I ran across your site as i was finishing my book/Art project and found your philosophy of interest as resonating with my own.

I reach out here to introduce myself and project - below please find the abstract and the book which is freely observable on line

Many thanks

John

3.0 i: Abstract/Letter of Introduction

Greetings fellow sojourner seeking,

Please pardon my interruption; I wanted to take the

opportunity to briefly introduce myself through my art

and, as such, invite you to peruse my book project with

title: i, in the palm of my mind : the chapters are

available to observe and consider online at

www.eidolononesuch.com

In my book, I explore - through various writing and

art formats - a series of desperate tho related concepts

ranging from cosmology to consciousness and free will.

And I propose and explore some intriguing models

you may want to consider such as regarding time and

how it results in the apparent EPR paradox and, as well,

a structural and mechanistic model for how matter and

mass connect as well as provide some detail on the

relationships of time/gravity and other forces.

Specifically,

I propose time as a 3-dimensional quasicrystalline net

of collapse events against the fabric of a fully collapsing

modular host pattern and describe where said pattern resides

I describe how to extract time from the pattern and evolve

a universe such as ours from a point containing

modular maths such as elliptics

I propose a unique model for the electron

(and nucleon components) as a resonant folded

wave/anti-wave (4:1 ratio in the electron) pattern in

the motif of a tetrix: a tetrahedral pyramidal fractal fold

of mass/void and the consequences of such regarding

the observed matter dominance in our universe and

its evolution

I describe the w/~w basis of the 3-state equilibrium

of photon/electron interaction as the tetrix tetrahedral

fold equilibrates with a cubic fold allowing point collapse

of part of the electron folded wave and how this yields time

and the EPR/Bell's inequality observations as waves and

anti-waves transition through the collapse state and

invert to yield the changed state

I explore how neutrinos may be the mechanism of

motion/momentum for the folded-matter waves and

how motion may be realized on a fully collapsing,

modular host with implications for how gravity

differs fundamentally from other forces

I elucidate a system - derived from neutrino oscillation

- detailing how rotational inertia is related and maintained

relative to linear momentum in a universe where the only force

is simplification and describe how momentum is prone to condense

with the greater frame of reference

I describe how the universe relies on de-construction

of its core information pattern, where the 'particle' machines

ur-data is extracted, sending the information by two mechanisms

to distant location and re-combining to yield the collapsible cubic

architecture: this results in alteration, temporarily, of the pattern

that consequently inflates our universe and this process can

occur reversibly without wave inversion beneath the

time collapse events

I describe entanglement as superposition/co-collapse

of mirrored, adjacent waves thus creating linkage to

subsequent collapse with inversion required as

observed time events

I propose straight-forward bases for the dark matter

and dark energy observations and describe the cycling

of universe iterations at our local site in the uberverse

including provenance of the high negative entropy

that is energy

Those are in part I of the book's triptych; if you find

these topics of interest, there are others that I find even

more intriguing in the remainder:

For example, I describe a functional definition of soul and

point to cryptic components, such as our ur-brain memory:

a cross-generational repository/information system which

provides survival utility as a fundamental evolutionary tool

This is interpreted in relation to the concepts of free will/choice

And I introduce potential reasons to question whether digital as

fundamentally differing, with relevance, from IRL

Please enjoy as you wont - it is intended purely and simply as art

and as such, simply and purely to inspire your art

Many thanks for all your good works,

J.

* June/July 20/20, JSM ]]>

On the one hand, we have BG the space, or the BG the “delooping” one-object groupoid with morphisms G, which we might write G => *. These are closely related; the former is the geometric realization of the nerve of the latter.

On the other hand we have BG the classifying topos or stack, which is (I think) the category of all principal G-bundles.

The notation and similar role played by those objects suggest they are versions of the same thing. On nLab, we find in classifying topos it reads says that the correspondence of toposes GBund(X) = Topos(Sh(X), G) is analogous to the correspondence pi0 GBund(X) = pi Top(X,BG).

Ok but is it just an analogy, or is there some kind of stackification or Yoneda process that turns BG the space/groupoid into BG the topos/stack? Or is there some kind of truncation or geometric realization process that turns BG the stack back into BG the space?

In the article moduli stack it says the moduli stack *//G is the base of the universal principal bundle. Does that mean in the category of stacks? What’s the “total space” over *//G? Is it a stackified version of EG?

It’s hard to believe that these theories are so utterly parallel just by coincidence without a literal connection.

]]>New entry representable morphism, in the sense of Grothendieck school. The notion is used at closed immersion of schemes where I just made some changes.

]]>Created the stub *germ of a space*, mainly to record the (trivial) insight that the category of germs of spaces is a localization of the category of pointed spaces.

Note that this is not yet a good stub, as it is not interlinked very well. I’m not quite sure where to put it in the table at *germ*.

From the definition of directed topological space it follows that the unit circle with $2n$ circumference clockwise paths ($n\in\mathbb{N}$) is a d-space.

This d-space is “nonlocal” that is not determined by small fragments of the path.

“Regular” clockwise circle with $n$ circumference clockwise paths ($n\in\mathbb{N}$) is a d-space too. And this one is “local”.

I ask you to help me define “locality” or “nonlocality” of d-spaces. What is the definition and how is it called?

]]>I updated separable space. I have two questions:

- Is it possible to proof that a separable space is Lindelöf without any form of AC?
- I do not understand how the theorem separable$\Leftrightarrow$second countable is subsumed by Theorem 2.

New entry spectral cookbook with sketch of some *very* nice constructions of A. Rosenberg. New stub sheaf on a noncommutative space, pretty contentless so far, and a redirect page noncommutative sheaf, where the latter may have a different meaning (that is why a separate page).

Stub for quotient space.

]]>Should the predicate $\Diamond$ on a formal topology be regarded as making it into an overt space?

]]>I’ve been looking a little bit at diffeological spaces and am becoming a fan of the idea. I’ve got some notes on my personal web too.

Quick question…

Given any two smooth spaces $X,Y$, we can form something of a canonical mapping “T” diagram:

$\array{ X & \stackrel{\pi_1}{\leftarrow} & X\times [X,Y] & \stackrel{ev}{\rightarrow} & Y \\ {} & {} & \mathrlap{\;\;\;\scriptsize{\pi_2}}{\downarrow} & {} & {} \\ {} & {} & [X,Y] & {} & {} }$which is also discussed on transgression.

I drew this with “plots” in mind, so I had arrows like

$\array{ {} & {} & U & {} & {} \\ {} & \swarrow & \downarrow & \searrow & {} \\ X & \stackrel{\pi_1}{\leftarrow} & X\times [X,Y] & \stackrel{ev}{\rightarrow} & Y \\ {} & {} & \mathrlap{\;\;\;\scriptsize{\pi_2}}{\downarrow} & {} & {} \\ {} & {} & [X,Y] & {} & {} }$with another arrow (not shown) from $U\to [X,Y]$.

This made me think that $U$ was actually the limit of the mapping “T”

$\array{ X & \stackrel{\pi_1}{\leftarrow} & X\times [X,Y] & \stackrel{ev}{\rightarrow} & Y \\ {} & {} & \mathrlap{\;\;\;\scriptsize{\pi_2}}{\downarrow} & {} & {} \\ {} & {} & [X,Y] & {} & {} }$So, my question is “What is the limit of this diagram?” Is it $\mathbb{R}^\infty$ or something?

Thanks for any words of wisdom.

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