Harmonics of Nature: The Etiology of Natural Patterns

This is the degrees of freedom uncertainty rule [which actually allows us freedom]. We can never be sure which individual went this way and which went the other way [that is what entropy and Carnot’s ‘jinks’ on Maxwell’s demons is all about]. This is a statistical population; there are enough members to apply the statistical rule [the rule of large numbers]. That is the same rule [just inverted] as the degrees of freedom uncertainty principle [which says that you cannot specify Newtonian activity on populations that provide excellent statistical results because of the same theory of large numbers. - You can’t have your cake and eat it too [precisely what Carnoy meant]. Also, the difficulties with this rule could be resolved easily; by applying the viewpoint of harmonics.

So, under the degrees of freedom uncertainty [when that applies {strongly enough}] you have harmonics. This is the fact that systems under the rule of degrees of freedom uncertainty and that are constrained [in certain natural or “harmonics” ways.] can form “natural” patterns. Harmonics [the name] refers to the patterns since they form in harmonic kine [a set of eigenfunctions]. The pattern does not specify where any part [molecule] is at or how fast it is going. The pattern is an envelope of probability distribution for the randomly distributed contents. This does not allow Maxwell's Demons to sneak some particles into a special place to violate equilibrium rules.

Harmonics

Regular Newtonian Only differential equations cannot measure or determine anything that is caught up in the degrees of freedom uncertainty [perhaps refer to it as the Rule of Large Numbers {only the flip side of the coin}]. The equation itself is dealing with specifying or measuring the position and velocity of a particle whose position or velocity cannot be specified or measured because of the degrees of freedom uncertainty rule. You see that some things are happening as you watch wave action closely [like surfers do] but it is hard to understand the action from our phenomenalistic understanding of the universe. We have been taught to recognize Newton Only but the these phenomena are strange [It just doesn’t look right to me!], but beautifully threatening.

Once the swell that are controlling the “waves” hits the shoreline bottoms the wave equation collapses. The problem is that momentum is then loosed in the waters and their molecules. This causes a set of “harmonic eddies” [harmonics and eddies sort of are the same thing but two different perspectives - so saying it twice is a reminder to see it both ways] to occur in a fairly standard path. The photographer, above, is doing well at showing the pipelines with each set of waves since those are the eddies that makes surfing fun. But here, in this set of waves, the eddies are too unstable to dare get inside of. And, when the wave is throwing you down it is unto the sand of the beach - ouch. That shore breaker effect is due to the fast drop in the undersea bottom just off Waimea Beach [yes, part of the equation].

The Etiology of Natural Patterns 

 Symmetry [although it is always some kine of natural symmetry] is pervasive in living things. Nature provides a number of different patterns: spirals, ripples, patterns on birds feathers, and spots and stripes on animals.

In high speed photography we can see the crown-shaped splash pattern formed when a drop falls into a pond. We see five-fold symmetry is found in such creatures as starfish, sea urchins, and sea lilies. Snowflakes have striking six-fold symmetry. Dunes may form crescents, very long straight lines, stars, domes, parabolas, and longitudinal or sword shapes. There are also symmetries, like: trees, spirals, meanders, waves, foams, cracks, spots, and stripes. But natural means straight lines are never straight, curves are never perfectly curved.

From the common understanding of entropy, we expect most things in this world to be random instead of ordered, and these random distributions should show dissipation and not order. It takes energy to create order.

Ramsey Theory says that order is the inevitable result of a large amount of random trials. Hungarian biologist Aristid Lindenmayer, and French American mathematician Benoît Mandelbrot showed how the mathematics of fractals could create patterns that appear to be natural in computer printouts. These are just the beginnings of understanding the harmonics of nature.

This book looks into the patterns in nature. Instead of just listing the interesting patterns, I am concerned about demonstrating a general etiology (the cause or reason for something to happen) of those patterns. This is a new way of looking at the physical universe itself to understand not only the etiology of harmonics but the general physics of those patterns. Thus we can see a set of characteristics that allows us to understand, predict, and use the processes of these patterns.

Dr. Jerome Heath