## Discontinuous Innovation

I’m reading a book on math for biology majors. The first chapter discrete time dynamical systems was great. It tied back to phase graphs in the book on Chaos I read back a few years ago. The next chapter is about derivatives. I was going to skip it, but I’m glad I didn’t. I takes a completely different approach. It’s not trying to make you into a mathematician. So I get to the part about continuity. Boring, except it wasn’t.

Instead, I found myself looking at a graph that was simply shocking. I must have seen this before, but no, in my math books discontinuities were open points omitted from the domain or range. Not this time.

In the earlier chapter, we went looking for equilibriums and in a certain situation, there are none. That situation, a discontinuity between two parallel intervals.

So this time, we have two intervals with a vertical gap, a discontinuity between them. Of  course, that wasn’t the shock. Instead, it was putting this in the context of trying to explain discontinuous innovation. First, the graphic. Then, the build to what it demonstrates.

The function we graphed was a step function:
f(x)=2Vt if x≤20 and f(x)=3Vt+20 if x>20.
The major point here is that they don’t intersect.

Next, we throw the marketing at it.

From a marketing perspective a discontinuous innovation is about a new formerly unserved population, a population that wasn’t interested in your offers before this one came a long, a population you weren’t interested in, and populations that are not known to each other either in terms of serving as a reference base for the other. Like the demographers and ethnographers trying to converge into a new discipline that I mentioned in another post. Still calling each other names. The technology under the hood isn’t similar to that of the existing population’s tech. The technology might not even be as good, yet. But, this discontinuity is wonderful, because it lets you create a new category and be the next near-monopoly exemplar corp in the biz press, a decade from now. Yeah, it’s not a next quarter thing.

But, back to the graph. The thick brown lines represent step functions that have been associated with their populations. I color coded the areas under those functions with aqua and purple. And, I show the vertical gap, the discontinuity in gray. Then, thinking about alleles, I differentiate the functions with a single bit, summarzing all the bits it takes to make those two function lines happen in a product.

The gray area represents a curriculum problem, a content problem, absence of an old-new contract. When Relativity came a long, they were the new population. The adopters had to make a knowledge leap and believe in the stuff, but doing so did help them, so they did it. There was no road from Newtonian to Relativity. To move the prior population, was to teach them, and retire those that wouldn’t learn. This stuff happens with our technologies as well. Take object-oriented programming (OOP). Initially, OOP was radical. So radical, that my CS profs wouldn’t go there until later, not with us undergrads anyway. But, it finally fell to MS to adopt OOP in there API. When they did, the did it in a continuous manner, and OOP stopped being radical. OOP wasn’t the same either, so today you still hear object thinkers trying to recapture the promised upsides of radical OOP. Oracle helped norm OOP as well by killing off the object-oriented database management cateory. Yes, to persist is a verb, or something that programmers still have to mess with, because OOP doesn’t do what was promised.

Oddly enough, back seven years ago, I was reading Seeing What’s Next, one of Christensen’s book in the delimna series. I posted a blog talking about how discontinuous was lexical, a decision about an approach. Christsen had a graph of S-curves. I redrew it. I put the old S-curve on the background, and the new S-curve on the forground. The middle ground was the lexical space. The middle ground was the discontinuity. Eliminating that middle gound collapses the radical, the discontinous into the continuous. Eliminating the middle ground changes the economic outcomes, because without it, you don’t need new value chains, and eliminating it changes the geography so it Euclidean or spherical depending on the size of the company pushing the underlying technology. Eliminating also takes the tornado allocated market leadership with it. Nah, without that middle ground, all you get is another market allocation in an existing category, aka a very small allocation of miniscule marketshare.

The discontinuity on the graph is the same as the middle ground in my long ago illustration. That discontinuity is gray. There are no bits here. This is the unknown. But, here is the thing, we actually decided to not extend the graph of the interval on the left, so that it would intersect the interval on the right. We decided to keep the middle ground, and to keep the populationos mutually exclusive. We decided to separate. Unfortuately, the business orthodoxy doesn’t let us separate. They’ll tell us that it costs too much. Then, the innovation fails to achieve it’s business objectives, and it was the innovation’s fault. Sorry management, but no. Christensen has not won the war on the separation concept, so we will all lose until we get this right. Separation is necessary. The point of separation is to create wealth, to create those value chains, not to capture cash, or pretend to be a bank like all those sigma 30 to 40 public companies out there, companies with no margins and an absolute need for cheap labor. But, the orthodoxy will wear you down. It was Moore that used to tell us that discontinuous innovation is about creating wealth. The Chasam Companion was about this wealth creation via value chain concept. It was also Moore that disavowed separation as being too expensive in his last book, a book where he turned his technology adoption lifecycle inside out for the sake of the orthodoxy he’s been working for since the Web 1.0 dot bust. Who can blame him? Nobody does real technological innovaiton anymore. We are replicants now.

But, there it is in gray, separation.

So if the discontinutity is a choice, what of continutity?

So here we are with our situation no longer discontinuous, no longer radical, not longer about creating wealth. Loads of cash, sure. And, how did we do this. We decided. We decided to let the function on top keep going until it intersected with the other function. We changed
f(x)=3Vt+20 to f(x)=3Vt+10.

I’ll have to check those functions and the conditionals, but that’s what I remember right now.