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.
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
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.
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.)
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.
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
Universal Constants, Variations and Identities
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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.
Universal Constants, Variations and Identities
Universal Constants and Variances
#11 Observation is communication between its participants (observer and observed). (Reference)
See http://mathesis-universalis.com for more information.
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.
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
Heurist.me (Carey G. Butler) 