This collection of books is a small, but growing example of the millions of books, journals, periodicals, and academic papers we are currently tracking and indexing. We are updating this library constantly. Please return often and review this library as it evolves.
This library is the first step on our way to making Mathesis Universalis (the long-sought search for a unifying principle in all that we know and experience) a reality. Soon our knowledge representations, in their many forms, will be accessible from the pop-up dialogues which appear when you click/tap on a book’s entry in the overview you see. Other types of knowledge sources; such as social media activity, websites, E-Mails, audio, video,… are also going to be included in our tracking and indexing system.
I, Carey G. Butler, have been working on this idea since 1989 during my study of Foundational Mathematics and Complex Analysis. I then moved to Germany in 1990 to continue my study (this time in the original German language) of many German mathematicians and philosophers such as Carl Friedrich Gauss, Bernhard Riemann, Gottfried Wilhelm Leibniz,… During that first year I began to formalise the idea as I began to learn the German language more intensively.
The journey has been a long one and was finally conceptually refined in March of 2009. The journey has taken many, many turns in the years since. I have made several key discoveries in mathematics, philosophy, and linguistics along the way which I, due to my concerns about priority, have not yet published. A few of these discoveries are documented elsewhere though, but I have been very careful to withhold many aspects of their details until I was able to find and/or adapt current technologies to bring them to a useful expression and application in their fullness. I was confronted with many obstacles and challenges, but I never gave up. For more information about my plans, please visit our website at Mathesis Universalis in English or Mathesis Universalis auf Deutsch.
As it stands, we could have created this library application a year ago. It is, in itself, nothing very special for programmers who know how to build applications like it. However, as we developed and tested the predecessor to this application, it soon became very clear that the sheer volume of data being manipulated was creating increasing demands on the conventional technology we were using at the time. Our concerns about processing time, network speed, and infrastructural demands forced us to step back and create a better foundation which could be scaled to any degree. We have spent the last 8 months (August 2021 – April 2022) building a ‘symphony’ of cloud applications and an infrastructure which is now fast, reliable, and scalable.
Towards that aim, this library represents the ‘orchestration’ of a collection of cloud apps we created or have forked and modified for our purposes that is distributed over several servers. Its backend is primarily driven by a distributed Couchbase database to store and to manipulate the massive amount of data. Also other kinds of databases are implemented for temporary storage or for the frontend’s presentation and housekeeping.
We are currently developing a Progressive Web App which will use this library as one of its sources to present our knowledge representation.
Finally, after 13 years of investment of all kinds and, on the 8th birthday of one of my most important discoveries (‘We Have a Heartbeat‘),…
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.
Words are symbolic indications and/or conveyors of meaning and are not that meaning in themselves.
Meaning is found, stored, and manipulated in our minds. This is why different languages are capable, in varying degrees of usefulness, to convey meaning which is very similar to that found via the symbols of any other.
It It is also the reason why there are words indicating meaning that are not found in other languages; or, if found in a different language, the other language requires more of its own structure, dynamics, and resonance to convey the same meaning.
For example: the words ‘déjà vu’ in French are found in German ‘schon gesehen’ and in English ‘already seen’, but these phrases do not convey the full meaning found in the French version. To counter this deficit, their meaning in other languages must be ‘constructed’ out of or ‘fortified’ by the careful use of longer strings of symbols. This additional construction and/or fortification may even fail at times. This is often where the word phrase from a different language is simply added to the language in which the concept is missing.
This same situation is found in the literature of many languages. The words used to convey meaning are condensed and may contain more meaning than is usually the case. In this regard, even the person reading/hearing the words may not possess the competence necessary to catch this condensed meaning in its fullness.
Mathematical expressions, albeit more precise, are also indications of meaning. They are more robust in their formulation, but at ever-increasing depth or scope, even they may fail to reliably or conveniently convey meaning.
Our understanding of what words mean is not always accurate, but where our mutual understanding of the meaning of words overlaps, and the degree to which they overlap, is where their meaning can be shared.
Our own personal understanding of words is measured by our ability to apply their meaning in our lives.
There is also a false meme, which I would like to clarify.
“Knowledge is Power!”
It is wrongly said that ‘Knowledge is power’. The truth is another: Knowledge is the measure of usefulness of what we understand and is the only true expression of its ‘power’.
The value of Knowledge is found in its usefulness and not in its possession.
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.
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.
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 taughtthat 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
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.
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 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.
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 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’
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.
“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.”
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.”
Precursors Of Knowledge
Fractal fields provide a nice framework in which to think about knowledge. They are not all we need for precision, but they are helpful in a generic way. I’ll be posting more on them as the knowledge representations are published, because there are many ‘gaps to fill’ to show how these relate to knowledge.
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.
Information Visualization Is Not Knowledge Representation
This great video from Lynda.com shows how the processing language/interpreter is great for modeling information.
With such a multitude of interesting ways to model data, we find it hard to resist the temptation to call this knowledge, but it’s not!
All of the wonderful representations here still require us to interpret their meaning!
What if there were a way to present knowledge in which our own understanding is not required to interpret them? What if our understanding of what we have presented to us becomes part of the presentation itself, and in fact, influences what we take from that representation?
We obviously need knowledge representation that can provide their meaning on their own for only they can provide a true understanding of their inherent structure and dynamics.
You see real understanding is the personalization of knowledge into your own mind. If your mind cannot dialog with that knowledge, it’s not really yours and if your mind does all the work, it’s only information.
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…)
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!
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.
[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!)] 😉