Diversions in Pure Theoretical Physics
If cancer can sometimes result from a single mutation in a base pair along the DNA data set that contains over 3 billion base pairs, within a single cell that is just one of roughly 30 trillion cells in the body, then we need to have a physics built from terms that are true to at least one part in 10^22. Neither Newtonian physics, nor special and general relativity, nor quantum mechanics are true to that level of certainty. In fact, that is about where they begin to break down. This is not surprising since most of our definitions evolved from a very practical need to truncate the finescale data associated with nonlinear activity  data that is otherwise too difficult to manage. If our organisms evolved within a physics environment that was fundamentally true  or, at least true to the order of the Planck Scale  then it is worth exploring conjecture about ways we might extend our current definitions into the mathematically more complicated, nonlinear, and selforganizing domain of the cell.
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PI: Pythagoras in the Real World?
The Pythagorean theorem tells us how we should define the distance between the free endpoints of two line segments that are joined to form a right angle. It has served as the basis for differential geometry and the launching point for defining spacetime curvature in modern gravitational theories. We are not going to second guess the use of the Pythagorean theorem as it applies to idealized geometries built from points and lines  but we are going to inquire whether the theorem is valid to apply to discrete systems. Might we view the Pythagorean theorem as valid only in the limit where [dx~0]? (Posted: 2.10.17)

PII: Modified Definitions of Curvature and Acceleration in a Discrete Medium?
Rotation is a property we associate with movement along an arc. However, curvilinear motion is a deduction we make by observing the position of a system over two or more intervals. In complex systems comprised of identical particles, we sometimes make the assumption that the motion of each particle follows curved trajectories because that is the simplest way to describe the change in the state of the system. But such motion is not necessarily fundamental to the system. When there is an underlying finite gauge to intervals, terms that would normally be eliminated due their extreme smallness, become important to retain.
The equations for kinetic energy and for angular momentum of gauged orbital motion are referenced to the idealized path of point particles traveling along infinitesimal arcs. Since objects in a discrete medium rarely travel along paths where the free path between collisions is infinitesimal, it makes more sense to reference local motion to the average gauge of the medium. When so referenced, there is a chord potential U(l) that emerges that provides an energy incentive for 'rotational' motion that is nonNewtonian in nature. (Posted: 2.10.17)

PIII: Observations Regarding the Kelvin Temperature Scale?
In the midnineteenth century, the Kelvin temperature scale was invented; it was defined as the absolute temperature scale. Can it be justified that  at a time prior to the discovery of the nucleus, prior to relativity, prior to quantum mechanics, and prior to discovering nuclear forces  that the knowledge scientist obtained by observing changes in water over a range of a fewhundred degrees was sufficiently fundamental to apply to the energy changes in stars that range of millions of degrees and more generally to the universe as a whole? (Posted: 2.10.17)

PIV: Discordant Tidal Characteristics Between the Lithosphere and the Asthenosphere as a Possible Generator of PlateDriving Forces?

PV: The Newtonian Definition of Mass in a TimeAveraged Environment?

PVI: The use of Harmonic Mean Length for Biological Scales?

PVII: Quantum Origins and the XY Axis?