Joshua Rothman’s *“Are Things Getting Better or Worse”* talks about an interesting reality of human perception. Things get better, but we don’t see it. Better happens on the scales larger than the individual. Worse happens on the smaller scale of the individual. We have to reach to see that better.

The article mentioned the statistical view of normal distributions with their thin tails as constants contrasting them with thick tails as underestimated surprises. Yes, once a distribution achieves normality slightly south of n = 2 11 data point where skew is gone, and excess kurtosis is gone as well, surprise is slow and resisted. A normal distribution becomes a Cauchy, aka a thick-tailed, distribution when some epsilon asserts itself under the normal when some logic erodes, or some new logic is birthed when as a new subgraph inserts itself in the graph defining the undermined normal.

Rothman went on to mention the population bomb whose explosion we managed to defuse. He frames it as a debate, as A vs B, as in A XOR B, two rhetorically mutually exclusive outcomes, Borlaug’s and Vogt’s, except that they were simultaneous and independent. The world decided to do both. The world adopted both.

The underlying beliefs required the adoption of Borlaug’s greening and agricultural innovative technologies and simultaneously adopting Vogt’s population control mechanisms, which beyond China turned out to be the spread of prosperity. The opposing adoptions involved two categories each with their own technology adoption lifecycles (TALC). The innovations exploded outward from the problem they resolved.

In the figure above, I made no determinations as to what phases the technologies were in. Those technologies are commodities now. And, the wins were determined after the fact, long after the problem was addressed. Realize that there are n dimensions to the problem and some m < n dimensions, fewer, technologies being adopted to address the problem.

That mutually exclusive framing struck a chord with me. That XOR sits between two things, the meat between two pieces of bread, aka a sandwich.

Sandwiches turn out to be typical of mathematics. Ranges like **0 < 3x + 5y < 187** are sandwiches. Once a mathematician finds one such object, the next mission is to delineate an extent. For a biologist, finding a previously uncataloged squirrel is the existence moment. The next question is how many of them are there and where do they live which resolve into a collection of ranges. In the technology adoption lifecycle, a phenomenon organized by the pragmatism of the underlying populations, again we see ranges. And ranges are sandwiches. A value chain or an ecology is a collection of sandwiches. Is it in or out of the meat of the matter?

The immediate example of a sandwich is linear algebra or more precisely linear programming. There can any number of constraints operating on a given problem. The solutions to the problems are the areas bounded by the collection of constraints, each constraint being a linear equation involving inequalities.

Every constraint has its own technology adoption lifecycle. It might be that a constraint is completely new or discontinuous. More typically, a constraint will be moved by continuous innovation or normal science. As an area is defined by any number of constraints, we have numerous dimensions in which to innovate.

Enjoy.