Dear Robert Shour,

What you call scale, which I call zoom, I use in my work as if it were a dimension and I get very expectant results and explanations to things that currently do not have it, maybe you are interested in reading my work.

Best regards

When we observe the mater in its part, we often focus our research and understanding on one level of it: subatomic particles, atoms, ions, molecules, macromolecules, proteins, cells, crystals, tissues, polycrystals, organs, bodies, ecosystems. We commit emergence as a process that naturally arises higher-level building blocks through interactions of those on the lower-level constituting parts.

Self-organization, self-assembly, and emergent structures are mighty processes that create higher and higher levels. Once we start at the bottom with processes (constituting entities) there the rest arises automatically.

For example, this led to the discovery of statistical physics of gases. It is present in almost all matter if not in all of it.

The ONLY PROBLEM :-) is that we are often unable to construct the mathematical theories describing it. It is exactly what is driving a massive development of research related to complex systems.

Complex systems along with self-organization, self-assembly, emergence, emergent structures, self-replicating structures are the places where I recommend to start your discovery of scaling properties of matter in its all forms.

Sydney Ernest Grimm

Thank you for your explanation of your fractal comment.

I know little about QM let alone a Higgs field but your explanation has some connections to articles I have posed on RG. You mention 2 kinds of cosmological space. The RG articles note that one dimensional motion added to three spatial dimensions gives a four dimensional space. Static space which might be considered a matter space has three dimensions. Hence one space has 4 dim, the other 3 dim. The space with motion (4 dim) might transmit energy to the space without motion (3 dim). Thus the space (3 dim) without motion has 4/3 the energy per dim as does the space with 4 dim. This is speculative but with some curious aspects. First, the 4/3 ratio arises in a variety of different phenomena (Stefan's Law, an 1860 paper of Clausius, Richardson wind eddies, the fractal dim of Brownian motion, among others). Second, the ratio of radiation energy density to matter energy density, which is Omega_gamma / Omega_m should be for the same energy E, ( E/1^3) / (E/ (4/3)^3) which is about 0.7033/ 0.2967 which is about the same as the ratio observed recently (Betoule 2014); and the 1998 SN 1A observations that led to the inference that there was DE found that SN were 25% dimmer than expected, which could be explained by 2 kinds of space, one of which stretches by 4/3 relative to the other.

As well, if the 4 dim space has 4 degrees of freedom and the 3 dim space has 3 degrees of freedom, then the fractal dim of one to the other is 4/3, which connects to your observation about fractality.

Papers that mention this include: The Theory of Dark Energy: Introduction; A preliminary history of dark energy and the 4/3 law.

Your observations have some curious and interesting connections to some of the ideas in my articles.

Best wishes.

Bob Shour

Things scale not only among two different parameters such as volume and area, but also within one only parameter. For example, far more small cities than large ones, for more short streets than long ones, far more low buildings than high ones, far more poor people than rich people, far more ordinary people than extra-ordinary people. I formulated scaling law - a universal law - based on this notion of far more smalls than larges. Together with another law so called Tober's law, these two laws constitute fundamental laws of living structure or wholeness that appears in all things ranging from the smallest (with Planck's length) to the largest (of universe).

Article A Complex-Network Perspective on Alexander's Wholeness

Presentation Scaling Law and Tobler's Law for Characterizing Asymmetry in Geography

These two laws apply not only to nature and biology, but also what we made or built (of course, excluding modernist buildings and arts). Truly beautiful or living things are governed by these two laws. In line with these two laws, there are two design principles - differentiation and adaptation - for creating living structures for built environment and arts.

Presentation A Mathematical Model of Beauty for Sustainable Urban Design

If you are interested in this topic, we would love to hear from you for the call for papers:

Poster CALL FOR PAPERS: New Applications and Development of Christo...

Scaling: "volume scales differently than area, which scales differently than length. Scaling sometimes seems to occur with a fractional exponent."

In physics and math, of course the scaling of length is linear, area scales at pi r2 ,

and volume at pi r3 . Depending upon the equations and format new elements are being scaling into, one needs to fit the size element with the other factors that may be involved regardless of the science. This could involve a fractional multiplicand, or exponent factor, which fits ones input with the data information already there. For this one has to understand the reason for this change in scaling size. Scaling change could also relate to proposed fractal aspects of a system.

