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
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.
Getting Hypertension About Hyperreals
(Links below)
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.
https://www.youtube.com/watch?v=rJWe1BunlXI (Part1)
https://www.youtube.com/watch?v=jBmJWEQTl1w (Part2)
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…)
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.
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.
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
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, Variations and Identities #13 (Knowledge)
Universal Constants, Variations and Identities
#13 Knowledge is what awareness does. (Knowledge)
I’ve published this before elsewhere, but it must be restated now for what is to follow (I’m starting a new octave).
#Knowledge #Wisdom #Understanding #Learning #Insight #Constants #Variances #Metaphysics #Philosophy #MathesisUniversalis #ScientiaUniversalis #PhilosophiaUniversalis #LogicaUniversalis #MetaMathematics #MetaLogic #MetaScience #MetaPhysics #MetaPhilosophy #Awareness
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.
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.
I’m a mathematician and can tell you that common ordinary language is quite capable of explaining physics. Mathematics is simply more precise than common language. It pays the price for that precision by being subservient to the 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. 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 monological gaze with its incipient ontological foundation, as found in 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 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…)
Complexity At the Cost of Being Simple
Complexity At the Cost of Being Simple
There are grievous problems with complexity ‘science’. Some of those problems are apparent here. I will note a few of them.
Reductionism at @13:00 is completely annoying. Epiphenomenological aspects of the problem are completely missing when you reduce into pure binary! It’s like taking you and your emotional life (with its incipient impact on your immune system) and reducing it down to DNA!
“There are way more problems than there are solutions.” @17:00!Sure! When you peel away the contextual embedding of any problem (via reductionism), then you’ve just committed a sort of lobotomy!
The definition of NP at @23:00 while correct, reveals how misguided this theory is. Not all choices are guesses, and correct answers aren’t always ‘lucky’.
Check out the response one receives from the system (algorithm) at @25:11.Did you notice something’s wrong or what?
@26:51 Does anyone notice who is supplying the criterion for the value of ‘correct’? The algorithm is being falsely attributed with properties it can only be endowed with and not arrive at on its own!
@30:00 The rules to Tetris are known by both (algorithm and human) however, the proof of a truth value cannot be computationally arrived at in NP, yet the proof – via a human being AND the skills necessary to ‘prove’ anything can do it in P! It should be obvious that we are going about the whole thing in the wrong way by now!
@31:00 the P<>NP Problem is described. The problem is meaningless and yet you’ll get a Millenium Prize for solving it! (Even sane and not sane find themselves in the balance! Whoa!) If you continue listening to the justification, you might want to be near a bathroom.
@32:27 Check out how NP is being determined to be ‘more’ than P! “Nobody in their right mind…”, “Obviously insane…”,… so naturally NP must be more than P!
Sounds reasonable? I don’t think so…
@32:37 Watch the disappointment: “…very annoying…” and I wonder why? The question is meaningless! Other phrasings of the P<>NP Problem are nothing special and are completely obvious: “You can’t engineer luck.” (Excuse me, but isn’t that the definition of luck in the first place?) and “Solving problems is harder than checking them.”
@34:17 “What could we possibly say… this is all kind of weired…” I don’t know anymore either and I sure hope you don’t tell me! Are we at the end of the lecture already?
@35:53 Now we are getting to the ‘meat of the potato’. If we just “believe in… have faith in…” P<>NP, then Tetris is within NP-P! Wait a minute? That doesn’t sound like any proof to me… perhaps it’s an axiom? We’ll see. It sure looks like begging the question, but I want to be convinced so I’ll just have to wait.
@36:43 He then moves on to a ‘proof’ that looks more like a set of definitions! NP-hard and NP-complete are correctly defined, but they do not prove anything! Tetris and chess act like a definitions, as well!
