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.
Strictly Speaking Can’t! Natural Language Won’t?
Physics is only complex, because it’s in someone’s interest to have it that way. The way to understanding, even if you don’t understand science, was paved with words. Even if those words led only to a symbolic form of understanding.
Common ordinary language is quite capable of explaining physics. Mathematics is simply more precise than common language. Modern Mathematics pays the price for that precision by being overly complex and subservient to causal and compositional relations. These are limitations that metaphysics and philosophy do not have.
Words in language have a structure that mathematics alone will never see as it looks for their structure and dynamics in the wrong places and in the wrong ways. Modern pure mathematics lacks an underlying expression of inherent purpose in its ‘tool set’.
With natural language we are even able to cross the ‘event horizon’ into interiority (where unity makes its journey through the non-dual into the causal realm). It is a place where mathematics may also ‘visit’ and investigate, but only with some metaphysical foundation to navigate with. The ‘landscape’ is very different there… where even time and space ‘behave’ (manifest) differently. Yet common language can take us there! Why? It’s made of the ‘right stuff’!
The mono-logical gaze with its incipient ontological foundation, as found in (modern) pure mathematics, is too myopic. That’s why languages such as Category Theory, although subtle and general in nature, even lose their way. They can tell us how we got there, but none can tell us why we wanted to get there in the first place!
It’s easy to expose modern corporate science’s (mainstream) limitations with this limited tool set – you need simply ask questions like: “What in my methodology inherently expresses why am I looking in here?” (what purpose) or “What assumptions am I making that I’m not even aware of?” or “Why does it choose to do that? and you’re already there where ontology falls flat on its face.
Even questions like these are met with disdain, intolerance and ridicule (the shadow knows it can’t see them and wills to banish what it cannot)! And that’s where science begins to resemble religion (psyence).
Those are also some of the reasons why philosophers and philosophy have almost disappeared from the mainstream. I’ll give you a few philosophical hints to pique your interest.
Why do they call it Chaos Theory and not Cosmos Theory?
Why coincidence and not synchronicity?
Why entropy and not centropy?
…
Why particle and not field?
(many more examples…)
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:
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
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.
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.
Obfuscation In A ‘Nut’ Shell
Distinctions that are no differences, are incomplete, or are in discord.
In knowledge representation these ‘impurities’ (artificiality) and their influence are made easy to see.
In groks you will see them as obfuscation fields. That means darkening and/or inversion dynamics. The term refers to the visual representation of an obfuscated field, and can also be represented as dark and/or inverted movements of a field or group. I concentrate more on the dark versions here and will consider the inversions (examples of lying) in a future post.
They bring dynamics that are manipulative, artificial, or non-relevant into the knowledge representation. Their dynamic signatures make them stand out out like a sore thumb.
Cymatic images reveal these dynamics too. There are multiple vortexes, each with their own semantic contribution to the overall meaning to a knowledge molecule or group.
Here is an example of a snow flake (seen below) https://www.flickr.com/photos/13084997@N03/12642300973/in/album-72157625678493236/
From Linden Gledhill.
Note that not all vortexes are continuous through the ‘bodies’ of the molecules they participate in. Also, in order to correctly visualize what I’m saying, one must realize that the cymatic images are split expressions. That means to see the relationship, you must add the missing elements which are hinted at by the image.
Every cymatic image is a cut through the dynamics it represents.
We are in effect seeing portions of something whole. Whole parts are dissected necessarily, because the surface of expression is limited to a ‘slice’ through the complete molecule.
(Only the two images marked ‘heurist.com’ are my own! The other images are only meant as approximations to aid in the understanding of my work.)
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…]
Universal Constants and Variances
Universal Constants and Variances
#1 Awareness is primary and fundamental. (Substrate)
#2 All awareness is non-dual unless it is dual. (Duality)
#3 There is no inside without an outside nor outside without an inside. (Interiority/Exteriority)
#4 Duality is bounded, non-duality is boundless. (Boundary)
#5 Boundaries arise in a spectrum from diffuse to concise. (Crossing)
[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.
Knowledge Is What Awareness Does – Knowledge Representation as a Means to Define Meaning Precisely
Knowledge Representation as a Means to Define Knowledge Precisely
Video is finally here!
Knowledge Representation – Self and Other
Knowledge Representation of Self and Other
This knowledge representation, which I made for a presentation in Nürnberg on April 29th, 2013, depicts a partial resonance domain with respect to sentient relation and orientation. The representation is not designed to be comprehensive in any respect, rather it is intended to help those who are not accustomed to viewing knowledge in this way.
It shows how, to quote Carl Sagan: “One voice in the Cosmic fugue.” can be represented more generally. There are certainly other possibilities with respect to relation and orientation between self and other.
You may need to stop this video occasionally as some of the transitions occur very quickly.I’ve indicated what is happening in the representation to aid in the interpretation of what is being shown.
I would appreciate any feedback you may want to give. I’d be pleased to answer any questions that may arise.
Thank you for watching!
UPDATE:
A question has come in from an anonymous source asking for clarification on the use of “Resonance Domain”.
A resonance domain is comprised of resonance fields. When one or more fields are being examined, the group is called a domain.
For further clarity I’d like to add that we are looking at two separate fields (sentient beings) in terms of the relation they participate in and the orientation they share with each other.
Fields are always composed of other sub-fields and contain even partial fields from other sources!
UPDATE: “Why do you use the word ‘sentient’ in your description?”
There are basically three types of entities in our universe:
1) Having some measure of interiority (concept of self).
2) Artifacts
3) Heaps
‘Self and other’ can come in any number of combinations:
The knowledge representation above requires that at least two of the participants are of type 1 (sentience) for this knowledge representation to hold.
Examples:
Type 1) human and type 1) dog will work.
Type 1) human and type 2) book will not work.
Type 1) human and type 3) rock will not work.
This way of looking at our Kosmos (multiverse) is called Mathesis Universalis.
For those interested in more on the subject, go to http://mathesis-universalis.com.
[PS: There are also the conditions that both participants are conscious of each other and that their shared consciousness is such that differences in semantics between them are ‘reconcilable’ (coherence). (for the scientists/mathematicians among us!)] 😉
Heurist.me (Carey G. Butler) 