Universal Constants, Variations, and Identities #10 All holons have at least six fundamental capacities. (Revised)

#10 All holons have at least six fundamental capacities. (Revised)

Horizontal:
1) Agency (Maintaining wholeness/identity) Pull to wholeness
2) Communion (Maintaining partness/relationship) Pull to partness

Vertical:
3) Transcendence (Becoming more wholeness) Pull upwards
4) Dissolution (Breaking down into constituent parts) Pull downwards

Lateral (Transverse - Direction of Change):
5) Change towards or within its interior (enfolding/recursion)
6) Change towards or without its exterior (unfolding/emergence)

(see #6 for definition of holon)

See heurist.org and mathesis-universalis.com for more information.

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Why is it so hard to prove that e+pi or e*pi is irrational/rational?

The reason why it is so hard to prove is actually very easy to answer. These constants, identities, and variations being referred to in this post, and others like it, all lay embedded in a far deeper substrate than current mathematics has yet explored.

Mathematics has been, and always shall be my ‘first love’, and it has provided for me all of these years. I am not criticising mathematics in any way. It is my firm belief that mathematics will overcome this current situation and eventually be quite able to examine these kinds of questions in a much more expansive and deeper way.
 
We need to extend our examination of mathematical knowledge, both in depth and in scope, out farther and in deeper than numbers (sets and categories as well - even more below) have yet done. I’ll introduce you to a pattern you may have already noticed in the current stage of our mathematical endeavour.
 
We all know there are numbers which lay outside of $Q$ which we call Irrational numbers. There are also numbers which lay outside of $R$ which we call Imaginary numbers. They have both been found, because the domain of questioning exceeded the range of answers being sought within the properties each of those numbers. This pattern continues in other ways, as well.

We also know there are abstractions and/or extensions of Complex numbers where the ‘air starts to get thin’ and mathematical properties start to 'fade away': Quaternions, Octonians, Sedenions,…

This pattern continues in other ways: Holors, for example, which extend and include mathematical entities such as Complex numbers, scalars, vectors, matrices, tensors, Quaternions, and other hypercomplex numbers, yet are still capable of providing a different algebra which is consistent with real algebra.

The framing of our answers to mathematical questions is also evolving. Logic was, for example, limited to quite sophisticated methods that all were restricted to a boolean context. Then we found other questions which led to boundary, multi-valued, fuzzy, and fractal logics, among a few others I haven’t mentioned yet.

Even our validity claims are evolving. We are beginning to ask questions which require answers which transcend relationship properties such as causality, equivalence, and inference in all of their forms. Even the idea of a binary relationship is being transcended into finitary versions (which I use in my work). There are many more of these various patterns which I may write about in the future.

They all have at least one thing in common: each time we extend our reach in terms of scope or depth, we find new ways of seeing things which we saw before and/or see new things which were before not seen.
 
There are many ‘voices’ in this ‘mathematical fugue’ which ‘weaves’ everything together: they are the constants, variations, identities, and the relationships they share with each other.
 
The constants $e, \pi, i, \phi, c, g, h$ all denote or involve ‘special’ relationships of some kind. Special in the sense that they are completely unique.

For example:

• $e$ is the identity of change (some would say proportion, but that’s not entirely correct).
• $\pi$ is the identity of periodicity. There’s much more going on with $\pi$ than simply being a component of arc or, in a completely different context, a component of area...

These relationships actually transcend mathematics. Mathematics ‘consumes’ their utility (making use of those relationships), but they cannot be ‘corralled in’ as if they were ‘horses on the farm’ of mathematics. Their uniqueness cannot be completely understood via equivalence classes alone.

• They are ubiquitous and therefore not algebraic.
• They are pre-nascent to number, equivalence classes, and validity claims and are therefore not rational. 

These are not the only reasons.

It’s also about WHERE they are embedded in the knowledge substrate compared to the concept of number, set, category…. They lay more deeply embedded in that substrate.

The reason why your question is so hard for mathematics to answer is, because our current mathematics is, as yet, unable to decide. We need to ‘see’ these problems with a more complete set of ‘optics’ that will yield them to mathematical scrutiny. 

Question on Quora

A Universal Paradox - Choice

Another universal constant here involving a causal relationship within which choice is embedded.

It doesn't get a number, because I haven't formalised it yet. Stay tuned though; I have new constants, variations, and identities which I haven't posted. I'm just too busy right now building my databases for the knowledge representations, that I haven't had the time to post them.

Universal Constants, Variations, and Identities #19 The Inverse Awareness Relation

Universal Constants, Variations, and Identities
#19 The Inverse Awareness Relation

The Inverse Awareness Relation establishes a fundamental relationship in our universe:

Micro Awareness = $\dfrac {1}{scope}$

and

Macro Awareness = $\dfrac {1}{depth}$

or

$\dfrac {Micro Awareness}{Macro Awareness} = \dfrac {depth}{scope}$

Which essentially state:

The closer awareness is in some way to an entity, the more depth and the less scope it discerns.

The farther awareness is in some way to an entity, the more scope and the less depth it discerns.

(Be careful, this idea of closeness is not the same as distance.)

