## 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 identity of change (some would say proportion, but that’s not entirely correct).
• π 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

This system is quite interesting if we allow ourselves to talk about the qualities of infinite sets as if we can know their character completely. The problem is, any discussion of an infinite set includes their definition which MAY NOT be the same as any characterisation which they may actually have.

Also, and more importantly, interiority as well as exteriority are accessible without the use of this system. These ‘Hyperreals’ are an ontological approach to epistemology via characteristics/properties we cannot really know. There can be no both true and verifiable validity claim in this system.

## Knowledge Representation – Holographic Heart Torus

Holographic Heart Torus by Ryan Cameron on YouTube

## Knowledge Representation – Fractal Torus 1

Fractal Torus 1 by Ryan Cameron on YouTube

## Which questions does Category Theory help us answer?

Another chapter in my attempt to help break the ‘spell’ of the category theoretical ‘ontologicisation’ of our world.

This may seem to many as a purely academic question, but we all need to realise that all of what we consider a modern way of thinking rests upon ‘mental technologies’ such as Category Theory.

Academics are literally taking the ‘heart’ out of how our world is being defined!
If we don’t pay attention, humanity will continue losing its way.

Category theory is a wonderful and powerful tool; nevertheless category theory, with all of its utility, is purely ontological. It can masterfully answer questions such as ‘Who?’, ‘What?’, and ‘How?’.

However; it is regretfully inadequate to form a comprehensive representation of knowledge, for it lacks expression of epistemological value, which are the very reasons for is use. Epistemology is about answering the questions of ‘Why?’, ‘What does it mean?’, ‘What is my purpose?’,…
Answers to questions of this kind are implicitly supplied by us during our consumption of the utility afforded by category theory. We often are so beguiled by this power of categorical expression that we don’t realise that is we ourselves who bring the ‘missing elements’ to what it offers as an expression of knowledge.
It does a wonderful job with exteriority (ontology), but cannot sufficiently describe nor comprehensively access interiority (epistemology). Therefore, it has limited metaphysical value with respect to philosophy in general.

Philosophies of mind, of language, or of learning are not comprehensive using only category theoretical tools.
Categorical structures are highly portable, but they can describe/express only part of what is there. There are structures, dynamics, and resonance that the ontology and functionalism in category theory completely turns a blind eye to.
More general than category theory is knowledge representation. It includes and surpasses category theory in many areas, both in scope and depth, but in particular: knowledge representation includes not just the ontological aspects of what we know, it goes further to describe the epistemological as well.
The qualities of Truth, Goodness, Beauty, Clarity,… can be defined and identified within a knowledge representation if the representation is not restricted to ontology. When category theory is used for the purpose of defining qualia, the objects must first be ontologised and functionally reduced. Trying to grasp them with tools restricted to category theory (or even semiotics) is like grasping into thin air.

Category theory, although very powerful, is no match for the challenge of a complete representation of knowledge. Category theory will tell you how to tie your shoes, but it can’t tell you why you are motivated to do so.

## 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:

### $i^8 = i^4 \cdot i^4 = (1)(1) = 1$

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.

## Does Division By Zero Have Meaning?

Yes, in knowledge representation, the answer is the interior of a holon.

Ontologies go ‘out of scope’ when entering interiority. The common ontological representation via mathematical expression is 1/0.

When we ‘leave’ the exterior ontology of current mathematics by replacing number with relation, we enter the realm of interiority.

In the interior of relation, we access the epistemological aspects of any relation.

As an aide to understanding – Ontology answers questions like: ‘What?’, ‘Who?’, ‘Where?’, and ‘When?’. Epistemology answers questions like: ‘Why?’ and ‘How do we know?’

In vortex mathematics 1/0 is known as ‘entering the vortex’.

There are other connections to some new developments in mathematics involving what is called ‘inversive geometry’.

Example: (oversimplified for clarity)

If we think of say… the point [x, y, z] in space, we may assign x, y, and z any number value except where one of these coordinates gets involved in division where 0 is not allowed (up to this point in common mathematics) as a denominator. x/z is not allowed when z=0, for example.

Now, if we are dealing with interiority, numbers are replaced by relationships, such as [father, loves, son].

What if the son has died? Is the relationship still valid?

The answer to this question lies within the interior of those involved in the relation.

## Are sets, in an abstract sense, one of the most fundamental objects in contemporary mathematics?

Yes and no.

The equivalence relation lies deeper within the knowledge representation and it’s foundation.

There are other knowledge prerequisites which lie even deeper within the knowledge substrate than the equivalence relation.