@40:33 Now he wants to talk about reductions. Wait, weren’t we talking about them already? Let’s take a look…
Yes, we stand upon giants [Authoritarianism]@46:15(Karp’s 3-Partition) and don’t need to think about it anymore and just reconfirm that all NP-complete is reducible to each other! You find some problem that was defined by a “giant” to be a member of your classification and then show that yours is at least as hard @48:47.
If we happen to find a better solution to a member of NP-complete, then either the whole house of cards falls down or we simply reclassify (by reduction) it to P! Now believe it or believe what you want, okay?
There will be a time when we have to revisit mathematics and do a house cleaning of this ‘cuddle muddle’.
Music For the Ears… and Eyes!
This is one of a growing number of representations for music. Listen, see and enjoy the wonder.
This isn’t the only kind of sound representation being done. I will be publishing my own in the near future.
Here is another source that is just as significant: https://www.youtube.com/channel/UC2zb5cQbLabj3U9l3tke1pg
Good News! It’s Not Just Particles! It’s Properties and Patterns of Particles! – Max Tegmark
“Consciousness is a mathematical pattern.”
Is it possible to explain the phenomenon of purpose away with another phenomenon of emergence?
I wonder how he defines purpose itself?
Isn’t consciousness more than our senses?
Why are we only looking at states of matter and leave out stages, lines, levels, types,…?
Who is doing the “feeling” he’s describing?
Who gives the particles their work to do?
How are the particles different between dead and living beings?
So we are to replace our questions with a certainty of the phenomenon of consciousness and then explain that in terms of an interpretation of same?
I’m not a religious person, but the video is starting to sound like I should be one!
Is this what we get when a physicist tries to do philosophy? Oh my!
I Really Want To Agree… But I Just Can’t! – Max Tegmark – Cahners Theater
I did it again (for a friend) and tolerated another hour of this man’s presentation (see my post following this one where I cover the one I watched on August 31st).
Beyond the Higg’s Boson, which is not a convincing ‘discovery’, is his claim that the universe is mathematical at (31:00). “In the sense that it [universe] is a mathematical structure.”
Mathematics is simply a precise language!
Here’s one avenue, but I can give others, that may help understand why mathematics cannot be the universe, rather a means to represent it.
Patterns and shapes can be described mathematically just as they are now being described with my words. When he widens his definition to include them (shapes and patterns, structure,…) they represent literally everything and become part of his definition!
He also assigns humanity as a whole as the designer for technology that our amok running corporations have made (and have led the rest of us who ‘enjoy’ employment with them to build for them). The Cuban Missile Crisis isn’t a problem created by humanity as a whole, rather was created by corporations who work for banksters to further their ends.
Causality is all wrong throughout his presentation. Believe me, I wanted to be enthralled by his wisdom, but I’m left disappointed for many reasons… many for which I’ve made no mention.
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!
Self-referential Paradoxum In Knowledge Representation
What do these two pictures share in common?
They represent structure and dynamics (continuity, connectedness, and boundary [of which topology is only ONE example!]) distributed over multiple and partial dimension. That’s why they interest me and are of use. I use them to represent knowledge, because they are found in our knowledge!
They always have a concealed twist (internal dynamics). You need to leave our 3D rational domain to capture their meaning though. I’ve studied these shapes for a long time now and use them in my work. Break the figures or logic apart and notice how you can tuck the parts into a cloud shape (ambiguity) and make the systems work.
A Precise Definition of Knowledge – Knowledge Representation as a Means to Define the Meaning of Meaning Precisely
A Precise Definition of Knowledge
Knowledge Representation as a Means to Define the Meaning of Meaning Precisely
Copyright © Carey G. Butler
August 24, 2014
What is this video about?
In this introductory video I would like to explain what knowledge representation is, how to build and apply them. There are basically three phases involved in the process of building a knowledge representation. Acquisition of data (which includes staging), collation and the representation itself. The collation and the representation phases of the process are mentioned here, but I will explain them further in future videos.
