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?

The Gap

April 29, 2015

In the AI of the ’80s, the goal was to solve the problem by various means, but mostly by making the problem small enough to solve. It turned out that most problems were too big. Consider that the point of HTML was to feed knowledge to AI machines without spending the money to encode the world’s knowledge on your dime. All this human reading, commerce and ad service was besides the point. Hell, a server log was an accident.

So we start out looking at the world. Actually, the world is large, so we start by focusing and tightening up our scope until we get to a comprehensible world.

00 A World

Yes, we’ll start where Euclid started. Well, he may have started with a point, instead of a line, but lines and points define each other. To get to a single point, we draw another line, not shown this time.

01 00 A Point In A World

We might think of a point, as being the result of an argument. And, while we are arguing we’ll stick with the real world, no concepts allowed. So the argument is all about taxonomy. “You’re an idiot.” “No, I’m not.” But then, idiot would necessitate that such a thing really existed, and no, not the concept of an idiot. Better to name it a rock, so we can keep our argument simple and non-conceptual.

01 01 A Point In A World

But,  somehow, we’ve admitted the concept of an idiot. So now are stuck with maintaining a taxonomy and an ontology. We end up with two worlds: the world of ideas, and the world of realizations. Realizations happen long after we get everyone on the same page as to the idea. There is some spatio-temporal notions of distance and time involved in getting everyone of the same page. And, that is pre-idea. Post-idea, post-implementation, that distance and time is tied up in the technology adoption lifecycle, even if we are talking product as opposed to the technology. Getting back to the taxonomy and ontology involved, they are different and separate worlds.

01 02 A Point In A World

Between those two worlds is a gap. We should be glad the gap is there since it’s where economic value comes from. Products reduce the impedance a constraint presents us with. Products might eliminate that impedance in its entirety. But, Goldratt’s Theory of Constraints tells us that there is always another constraints. We should be happy about that as well, because we won’t run out of work–ever. So why are we unemployed? Well, it’s not globalism, robots, computers, or laziness.

01 03 A Point In A World

But, back to the gap. Those lines are not straight. We might use matrix algebra to straighten them out, but really, they curve. We don’t even try to cross a gap until someone can see or imagine the other side.

01 04 A Point In A World

In the gap, we find value. We make the unknown a little more known. We generate few more bits in the crossing.

01 05 A Point In A World

When we can cross a gap without tossing aside yesterday’s world, when we innovate continuously, we capture cash. When the freight hauling train gets stuff to a port, billing captures some cash, eventually. But, wealth was created when the railroads were built, when railroads were a discontinuous innovation. Railroads might be a bad example, because they were vertically integrated and tended to capture all the cash involved. Today, we are no longer vertically integrated, so the cash is captured by each members of a value chain. Wealth doesn’t get captured in a single set of books. No entity gets all the cash.

One of the core jobs when getting an innovation, a discontinuous innovation, adopted is building that value chain and creating that wealth that feeds the coming cash capture. Too much of what we do today is about cashing out on yesterday’s wealth.

Back to those taxonomies and ontologies, they involve decisions. Those decisions define the terrain. The terrain isn’t even known. On that map of travel times out of New York, you got out west where the map went blank. There was terrain there, but nobody had surveyed it, mapped it, defined the features and the data that we encode in our maps. I’ve drawn the taxonomy and ontology used here as in the leaf nodes attaching to the terrain elevation lines. I’m left wondering if the taxons and ontons, the decisions, are a better place to run the terrain. Do we reach a place, or do we go up and down hills? That question seems to be the distinction between discontinuous and continuous innovation. Did we stop somewhere, or did we keep moving? Did we engage in trench warfare, or the war of fluid tank battles with no rear or forward areas? The point here is that you draw your on taxonomies and ontologies and put the terrain features where you want them. Just use a consistent set of rules for doing so.

