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.
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.
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:
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
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.
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.)
The Creation Of ‘Care’
The Creation of ‘Care’
The 8th Principle of Natural Law: Care
The ‘container’ in which all of the principles of natural law exist.
What we care about on a daily basis acts as the driving force of our thoughts and actions.
Care+Knowledge+Action (Feeling, Mind, Being)
This is the reason my mother named me ‘Care-y’. She told me as a child when I asked her why she named me Carey that I would be the one who cares.
Note how this is the opposite of what our parasitic slave owners want. They even celebrate the opposite. They call it the ‘Cremation of Care’. Here a description on WikiLies): https://en.wikipedia.org/wiki/Cremation_of_Care
Actual footage of the ceremony here:
https://www.youtube.com/watch?v=r5dHhvpHIjM
The parasites sucking us dry for centuries now have the religion to make us want to not care any more. “Stand down and accept your chains… that’s what their religion is there for.” – Mark Passio
Mark Passio’s brief introduction.
https://www.youtube.com/watch?v=1Bs6sWFvJbU
Go to @42:43 in the video for ‘Care’.
Full Version of his Natural Law seminar is here:
https://www.youtube.com/watch?v=dIEemKcy-4E
Maritime Admiralty Law in 10 Minutes
Maritime Admiralty Law in 10 Minutes
You are ‘owned’ just by acquiescing to that ‘ownership’.
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…
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.
Good Intentions – False Causality – Sadly, Therefore Meager Cure
Good Intentions – False Causality – Sadly, Therefore Meager Cure
Earth Day: This is another brilliant video that unfortunately assigns the condition of our world to humans as a whole.
Certainly WE ALL are responsible by allowing it to happen in OUR name, but the corporations (artificial persons) and the banksters (which run the corporations) are who have performed the deed!
Yes, WE looked on, but we trusted them and they failed us all. Now WE must do something about it! He is absolutely wrong in that we must NOT look away from how our governments are dictated by corporations! (which have become the real countries)
We are losing our individual and collective sovereignty through ruses like ‘Climate Change’ (Global taxing scheme).
We should now take the corporations down and replace them with real humans and not the 1871 version that allows them to enjoy those rights of being human and yet are exempt from the responsibilities that real humans must answer to.
http://byronwine.com/files/1871.pdf
http://drrichswier.com/2015/04/21/15-supreme-court-decisions-that-shredded-the-constitution/
This man is well intentioned, but not up to par on what needs to be done. He is passionate, but unfortunately not enlightened. The onus is on us for allowing it to continue, but the onus is on the corporations and banksters, for directing humanity towards where we have come!
Why is Fukushima no longer in the news?
Why is the Gulf spill no longer in the news?
Why do we no longer think about them?
Here is where WE ALL are responsible!
http://collectivelyconscious.net/articles/the-gulf-oil-spill-you-never-heard-about-may-be-the-largest-ever/
https://www.youtube.com/watch?v=dK_EJqat1sc
The Parasites ‘Need’ a Pow Wow
The Parasites ‘Need’ a Pow Wow The ‘need’ (control/fear fetish) for full-spectrum dominance. We must live out their nightmare so that they can save us. Will they be proud of their ‘work’ in a galactic context when our neighbors see what we’re up to?
We suffer from an awful shortage of humans in the universe, but they tell us there’s too many of us! It’s all an expression of their fear and need to control others. Even where there are no problems, they will create them so that they may mark them, touch them and make them ‘safe’.
Our problem isn’t a lack of resources, it’s the hoarding of them!
Scarcity Fetish Served Hot and Dry
Image Credit: © Cecilia Lim / Fotolia (see original source)
Scarcity Fetish Served Hot and Dry
More artificial scarcity. Why don’t we try ridding ourselves of just one medium sized weapons system. Then we could feed everyone in the world.
Then we could stop suppressing free energy. When we do that we could harvest water out of the air, use it for fuel and drink the exhaust!