The concepts of a boundary, of quantity, membership, reflexivity, symmetry, transitivity, and relation are some examples.

http://bit.ly/2wPV7RN

## Limits of Category Theory and Semiotics

They are wonderful tools to explain much of our world, but lack ‘The Right Stuff’ to handle the metaphysical underpinnings of anything near a Philosophy of Mind, Philosophy of Language , or a Philosophy of Learning.

This is, because Category Theory specialises on roughly half of the Noosphere. It does a wonderful job on exteriority, but cannot sufficiently describe nor comprehensively access interiority.

Therefore, as is the case with Semiotics, has limited metaphysical value with respect to philosophy in general.

For example: philosophies of mind, language, or learning are not possible using only category theoretical tools and/or semiotics.

Here is an example of one attempt which fails in this regard: http://nickrossiter.org.uk/proce…

(and here: VisualizationFoundationsIEEE)

Here are two problems (of many) in the paper:

4.4.2 Knowledge is the Terminal Object of Visualisation states:

“The ultimate purpose of the visualisation process is to gain Knowledge of the original System. When this succeeds (when the diagram commutes) then the result is a ‘truth’ relationship between the Knowledge and the System. When this process breaks down and we fail to deduce correct conclusions then the diagram does not commute.”

I want to also comment on Figure 3 (which also exposes missing or false premises in the paper), but I will wait until I have discussed the assertions in the quote above which the authors of this paper reference, accept, and wish to justify/confirm.

1) The purpose of a representation is NOT to gain knowledge; rather, to express knowledge. Also, truth has nothing to do with knowledge except when that value is imposed upon it for some purpose. Truth value is a value that knowledge may or not ‘attend’ (participate in).

1a) The ‘truth value’ of the System (‘system’ is a false paradigm [later, perhaps] and a term that I also vehemently disagree with) does not always enter into the ‘dialogue’ between any knowledge that is represented and the observer interpreting that knowledge.

2) The interpretation of a representation is not to “deduce correct conclusions”; rather, to understand the meaning (semantics and epistemology) of what is represented. ‘Correct’ understanding is not exclusive to understanding nor is it necessary or sufficient for understanding a representation, because that understanding finds expression in the observer.

2a) ‘Correct’, as used in this paragraph, is coming from the outside (via the choice of which data [see Fig. 3] is represented to the observer) and may have no correspondence (hence may never ever commute) whatever to what that term means for the observer.

The authors are only talking about ontologies. That is a contrived and provincial look at the subject they are supposing to examine.

There may (and usually are) artefacts inherent in any collection and collation of data. The observer is forced to make ‘right’ (‘correct’) conclusions from that data which those who collected it have ‘seeded’ (tainted) with their own volition.

‘System’ (systematising) anything is Reductionism. This disqualifies the procedure at its outset.

They are proving essentially that manipulation leads to a ‘correct’ (their chosen version) representation of a ‘truth’ value.

I could tie my shoelaces into some kind of knot and think it were a ‘correct’ way to do so if the arrows indicate this. This is why paying too much attention to a navigation system can have one finding themselves at the bottom of a river!

The paper contains assumptions that are overlooked and terms that are never adequately defined! How can you name variables without defining their meaning? They then serve no purpose and must be removed from domain of discourse.

Categorical structures are highly portable, but they can describe/express only part of what is there. There are structure, dynamics, and resonance that ontology and functionalism completely turns a blind eye to.

The qualities of Truth, Goodness, Beauty, Clarity,… (even Falsehood, Badness, Ugliness, Obscurity,…) can be defined and identified within a knowledge representation if the representation is not restricted to ontology alone.

In order to express these qualities in semiotics and category theory, they must first be ontologised funtionally (reduced). Trying to grasp them with tools restricted to semiotics and category theory is like grasping into thin air.

That is actually the point I’m trying to make. Category Theory, and even Semiotics, each have their utility, but they are no match for the challenge of a complete representation of knowledge.

## 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:

## Does Knowledge Become More Accurate Over Time?

Change lies deeper in the knowledge substrate than time.

Knowledge is not necessarily coupled with time, but it can be influenced by it. It can be influenced by change of any kind: not only time.

Knowledge may exist in a moment and vanish. The incipient perspective(s) it contains may change. Or the perspective(s) that it comprises may resist change.

Also, knowledge changes with reality and vice versa.

Time requires events to influence this relationship between knowledge and reality.

Knowledge cannot be relied upon to be a more accurate expression of reality, whether time is involved or not, because the relationship between knowledge and reality is not necessarily dependent upon time, nor is there necessarily a coupling of the relationship between knowledge and reality. The relationships of ‘more’ and ‘accurate’ are also not necessarily coupled with time.