In biology, economics, and data networks, elements can and do grow or shrink in size over time. In physics molecular aggregations can increase or decrease in size over time as well as energy factors, etc. In cosmology scale-changing models can relate to expanding space etc., and at atomic, quantum scales as well as in cosmology, the scale-changing of elemental size is a theoretical concept in the absence of other applications.

Scaling: "volume scales differently than area, which scales differently than length. Scaling sometimes seems to occur with a fractional exponent."

Of course the scaling of length is linear, the scaling or area involves

Concepts of science such as "laws of Nature" come not from Nature itself, which has no laws at all, as Kant, Bergson and others already understood, but rather from objects of our attention, resulting in turn from our implied actions. In particular in physics, one can dispense with metric concepts like length, area, volume, time duration etc. as measured with rulers and clocks (see my book 'Irony of the Method'). It is possible to make predictions solely by means of counting oscillations numbers ratios of the top-speed signal.

The so-called "entropy " doesn't exist at all.

During the process of deriving the so-called entropy, in fact, ΔQ/T can not be turned into dQ/T. That is, the so-called "entropy " doesn't exist at all.

The so-called entropy was such a concept that was derived by mistake in history.

It is well known that calculus has a definition,

any theory should follow the same principle of calculus; thermodynamics, of course, is no exception, for there's no other calculus at all, this is common sense.

Based on the definition of calculus, we know:

to the definite integral ∫T f(T)dQ, only when Q=F(T), ∫T f(T)dQ=∫T f(T)dF(T) is meaningful.

As long as Q is not a single-valued function of T, namely, Q=F( T, X, …), then,

∫T f(T)dQ=∫T f(T)dF(T, X, …) is meaningless.

1) Now, on the one hand, we all know that Q is not a single-valued function of T, this alone is enough to determine that the definite integral ∫T f(T)dQ=∫T 1/TdQ is meaningless.

2) On the other hand, In fact, Q=f(P, V, T), then

∫T 1/TdQ = ∫T 1/Tdf(T, V, P)= ∫T dF(T, V, P) is certainly meaningless. ( in ∫T , T is subscript ).

We know that dQ/T is used for the definite integral ∫T 1/TdQ, while ∫T 1/TdQ is meaningless, so, ΔQ/T can not be turned into dQ/T at all.

that is, the so-called "entropy " doesn't exist at all.

Dear Shufeng Zhang,

Diverting from the subject at hand a little, entropy is more than just a calculation, it is also a meaningful word. In thermodynamics entropy is the portion of a heated system representing the unavailability of this part of the system's thermal energy which cannot be converted into mechanical work, as well as the rate of this digression, which can tell us a lot about the system. The degree of disorder or randomness in the system.is based upon its gradual decline from an ordered system.

How entropy should be calculated, by convention or otherwise, is a matter of the usefulness of the results obtained.

As to the usefulness of describing the universe in terms of entropy, I agree, entropy cannot apply to the universe in the least. The major aspect of the universe works contrary to entropy, this being gravity. Disorder comes together into order. A minor one, but not to us, is life, again disorder comes together into order.

Now, back to the subject at hand: Why do things scale ubiquitously in science?

On the planetary scale there is a general understanding of "why" scaling produces generally the same results everywhere, with only minor variations depending upon changing variables. As to the observable universe, the aspect of the cosmological principle characterizing the universe as being uniform everywhere, would apply. This is an assumption. As to why we believe this is the case for the universe is because most astronomers believe it appears to be that way based upon our numerous observations using many different instruments.

Even if for all past time frames things would have appeared the same in past times as they now appear to us, does not mean that the scale of matter has not changed over time. An undetectable diminution in the size of matter (the scale) over a great span of time, for instance, would make it appear to us that space was expanding, not only that, if this rate of diminution of matter were uniform, the expansion of the universe could appear to us to be non-uniform, fancy that :)

with regards, Forrest

The fractal scaling seems more like a postulate that seems true. Carried a bit more we might say the quantum world should obey basic equations of the classical realm. Therefore, the weird (not intuitively seen in our size world) should be manifestations of some process seen in our size world. The walking drop may be one such example. Also,

Article STOE assumptions that model particle diffraction and that replaces QM

Dear Forrest Noble,

Enjoy yourself !