Infinite Self-Similar Recursion Over Scales (By Ian Beardsley)

Oleg Evdokimov has taken my work to a whole new level, really to what

is necessary for a complete formulation by doing it topologically

deriving from the source, the master equation formulation for the mass

of a proton as a knot in the primordial field, as based on his OFN

theory. I do have to say I offered up a how, but only on a classically

mechanical level, which we went into in our joint paper. I suggested:

We suggest inertia arises because objects move at constant speed

through spacetime with their velocity vector rotating between temporal

and spatial components. A particle presents a cross-sectional area

(like for a proton) Aₚ=πrₚ² to a normal force Fₙ=h/(ct₁²), where

t₁=1second as it moves through time. Work done by this force is

mediated by the gravitational constant G. This gives that inertia

expressed as the mass of a proton is from such a description of

inertia (mass pushes back when we push on it, the more of it, the more

it pushes back):

mₚ=κₚ√(πrₚ²Fₙ/G)

I show this is directly derived from:

1second=(1/6α²)(rₚ/mₚ)√(4πh/[Gc] )%

And,%

1second=(1/3)h/α²√(ϕπrₚ²/[Gmₚ³] )%

I then say we know these two equations are right because they also accurately produce the

radius of a proton (setting the right sides equal) to be%

rₚ=ϕh/(cmₚ)%

I suggest the proton puzzle may have its solution in ϕ taking ﬁbonacci approximations to it:

2/3, 5/8,…for its diﬀerent states as a fuzzy cloud whose size changes with the physical

conditions. We also know it is right because this equation for the radius of a proton follows

from:%

E=hνₚ

E=mₚc²

if we introduce the factor of ϕ. I explain this factor by invoking Kristin Tynski, her paper titled:

One Equation, ~200 Mysteries: A Structural Constraint That May Explain (Almost) Everything.

Tynski shows that for any system requiring consistency across multiple

scales of observation has the recurrence relation:

scale(n+2)=scale(n+1)+scale(n)

Which she says leads to

λ²=λ+1

Whose solution is ϕ. I provide a little in my paper of why this might ϕ might be, but more

explicit mechanics are required.%

I indeed find the one-second invariant results from formulating

Newton’s Universal Law of Gravitation with Planck length lₚ and Planck

mass mₚ, which result in:

t₁=2√([1/κₚ][1/G][tₚ/t꜀][h/c])mₚ/lₚ

Which uses minimal coherent time tₚ (Planck time) and the quantum

temporal scale t꜀ (Compton time). So, I didn’t exactly guess at all of

this, but reasoned it. This is all presented more explicitly in my

paper at:

https://doi.org/10.5281/zenodo.18444538

Or,

https://www.academia.edu/156994531/

The_Sublime_and_Mysterious_Place_of_Humans_in_the_Cosmos_A_Work_in_Exo

archaeology

One of the main motivations for this was to work on recursive self-

similarity of forms from the proton to the atom to to the solar system

because I have found the one-second invariant in the Earth-Moon-Sun

System. For example:

1second=[ħ_⊙²/(GMₘ³)][1/c]

Where ħ_⊙ is a Solar System type Planck constant given by 1 second and

the earth’s orbital kinetic energy;

ħ_⊙=(1second)KEₑ

Further we have

1second=(KEₘ/KEₑ)(EarthDay)cosθ

Using the kinetic energies of the moon and earth and the earth

rotation period (earth day=24hrs) and θ=23.5 deg is the earth’s

inclination to its orbit. This equation is pivotal in the paper.

We talked about some of this in our joint paper about my “how" of the

normal force. Which is at:

https://doi.org/10.5281/zenodo.18405270

Or,…

https://www.academia.edu/146203559/

Cosmic_Knots_as_Torsional_Solitons_in_the_Fundamental_Network_Unifying

_the_One_Second_Invariant_Phi_Scaling_and_Baryogenesis

But, yes, Oleg formulates this in his Ontology of the Fundamental

Network (OFN) in a very complete sense saying

“We demonstrate that the discrete spectrum of stable Cosmic Knot

states, characterized by a dimensionless

connectivity parameter sigma, naturally yields the one-second

invariant and phi scaling as signatures of topological optimality.”

