## Knowledge Representation – Holographic Heart Torus

Holographic Heart Torus by Ryan Cameron on YouTube

March 11, 2018 | Categories: Fractals, Holons, Holors, Hyperbolic Geometry, Knowledge, Knowledge Representation, Language, Learning, Linguistics, Mathematics, Mathesis Generalis, Mathesis Universalis, Metamathematics, Philosophy, Philosophy of Language, Philosophy of Learning, Philosophy Of Mind, Semantic Web, Semantics, Understanding, Wisdom | Tags: knowledge, Language, learning, Philosophy, understanding | Leave a comment

## Knowledge Representation – Fractal Torus 1

Fractal Torus 1 by Ryan Cameron on YouTube

March 11, 2018 | Categories: Fractals, Holons, Holors, Hyperbolic Geometry, Knowledge, Knowledge Representation, Learning, Linguistics, Mathesis Universalis, Philosophy of Language, Philosophy of Learning, Philosophy Of Mind, Semantic Web, Semantics | Tags: knowledge, Knowledge Representation, learning, Mathesis Generalis, Mathesis Universalis, Philosophia Universalis, Philosophy of Language, Philosophy Of Mind, Semantics, understanding, wisdom | Leave a comment

## Lateral Numbers – How ‘Imaginary Numbers’ May Be Understood

First, allow me to rename theses numbers during the remainder of this post to ** lateral numbers**, in accordance to the naming convention as was

**recommended by Gauss**. I have a special reason for using this naming convention. It will later become apparent why I’ve done this.

If we examine lateral numbers *algebraically*, a pattern emerges:

When we raise lateral numbers to higher powers, the answers do not get higher and higher in value like other numbers do. Instead, **a pattern emerges after every 4th multiplication.** This pattern never ceases.

**All other numbers, besides laterals, have a place on what currently is called the ‘Real number line’.**

I qualify the naming of the Real Numbers, because even their conceptualisation has come into question by some very incisive modern mathematicians. That is a very ‘volatile’ subject for conventional mathematicians and would take us off on a different tangent, so I’ll leave that idea for a different post.

If we look for laterals on any conventional Real number line, we will never ‘locate’ them.** ***They are found there,** but we need to look at numbers differently in order to ‘see’ them.*

**Lateral numbers solve one problem in particular: ***to find a number, which when multiplied by itself, yields another negative number.*

Lateral numbers** **‘

**’**

*unify*

*the number line with the algebraic pattern shown above.*2 is positive and, when multiplied by itself, yields a positive number. It maintains direction on the number line.

When one of the numbers (leaving squaring briefly) being multiplied is negative, the multiplication yields a negative number. The direction ‘flips’ 180° into the opposite direction.

Multiplying -2 by -2 brings us back to the positive direction, because of the change resulting in multiplying by a negative number, which always flips our direction on the number line.

So, it appears as if there’s no way of landing on a negative number, right? We need a number that only rotates 90°, instead of the 180° when using negative numbers. **This is where lateral numbers come into play.**

If we place another lateral axis perpendicular to our ‘Real’ number line, we obtain the desired fit of geometry with our algebra.

When we multiply our ‘Real’ number 1 by *i*, we get *i* *algebraically*, which *geometrically* corresponds to a 90° rotation from 1 to *i*.

Now, multiplying by i again results in i squared, which is -1. This additional 90° rotation equals the customary 180° rotation when multiplying by -1 (above).

We may even look at this point as if we were viewing it down a perpendicular axis of the origin itself (moving in towards the origin from our vantage point, through the origin, and then out the back of our screen).

###### [If we allow this interpretation, we can identify the ‘spin’ of a point around the axis of its own origin! The amount of spin is determined by how much the point moves laterally in terms of *i*.

We may even determine in which direction the rotation is made. I’ll add how this is done to this post soon.]

Each time we increase our rotation by multiplying by a factor of* i*, we increase our rotation another 90°, as seen here:

and,

The cycle repeats itself on every 4th power of *i*.

**We could even add additional lateral numbers to any arbitrary point. This is what I do in my knowledge representations of holons. **For example a point at say 5 may be expressed as any number of laterals *i, j, k,… *simply by adding or subtracting some amount of* i, j, k,…:*

*5 + i + j +k +…*

Or better as:

[*5, i, j, k,…*]

**Seeing numbers in this fashion makes a point*** n***-dimensional.**

November 14, 2017 | Categories: Constants, Holons, Holors, Hyperbolic Geometry, Knowledge, Knowledge Representation, Language, Learning, Linguistics, Mathematics, Mathesis Universalis, Metamathematics, Philosophy of Language, Philosophy of Learning, Philosophy Of Mind, Semantic Web, Semantics | Tags: Mathematica Generalis, Mathematica Universalis, Mathesis Generalis, Mathesis Universalis, Metamathematics | Leave a comment

## Universal Constants, Variations, and Identities #19 (Inverse Awareness)

**Universal Constants, Variations, and Identities**

#19 **The Inverse Awareness Relation**

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

```
```and

Macro Awareness =

or

```
```

```
```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.)

```
```
May 15, 2017 | Categories: Discernment, Holons, Holors, Hyperbolic Geometry, Identities, Insight, Knowledge, Knowledge Representation, Language, Learning, Linguistics, Mathesis Generalis, Mathesis Universalis, Metamathematics, Metaphysics, Philosophy, Philosophy of Language, Philosophy of Learning, Philosophy Of Mind, Semantic Web, Semantics, Understanding, Universal Constants, Variations, and Identities, Variations, Wisdom | Tags: knowledge, Language, learning, Linguistics, LogicaUniversalis, Mathesis Universalis, Philosophia Universalis, Philosophy, Philosophy of Language, Philosophy of Learning, Philosophy Of Mind, understanding | 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

September 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

## 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.

August 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

## A New Kind of Knowledge Representation Is Coming to Be!

The project is now coming to conclusion (finally). In this video I show an example knowledge molecule being ‘examined’ by the knowledge representation.

I’ve hidden the other actors in this demonstration and have simplified the instrumentation to preserve my priority on my work.

Be patient! It won’t be long now… I have the theoretical underpinnings already behind me. Now it’s only about the representation of that work.

August 12, 2016 | Categories: Big Data, Holons, Holors, Knowledge, Knowledge Representation, Language, Learning, Linguistics, Long Data, Mathematics, Mathesis Generalis, Mathesis Universalis, Meta Logic, Metamathematics, Metaphysics, Philosophy, Semantics, Understanding, Wisdom | Leave a comment