01 07 A Point In A World

Once you have your map, you can put your value chain on the terrain as well. Here I’m using circles as a Fourier analysis of the value chain. I’ve followed the Styrofoam cup as microphone notion of saying the circles fit the largest area between the constraining elevations of both the taxonomy and the ontology. We end up with the largest possible circles, the highest frequencies you can get. Now, we might not sense that tightly. We might sense smaller. But, sensing larger is a fail in the game theory sense. We’ve gone too far. We won’t notice, except that our gut instinct will tell us something is wrong.

01 08 A Point In A World

In the figure, the purple points represent the points of contact between our sensors and our terrain. The small circle is our peak. Well, hopefully, it is our peak, because it represents the top of the value chain, where you want to be. The circles are eccentric. That means that depending on their direction of approach a competitor might surprise you.

Enjoy. Comments?

Spatio-temporal Product Management

April 23, 2015

Reading 101 Things I Learned in Fashion School, brought to mind Architectural Drawing, 2nd ed. The latter book talks about architectural drawing in the post-building information system era. CAD system changed drafting and illustration for architects. CAD systems went on to change how buildings got built. CAD systems went beyond all that. CAD systems disrupted drawing as thinking. But after so many generations of Gartner’s hype cycles, drawing made a come back. Drawing found it’s place in a mixed analog-digital process. Analog drawing found its value amid the digital.

One way to think about this is in the sense of value projected, as in the post on projected value. CAD started simply as a different way to draw. CAD went on to be different way to compute, nomography no more. CAD became CAD-CAM. With Eisenman, CAD became an animation and rules-based system that moved buildings from static to dynamic. Each of these projections through other systems.

But, what were these value projections projected through? Space. How long did it take? Time. Value was projected through a terrain having a spatio-temporal reality. CAD had to meet CAM. CAD-CAM had to meet other elements before building information systems were realized.

As a product manager, you can look into the future and make that future happen, or you can let the future surprise you. But, it will be the vendor that reaches out to that next population that gets economics of scale, that gets there first, in the marketing sense, that gets the monopoly position and the immunity that monopoly brings you from the promo spenders. That first company gets to create wealth. The followers get to capture cash. Oh, well.

Once you layout your spatio-temporal product roadmap, you’ll start to see the research agendas that already contribute to your product as spatio-temporal maps. How long will the next advancement of display resolutions take to arrive? How will that impact your offering, beyond richer colors? How will an n time sort algorithm change your product? When net neutrality goes away, how will you code around that?

Now, back to the fashion book. I’ve read other books in this series. Each book tells you about the point of view of a given domain. Design for art, design for fashion, design for the engineer, and design for the MBA are very different things. Each of these domains defines the world its way, aka each has its own culture. I’ve called these functional cultures long before I came across a journal on epistemic cultures.

I’ve gone back to a long ago interest in photography and ran into HDR, high dynamic range photography. I can’t help but wonder how HDR ties to data warehousing, and big data.

As a final note, I’ll answer a question tweeted to me by an old friend. We were tweeting about how globalism needs to be addressed by managers and investors today. We need discontinuous innovation. Continuous innovation won’t bring globalized jobs back to our shores, or make up for all the jobs lost to globalization. So where do you find the companies doing that?  Start by reading the research front of a field you want to invest in, make or get a  spatio-temporal map of that field’s research terrain, know who is who in the field, and harder, know who the students are. Then, watch the sales tax permit applications. Join the community. It will take a lot of work. It won’t be easy, but following Moore’s guerilla game strategy, get there.

Comments?

More Spatio-Temporal Maps

April 15, 2015

Last night I came across a spatio-temporal map on the web showing travel time back 200 years ago or so. I can’t find the page, so we’ll have to let the when slide. I should have put the citation on the graphic itself. Note to processes.

As a kid, we’d be out of country for a long time. We’d maintain our connections to America via the Sears catalogue, the Armed Forces (radio) Network, and the movies that ran at the base theater. And, something called white bread. I was great stuff unlike white bread you buy at the grocery store today. We’d fly out of McGuire AFB in New Jersey. Once we flew out of somewhere else. But, we’d always fly back to McGuire. We’d end up in Newark, and Brooklyn Heights in NYC. More germane, we’d drive from New Jersey to the Alabama-Florida border where the stateside family lived.

