around a standard normal appear as a donut or, a torus. Those curvatures are the same all the way around the normal in a 3-D view. That same donut around a skewed normal appears as a deformed donut, or a ring cyclied. In the skewed normal the curvatures differ from one side to the other. These curvatures differ all the way around the donut.

The curvature donut around the standard normal sits flatly on the x-axis and touches the inflection points of the normal curve. Dropping a line from the inflection points down to the x-axis provides us with a point where a line 45 degrees above the x-axis is where the origin of the circle of the particular curvature would be.

The curvature donut of a skewed normal would sit flatly on the x-axis, but might be tilted as the math behind a ring cyclied is symmetrical to another x-axis running through the centers of the curvatures. In January’s Kurtosis Risk, we looked at how skew is a tilt of the mean by some angle theta. This tilt is much clearer in More On Skew and Kurtosis. That skewness moves the peak and the inflection points but the curve stays smooth.

So I’m trying to overlay a 2-D view of a skewed distribution on a 3-D view of ring cyclied.

Ring Cyclide

I’ve used a red line to represent the distribution. The orange areas are the two tails of the 2-D view. The curvatures show up as yellow circles. The inflection points on the distribution are labeled “IP.” The core is likewise labeled although the lines should match that of the tilted mean.

I think as I draw these figures, so in this one, have a gray area and a black vertical line on the ring cyclied that are meaningless. Further, I have not shown the orientation of the ring cyclied as sitting flat on the x-axis.

The ring cyclied occurs when skewness and kurtosis occur. A normal distribution exhibits skewness and kurtosis occur when the sample size, N, is less than 36. When N<36, we can use the Poisson to approximate or estimate the normal. Now, here is where my product management kicks in. We use Poisson games in Moore’s bowling ally to model Moore’s process as it moves from the early adopter to the chasm. The chasm being the gateway to the vertical market that the early adopter is a member of. We stage gated that vertical before we committed to creating the early adopter’s product visualization.  We get paid for creating this visualization. It is not our own. The carried component always belongs to the client. The carrier is our technology and ours alone.

So let’s look at this tending to the normal process.

Conics as Distribution Tends to Normal

I was tempted to talk about dN and dt, but statistics kids itself about differentials. Sample size (N) can substitute for time (t). The differentials are directional. But, in statistics, we take snapshots and work with one at a time, because we want to stick to actual data. Skew and kurtosis go to zero as we tend to the standard normal, aka as the sample size gets larger. Similarly, skew risk and kurtosis risk tend to zero as the sample size gets larger.

The longer conic represents the tending to normal process. The shorter conic tends to work in the inverse direction from the normal to the skewed normal. Here direction is towards the vertex. In a logical proof, direction would be towards the base.

The torus, the donut associated with the standard normal, like its normal is situated in Euclidean space. However; the ring cyclide is situated in hyperbolic space.

An interesting discussion on twitter came up earlier this week. The discussion was about some method. The interesting thing is what happens when you take a slice of the standard normal as a sample. The N of that slice might be too small, so skew and kurtosis return, as do their associated risks. This sample should remain inside the envelope of the standard normal; although it is dancing. I’m certain the footprints will. I’m uncertain about the cores in the vertical sense. Belief functions of fuzzy logic do stay inside the envelope of the base distribution.

Another product manager note: that slice of the standard normal happens all the time in the technology adoption lifecycle. Pragmatism orders the adoption process. Person 7 is not necessarily seen as an influencer of person 17. This happens when person 17 sees person 7 as someone that takes more risk than they or their organization does. They are in different pragmatism slices. Person 17 needs different business cases and stories reflecting their lower risk willingness. These pragmatism slices are a problem in determining who to listen to when defining a product’s future. We like to think that we code for customers, but really, we code for prospects. Retained customers do need to keep up with carrier changes, but the carried content, the use cases and conceptual models of carried content rarely the changes. The problem extends to content marketing, SEO, ancillary services provided by the company, and sales qualifications. Random sales processes will collide with the underlying pragmatism structure. But, hey, pragmatism, aka skew and kurtosis, is at the core of problems with Agile not converging.

In terms of the technology adoption lifecycle, the aggregated normal that it brings to mind is actually a collection of Poisson distributions and a series of normal distributions. The footprint, the population of the aggregated normal does not change over the life of the category. Provided you not one of those to leave your economy of scale with a pivot. Our place in the category is determined in terms of seats and dollars. When you’re beyond having sold 50% of you addressable population you are in the late market. The quarter where you left the early market and entered the late market is where you miss the quarter and where the investors are told various things to paper over our lack of awareness that lost quarter was predictable.

