lf acceptance of this idea does not constitute a problem for the reader (and you do

lf acceptance of this idea does not constitute a problem for the reader (and you do not find it fun to follow along with a computer math program and/or a pencil), then the following several paragraphs can be quickly scanned or skipped entirely. The computations of H; and Hy begins with keeping track of how many 0 > 1 and 1 > 0 transitions are found going from left to right in the binary series. For example, in the binary expression of 729, 1011011001, one starts counting with a 1— 0 transition followed by a 0 + 1 transition and then a 1 — 1 transition and so on. A useful way to record the count is via entries into a 2 x 2 matrix for score keeping in which the horizontal rows are labeled 0 on top and 1 below and the vertical columns are labeled O on the left and 1 on the right. The number of each kind of transitions (from the vertical label to the horizontal label) are counted and summed in the appropriate box of the two box by two box matrix; for examples: for a 0 > O transition, a tally mark is entered in the upper left corner of the matrix; for a 0 —>1 transition, a tally mark is entered in the upper right corner; a 1— 0 tally goes in the left lower corner and a 1-> 1 Is tallied in the right lower corner. The resulting transition incidence counting matrix, M; for the 729 binary transformation series 1 3 looks like M; = 32 indicating one 0 — O, three 0 > 1, three 1 > 0, and two 1 > 1 transitions have been tallied. Although this series alone is too short for computing reliable statistical measures, if we assume that the pattern of transitions observed in this short series is stationary, that is its transition behavior will remain the same if the binary series continued on to be infinite in length, the assumption being that the dynamics of now will be the same as always, 729 will stay 729, then we can use two forms of this transition matrix in the computation of the topological entropy reflecting the growth rate of the possible, H;, and the metric entropy from the statistical weights of allowed choices among them, the probable, Hy. To obtain the entropy representing the growth rate over time of the new possibles, the computation of H7, the topological entropy, involves first transforming M; into an transition incidence matrix, Mz; a 0 or 1 matrix indicating whether each box has been entered at all (or not). Since in the binary representation of 729, all 107 HOUSE_OVERSIGHT_013607