The first time we came back it was on a boat. The next time we went it was on a prop plane. The next time it was on a jet. A week got compressed into a few hours…. But, here we were in New Jersey driving the interstates. They didn’t go everywhere. We never picked the places we were going so they were right off the interstates. No. We drove through lots of little towns. Lots of zigs and zags. Lots of late nights leaving the pitch black, entering the neon-lit burges, plunging back into the pitch black. There was a whole lot of spatio-temporal. Like that country song, “The world must be flat, people leave town and never come back….” Not really, but when they leave a product, they never come back.

So on to the map.

spatio-temporal map

Notice that we are talking land travel times, and earliest possible arrivals. Had they put travel by ship on here, the maps would be different. Travel and communications constraints made for dialect. You talked like all the people in your town. Widening that to say, your state wouldn’t make much sense, since different parts of your state where reached on different days. Your town might be isolated like far northwest South Carolina, which might be on the other side of the Appalachian mountains from the rest of the state. Those mountains were a considerable constraint. You went where the trails went, where the roads went, and before the railroads, you went where the canals and rivers went. Maybe you had a horse and went where the hell, you wanted to go.

Your travels where not a random walk. They were typically Levy flights. You were already in a fractal space. You were already in a world filled with Bayesian priors, unless of course, Joe of Joe’s Garage fame said, “Oh, no sir, you can’t get there from here.” Laugh, except that in the middle of the night, pre-interstate, east bound out of New Orleans, it was true. Dad always got lost there. But, don’t take my word for it. Try driving EB White’s coastal Maine.

Joe was just injecting some Gaussian noise, aka randomness into your Bayesian priors. So why do I not stop for directions?

But we are lucky, someone before us built roads, bridges, and tunnels. That “You can’t get there from here, not today.” was real. Today, we build stores and magazine stands on the side of an internet cable, on top of some API, running in one or more clouds somewhere on who knows how many servers at any given moment. We have a standard platform. We have whole product. When we improve it, those elevation lines on the map get closer together. When we improve it, we create wealth, create a monopoly, capture some cash, and become hero’s for some part of fifteen minutes. Being a hero twice doesn’t get you another fifteen minutes of fame. The terrain is out there. We just don’t have a mapping company willing to take on that project. No areal photos, no maps–apparently.

Notice the unknown, aka six weeks and beyond. There were keywords out there egging people on. The Santa Fe Trail, oh, yeah, a wide patch of grass in an otherwise rocky terrain. Follow the grass. Follow the wagon up ahead. Imagine having a teenager in your wagon. That fuzziness we reach at the six week mark is where that Gaussian normal and our Bayesian normal fight it out for statistical significance. Where our Poisson distributions and associated vectors leave us in the creative moment of creating a generative grammar for those following us. “Yeah, the lore says, cross this river to the south.” So another wagon shifts to the south. The rest of the wagons following that one shift as well. Tomorrow’s wagons, who knows.

Those elevation lines are still relevant today. I know that the drive through Chicago took three hellish hours, and that Erie, PA, I’d call it a day–a long spatio-temporal day of topological transforms. “It looked straight, until I changed maps.” Like, trying to drive west in Maryland or north in Nebraska. “You can’t get there from here.” Well, not until we put the interstate through. When we upgrade our roads, the steep, up and down two-lanes cut the hill tops off for fill, the bottoms get culverts and fill, the lanes multiply–the experience becomes flat. The same thing happened on the internet. Expectations rise. And, our look back machine considers the old stuff as lame, but back then it wasn’t lame–a historical elevation line runs through that.

The map above aggregated the data from tons of travelers. The data wasn’t just where New Yorkers went.

That added day running through north central Alabama was a mountain range between Huntsville and Birmingham. People in Huntsville don’t drive the hour or hour and a half to jobs in Birmingham. Yet, people make those kinds of drives in Houston all the time. Flat matters. In Houston, the roads a likely to be under water. Building culverts matter.

