The Grid

It’s been said of mathematical proofs that they start somewhere and end somewhere else. Grids behave in the same manner. Grids might be rectangular or square.

Grid 4x10Grids might be laid out on some modulo, which greatly restricts their shape and how they shape the content they contain or in our verbiage “carry”. In the end, a grid starts somewhere and ends somewhere else.

Mod 10 Grid

Each of the rows could have kept on going, but the rule about row population prevents this, and instead, puts the red numbers on the next line.

A table of z-scores takes an infinite ray and chops it up at decreasing and later increasing intervals. The z-score table in the back of my statistics book gives the wrong impression when it chops the entries up ten z-scores to rows of modulo 10. The shape of the table controls the shape of the carried z-scores. The z-scores have their own shape, but it is lost here.

Table As Media

Just to make the table as media reality clearer, I’ve changed the carrier, the grid, as I changed the number of columns. I changed the metadata or meta carrier to change the number of columns. Being a carrier or the carried is a matter of shifting contexts in the stack.

Table Carrier Modified Meta Carrier

Oops! This carrier is smaller than the last. We’ve run out of carrier before we’ve ran our of carried content. Those excess numbers fall into a jumble on the floor. Some of the numbers that remained in the table did not move. Other’s moved. I’ve highlighted the ones that did not move. They remind me of Ito processes, processes with fixed sized memories. A Markov process is an Ito process with zero memory (n=0). In our table, the rows are memories that vary between zero and ten (0 ≤ n ≤ 10). This memory problem is what the Hilbert Curve was invented to solve. A value placed on a Hilbert space-filling curve never moves. Hilbert curves forget nothing in our Ito process sense even as the resolution or densities vary. In terms of the last post, Matrix Composition, matrix compositions, the processes never move even as the customers and the products move on.

Table Sequence and Memory

When the carried is a sequence, it remains a sequence. The grid becomes sparse or ceases to be a rectangle or a square when the sequence dances. z-scores are such a sequence. The z-score sequence is really a collection of sequences.

Sequence of Differences Without Modulo 04

Here I’ve put each sequence making up the larger sequence on its own line. Here we put a parsing rule in place. The first number that is larger than the previous number goes to the next line. Then, we add the next equal in value numbers pushing back to the front indicated by the red vertical line. This works until the new line is longer than the prior lines. Then we add another rule. Push the front of the lower value number further to the right and add spacers or holes on the lines above where necessary, so the lower values are aligned at their front. Spacers change the shape of the surface of the curve. Holes run through the solid mass of the curve. Those two rules let the sequences express their “natural” shape. The grid is going where it will. The shape of the curve, the shape the grid will follow, might surprise you.

Iterations and releases would behave similarly. If you put too much in an iteration, you end up pushing the boundary of the next iteration or release. Or you move the current iteration into the next release and ship what you have, a working iteration.

As a product manager, are you imposing a modulo on your roadmaps, or are your roadmaps going where they go without enforcement? Are you mining the shape of your roadmaps for surprise? Yes, we impose some rules about delivering value in each release. We have an upgrade tempo, but the functionality carried by the roadmap dances to its own shape.

Are your carriers clearly separated from your carrieds? Are your populations facing your carriers or your carrieds? Remember that the IT horizontal is carrier facing. Most of what we do these days is likewise carrier facing even though we might be selling to consumers. Are we turning consumers into administrators with this carrier focus?

The push rule provides a new kind of outcome if we were being probabilistic about outcomes. Z-scores have holes in them.

 

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One Response to “The Grid”

  1. A Discontinuity in a Sequence | Product Strategist Says:

    […] Beyond the orthodoxy. « The Grid […]

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