If you know anything about the ceiling problem, the sample distribution reaching beyond the parent normal let me know.

I’ve actually seen accounting visualizations showing how the Poissons tend to the normal.


The Postmodern UI

July 8, 2017

A tweet dragged me over to an article in The New Republic, a journal that I’m allergic to.  But the article, America’s First Postmodern President, an article I read with my product manager hat on, an article about the postmodern world we live in, that world one of constant, high-dimensional, directionless change. And, it became obvious to me that I’m not a postmodernist while Agile is exactly that, postmodernist, so our software products reflect that.

No politics here. The quotes might go that way, but I will annotate the quotes to get us past that. I’ll ignore the politics. Here the discussion will be product, UI, design, Agile.

For Jameson, postmodernism meant the birth of “a society of the image [textual/graphical/use case] or the simulacrum [simulation] and a transformation of the ‘real’ [the carried content] into so many pseudoevents.” Befitting the “postliteracy [Don’t make me read/YouTube it] of the late capitalist world,” the culture of postmodernism would be characterized by “a new kind of flatness or depthlessness [no heirarchy, no long proofs/arguments/logics/data structures/objects, a new kind of superficiality [the now of the recursion, the memorilessness of that recursion’s Markov chain] in the most literal sense” where “depth [cognitive model/coupling width/objects] is replaced by surface [UI/UX/cloud–outsourced depth].” Postmodernism was especially visible in the field of architecture, where it manifested itself as a “populist” revolt “against the elite (and Utopian) austerities of the great architectural modernisms: It is generally affirmed, in other words, that these newer buildings [applications/programs/projects/products/services] are popular works, on the one hand, and that they respect the vernacular of the American city fabric, on the other; that is to say, they no longer attempt, as did the masterworks and monuments of high modernism [No VC funded, logrithmic hits out of the financial ballpark], to insert a different, a distinct, an elevated, a new Utopian language into the tawdry and commercial sign system [UX as practiced now] of the surrounding city, but rather they seek to speak that very language, using its lexicon and syntax as that has been emblematically ‘learned from Las Vegas [for cash and cash alone, no technlogical progress/reproduction by other people’s means].’”


For Baudrillard, “the perfect crime” was the murder of reality, which has been covered up with decoys (“virtual reality” and “reality shows” [and UIs]) that are mistaken for what has been destroyed. “Our culture of meaning is collapsing beneath our excess of [meaningless] meaning [and carrier impositions], the culture of reality collapsing beneath the excess of reality, the information culture collapsing beneath the excess of information[multiplicities in the spherical geometry where every model models correctly in the financial/cash sense]—the sign and reality sharing a single shroud,” Baudrillard wrote in The Perfect Crime (1995)…[political cut].

What a mess. It helped that this morning in those Saturday morning, light-weight introspective moments the notion of objects being bad and the reassertion of functional programming was leaving us with data scattered in the stack via recursion, and the now of the current system stack with nothing to see of how we got here. But, hey, no coupling between functions through the data structure, something I never thought about until some mention in the last two weeks. Yes, the alternative to static would do that no matter how dynamic.

Those gaps, the architecture enabling us to escape those tradeoffs we make in our products, the slowness of feedback from our users, and the feedback from the managers as if  they were users–a flattening–all disappear when we go postmodern when we go flat. That jack in your car becomes worthless when your emergency tire goes flat.

Still, I don’t like surface without depth; the absence of a cognitive model; the painted on UI, the erasure of the deep UX/CX/BX/MX/EX, the surface of machine learning, and programmers writing up other people’s disciplines as if those disciplines don’t matter, as if those years spent in school learning that discipline doesn’t matter, that the epistemical/functional cultures don’t matter–but, of course, they don’t matter because the programmer knows all the content they encode, and management lays off all the content anyway ending their Markov chains and filling their resumes so full of cheap labor jobs so you can’t see the underlying person. Thirty years of doing something, the depth, forgotten because seven years have passsed, still leaves depth, but hiring passion over experience gets us to that postmodernist surface. Oh, well. When better is surface, when success is reality TV, when…

The danger of a sweeping theory like postmodernism is that it can produce despair.

But, that’s where we are this morning, sweeping theory, not despair.