The map shows populations connecting to other populations. Your personal map is covered by a single normal with a lot of vectors an Poisson distributions under it. Look up into the sky. You don’t see the distributions you’re under., not a single one.  The technology adoption lifecycle connects a few highly related populations. The Bayesian terrain is there. The typical corporation have their economies of scale, reusable populations. Reusing populations means discontinuous innovations are out. It means you’re stuck in NYC even as every other non-local elevation line got erased.

Our product road maps tend to be straight lines. Having no topological map, we don’t built s-curves to gently get us over the next mountain. No, we drive straight ahead into the ditch. Well, at least you drove past the party at the rest area.

That one week travel time elevation line has moved all the way to the west coast with pockets still isolated as ever in between.

Innovation eliminates or reduces the impact of a constraint. What you see on the old map was time being lost to physical constraints, constraints on transportation and communications, constraints on getting there and getting done. Knowing what the situation today shows us how successful or innovations in roads, bridges, tunnels, and culverts have been. You don’t have to have taken the road trip or have gotten lost on Hwy-90 to know that those innovations have moved the constraints many times in your lifetime. It happens close to home, right in the street in front of your house, and the utility right-of-way behind your house. It happens in your house, in the walls, in the unused telephone connections, and wifi. It happens right behind your screen. All of it will continue to change. It’s not a matter of putting up another retail store, or serving the consuming masses. Mostly, it’s about getting a map. Find an elevation line and move it.

Lets hope we can get there from here.

Comments?

Value Projected

April 11, 2015

When marketers talk about value, I’m like, “Oh, please.” None of these markets read Value Merchants or Value-based Fees. Besides the recession is over, so there is less downward pressure on price. Besides everything is free because we monetize everything in every way. Still, value persists independent of price, aka acquisition costs, all those other costs rolled into Gartner’s total cost of ownership (TCO), and all those costs that don’t get reflected in the TCO. And, the need to talk about value persists as well.

Out on twitter, somebody will ask if UX is where value lives. No. Value is out there somewhere.

I’m going to start far away from value and talk about data Then, I’ll talk about data and value at the same time–not that value comes from data. Oh, yeah, IT people think value comes from data.

So lets start with a point.

03 00 A Point

Yeah, that point. We all know that point. But, we might ignore the notion that a point is made. It took Euclid two lines to make a point. These days we use Excel or maybe R to make a point. Then, we use points to make a point, alas a different  species of point. We might keep a point under a distribution for later use.

Actually, a point is born in a sensor. We’ll call a survey a sensor just in case a thermocouple just doesn’t tell you what you need to know.

03 12 A Point - Sensor

But, a lot of sensors require the sensed entity to be illuminated. A camera doesn’t do much in the dark.

03 13 A Point- Illuminator - Sensor

So now we have an illuminator, the point being sensed and a sensor. A political pollster might ask a slanted question, provide slanted answers to that question, and expect you to fill in those dots all before sending those forms to the reader, aka the sensor. That was a lot of illumination to make some bad points.

We might even sense an alias that is related to the thing we really want to sense, but can’t. You were out of town, so we asked your significant other. We’ll put some words in your mouth. It was only ten questions.

03 14 Proxy Point-Relation-Point

I use something I call the triangle model to talk about made things. It’s a decision tree. The base of the triangle is the made stuff. It could be a UX. Or, it could be the illuminator, sensor, and the point we made via a relation. So I redrew the above diagram.

03 15 Made Data

We have three triangles in this figure. I drew another figure with a forth triangle, because the relation was made. But how do these triangles interact? So another figure.

03 16 Triangle Model

In this figure, the illuminator’s triangle is shown in light gray. The thick gray line is the illuminator’s emitter. The sides of the illuminator’s triangle extend outward to the base of the sensor’s triangle. The proxy being sensed must be between the illuminator and the sensor. The relation projects through the sensor data processing it as it goes. After some calculation the relation produces the point.

The figure is demonstrating how the value of the proxy is conveyed through each component of the system eventually providing us with a point that can be used later. The components projected their value into the future into the distance from the functionality, UX, or realization. The point can be seen as the summation of the value the system captured and packaged. The point will be used a long way from the illuminator and sensor. The point will be used a long way from the relation as well. The point won’t tell anyone how it was built, but some of those details are needed before other’s can rely on that point.

