## 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, π, i, ϕ, 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(some would say proportion, but that’s not entirely correct).*identity of change**π*is the. There’s much more going on with than simply being a component of*identity of periodicity**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. **

Apr 25, 2018 | Categories: Holors, Insight, Knowledge, Knowledge Representation, Learning, Mathematics, Mathesis Generalis, Mathesis Universalis, Metamathematics, Philosophy of Language, Philosophy of Learning, Philosophy Of Mind, Understanding, Wisdom | Tags: insight, knowledge, learning, Mathesis Generalis, Mathesis Universalis, Metamathematics, Philosophy Of Mind, understanding, Universal Constants, wisdom | Leave a comment

## 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 a much more fundamental concept: **** 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 it 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

Sep 7, 2016 | Categories: Constants, Holons, Holors, Knowledge, Knowledge Representation, Language, Learning, Linguistics, Mathematics, Mathesis Generalis, Mathesis Universalis, Meta Logic, Metamathematics, Metaphysics, Perspective, Philosophy, Scalars, Semantics, Understanding, Variations, Wisdom | Tags: BigData, First Distinction, insight, knowledge, Knowledge Representation, learning, Logica Universalis, Mathesis Universalis, Metalogic, Metaphysics, Philosophia Universalis, Scalar Field, Scalars, Scientia Universalis, Semantics, understanding, Universal Constants, Variances, wisdom | Leave a comment

## Universal Constants, Variations, and Identities – #17 (Representation)

*#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.

Sep 6, 2016 | Categories: Constants, Identities, Mathesis Generalis, Mathesis Universalis, Meta Logic, Metamathematics, Semantics, Understanding, Variations, Wisdom | Tags: insight, knowledge, Knowledge Representation, learning, Logica Universalis, Mathesis Universalis, Metalogic, Philosophia Universalis, Philosophy, Scientia Universalis, understanding, Universal Constants, Universalis, Variances | Leave a comment

## HUD Fly-by Test

Don’t take this as an actual knowledge representation; rather, simply a simulation of one. I’m working out the colour, transparent/translucent, camera movements, and other technical issues.

In any case you may find it interesting.

The real representations are coming soon.

Aug 21, 2016 | Categories: Big Data, Holons, Holors, Hyperbolic Geometry, Knowledge, Knowledge Representation, Language, Learning, Linguistics, Logic, Long Data, Mathesis Generalis, Mathesis Universalis, Meta Logic, Metamathematics, Metaphysics, Philosophy, Understanding, Wisdom | Tags: BigData, Constants, Hyperbolic Geometry, insight, knowledge, Knowledge Representation, learning, Logica Generalis, Logica Universalis, Mathesis Generalis, Mathesis Universalis, Metalogic, Metamathematics, Metaphysics, Philosophia Generalis, Philosophia Universalis, Philosophy, Philosophy of Language, Philosophy of Learning, Philosopohy of Mind, Scientia Universalis, understanding, Universal Constants, Universalis, wisdom | Leave a comment

## 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.)

Feb 24, 2015 | Categories: Constants, Insight, Knowledge, Learning, Understanding, Wisdom | Tags: change, Creation, Identities, insight, knowledge, learning, Logica Universalis, Mathesis Universalis, Metalogic, Metamathematics, Metaphysics, Metascience, Philosophia Universalis, Philosophy, Scientia Universalis, understanding, Universal Constants, Universalis, Variances, wisdom | Leave a comment

## Universal Constants, Variations and Identities – #15 (Change/Time)

*#15 *** Time is a temporally ‘linear’ (directed) form of change that is not limited by dimension.** (Change/Time)

**Time has been arbitrarily and wrongly assigned to dimension. Change is not restricted to any dimension: therefore time is also not limited to it.**

I know it’s trendy to see time as a dimension, but dimension is something completely different. Stay tuned to find out what and why.

Update: There are many reasons why time needs a proper definition. Here are a few of them:

The chemical reactions in the vessel are not really effected by some mysterious thing called time, but by the number of contacts or collisions that take place in the soup of atoms or molecules. That is what the factor ‘T’ really stands for.

1) Eternity may be a somewhat mystical overarching reality outside of the physical universe, but time is not. Nor is time a thing that anybody can do anything to. In other words: it cannot be reified.

2) The universe doesn’t exist in time, but time exists in the universe.

3) The proper definition of time is exactly: the sequence of events in the material universe.

