Archive for May, 2015

Geometry

May 23, 2015

I was looking for the parameters of an eclipse earlier in the week. I ended up Wikipedia looking at the definition of Eccentricity. The parameter of interest is eccentricity. Right away eccentricity breaks down into four cases: circle (e=0), ellipse (0<e<1), parabola (e=1), and hyperbola (e>1). Notice that this aligns itself with the geometry of the space itself. Relative to the sum of the angles in a triangle we have three cases: hyperbolic (<180), Euclidean (=180), and spherical (>180). Notice also that this aligns itself with the definition of probabilities, as 0 ≤ p ≤ 1. And, footprints of distributions tie into eccentricity: normal as a circle, and Poisson as an ellipse. The distributions also tie into machine learning: Poisson giving us rule enforcement, and Gaussian (normal) giving us rule enforcement. Then, there is Ito processes: n = 0 giving us the Markov chain, n > 0 giving us an Ito process. The Markov chain is a special case of the Ito process. The holes in these associations is probably due to my having been exposed to that math yet. Everything in math is tied to everything else in Math.

I don’t have a correlation between the parabola and anything else. I’ll have to think about this single case.

The failures of a given innovation is excused by faulting innovation. But management as an idea was extended to innovation. Management as an idea was exclusive of innovation when Sloan created management. Nobody says management failed when an innovation fails. Christensen makes the case that managers excelling at management failed when their companies were disrupted. Ultimately what this boils down to is place, under a distribution in a specific geometry. I will finish this post talking about place, but I need to get back to eccentricity and geometry first.

In the Wikipedia post on eccentricity, there was an animation linking circles with ellipses, parabolas, and hyperbolas. Watch it several times, because I going to ask you to image the animation happening in a different order.

250px-Ellipse_and_hyperbolaThe animation begin with the circle. A blue dot represents the center of that circle. That dot goes on to represent the foci of the ellipse, the parabola, and the hyperbola. You can watch the dot move in each frame of the animation.

So now we can think about it in terms of the technology adoption lifecycle(TALC), or the processes organized by the lifecycle. We’ll start simply here. It will get messy as we go deeper. Start with a Poisson game. That’s when we are looking for those B2B early adopters in the TALC. That’s the second phase, the one adjacent to the technical enthusiasts.

A series of Poisson distributions generate a single Poisson distribution whose foot print is an ellipse. The major axis of the ellipse shows us a Markov process as the major axis grows. The major axis is a vector. We start with this Poisson distribution, because we are using a game-theoretic game to represent a game of unknown population, a Poisson game. You can play these games as Gaussian games, but my intuition is to go with discovery learning. Keep in mind that I’m talking about a discontinuous innovation here. Continuous innovations happen elsewhere in the TALC.

Now, this Poisson distribution starts off as a single infinite histogram, aka a point, in other words as a tiny circle. Markov chains are composed of Poisson distributions of arcs, whose pre-choice probabilities are taken from normal distributions of the nodes, small distributions. The Poisson would be external, while the normal would be internal.

We are representing the company and its customer base, as opposed to its prospect base as a Poisson distribution. Over time, that Poisson distribution tends to the normal. The ellipse gets longer and wider. The ellipse fits inside a rectangle that eventually becomes a square at which point the ellipse becomes a circle. The eccentricity changes from something between zero and one becoming zero. I’ve seen this in financial results of companies selling products to foster the adoption of discontinuous innovation. I trust this to be reliable.

The circle represents the vertical. The bowling ally is a collection of approaches to different verticals. The Poisson distributions of those approaches to their verticals point to their respective verticals, aka they walk to their vertical.  Arriving at the chasm is the event that correlates with the onset of the normal. The onset of the normal is also the onset of Euclidean space.

The circle goes on to represent the horizontal market. Consider it to be six sigma wide at the post tornado. Once it is larger than six sigma the geometry is spherical. The standard b-school case analysis becomes very reliable in spherical space. But, my focus is on why that same analysis fails us prior to the chasm. I hypothesize that the space prior to the Euclidean is hyperbolic.  We’ll go back to animation again, but this time I’ll capture the frames.

00 Research FrontThe animation ends with the hyperbola. Businesses don’t end with the hyperbola. They end in a spherical geometry usually with a black swan that makes their distribution contract. A category begins with a gap. Consider the space looking outward to the foci to be the gap.

I was going to show that the research front changed and call that period the research effort. But, the animation didn’t support that. The directrices moved instead. They do approach each other, but never converge. distance from one foci to the nearest directrix is equal to the eccentricity, which will be larger than one.

I’m going with the hyperbola, as it is unfamiliar and weird enough to lead to things like taxicab geometry where you can’t go straight there, instead having to stay on the grid. In the other geometries you can go straight there. I imagine linear algebra can make the hyperbolic linear, but I haven’t gotten to that math yet.

The time research takes would happen on a z-axis. The search that is research would happen on the surface of the research front. Notice I didn’t use the term R&D. Research gets us our technology and our s-curve. Products foster adoption of the technology. Technology is adopted. Products are sold.