You are now watching a simulation of the acquisition phase as it collects and stores preliminary structure from the data it encounters in terms of the vocabulary contained within that data. Acquisition is a necessary prerequisite for the collation phase following it, because the information it creates from the data are used by the collation algorithms which then transform that information into knowledge.
The statistics you are seeing tabulated are only a small subset of those collected in a typical acquisition phase. Each of these counters are being updated in correspondence to the recognition coming from underlying parsers running in the background. Depending upon the computer resources involved in the
acquisition, these parsers may even even run concurrently as is shown in this simulation.
The objects you see moving around in the video are of two different kinds: knowledge fields or knowledge molecules. Those nearest to you are the field representations of the actual data being collected called knowledge fields. They could represent an individual symbol, punctuation, morpheme, lexeme, word, emotion, perspective, or some other unit of information in the data. Each of them contain their own signature – even if their value, state or other intrinsic properties are unknown or indeterminate during the acquisition.
Those farther away from the view are clusters of fields which have already coalesced into groups according to shared dynamically adaptive factors such as similarity, relation, ordinality, cardinality,…
These ‘molecules’ also contain their own set of signatures and may be composed of a mixture of fields, meta-fields and hyper-fields that are unique to all others.The collation phase has the job of assigning these molecules to their preliminary holarchical domains which are then made visible in the resulting knowledge representation. Uniqueness is preserved even if they contain common elements with others in the domain they occupy. Clusters of knowledge molecules and/or fields grouped together are known as ‘knowledge domains’, ‘structural domains’,’dynamical domains’ or ‘resonance domains’, depending upon which of their aspects is being emphasized.
We now need a short introduction to what knowledge representation is in order to explain why you’re seeing these objects here.
What is Knowledge Representation?
Knowledge representation provides all of the ways and means necessary to reliably and consistently conceptualize our world. It helps us navigate landscapes of meaning without losing our way; however, navigational bearing isn’t the only advantage. Knowledge representation aids our recognition of what changes when we change our world or something about ourselves. It does so, because even our own perspective is included in the representation. It can even reveal to us when elements are missing or hidden from our view!
It’s important to remember that knowledge representation is not an end, rather a means or process that makes explicit to us everything we already do with what we come to be aware of. A knowledge representation must be capable of representing knowledge such that it, like a book or other artifact, brings awareness of that knowledge to us. When we do it right, it actually perpetuates our understanding by providing a means for us to recognize, interpret (understand) and utilize the how and what we know as it relates to itself and to us. In fact – knowledge representation even makes it possible to define knowledge precisely!
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? Their perfectly valid structure and dynamics are ignored by classifying them as something else than what they are. Differences in culture or language make 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 catalogs, 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 objects to which it corresponds! The knowledge is not coming from the data itself, it’s always coming from the observer of the data – even if that observer is an algorithm!
Therefore ontology-based semantic analysis can only produce the artifacts 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 acknowledgment. In fact knowledge cannot even be completely systematized, it can only be interacted with using ever increasing precision!
- What is knowledge then?
• Knowledge is what awareness does.
• Awareness of some kind and at some level is the only prerequisite for knowledge and is the substrate upon which knowledge is generated.
• Awareness coalesces, interacts with and perpetuates itself in all of its form and function.
• Awareness which resonates (shares dynamics) at, near, or in some kind of harmony (even disharmony) with another tends to associate (disassociate) with that other in some way.
• These requisites of awareness hold true even for objects that are infinite or indeterminate.
• This is why knowledge, the meaning of meaning, can be precisely defined and even provides its own means for doing so.
• Knowledge is, pure and simply: the resonance, structure and dynamics of awareness as it creates and discovers for and of itself.
• Awareness precedes meaning and provides the only fundamentally necessary and sufficient basis for meaning of meaning expressing itself as knowledge.
• Knowledge is the dialog between participants in awareness – even if that dialog appears to be only one-way, incoherent or incomplete.
• Even language, mathematics, philosophy, symbolism, analogy, metaphor and sign systems can all be resolved to this common denominator found at the foundation of each and every one of them.
More information about the objects seen:
The objects on the surface of the pyramid correspond to basic structures denoting some of the basic paradigms that are being used to mine data into information and then collate that information into knowledge. You may notice that their basic structures do not change, only their content does. These paradigms are comprised of contra-positional fields that harmonize with each other so closely that they build complete harmonic structures. Their function is similar to what proteins and enzymes do in our cells.
#Knowledge #Wisdom #Understanding #Learning #Insight #Semantics #Ontology #Epistemology #Philosophy #PhilosophyOfLanguage #PhilosophyOfMind #Cognition #OrganicIntelligence #ArtificialIntelligence #OI #AI
#Awareness
Does a Nobel Prize Automatically Make You Correct?
My attention has been recently brought again to the book: Thinking, Fast and Slow. There is so much ‘work’ out there to comment on that it would take many lifetimes to cover it all, but this one hits me right in the gut: it’s about heuristics. This post will delve into the misconceptions in the book regarding a heuristic and heuristics in general with respect to mind, thought and, most importantly, knowledge and its representation.
Of course there are many insightful aspects to the book and I hope this post induces people to buy and read the book! It is definitely worth that effort! There is much truth in the book and useful considerations regarding the psychology of thought (at least for me).
There is a universal constant in our universe that I call the ‘Near and Far Contraposition’. This constant is responsible for the effect we experience when we look at things close up verses far away. It ‘makes it’s appearance’ when we say things like; “He can’t see the forest for the trees.” I will describe this constant more below as time permits me to do so.
His System 1 (Intuition) is, in reality, taking relational bearing on entities involving deeper scope (among other factors) than in his System 2.
Whereas his System 2 is taking that relational bearing with entities involving more shallow scope (among other factors) to entities than in his System 1.
His systems will be shown to be completely unnecessary. There are ‘systems’ within consciousness, but they are not where Daniel says they are.
I’m amazed that someone of his depth is unable (or unwilling) to recognize this!
Your thoughts are welcome too. We all are impacted by this artificial environment created for us that causes stress and economy in our lives. It is possible to an extent to ‘divorce’ ourselves from these frenetic states, but when our customers do not ‘cooperate’ (due to different priorities, perspectives and needs) with our efforts, then it does present challenges for us.
A Disservice to Mathematics and Science For Over 100 Years and Counting…
“Today’s scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality. ” -Nikola Tesla
… and that isn’t the only area of ‘damage’!
I’ve been tracking Characteristica Unversalis, Philosophia Universalis, Mathesis Universalis, Logica Universalis and Scientia Universalis all of my working life (for a time not even knowing what these concepts were!).
These concepts are so vitally important and it is a wonder that they have been all but forgotten in our ‘modern’ and ‘post-modern’ era.
The people who are changing our education, science, mathematics and philosophy are most comfortable in an environment of fear and control. That’s why they teach us to frame ideas in terms like uncertainty, chaos, random, coincidence, normativity … all of these are artificial creations.
This is going to change! It must!
We need to be aware of the subtle changes being made to our science, mathematics, philosophy and logic over time and then bring them back to their intended purposes!
I believe we all have an edge (sometimes many) – even if it takes time or circumstance to find it.
That’s just one of the reasons why normativity is only of very limited use and its importance should be put back in its place, for just one example. Any group of humanity large enough to be considered a distribution (anything else for that matter) will exhibit shared traits and exceptions to them.
It is part of the structure of the universe that it is so! It is a natural constant
We are called upon to judge wisely what these traits are which we choose to measure, lest we miss those which are just as valid as any other, and yet remain unrecognized!
We haven’t even really begun seriously to investigate these wonderful differences in each of us that make each of us special ( #OI Organic Intelligence). Using the most frequently populated area of any particular group is a ‘measuring rod’ won’t get us there either!
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) 