Example: Eratosthenes calculated the circumference of the Earth long before Copernicus published. The ‘common knowledge’ of the time (Copernicus knew about Eratosthenes, but the culture did not) was that the Earth was flat.

## Is Mathematics Or Philosophy More Fundamental?

Is Mathematics Or Philosophy More Fundamental?

Answer: Philosophy is more fundamental than mathematics.

This is changing, but mathematics is incapable at this time of comprehensively describing epistemology, whereas, philosophy can.

Hence; mathematics is restrained to pure ontology. It does not reach far enough into the universe to distinguish anything other than ontologies. This will change soon. I am working on exactly this problem. See http://mathematica-universalis.com for more information on my work. (I’m not selling anything on this site.)

Also, mathematics cannot be done without expressing some kind of philosophy to underlie any axioms which it needs to function.

PROOF:

Implication is a ‘given’ in mathematics. It assumes a relation which we call implication. Mathematics certainly ‘consumes’ them as a means to create inferences, but the inference form, the antecedent, and the consequent are implicit axioms based upon an underlying metaphysics.

Ergo: philosophy is more general and universal than mathematics.

Often epistemology is considered separate from metaphysics, but that is incorrect, because you cannot answer questions as to ‘How do we know?” without an underlying metaphysical framework within which such a question and answer can be considered.

A knowledge representation system is required. I’m building one right now. Mathesis Universalis.

There are other tools which are useful, such as TheBrain Mind Mapping Software, Brainstorming, GTD and Knowledgebase Software

Products and technologies like TheBrain, knowledge graphs, taxonomies, and thesauri can only manage references to and types of knowledge (ontologies).

A true knowledge representation would contain vector components which describe the answers to “Why?” and “How does one know?” or “When is ‘enough’, enough?” (epistemology).

It is only through additional epistemological representation that tacit knowledge can be stored and referenced.

## 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

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.)

## Men And Their Semantics – Turning Meaning into Legos

Semantically speaking: Does meaning structure unite languages?

This work is a dead end waiting to happen. Of course it will attract much interest, money, and perhaps even yield new insights into the commonality of language, but there’s better ways to get there.

What’s even more sad is that they, who should know better, will see my intentions in making this clear as destructive criticism instead of a siren warning regarding research governed/originating through a false paradigm. These people cannot see or overlook the costs humanity pays for the misunderstandings research like this causes and is based upon.

It’s even worse in the field of genetic engineering with their chimera research. The people wasting public money funding this research need to be gotten under control again.

I don’t want to criticize the researcher’s intentions. It’s their framing and methodology that I see as primitive, naive, and incomplete.

I’m not judging who they are nor their ends; rather, their means of getting there.

“Quantification” is exactly the wrong way to ‘measure/compare semantics; not to mention “partitioning” them!

1) The value in this investigation that they propose is to extrapolate and interpolate ontology. Semantics are more than ontology. They possess a complete metaphysics which includes their epistemology.

2) You cannot quantify qualities, because you reduce the investigation to measurement; which itself imposes meaning upon the meaning you wish to measure. Semantics, in their true form, are relations and are non-physical and non-reducible.

3) Notice also, partitioning is imposed upon the semantics (to make them ‘measurable/comparable’). If you compare semantics in such a way then you only get answers in terms of your investigation/ontology.

4) The better way is to leave the semantics as they are! Don’t classify them! Learn how they are related. Then you will know how they are compared.

There’s more to say, but I think you get the idea… ask me if you want clarification…

## Typical Knowledge Acquisitions Node

Knowledge Representation

A typical knowledge acquisition node showing two layers of abstraction. Note how some of the acquisition field detection moves with the observer’s perspective. You can tell, due to the varying visual aspects of the fields and their conjunctions that it has already been primed and in use.

This node may be one of thousands/millions/billions which form when acquiring the semantics of any particular signal set.

Their purpose is to encode a waveform of meaning.

Basically it is these ‘guys’ which do the work of ‘digesting’ the knowledge contained within any given signal; sort of like what enzymes do in our cells.

The size, colour (although not here represented), orientation, quantity, sequence, and other attributes of the constituent field representations all contribute to a unique representation of those semantics the given node has encountered along its travel through any particular set of signal. The knowledge representation (not seen here) is comprised of the results of what these nodes do.

This node represents a unique cumulative ‘imprint’ or signature derived from the group of knowledge molecules it has processed during its life time in the collation similar to what a checksum does in a more or less primitive fashion for numerical values in IT applications.

I have randomized/obfuscated a bit here (in a few different ways), as usual, so that I can protect my work and release it in a prescribed and measured way over time.