02 Poisson GameOnce the directrices have converged to their minimum separation the weak signal is emitted and the Poisson games begin. I had to draw the figure myself, because the ellipse was too large since in the animation the ellipse starts with a circle. The hyperbola in the figure is there to show the system before the directrices converged. The big bang here is the signed contract with the B2B early adopter. We grow from nothing starting here.

As an aside, Levy flights happen at the find you’re underlying technology phase, aka before the technical enthusiast phase of the TALC.

Now, we’ll go back to the notion of place. In the animation, the blue dots that represent the origin and the foci moving across the geometries. In the TALC, a normal of normal, discontinuous technologies undergo adoption from left to right starting at the far left. All other types of innovation start in the random-access sense somewhere to the left, aka in a different place. Starting at the left means being a monopolist or exiting the category. Starting to the right means competing on promo-spend dollars against fast followers and other look alikes. Those are different places. Samsung will never be Apple even if they hire Steve Jobs. Different places. Different times. Different pathways.

I’ll talk about place in a later post. Tweets about design and brand drive me nuts. They are phase specific–place specific.

Comments?

Normal Approximating Whatever

May 13, 2015

I finally got back to a math book, Modeling the Dynamics of Life by Frederick R. Adler,  I’ve had it on hold for a long while. I’ve been at it for over a year. And, I still haven’t done the homework. The homework actually teaches beyond the text in a lot of math books. So I’ll be at it for a long time to come even though I’m starting the final chapter. It’s an applied textbook, so the author gets his point across without turning you into a mathematician, or at least tries to. The mathematician thing will happen if you pay attention, but who does that?

In the previous chapter, the book talks about approximating a Poisson distribution with a normal. That’s a very small normal since it fits inside that Poisson distribution it’s trying to approximate. It does the same sort of thing for the Binomial. And, again for the exponential. I drew the series of distributions for this latter exercise. It takes a lot of distributions added together to get that normal, a lot like 30 distributions. The thing that can get lost is the shape of the world holding the distribution.

In approximating the normal from an exponential, the exponential, aka long tail looked longer than it was tall. But adding two distributions brought us to a gamma distribution that was a little longer. Adding five distributions got us something that looked normal, but was wider still, and pdf was taller than the normal. Adding ten distributions, wider again and less tall. Adding 30, wider, practically on top of each other and shorter. If we kept on adding, it would get shorter and wider, aka it would get tiny, but the approximation and the actual would be close enough that we’d be collecting data and graphing things for entertainment.

This graph will be too small. But take a look.

Sum of Distributions Tending to Normal

At some point further calculation becomes pointless. Factor analysis shares this property. Does another factor tell you something actionable? Does more accuracy do the same?

Another thing that got talked about was the standard normal. You get to the standard normal from the normal via z-scores. You want all your distributions to have a normal approximation since your tools for approximating probabilities are based on the standard normal and its z-scores. To do hypothesis testing, you need a normal.

You can find those formulas for distributions. They tend to look messy. Try integrating them. Getting to a standard normal is easier. Another author in another book that I can’t cite, said that while the numbers convert via those formulas, the logic does not follow the flow of the calculations. Hypothesis testing in non-normal distributions is an active area of research. An example of calculation and logic not being consistent,  we have  machine learning, Markovian approaches discover, while Gaussian approaches enforce. That’s not really a matter of application. One is ontological while the other approach is taxonomic.

Notice that all these approximations and converging tos require a lot of data and a lot of distributions. We are using big data to estimate small data.

Enjoy! Comments?

More on the Gap

May 10, 2015

After posting “The Gap,” I kept going. I put the technology adoption lifecycle across the terrain. An idea gains adoption via some apostles in an invisible college, which gets the idea published in a peer-reviewed journal. But, that’s long before the idea shows up in a corporation pushing it out into some productization. That corporation wrestles with the idea. Someone has to convince someone. The idea has to gain adoption internally within the corporation. That corporation is staffed with people drawn from the larger world. The pragmatism scale organizing external adoption is also organizing the internal market. Someone will be the technical enthusiast. Someone will be the early adopter. Not everyone in the corporation has to adopt the idea. Once the corporation starts selling the idea, there will be some internal laggards, some phobics, some non-adopters.  But, before the corporation starts selling, it will have adopted the idea.

Before the corporation sells much, it is faced with external adoption. The forces of external adoption will be with the corporation until it abandons the idea’s  category.

01 09a A Point In A World

Internally, we have an ontology, a hierarchical definition of the idea, a definition delineating how it is different and how it is similar to other ideas. Patent applications are like that, differences and similarities. But patents are really about realizations. Ontologies organize ideas.

Taxonomies organize realities. External adoption uses different species of implementation in different product spaces. The realizations in external adoption get organized around differences and similarities with other products. The idea becomes implicit in the taxonomy.

Since external adoption sequences markets and contexts it also sequences whether the focus is on the vertical or the horizontal, on the carried or the carrier. The external adoption is itself a media that orchestrates the media of software.