I don’t know what he may think of my loose model where “inertia arises

because objects move at constant speed through spacetime with their

velocity vector rotating between temporal and spatial components. A

particle presents a cross-sectional area (like for a proton) Aₚ=πrₚ² to

a normal force Fₙ=h/(ct₁²), where t₁=1second as it moves through time…”

That is, I don’t know he sees that model as compatible to his cosmic

knot formulation. But this is a perfect opportunity to bring up my

view on this, which is used in a paper by Kunal Kishor Verma, and

myself at

https://www.academia.edu/144939647/

Nature_as_Infinite_Regress_A_Unified_Framework_of_the_Timeless_Energy_

Principle_and_the_Collapse_of_Abstract_Modeling

“We propose that Nature may be the manifestation of an infinite

regress of models, where every mathematical description of

reality inevitably generates a higher-order transformation that

escapes closure. Each model MMM of Nature evokes another,

T(M)T(M)T(M), that transcends it, yielding a limitless recursion.

This process defines existence itself: a continual emergence of

structure through self-referential regression. Building upon the

Timeless Energy Principle (TEP) which interprets the universe as a

self-transforming, a temporal energetic continuum - we reformulate

existence as the collapse of infinite abstraction.”

Now in light of this, whether we are considering a cosmic knot or

normal force created by exposure of the the proton cross-section to

the stiffness of space, or anything else that other theories have,

really such things are models, not solitary absolute truths, but the

collapse of infinite abstraction. I am just saying everything is a

model owing to mathematics being a formal system that is in the end

self-referential. There would be then an infinite number of possible

models that work, but they don’t say what reality is, only how you are

modeling it as a tool. So, a good example of this is we say space is

x=vt. If we want to say what distance x is we have to say velocity is

x/t, so we have x=(x/t)t=x. So in this formulation of reality, space

is space. So mathematics is a formal system and self-referential at

some point, so it can’t explain itself, thus preventing us from saying

what reality is. But models being tools, you use the one that opens

more doors for the given problem.

I think this infinite regress is connected to the problem of the

universe exists, but shouldn’t because you can’t have an uncaused

cause, or unmoved mover, but you need it to break out of the infinite

regress, but it is impossible, because you then have no cause and

effect. My point is that it may be counter productive to argue over

whose theory is right in an infinite regress.

But I feel the meaning to be had in reality will be found in

infinitely, self-similar recursion through scales, like I am

presenting here as findings in the 1-second invariant at the level of

protons, to atoms, to the solar system. It may be that this regression

is infinite going on to galaxies, and clusters of galaxies, and

clusters of clusters. We really don’t know for sure whether the

universe is infinite in extent, or finite with an infinite number of

them, and so on. But in the end, something strange has to be going on

that we are missing in that we seem to have a universe that is either

an uncaused cause, or has always existed, yet is a particular way. It

seems to be so, but the human mind cannot understand such a thing with

any form of reason.

With exoarchaeology I offer-up a platform that escapes the problem of

stopping moving forward when can’t explain something from first

principles by introducing the idea of an “artifact”. I find we find if

we accept something momentarily and move on, other discoveries arrive

and a coherent picture starts to form. This is much in the school of

abstract algebra. For instance we might find something takes the form

as an oscillator, but we don’t say whether it is due to springs, or

fields, we explain that after arriving at the form, and even then, the

explanation is only collapsing the infinite regress into a finite

closure that is self-referential. There could be an infinite number of

models that do the same thing. However, in exoarchaeology we can

arrive at something from first principles as well, as I have outlined

here with some my explanations for inertia. I am beginning to think

people shouldn’t be arguing over whose theory is right when really

there is no right in an infinite regress, which is what reality seems

to be. I don’t know if other people will like this approach, but I

find the archaeological approach is exciting because it finds exciting

models that point us in the right direction. Thus, I think don’t argue

over which models are right, but which model suits best the situation

at hand. These exciting models can point you in the right direction. A

direction this model has pointed me in is a Genesis Project, asking

what are the conditions for life hosting systems not just

biologically, but astronomically, and are the laws that follow part of

a common unfolding of life throughout the Universe.