Archive for January, 2016

Stuff Left Out

January 17, 2016

My review of math has me learning things that I was never taught before. There were concepts left for later, if later ever arrived.

We had functions. At times we had no solutions. Later, they become functions without the right number of roots in the reals, as some of the solutions were in the space of a left out concept, complex roots. For a while, after a deeper understanding of complex roots, I’d go looking for the unit circle, but what was that unit circle centered on? Just this week, I found it centered on c, a variable in those equations like ax2+bx+c. So that open question comes to a close, but is that enough of an answer? I don’t know yet.

We had trigonometry, because we had trigonometric functions. We have the unit circle and an equation, notice that it’s not a function, because as a function it would fail the vertical line test. When a function violates the vertical line test, we create a collection of functions covering the same values in a way that does not violate the vertical line test. Trigonometry does that for us without bothering to explain the left out concept, manifolds.

One of Alexander Bogomolny’s (@CutTheKnotMath) tweets linked to a post about a theorem from high school geometry class about how a triangle with it’s base as a diameter of a circle and a vertex on the circle had angles that added up to 180 degrees. Yes, I remembered that. I hadn’t thought about it in decades. But, there was something left out. That only happens in a Euclidean geometry.

Well, I doodled in my graphics tools. I came to hypothesize about where the vertex would be if it were inside the circle, but not on it, and the base of the triangle was on the diameter. It would be in a hyperbolic geometry was my quick answer; outside the circle, same base, spherical. Those being intuitive ideas. A trapezoid can be formed in the spherical case using the intersections of the circle with the triangle. That leave us with the angles adding up to more than 180 degrees.

I continued to doodle. I ended up with the bases being above or below the diameter, and the vertex on the circle. Above the diameter, the geometry was hyperbolic; below, spherical. I got to a point using arc length were I could draw proper hyperbolic triangles. With the spherical geometries there were manifolds.

The point of all this concern about geometries involves how linear analyses break down in non-Euclidean spaces. The geometry of the Poisson games that describe the bowling allies of the technology adoption lifecycle (TALC) is hyperbolic. The verticals and the horizontals of the TALC approach the normal. Those normals at say six sigma give us a Euclidean geometry. Beyond six sigma, we get a spherical geometry, and with it a redundancy in our modeling–twelve models all of them correct, pick one.

We’ve looked at circles for decades without anyone saying we were constrained to the Euclidean. We’ve looked at circles without seeing that we were changing our geometries without thinking about it. We left out our geometries, geometries that inform us as to our non-linarites that put us at risk (hyperbolic) or give us too much confidence (spherical). We also left out the transitions between geometries.

The circle also illustrates why asking customers about their use cases and cognitive models, or even observing, doesn’t get us far enough into what stuff was left out. Back in school, it was the stuff that was left out that made for plateaus, stalls, stucks, and brick walls that impeded us until someone dropped a hint that led to the insight that dissolved the impedances and brought us to a higher level of performance, or a more complete cognitive model.


January 8, 2016

I just finished reading a review of “Are we Postcritical?,” a book about literary criticism.  It mentions things like Marxism and Structuralism used as the basis of literary criticism. It goes further to mention a stack of critical frameworks.

These critical frameworks are applied to all art forms from literature to sculpture to architecture to “design” in its various outlets. You might find a Structuralist critique of the iPhone. Or, a Marxist critique of some computer game.

But, developers hardly go looking for the critical reviews of their own art. We hear it on twitter. Designers tell us the UI’s of the 80’s and 90’s suck. Well, sure, had we been trying to serve the same users we serve today. I’ve got news for you, they didn’t suck. They served the geeks they were intended to serve. Nothing today serves geeks. Sorry geeks, but we serve consumers today. So today, we can think about that same stack of critical frameworks that gets applied to “design.”

To get to this “design” as a form of art, we would have to be artists. Yes, some Agilists come across as artists in their demand to be free from management and economic considerations and purposes. But, back in the early phase of the technology adoption lifecycle this wasn’t so. Under the software engineering approach, we had a phase called “design!” Yes, we applied critical frameworks that had nothing to do with literary criticism that were just as critical as these art and artist-oriented critical frameworks.

Every domain has its own critical frameworks. Before we drop a bomb, we take a photo. We drop a bomb, then we send another drone to take a photo. That photo is graded via a critical framework, and bombing is assessed. We could if we like apply a structuralist framework during this assessment, but mostly we’ll ask “Hey do we need to send another drone to take the target out?” “No, it’s a kill. Tell PR there was zero collateral damage.” That being just an example of a geek’s critical framework.

More to the point we might say O(n), which becomes possible once we have true parallelism. Yes, everything will have to be rewritten to pass the critical framework of algorithm design. Oh, that word again, “design.”

Accountants have critical frameworks. Likewise, hardware engineers and software developers. They just don’t happen to be artist-oriented frameworks. It just kills me when an artist-designer puts down the design critiqued by some unknown to them critical framework. And, it kills me that these designers want to be the CEO of firms selling to consumers without recognizing all the other critical frameworks that a CEO has to be responsive to like those of the SEC, FCC, and various attorney generals.

Design is the demarcation of and implementation of a balance between enablers and constraints be that with pastels and ink; plaster and pigments, or COBOL. The artist wants to send a message. The developer wants to ship a use case. What’s the difference? At some scale, none at all. Design, in it’s artistic/literary senses has yet to reach the literate/artistic code of developers. Design, in that art sense, is an adoption problem. But, we do have computers doing literary criticism, so one day computers will do code criticism. Have fun with that.

And, yes, since this is a product management blog, some day we’ll have a critical framework for product management. We already do, but who in the general public will be reading that in their Sunday papers? Maybe we’re supposed to be reading about it in the sports section. The sportscaster calling out the use of, oh, that design pattern.

Yes, artist-oriented design is important, as is brand. Have fun there, but there is a place, and that place is in the late phases of the technology adoption lifecycle, not the phases that birthed the category and value chains that underlay all that we do today. Late is not bad, it’s just limited to the considerations of cash, not wealth–oh, an economic critical framework.