Author Archives: Bob H

Models and Reality by H. Putnam… More from Putnam… Click to access 03-Hilary-Putnam-Afterthoughts-on-Models-and-Reality.pdf Also worthy…Skolem and the Skeptic by P. Benaserraf …you’ll need a jstor account (free) to read it online. https://www.jstor.org/stable/4106752

We live in a world where time is real. In the real world there is no such thing as a “finished” infinity. There is no such thing as a boundary with no “holes”… a complete “manifold” of “fixed points”. That “Platonic universe” may be a useful fiction for some purposes, but it is just that,Continue reading ““R” is not a static “configuration space””

It is important to recognize the role of the “backward wave” in “wave propagation”. The role of the complement cannot be disregarded…it must be understood. Here are some links to papers that deal with the issue as a physical principle. Huygens’ Principle geometric derivation and elimination of the wake and backward waveForrest L. Anderson https://www.nature.com/articles/s41598-021-99049-7Continue reading “Huygens’s wave propagation principle and the Mott problem”

The discrete derivative is founded on the recognition that two complementary strings are a partition of the infinite string of 1’s. Starting with only 00000… and 111111… we get all the binary strings as complementary pairs between the two “parents”. Starting with “0” we get the counting numbers as partitions of “1”. Growth is alwaysContinue reading “The Discrete Derivative Tree”

The labels in this tree are 2×2 matrices and as such are representations of a geometric structure as explained in “Matrix Gateway to Geometric Algebra, Spacetime, and Spinors” by G. Sobczyk. There are many other sources for the same information, but his book is concise, accessible for an undergraduate in math or physics, and inexpensive.Continue reading “The Dyadic Monoid Tree”

The Stern-Brocot Tree starts with “virtual vertices” (labeled 0/1 and 1/0 below) appended to the basic binary tree structure… Labels are constructed/assigned via a “mediant” process…add the numerators and denominators of the vertices on each side above the vertex… The fact that we can use information from only the previous row without reference to anyContinue reading “The Stern-Brocot Tree”

The idea of “discrete” can be modeled by a binary tree…by the parent/child relationship. The space between branches are the “holes” in the structure or the two parts separated by a boundary (“branches” in a binary tree: the two “children” of the one “parent”). The idea starts with a blank tree devoid of labels. WeContinue reading “The Binary Tree”

The title of this blog entry: in as much as it assumes there is such a “thing” as a beginning it assumes a certain relationship between the discrete and the continuous. Which comes “first”, discrete or continuous, how do they relate? Does the discrete “generate” the continuous as in parent/child?…or is there a “smooth” transition,Continue reading “The Beginning”

Read the previous blog post Towers of Hanoi, then answer the question,” how many cuts does it take to divide a strip of paper into 4 parts, 8 parts, 16 parts?” Likewise, how many jumps does it take to get from the first entry in our lists of code to the last entry? Answer: obviously,Continue reading “How we put Humpty back together again”