Feb 7, 2015 | Categories: Constants, Insight, Knowledge, Learning, Understanding, Wisdom | Tags: change, insight, knowledge, learning, linear, Logica Universalis, Mathesis Universalis, Metalogic, Metamathematics, Metaphysics, Metascience, Philosophia Universalis, Philosophy, Scientia Universalis, temporal, understanding, Universal Constants, Universalis, Variances, wisdom | Leave a comment

## Universal Constants, Variations and Identities – #14 (Singular/Plural)

**Universal Constants, Variations and Identities**

*#14 *** Singular and plural arise together.** (Singular/Plural)

There is no singular without a plural representation except in the non-dual.

See http://mathesis-universalis.com for more information.

#Knowledge #Wisdom #Understanding #Learning #Insight #Constants #Variances #Philosophy #MathesisUniversalis #ScientiaUniversalis #PhilosophicaUniversalis #LogicaUniversalis #MetaMathematics #MetaLogic #MetaScience #MetaPhysics #MetaPhilosophy #Singular #Plural

Feb 3, 2015 | Categories: Constants, Identities, Insight, Knowledge, Learning, Mathesis Universalis, Metamathematics, Metaphysics, Philosophy, Wisdom | Tags: Constants, insight, knowledge, learning, Logica Universalis, Mathesis Universalis, Metalogic, MetaPhilosophy, Metaphysics, Metascience, Philosophia Universalis, Philosophy, Plural, representation, Scientia Universalis, Singular, Singular and plural, understanding, Universal Constants, Variances, wisdom | Leave a comment

## Universal Constants, Variations and Identities #13 (Knowledge)

**Universal Constants, Variations and Identities**

*#13 *** Knowledge is what awareness does.** (Knowledge)

I’ve published this before elsewhere, but it must be restated now for what is to follow (I’m starting a new octave).

#Knowledge #Wisdom #Understanding #Learning #Insight #Constants #Variances #Metaphysics #Philosophy #MathesisUniversalis #ScientiaUniversalis #PhilosophiaUniversalis #LogicaUniversalis #MetaMathematics #MetaLogic #MetaScience #MetaPhysics #MetaPhilosophy #Awareness

Feb 3, 2015 | Categories: Big Data, BigData, Identities, Knowledge, Knowledge Representation, Learning, Logic, Mathematics, Mathesis Universalis, Metamathematics, Metaphysics, Philosophy, Science, Understanding, Wisdom | Tags: Awareness, Constants, Identities, insight, knowledge, learning, Logica Universalis, Mathesis Universalis, Metalogic, Metamathematics, MetaPhilosophy, Metaphysics, Metascience, Philosophia Universalis, Philosophy, Scientia Universalis, understanding, Universal Constants, Variances, wisdom | Leave a comment

## Universal Constants, Variations and Identities

**Universal Constants, Variations and Identities**

*#12 *** The ends are determined by their means.** (Integrity of purpose)

(Dispelling the lie of: *“The ends justify their means.”* **The truth is that ends are inextricably tied to the means used to achieve them.** If we employ destructive means, then only destructive ends can result. Intention means nothing with regard to means… those who believe that learn: *“The road to Hell is paved with good intentions.”*

See http://mathesis-universalis.com for more information.

Feb 3, 2015 | Categories: Constants, Identities, Insight, Knowledge, Learning, Mathesis Universalis, Understanding, Wisdom | Tags: communication, Constants, Identities, insight, knowledge, learning, Logica, Logica Universalis, Mathematical Universe, Mathesis Universalis, Metamathematics, Metaphysics, Metascience, Philosophia Universalis, Philosophy, Philosophy of Language, Philosophy Of Mind, Real Science, Scientia Universalis, Universal Constants, Universalis, Variances, wholeness, wisdom | Leave a comment

## Universal Constants, Variations and Identities

**Universal Constants and Variances
**

*#11*

**(Reference)**

*Observation is communication between its participants (observer and observed).*See http://mathesis-universalis.com for more information.

Feb 1, 2015 | Categories: Constants, Identities, Insight, Knowledge, Learning, Mathesis Universalis, Understanding, Wisdom | Tags: communication, Constants, Identities, insight, knowledge, learning, Logica, Logica Universalis, Mathematical Universe, Mathesis Universalis, Metamathematics, Metaphysics, Metascience, Philosophia Universalis, Philosophy, Philosophy of Language, Philosophy Of Mind, Real Science, Scientia Universalis, Universal Constants, Universalis, Variances, wholeness, wisdom | Leave a comment

## Universal Constants, Variations and Identities

**Universal Constants and Variances**

*#10 **All holons have** at least *** four fundamental capacities. **(Potential)

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

(see #6 for definition of holon)

See http://mathesis-universalis.com for more information.