This is simply another attempt to get us to accept the privatization of water! We are the living Earth, but if we continue, we’ll all be renters on our own home!
Did we suffer from a shortage of electricity before Tesla showed us how to make use of it?
The parasitic banksters who fund our science (i.e. how we are taught to frame things) have been harping about overpopulation for over 5 centuries (it started during the time of Machiavelli). If they wanted a solution, we would have had one by now. They don’t want a solution to an artificial problem until they can sell us an artificial solution.
We should learn to see through this crap! They’re framing everything now in terms of scarcity and we lap it up like trendy mainstream pablum!
We are suffering from a shortage of humans in the universe. Do your share by having many children who don’t hoard like banksters.
http://overpopulationisamyth.com/
Rationally Bayesian Doesn’t Help You See The Elephant!
Here a proven social engineering device ‘conspiracy theory’ is being used to contrast Bayesian logic and fails miserably in discovering truth by doing so.
The example used for ‘conspiracy thinking’ was the ignorance of an elected official during WW2, California Governor Earl Warren https://en.wikipedia.org/wiki/Earl_Warren
Who interestingly enough, got placed on the Supreme Court by the parasitic class later in his career!
We literally swim in a world of conspiracies (look up LIBOR scandal, for just one example: http://www.liborscandal.org/index.html), yet we are supposed to marginalize each other with ridicule like ‘nut job’ and ‘conspiracy theorist’ to keep us in the ‘safe’ and ‘permissible’ trendy mainstream dominant social memes.
The criminal banksters and their corporations get to hide in plain sight and we police each other for crossing boundaries they have set for us! They can wreak havoc on our planet and blame humanity for their deeds. Note however, that Bayesian Logic can’t even grasp this structure and dynamics.
This shows how a statistical and frequency-oriented approach to looking at our world is no guarantee of even seeing the proverbial ‘elephant in the room’!
Hoarding Can Be Cancer Too
Hoarding Can Be Cancer Too
This short video’s symbolism and message is paradigm changing. The video stems from a religious message and also contains a bit of idealism, but has meaning even to agnostics and atheists alike.
The Universe is suffering from a shortage of humans right now. Please do your share to rectify this situation by having many children who do not need to hoard.
The true measure of the value of a society finds expression in how it treats its weakest members: the old, infirm, and children.
Universal Constants, Variations and Identities – #16 (Creation/Discovery)
Universal Constants, Variations and Identities
#16 Creation and discovery compliment each other and are the means in which the Universe fundamentally unfolds and enfolds itself (Creation/Discovery)
We tend not to identify them, because there are so many variations in their harmony. Please do overestimate your thoughts… as you will see they are the beginning of your expression to and of the world.
Both Creation and Discovery will work in unison, if we allow them.
Discovery is to recognize/relate what is in your world.
Creation is to transform/synthesize it too.
Each is alone without the other.
Creation=Right ‘brain’ (right+mind)
Discovery=Left ‘brain’ (left+mind)
Their ‘magick’ (sic.) manifests not when you synchronize them; rather, when you harmonize them.
(Please take the time to watch the 4 minute video.)
Universal Constants, Variations and Identities – #15 (Change/Time)
#15 Time is a temporally ‘linear’ (directed) form of change that is not limited by dimension. (Change/Time)
Time has been arbitrarily and wrongly assigned to dimension. Change is not restricted to any dimension: therefore time is also not limited to it.
I know it’s trendy to see time as a dimension, but dimension is something completely different. Stay tuned to find out what and why.
Update: There are many reasons why time needs a proper definition. Here are a few of them:
The chemical reactions in the vessel are not really effected by some mysterious thing called time, but by the number of contacts or collisions that take place in the soup of atoms or molecules. That is what the factor ‘T’ really stands for.
1) Eternity may be a somewhat mystical overarching reality outside of the physical universe, but time is not. Nor is time a thing that anybody can do anything to. In other words: it cannot be reified.
2) The universe doesn’t exist in time, but time exists in the universe.
3) The proper definition of time is exactly: the sequence of events in the material universe.