Ontologies and taxonomies organize their search spaces. Ontologies are generative. Ontologies diverge. Taxonomies are enforcing. Taxonomies converge. At each taxonomic decision, I am becoming more known. At each ontological decision, I become less known. Ontologies face into the unknown, the more to be known. Taxonomies face into the known.

Ontologies are convex; Taxonomies, concave. The book “Antifragile” tells us that concave is safe, while convex is unsafe. Sloan, the founder of GM, invented management. He was all about the concave. Sloan was not an innovator. GM bought the innovations it needed. Taxonomy is management. Ontologies are innovation. Innovation is exclusive of management. I’ve gone so far as to say that management inserts risk into innovation.

01 09b A Point In A World

The ontological spreads out across the search space. To realize an idea, we trim the tree that is the search space. We trim it enough to converge to a solution. That may be a point, or a line, or a shape. The figure is a little off. The solution, the thick dark blue line occurs before the external technology adoption lifecycle. It should occur inside he lifecycle.

01 09c A Point In A World

One last thing to do was to count the bits involved in crossing the gap. The idea uses 3 bits to document its search space. The realization, likewise, uses 3 bits. Those would be explicit bits. When differentiators become commoditized, their  bits become implicit. The number of bits involved will change as the idea moves through the technology adoption lifecycle.

01 10 A Point In A World

Enjoy. Comments?

A Point, Unquantifiable Datum

May 4, 2015

Data is made. When you take out your tape measure and measure twice before you cut, you have taken all the bits that it took to make that particular tape measure and projected them on to the tick mark where you will cut. You do that twice. You go even further by taking the bits involved in making the saw and projecting them on to the line that gets cut. Seeing a nice flat surface, a surface that doesn’t exist in nature, should remind us that data is made, manmade. Well, more than likely, robot made.

So lets start at a point and look, once again, at a point, a point in some multidimensional space, a point in an argument, a number of bits.

03 00 A Point

So we have the point again.

03 01 A Bit

When there is a point, there is at least one bit. We’ll just call zero bits ground.

03 02 A Bit

Where there is a bit, there is a decision. If such and such. Never mind the behavior associated with that bit for now. If there is a decision, there is always at least one consequence. “There’s a spot on this glass.” “Then, wash it.” Just one point and already you need a dishwasher, a water softener, and dish towel.

03 03 Two Bits

And, of course, where there is one bit, there will be more. Consider how much money is spent on systems to move bits around that boil down to that single bit, “Hey, are we still in business?”

03 03a N Bits

The real problem with bits is consciousness. We tend to treat explicit bits differently than implicit bits. We talk about assumptions, aka the criminal alias of implicit bits. But consciousness moves around. One bit is important right now. Another bit later on. We have limited focus as humans and those limits demand implicit bits. It’s the world size problem. We put some number of bits inside our world at a given moment and assume the rest.

03 03b N Bits

We focus on the foreground. We let the midground and background slip into the implicit in varying degrees. We let those assumptions fly.

03 03c N Bits

Then, there is the whole mess of carrier and carried, of software as media, of product as media, of company as media, of stock prices as media.

03 03d N Bits

It’s like a cave. You have a floor of implicit bits under you, and a ceiling of implicit bits above you. The space you can stand up in is that of your explicit bits. If you’re ever a coal mine tourist, keep the exits in mind.

03 03e Multiple Carriers

The software as media model comes into this notion of habitable space. There are many carriers. A startup that has its own technology undergoing adoption starts out as two people and three bivectors: company, product, and market. Oh, four: the technology. Whole product people can skip the fourth. To position the point is to build the company, product, and market. So all those bits roll up into that point. Fuse me some data.

03 03f Multiple Carriers FA

Here I simplified the carrier and content aspects. I’ve also applied some hypothetical factor analysis to the system. Each aspect is different in terms of how important it is. The hole is not round. As much as designers dislike radar diagrams, sometimes it takes a radar diagram to illustrate where the point is. Then, again, the point isn’t always in the middle.

51 01 Design

When you have a dimension and you are optimizing it in some way, you have the physical aspect, aka the media, presenting you with some impedance. The ribbon in MS Word does this to me all the time. I’m like, “Where the hell is the control?” I know how to move that impedance, I’m just lost on the topic of finding it. Design is the process of establishing how much the enabler will have to push against the impedance. Bits vs bits. Design in this definition is general enough to work for software or art. The criteria define the impedances. Design is a point.

51 02 Design

Since we usually design in multidimensional spaces, we end up with a multidimensional surface. That surface having explicit and implicit components, a foreground, midground, and background. That is a surface of bits. The red column of enabler bits is the technology that made this product possible, that enabled the work. The rest are context.

51 03 Design

A multidimensional design will be built on a multidimensional analysis having some tiling and some population(s

). Change the tiling and the populations and you will need a different design. These are the keys to finding a market for a fast follow. Adding  a new technology of your own will get you a different design as well. In the end, they are collections of bits, collections of points.

Oh, why did I say unquantifiable? The implicit bits are not counted. Psychological processes don’t count bits. We have no idea how many bits make up our floors or our ceilings. The poets connotations float, as do we.

Enjoy! Comments?