# Scientific & Mathematical Explorations

## don lehman jr.

This website contains the results of my scientific and mathematical pursuits over more than 4 decades (1978 - 2023). My research ultimately coalesced into a series of Books, each consisting of multiple numbered Notebooks (links at left). Each Notebook consists a variable number of numbered Articles.

Each Book (series of Notebooks) has a unique focus, e.g. habit formation, maximizing a creative session, and how life digests information. A single mathematical system, Data Stream Dynamics (DSD), unites this diversity under a common umbrella.

Why this common thread? Life via Attention employs an image overlay process (IOP) to digest information. The Living Algorithm (LA) is the mathematical realization of this IOP process and DSD derives from LA. As evidence for this model, evolutionary forces operate upon DSD to enhance living potentials, e.g. survival and reproduction.

The process that Life employs to digest information (IOP) generates a second dimension of time. Matter only exists in time's inexorable linear (horizontal) dimension. In addition to horizontal time, Life also exists in time's cyclical (vertical) dimension. Accompanying time's vertical dimension is a temporal sense that enables meaning, purpose and choice.

Following is a brief description of 7 of these books with a link to a table with Notebooks and articles.

I: Data Stream Momentum (1994) The first collection of 5 Notebooks (#1>5) develops the potentials of the Living Algorithm. The articles produce insights and derive equations that ultimately provide the basis for Data Stream Dynamics, which is so important for my Theory of Attention. This unique mathematical system generates some models that shed light on abusive relations, the conversion experience, the influence of boredom on civilization, and the effective use of will to change habit patterns, including diet.

II: Directionals: Content, Context & Beauty (1994) The second collection of 5 Notebooks (#6-10) is a mathematical exploration of the decay-based central measures that were derived in the first work. Some beautiful equations, which ravel and unravel, furl and unfurl, actually turn into a beautiful picture-equation that mimics nature.

III. The Creative Pulse (2002) The third collection of 3 Notebooks (#11>13) is an extension of the discoveries of the mathematics of behavior that were laid out in the first book. It develops a new notion - the power of sustained Attention, which results in the Creative Pulse. The Creative Pulse is a feature of Data Stream Dynamics. This mathematical model makes distinct predictions about the nature of the Zone, whether athletic, intellectual, artistic, or emotional, positive or negative.

IV: Root Beings & The Internal Structure of Numbers (1995, 1999) This collection of 4 Notebooks (#21>24) is a mathematical study of iterative equations based in infinite continued fractions. These mimic the quest for mastery or even enlightenment. Mathematical proofs indicate that rationals, irrationals, and patterned transcendentals, all belong to the same family of numbers.

V: The Triple Pulse & Attention Dynamics (2010-2012) This collection of 8 Notebooks (#32>39) extends the insights of earlier Scientific Pulses. They establish patterns of correspondence between Data Stream Dynamics (DSD) and many scientific facts from living behavior, biology and evolution. DSD derives from the Living Algorithm and is based upon and inspired by the same architecture of constructs as Newtonian dynamics. The cross-disciplinary strength and stability of this Math/Fact Matrix indicate that Living Systems employ the Living Algorithm as a computational interface to derive dynamic meaning from sensory and ideational data streams.

VI. The Realm of Attention (2016-2018) The primary goal of this collection of 4 Notebooks (#40>43) is to provide support for the hypothesis that there is a Realm of Attention that is on a par with the Material Realms, i.e. Subatomic and Atomic. The Living Realm exists at the intersection of the Material Realms and the Realm of Attention. The Realm of Attention has its own mathematical system, Data Stream Dynamics. It seems that the Rhythms of Attention are entrained to the rhythms of Data Stream Dynamics. These naturally occuring rhythms exert an influence on behavior, biology and evolution.

VII. Life's Information Digestion System (2020-2021) The primary goal of this collection of 7 Notebooks (#44>50) is to provide support for the hypothesis that living systems have an Information Digestion System (ID system) that is on a par with our physiological systems. Extending insights from Spiral Time (Notebook #1), we develop the notion that Life's two types of systems, i.e. info and material, operate in different dimensions. The ID system operates in Time's Vertical Dimension, while Matter operates in Time's Horizontal Dimension.