In April I will be entering the 7th year of working on this phase of my work. I didn’t intentionally plan it this way, but the number 7 does seem to be a ‘number of completion’ for me as well.

The shape of the model was not intended in itself. It ‘acquired’ this shape during the course of its work. It could have just as well been of a different type (which I’m going to show here soon).

Important is the ‘complementarity’ of the two shapes as they are capable of encoding differing levels of abstraction. The inner model is more influenced by the observer than the outer one, for example. The outer shape contains a sort of ‘summary’ of what the inner shape has processed.

## A Holon’s Topology, Morphology, and Dynamics (2a)

A Holon’s Topology, Morphology, and Dynamics (2a)

This is the second video of a large series and the very first video in a mini-series about holons. In this series I will be building the vocabulary of holons which in turn will be used in my knowledge representations.
The video following this one will go into greater detail describing what you see here and will be adding more to the vocabulary.

This is the second video of a large series and the very first video in a mini-series about holons. In this series I will be building the vocabulary of holons which in turn will be used in my knowledge representations.

## Ontology: Compelling and ‘Rich’

Ontologies are surfaces… even if ‘rich’. (link)

Ontology: Compelling and ‘Rich’
They are only surfaces, but they seem to provide you with depth.

This exquisite video shows how the representation of knowledge is ripe for a revolution. I’ve written about this in depth in other places so I won’t bore you with the details here unless you ask me in the comments below.

Stay tuned! I’m behind in my schedule (work load), but I’m getting very close just the same. I will publish here and elsewhere.
I’m going to use this video (and others like it) to explain why ontologies are not sufficient to represent knowledge.

Soon everyone will acknowledge this fact and claim they’ve been saying it all along! (In spite of the many thousands of papers and books obsessively claiming the opposite!!!) They do not know that how dangerous that claim is going to be. Our future will be equipped with the ability to determine if such claims are true or not. That’s some of the reason I do what I do.

## Knowledge Representation Foundations

Knowledge Representation Foundations
It’s also stuck in ontological framing, but the approach and results are fascinating.

“This map was constructed by sorting roughly 800,000 published papers into 776 different scientific paradigms (shown as pale circular nodes) based on how often the papers were cited together by authors of other papers.”

“Links (curved black lines) were made between the paradigms that shared papers, then treated as rubber bands, holding similar paradigms nearer one another when a physical simulation forced every paradigm to repel every other; thus the layout derives directly from the data.”

“Larger paradigms have more papers; node proximity and darker links indicate how many papers are shared between two paradigms. Flowing labels list common words unique to each paradigm, large labels general areas of scientific inquiry.”

Others doing work on this:
http://www.mapofscience.com/

https://www.flickr.com/photos/7446536@N03/430561725/

Paper on Illuminated Diagrams:
http://www.textarc.org/appearances/InfoVis02/InfoVis02_IlluminatedDiagrams.pdf
(Also one in German that is VERY comprehensive!)
http://gerhard_dirmoser.public1.linz.at/Anwendungskontext_Diagrammatik.pdf

Enjoy!!!

Introduction.
Manuel DeLanda. 2015. Philosophical Chemistry: Genealogy of a Scientific Field. Bloomsbury
“There is no such thing as Science. The word ‘Science’ refers to a reified generality that together with others, like Nature and Culture, has been a constant source of false problems: are controversies in Science decided by Nature or Culture?”

“Avoiding badly posed problems requires that we replace Science with a population of individual scientific fields, each with it own concepts, statements, significant problems, taxonomic ad explanatory schemas. There are, of course, interactions between fields, and exchanges of cognitive content between them, but that does not mean that they can be fused into a totality in which everything is inextricably related. There is not even a discernible convergence towards a grand synthesis to give us hope that even if the population of fields is highly heterogeneous today, it will one day converge into a unified field. On the contrary, the historical record shows a population progressively differentiating into many subfields, by specialization or hybridization, yielding an overall divergent movement.”

## Coming Soon To A World Near You

Coming Soon To A World Near You

The time is coming when we will exchange massive amounts of knowledge between us without any corporation standing in between.
My life’s work is dedicated to this vision and I’m actually carrying it out right in front of you!

We will not only create and share our books, documents, web sites, search results, and media with each other – we will be sharing their conceptual landscapes.

## 3D Scientific Visualization with Blender

3D Scientific Visualization with Blender
It’s a book everyone in knowledge representation should at least know about. It has great tips and clarifications inside.

Unfortunately it is also based solely on ontologies so it provides only limited value for what I’m doing, but it is a valuable resource for understanding and creating visualizations just the same.

Video – Rendering a data cube: