## 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

## 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:

Micro Awareness = ```$\dfrac{1}{scope}$ and Macro Awareness = $\dfrac{1}{depth}$ or $\dfrac {Micro Awareness}{Macro Awareness} = \dfrac{depth}{scope}$ 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 ```
``` Is Real World Knowledge More Valuable Than Fictional Knowledge? No. Here an excerpt from a short summary of a paper I am writing that provides some context to answer this question: What Knowledge is not: Knowledge is not very well understood so I’ll briefly point out some of the reasons why we’ve been unable to precisely define what knowledge is thus far. Humanity has made numerous attempts at defining knowledge. Plato taught that justified truth and belief are required for something to be considered knowledge. Throughout the history of the theory of knowledge (epistemology), others have done their best to add to Plato’s work or create new or more comprehensive definitions in their attempts to ‘contain’ the meaning of meaning (knowledge). All of these efforts have failed for one reason or another. Using truth value and ‘justification’ as a basis for knowledge or introducing broader definitions or finer classifications can only fail. I will now provide a small set of examples of why this is so. Truth value is only a value that knowledge may attend. Knowledge can be true or false, justified or unjustified, because knowledge is the meaning of meaning What about false or fictitious knowledge? [Here’s the reason why I say no.] Their perfectly valid structure and dynamics are ignored by classifying them as something else than what they are. Differences in culture or language even make no difference, because the objects being referred to have meaning that transcends language barriers. Another problem is that knowledge is often thought to be primarily semantics or even ontology based. Both of these cannot be true for many reasons. In the first case (semantics): There already exists knowledge structure and dynamics for objects we cannot or will not yet know. The same is true for objects to which meaning has not yet been assigned, such as ideas, connections and perspectives that we’re not yet aware of or have forgotten. Their meaning is never clear until we’ve become aware of or remember them. In the second case (ontology): collations that are fed ontological framing are necessarily bound to memory, initial conditions of some kind and/or association in terms of space, time, order, context, relation,… We build whole catalogues, dictionaries and theories about them: Triads, diads, quints, ontology charts, neural networks, semiotics and even the current research in linguistics are examples. Even if an ontology or set of them attempts to represent intrinsic meaning, it can only do so in a descriptive ‘extrinsic’ way. An ontology, no matter how sophisticated, is incapable of generating the purpose of even its own inception, not to mention the purpose of the objects to which it corresponds. The knowledge is not coming from the data itself, it is always coming from the observer of the data, even if that observer is an algorithm. Therefore ontology-based semantic analysis can only produce the artefacts of knowledge, such as search results, association to other objects, ‘knowledge graphs’ like Cayley,… Real knowledge precedes, transcends and includes our conceptions, cognitive processes, perception, communication, reasoning and is more than simply related to our capacity of acknowledgement. In fact knowledge cannot even be completely systematised; it can only be interacted with using ever increasing precision. [For those interested, my summary is found at: A Precise Definition of Knowledge – Knowledge Representation as a Means to Define the Meaning of Meaning Precisely: http://bit.ly/2pA8Y8Y May 11, 2017 | Categories: Consciousness, Insight, Knowledge, Language, Learning, Linguistics, Mathesis Generalis, Mathesis Universalis, Metamathematics, Metaphysics, Philosophy, Philosophy of Language, Philosophy of Learning, Philosophy Of Mind, Semantic Web, Semantics, Understanding, Wisdom | Tags: Big Data, Characteristica Universalis, insight, knowledge, Knowledge Representation, Language, learning, Linguistics, Logica Universalis, Mathematica Universalis, Mathesis Universalis, Metaphysica Universalis, Metaphysics, Philosophia Universalis, Philosophy, Philosophy of Language, Philosophy of Learning, Philosophy Of Mind, Scientia Universalis, Semantic Web, Semantics, understanding, wisdom | Leave a comment What About Tacit Knowledge? 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.   May 5, 2017 | Categories: Knowledge, Knowledge Representation, Language, Learning, Linguistics, Mathesis Generalis, Mathesis Universalis, Metamathematics, Wisdom | Tags: Big Data, Characteristica Generalis, Characteristica Universalis, insight, knowledge, Knowledge Representation, learning, Linked Data, Logica Generalis, Logica Universalis, Mathesis Generalis, Mathesis Universalis, Metaphysica Generalis, Metaphysica Universalis, Philosophia Generalis, Philosophia Universalis, Scientia Generalis, Scientia Universalis, Semantic Web, Smart Data, Tacit Knowledge, understanding, 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 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 Link to video. 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! Link to video 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 « Older Entries ```
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