Universal Constants, Variations, and Identities #18 (Dimension)

 

Universal Constants, Variations, and Identities (Dimension)

#18 Dimension is a spectrum or domain of awareness: they essentially build an additional point of view or perspective.

We live in a universe of potentially infinite dimension. Also, there are more spatial dimensions than three and more temporal dimensions than time (the only one science seems to recognize). Yes, I'm aware of what temporal means; 'Temporal' is a derived attribute of much more fundamental concepts, such as: Sequence and Change.

[One important caveat: please bear in mind that my little essay here is not a complete one. The complete version will come when I publish my work.]

The idea of dimension is not at all well understood. The fact is, science doesn't really know what dimension is; rather, only how they may be used! Science and technology 'consume' their utility without understanding their richness. Otherwise they would have clarified them for us by now.

Those who may have clarified what they are get ignored and/or ridiculed, because understanding them requires a larger mental 'vocabulary' than Physicalism, Reductionism, and Ontology can provide.

Our present science and technology is so entrenched in dogma, collectivism, and special interest, that they no longer function as they once did. The globalist parasites running our science and technology try their best to keep us 'on the farm' by restricting dimension, like everything else, to the purely physical. It's all they can imagine.

That's why many of us feel an irritation without being able to place our finger on it when we get introduced to dimension. We seem to 'know' that something just doesn't 'rhyme' with their version.

Time and space may be assigned dimensionality, in a purely physical sense if necessary, but there are always underlying entities much deeper in meaning involved that are overlooked and/or remain unknown which provide those properties with their meaning. This is why the more sensitive among us sense something is wrong or that something's missing.

Let us temporarily divorce ourselves from the standard 'spatial' and 'temporal' kinds of ‚dimension’ for a time and observe dimension in its essence.

Definitions are made from them: in fact, dimensions function for definitions just as organs do for the body. In turn, dimension has its own set of 'organs' as well! I will talk about those 'organs' below.

Dimension may appear different to us depending upon our own state of mind, level of development, kind of reasoning we choose, orientation we prefer, expectations we may have,... but down deep...

Everything, even attributes of all kinds, involve dimension. We must also not forget partial dimension such as fractals over complex domains and other metaphysical entities like mind and awareness which may or may not occupy dimension. Qualia (water is 'wet', angry feels like 'this', the burden is 'heavy') are also dimensional.

Dimensions are 'compasses' for navigating conceptual landscapes. We already think in multiple dimension without even being aware of it! Here's is an example of how that is:
[BTW: This is simply an example to show how dimension can be 'stacked' or accrued. The items below were chosen arbitrarily and could be replaced by any other aspects.]

♦ Imagine a point in space (we are already at 3d [x,y,z]) - actually at this level there are even more dimensions involved, but I will keep this simple for now.
♦ it moves in space and occupies a specific place in time (now 4d) 3d + 1 time dimension
♦ say it changes colour at any particular time or place (5d)
♦ let it now grow and shrink in diameter (6d)
♦ if it accelerates or slows its movement (7d)
♦ if it is rotating (8d)
♦ if is broadcasting a frequency (9d)
♦ what if it is aware of other objects or not (10d)
♦ say it is actively seeking contact (connection) with other objects around it (11d)
♦ ... (the list may go on and on)

As you can see above, dimensions function like aspects to any object of thought.

Dimensionality becomes much clearer when we free ourselves from the yoke of all that Physicalism, Reductionism, and Ontology.

Let's now look at some of their 'organs' as mentioned above as well as other properties they have in common:

• They precede all entities except awareness.
• Awareness congeals into them.
• They form a first distinction.
• They have extent.
• They are integrally distributed.
• They have an axial component.
• They spin.
• They vibrate.
• They oscillate.
• They resonate.
• They may appear as scalar fields.
• Their references form fibrations.
• They are 'aware' of self/other.
• Their structural/dynamic/harmonic signature is unique.
• They provide reference which awareness uses to create perspective meaning.
• Holons are built from them.

http://mathesis-universalis.com

Sacred Geometry 29 by Endre @ RedBubble:
http://www.redbubble.com/people/endre/works/6920405-sacred-geometry-29?p=poster

Universal Constants, Variances, and Identities - 17 (Interiority/Exteriority)

 

Universal Constants, Variations, and Identities

#17 Interiority and Exteriority arise together. (Representation)

For every interior representation there is always an exterior representation that compliments it. For every exterior representation there is always a corresponding interior one.

Universal Constants, Variations, and Identities – #16 (Creation/Discovery)

 

Universal Constants, Variations and Identities

#16 Creation and discovery compliment each other and are the means in which the Universe fundamentally unfolds and enfolds itself. (Creation/Discovery)

We tend not to identify them, because there are so many variations in their harmony. Please do overestimate your thoughts... as you will see they are the beginning of your expression to and of the world.

Both Creation and Discovery will work in unison, if we allow them.
Discovery is to recognize/relate what is in your world.
Creation is to transform/synthesize it too.
Each is alone without the other.

Creation=Right 'brain' (right+mind)
Discovery=Left 'brain' (left+mind)

Their 'magick' (sic.) manifests not when you synchronize them; rather, when you harmonize them.

(Please take the time to watch the 4 minute video.)