Universal Constants, Variations and Identities – #14 (Singular/Plural)
Universal Constants, Variations and Identities
#14 Singular and plural arise together. (Singular/Plural)
There is no singular without a plural representation except in the non-dual.
See http://mathesis-universalis.com for more information.
#Knowledge #Wisdom #Understanding #Learning #Insight #Constants #Variances #Philosophy #MathesisUniversalis #ScientiaUniversalis #PhilosophicaUniversalis #LogicaUniversalis #MetaMathematics #MetaLogic #MetaScience #MetaPhysics #MetaPhilosophy #Singular #Plural
Science As a New Tower of ‘Babble’
Complexity – a patchwork quilt of misunderstanding and confusion tied together ‘by hook or by crook’.
https://en.wikipedia.org/wiki/By_hook_or_by_crook
Complex systems are the result of our collective blindness to the simple interconnectedness of our universe.
Why is the emerging view of our universe – no longer a Cosmological and Cosmogonic garden of the good, true and beautiful – now turning into this phantasm of complexity?
Where did we go wrong?
Was it the creation and maintaining of the expectation that we could comprehend and grasp the whole of our Cosmos within one perspective?
Were the applications of the science we created so profit bearing that we began to take more than our fare share?
Was it the tempo at which our scientists – not even slowed down by the ethical and moral considerations which constitute our navigation systems down the roads of evolution – that have brought us to this place much too soon and with so much needless suffering (for animals and humans)?
Are we to continue abandoning our organic (and real) ascendancy for artificial (and synthetic) correlates?
The ends are NOT justified by their means! They are determined by them.
Image1:
Hiroki Sayama, D.Sc. – Created by Hiroki Sayama, D.Sc., Collective Dynamics of Complex Systems (CoCo) Research Group at Binghamton University, State University of New York
Image2:
By Brian Castellani (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)%5D, via Wikimedia Commons
Universal Constants, Variations and Identities
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Universal Constants, Variations and Identities
#12 The ends are determined by their means. (Integrity of purpose)
(Dispelling the lie of: “The ends justify their means.” The truth is that ends are inextricably tied to the means used to achieve them. If we employ destructive means, then only destructive ends can result. Intention means nothing with regard to means… those who believe that learn: “The road to Hell is paved with good intentions.”
See http://mathesis-universalis.com for more information.
Universal Constants, Variations and Identities
Universal Constants and Variances
#11 Observation is communication between its participants (observer and observed). (Reference)
See http://mathesis-universalis.com for more information.
There Is Only Now
New Theory Suggests That We Live In The Past Of A Parallel Universe
There Is Only Now
Here they confuse the issue… Badly!
More psyence mumbo jumbo to get you confused. If you would have said this before publication, you’d have been called a ‘nut job’ or ‘wacko’. But as you see, dogma does change.
They have time and space all whacked out and call people who have better explanations wacko!
The idea of a parallel universe does have uses. For example when we decide something or imagine how something may be different. We construct them in order to compare outcomes (or other aspects) with each other.
The problem with the article, for me, is that today’s science use them to reduce possibility and novelty to outcomes (or other aspects) that must preexist in some form!
They want everything to be non-personal 3rd. person ‘its’ running around interacting from some set of initial conditions! That’s one of the reasons why these parallel universes need to exist for them.
Otherwise they would have to account for some creative or imaginative process which would require a thinking being and not some 3rd. person ‘it’.
Universal Constants, Variations and Identities
Universal Constants and Variances
#10 All holons have at least four fundamental capacities. (Potential)
Horizontal:
1) Agency (Maintaining wholeness/identity) Pull to wholeness
2) Communion (Maintaining partness/relationship) Pull to partness
Vertical:
3) Transcendence (Becoming more wholeness) Pull upwards
4) Dissolution (Breaking down into constituent parts) Pull downwards
(see #6 for definition of holon)
See http://mathesis-universalis.com for more information.
Heurist.me (Carey G. Butler) 