Here is another figure illustrating the projection of value.

03 17 Triangle Model

Here we have someone using out point in a report. The person writing the report projected the report through a word processing app. That app projected value through a machine. The point was projected through the report after the point was projected from the proxy thought the illuminator-sensor plane. Lots of value projected from various sources from various distances and points of view.

Yeah, not at the UX at all.

Comments?

Noise and Knowlege

April 7, 2015

I started reading something on topology and statistical distributions. This is one of my research topics. My intuition tells me there is something to the notion that linear analyses fail when the space is hyperbolic, and succeed despite themselves when the space is spherical. In this reading the author said that the distribution sits on a manifold. Why a manifold? I’ll take that under advisement and wait for it to become more meaningful.

I’ve sketched tons of graphics. Some of those I’ve used in this series of posts on the normal distribution. We’ll look at one more, a normal distribution on a small sphere. The tails get longer, but like a squeezed water balloon, the noise that fills that additional length had to come from somewhere. We usually think of the distribution as sitting on a flat Euclidean plane. When the distribution is sitting on a sphere, flat goes out the window. The noise comes from the bottom of the distribution moving outward from the mean.

49 Normal on a Sphere

The figure shows how the shape of the distribution would change and how the tails reach around the sphere. In the figure, the increase in tail length is projected back a Euclidean plane. Lost in this is the height loss that happens as the number of standard deviations, or sigmas increase, as the firm grows larger.

Notice that in this particular figure, I’m taking the Frequentist point of view that of a distribution containing random noise, rather than knowledge.

Back in my radar mechanic days, the story about using a Styrofoam cup and a microwave transmitter as a bug was making it’s rounds. Microwaves are fun stuff. If you change the shape of the container, you change the frequencies emitted. That container is typically a metal waveguide. These waveguides are firm. They don’t get deformed in typical usage. But in this application as a bug, the lack of firmness is essential. A room vibrates, so the cup vibrates. Sound waves bounce around the room, so they eventually deform the Styrofoam cup. Those deformations clip frequencies from the square microwave pulse filling the cup.

Coffee Cup 03

The figure shows the opening of a Styrofoam cup in blue. The red sphere fits inside the cup. When you pick the cup up, the cup is deformed. The deformation makes the opening thinner, but longer. The frequencies that were the size of the red sphere are now clipped as only frequencies the size of the brown sphere can fit into the cup. You could use that Styrofoam cup to squeeze out some Morris code.

In the last two posts I wrote about how black swans clip the tail of the distribution. Black swans are typically big price/valuation losses on in the financial markets, aka missed quarters and such. But, these black swans are like setting an epsilon in calculus when you are trying to find the convergence of a function, so these tail movements happen all the time by tiny price fluctuations that happen every day once you’re a public company. Your normal distribution is like that Styrofoam cup. Your price constantly vibrates. This also means that your outliers might be under the distribution one day and not the next. Your real option tracking portfolio would act similarly, so the strategic decisions driven by those real options would oscillate as well.

Given that a statistical distribution has a surface defined by a function, and functions can be analyzed via a Fourier analysis, the shape of the distribution is doing the Styrofoam cup thing inside the distribution, not just relative to the outliers at the base of the distribution.

31 01 Randomness Structured

In this figure, I’ve drawn the largest sphere, the largest frequency, that could fit under the distribution. I also drew a much smaller sphere. Notice that with an unlimited budget, there is no physical limit to how small that smaller sphere could be. Alas, at some point you end up with a laser, aka another way to pick up the vibrations from a Styrofoam cup. But, budget and significant use keep us from getting smaller frequencies into our Fourier analysis. This is much like doing a factor analysis. There is always another factor, but the smaller those factors get, the more expensive it is to capture the underlying data. Beyond budget, you might want to ask just how much company cognition you can dedicate to ever finer factors.

I did not show the spheres between the largest and smallest that would fit or pack under or inside the distribution. Also not shown are the lifecycle of the distribution. The largest sphere gets smaller as the company gets larger. The spheres start out small in a Poisson distribution and get larger as those Poisson distributions tend to the normal.

32 02d Poisson Distributions Tending to the Normal

The above figure roughly lays out the Poisson distributions under the normal while those Poisson distributions tend to the normal. Frequentist probabilities use the law of large numbers to find macro-level behavior, and the law of small numbers to find micro-level behavior. Poisson distribution provide the basis for Markov chains. Markov chains begin chipping away at the notion of that a distribution only contains random noise. Markov chains begin to structure the contents of a normal  distribution, the normal distribution being large. Poisson distributions, aka small distributions constitute traversals of the area under the distribution, aka vectors, like a vector of differentiation.

32 02c Imposing a Structure Under the Normal

The Poisson distribution here starts as an outlier. It follows a chain of vectors until it gets to the mean. It could be a random walk under the normal. It need not pass through the mean. When we seek out our next discontinuous technology, our random walk would be a Levy flight. Imposing structure happens as we gain knowledge of the systems under the normal. As this structure is imposed, the probabilities become less Frequentist and more Bayesian.

The next few figures illustrate how the technology adoption lifecycle imposes structure on the contents of the normal distribution, on the once random variables.

32 02a Normal Distribution Footprint Outliers32 02b Imposing a Structure Under the Normal32 04 Imposing a Structure Under the Normal

Here I wanted to show how the B2B early adopter was an outlier. Yes, I called that early adopter a weird person. They don’t make a good reference case for other prospects in their vertical. The technology adoption lifecycle is organized by pragmatism. Marketing would set the width of each slice of pragmatism. Those widths can change. But, business cases and other reference data needs to be generated for each slice. Market to a few, since traversal across the market takes time, but try selling to just one at a time. Requirements collection needs to be bound by the width of the pragmatism slices as well.

32 03 Imposing a Structure Under the Normal

In the above figure I’ve put the B2B early adopter, who is an outlier in our category’s normal distribution, is also an outlier in the normal distribution of the vertical that that B2B early adopter does business in. In the bowling ally, the seats and dollars you will take from that vertical is the only workable stage gating you’d want to do before deciding to take on building that B2B early adopter’s product visualization.

Structure comes out of nowhere, well, out of the daily operations, experimentation, and other efforts to reduce the uncertainty of the innovating organization. Geometries change, the shapes of the noise change, distributions change, but they change in organized ways. Frequentist probabilities are not the only ones out there. Some people have found that they have topological problems. Know who to call.

 

Enjoy? Comments?

 

Learn and Forget

April 4, 2015

One of the ideas you hear a lot for a long time now is how you have to keep learning going into the future. Have fun with that.

The technology adoption lifecycle, aka the normal distribution says something else about the future. The transition from early to late moves the focus from carrier to carried, from IT to the departments doing other work, from the horizontals to the verticals, from geeks to consumers, from players to payers, from firewall disdainers to firewall payers. All of this happens at the mean of the normal. At the mean, we have to forget.

The transition from early to late also does other things. It switches your stock price outlook from growth to decline. IPOs were big, but now will be smaller, as the premium goes away. And, you miss a quarter, because you forecast continuing growth, but now having sold more than 50% of your available market, you have fewer prospects ahead, more pragmatic prospects, smaller companies ahead, and marketing pushing the wrong people down your pipeline. Sales might even feel like going for the CxO sale, which slows down the deal flow immensely.

So you missed your quarter, so stock price effects happen as well. You have to take your employees off of stock option compensation, since those stock options are worth less and will not grow, which means you’ll be renegotiating salaries upward. You look like an ordinary company. You are not a startup anymore. It happens. You’re VCs will be pushing for your M&A, if you took VC money. Yes, your company could have a 10x larger market after you’re acquired, but that accrues to the acquirer. Much happens crossing from early to late, aka crossing the mean.

But, lets get back to what your product team learns and forgets. Lets bring this home.

25 World as  Bits 02

In this figure we look at what the development team is doing right now. The x-axis is time. Below the x-axis is functionality provided by your value chain suppliers, say your cloud vendor. The world that development created includes their code, above the x-axis and the bits provided by the value chain, the whole product. Make is above the x-axis. Buy is below it. A lot of coordination is required at the x-axis, maintenance windows, et.al.

Now is a vertical line slicing through the distribution. Inside the distribution is what was just released, or what will be released the next time. It is what we are making now. Below the x-axis is what we are buying now. Above the normal is a population we will come to serve in the future. The buy portion of the line also has a segment looking to the future and what will be bought in the near future. Consider that your value chain providers likewise operate under their own normal distribution. Your future buy is their future sale.

To code for the future populations, aka make, and to buy for the future populations is learning via accretion or accumulation, as described in Stewart Brand’s, How Buildings Learn. Yes, your organization learned its way across the technology adoption lifecycle (TALC), as it sold its way across it as well. When I’m talking about the TALC as a normal, I’m talking Bayesian probabilities, where there is knowledge under the distribution, rather than the frequentist’s randomness.  Moore said that pragmatism organizes the TALC, so the lifecycle is not random. I did have a sales rep describe his lead-handling process as a random one. Marketing is Bayesian, aka not random, while Sales is Frequentist, aka random–A fundamental conflict. Likewise, content marketing lays out content under the normal, so consistent with marketing’s inescapable approach, it’s knowledge under the distribution where time and pragmatism is the coordinates of place, and learning.

So let’s cross the mean and look at the other side.

25 World as  Bits 03

Here now is right of mean, deeper into the future. I think of those bits I mentioned earlier as the size of the world. Here the world is large in the sense of total bits, but most of those bits are not relevant any longer. We have left customers behind. We have dropped the geeks as our market. Sure they are still there, but we don’t serve them. We’ve even been charging for our services, because our consumers pay for things. Free doesn’t fit anymore.

On the figure, I’ve labelled the forgetting, since that is what we are doing. As me move into laggard, phobic, and non-adopter spaces, we are disappearing into the stack. It’s hard to disappear if you are a media operation striving to capture attention in your content layer as your carrier layer is disappearing. Beware of your monetizations when they run contrary to forgetting. We have forgotten things in the past. We have ongoing forgetting operations. Making the future is just there to accommodate the forgetting. When we first crossed over the mean from early to late, we had to hide controls, while retaining the power of our application. Moore called this task sublimation. Look at all the things we don’t do in our mobile apps that we used to do. We don’t save files anymore. Everything is in a database that we don’t administer. We make a little for now. Our buying side undergoes the same forgetting pressures. Our supply chain has to survive on selling less, not more. Their bits are disappearing just like ours. So the right side of the normal is about forgetting.

Next, I’ve put both sides on the same figure.

25 World as  Bits 05

And, I sum up some points next.

25 World as  Bits 06

The world we made traverses the normal from left to right, from the past to the future. We consume bits converting them to dollars, as we consume customers. We have a scorched earth approach to consuming customers. We only have one initial sale. We retain them, but it is the initial sale that moves across the x-axis. The customer is the tick of our clock. The bigger the customer the sooner we get to the mean. Crossing the mean we begin to reduce the size of our world. We stop growing the number of bits. We undergo bit reduction. Oddly, our organization concocts a growth myth, so it can stay larger as it depreciates bits. The organization gets larger in terms of standard deviations, which lowers the ceiling under the distribution as our margins get thinner.

Notice that I labeled a particular point on the surface of the distribution with the word “Stop.” In calculus, we approach a limit defined by an arbitrary height epsilon. Epsilon is what I’m calling “min.” We need a minimum amount of cash to keep going. You can only layoff so much. “Stop” is where the normal converges with our burn rate.

The TALC is the lifecycle of a category. Blue oceans happen near that epsilon convergence. Crossing the mean should have us looking for the next discontinuous technology to ride. Today we are comfortable with capturing cash, instead of creating wealth, building entirely from other people’s whole product, starting out to the right of the mean. We are comfortable with stasis. We live in small worlds with rich pasts. We look back at that past and forget that it taught us. It fit the populations it served. If it didn’t we wouldn’t remember it at all. It didn’t lack design. The ethic was different.

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