Jan 7, 2015 | Categories: Constants, Identities, Insight, Knowledge, Learning, Mathesis Universalis, Understanding, Wisdom | Tags: Constants, Identities, insight, knowledge, learning, Logica, Mathematical Universe, Mathesis Universalis, Metamathematics, Metaphysics, Metascience, Philosophia Universalis, Philosophy, Philosophy of Language, Philosophy Of Mind, Real Science, Scientia, understanding, Universal Constants, Universal Variances, Unversalis, Variances, wholeness, wisdom | Leave a comment

## Universal Constants, Variations and… Identities

**Universal Constants, Variations and… Identities**

7) pi is the identity of periodicity

8) e is the identity of change

9) phi the identity of proportion

Dec 24, 2014 | Categories: Constants, Identities, Insight, Knowledge, Learning, Understanding, Wisdom | Tags: Constants, Identities, knowledge, learning, Logica, Mathesis, Mathesis Universalis, Metalogic, Metamathematics, Metaphysics, Philosophia Universalis, Philosophy, Philosophy of Language, Philosopohy of Mind, Scientia, Scientia Universalis, understanding, Universal Constants, Universalis, Variances, wisdom | Leave a comment

## Universal Constants and Variances

*#6 *** Reality is composed of whole parts.** (Holons)

Arthur Koesler coined the term ‘Holon’ that refers to entities as both wholes and parts of some other whole.

https://en.wikipedia.org/wiki/Holon_%28philosophy%29

For example: a whole atom is part of a whole molecule, which is part of a whole cell, which is part of a whole organism,… **Each of these entities are neither a whole or a part; rather, a ***whole part*** or ***Holon.*

There’s a 2000 year old philosophical squabble between *atomists* and *holists:* “Which is ultimately *real* – the *whole* or the *part?”* The answer is *neither* or *both,* if you prefer…

**There are only ‘whole-parts’: Holons.**

[More are coming soon in a new post…]

Dec 19, 2014 | Categories: Holons, Knowledge, Mathematics, Mathesis Universalis, Metamathematics, Metaphysics, Philosophy, Understanding, Wisdom | Tags: Constants, Holons, knowledge, learning, Logica, Logica Universalis, Mathesis, Mathesis Universalis, Metalogic, Metaphysics, Philosophia, Philosophia Universalis, Philosophy, Scientia, Scientia Universalis, understanding, Universal Constants, Universalis, Variances, wisdom | Leave a comment

## Universal Constants and Variances

**Universal Constants and Variances**

*#1 *** Awareness is primary and fundamental.** (Substrate)

*#2*

**(Duality)**

*All awareness is non-dual unless it is dual.**#3*

**(Interiority/Exteriority)**

*There is no inside without an outside nor outside without an inside.**#4*

**(Boundary)**

*Duality is bounded, non-duality is boundless.**#5*

**(Crossing)**

*Boundaries arise in a spectrum from diffuse to concise.*[More are coming soon in a new post…]

A few of those who have followed my posts have been asking for more information about my work. Towards that end, I’m going to start publishing my growing list of universal constants and variances. **It is these constants and variances that form the foundation of my work.**

There are about as many of them as there are stars in our universe (if you count the primary and derived together), so I don’t think I’ll run out of them! Most of them are self-explanatory, but if you have any questions, please don’t hesitate to ask in the appropriate thread. The numerical ordering is not yet important, as I’m still collecting and collating them as I discover them.

I have no tolerance for trolling or people who abuse others in my threads; especially on these threads about the constants and variances! So if you plan to wreak havoc here, you’ll get bumped real fast. I don’t mind criticism or skeptical opinions at all, but please *be civil* with everyone (including me).

See http://mathesis-universalis.com for more information.

Dec 13, 2014 | Categories: Holons, Knowledge, Language, Learning, Linguistics, Logic, Mathematics, Mathesis Universalis, Philosophy, Semantics, Understanding, Wisdom | Tags: Constants, knowledge, learning, Logica, Logica Universalis, Mathesis, Mathesis Universalis, Metalogic, Metamathematics, Metaphysics, Philisophia Universalis, Philosophia, Philosophy, Scientia, Scientia Universalis, understanding, Universal Constants, Universalis, Variances, wisdom | Leave a comment