Project under development
Evolving and coalescing
"By trying and erring, by groping and stumbling  so progressed our knowledge. Hampered and yet spurred by a hard struggle for existence, a plaything of the environment and a slave to the traditions of the time, human beings were guided in this progress not by logic but by intuition and the storedup experience of civilization. This applies to all things human, and I have made painstaking efforts to show that mathematics is no exception."
Very slightly edited for sensitivity to gender
Tobias Dantzig, Number: The Language of Science, 1930, p.187
http://originresearch.com/docs/number_the_language_of_science.pdf

The Closed Loop project has been evolving for many years as studies in conceptual structure and categories, and is only recently beginning to take shape within the definitions and boundaries of the Closed Loop concept.
We are now approaching the project as a process of topdown integration, where after repeated testing and confirmation, we are tending to presume that this design makes sense, and it is indeed reasonable to pursue its highly inclusive objectives based on this approach to a universal container and integrated body of definitions.
Some of the original work on category theory and synthetic dimensionality can be found at http://originresearch.com
What is an interval??
https://en.wikipedia.org/wiki/Line_segment

A vast jigsaw puzzle
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This project combines hundreds or thousands of small specialized ideas ("concepts"), which we seek to combine into a single integrated framework with a perfectly smooth connection between all the pieces.
We want to define these pieces as emerging from the continuum, driven by human motivation and taking infinitely fluent form, capable of describing absolutely anything to any desired/motivated degree of detail.
Of course, this is an amazingly difficult challenge, something like a dream out of mythology. Philosophy and mathematics and indeed the entire world of human thinking today and throughout history are and always have been fragmented into endless numbers of little pieces, combined in locallyspecific ways as makedo heuristics that were good enough to meet immediate needs.
But we are following the alluring magnetism of a comprehensive vision of wholeness, of integration, of unity, of "truth and beauty". We think this is motivated. We think it is part of collective human evolution  something like "the destiny of civilization".
And it seems that collective evolution today is reaching a critical point. Yes, we have "soiled our nest", like baby birds. Throughout history, we took what we needed, and we acted in a local and immediate context, with a shortsighted perspective, without respect to "the whole"  at least partly because we had no idea that the whole even existed.
But now we do. We "saw the earth from space" and life was transformed. Immediately, projects based on "The Whole Earth" began to emerge. A new ethic of wholeness began to emerge at the leading edge. Our awareness of largescale issues has been growing for at least fifty years, as scientists began defining and announcing critical globalscale issues like "the ozone layer". Hundreds of similar influences are shaping leadingedge thinking today.
This vision was formed many years ago under the influence of social and cultural transformation, and the emerging new capacity of electronic networks. Computer science has been fascinating and potent since its birth, and today it is reaching amazing levels. And correspondingly, the collective human crisis of shortsighted evolution is reaching critical levels.
Today, this project, running in a highcapacity intent database system, supports what I like to call a "mind storm"  a kind of largescale and semichaotic process that involves bringing many pieces together into creative relationship, and letting inspiration and creativity respond to emerging new combinations that seem to make sense.
As I work on this project, I create new categories. I add features any time I can think of one, and think it is worth doing. This framework seems scalable. I can "stick new stuff in there" any time the inclination arises. The Closed Loop ideal and vision is pretty amazing. Yes, it is mindblowing, and "something entirely different" from the way we have always understood reality. But I find it inspiring and its credibility and feasibility seem to be growing. I am excited about this creative process. Given time and endurance, I think it's fair to expect something of consequence...
Sat, May 8, 2021

The closed loop vision
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We are exploring and proposing a generalization of mathematical and semantic space, based on a single algebraic/topological form which we are supposing can contain in a compressed format all definitions and partitions and distinctions which combine to form the world of mathematics and abstract symbolic representation (language and semantics).
Every value is defined as an interval in a bounded range.
Hierarchy of meaning structure:
 One, the whole
 Meaning  complex "points" made in complex highdimensional space, somewhere within the common space
 Dimensions
 Words
 Alphabets
 Numbers
 Bytes
 Bits
 0 or 1
 The continuum
Everything is constructed in digital terms, in strict digital mathematics
In a simple interpretation of the way computer systems model numbers and alphabets and arithmetic processes
Sat, May 8, 2021

Why do we need a database?
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This project is extremely ambitious, spanning the full breadth of deep intuition and modern mathematics and science.
That is a vast span, and attempting to bridge it  or even talking about this attempt  is for good reason likely to prompt immediate skepticism or even ridicule. Indeed, defined in this way, the project may be impossible.
But here in this online context, with a vast ocean of data available with instant highbandwidth access, including billions of references through Google, with a vast pool of graphic images from everywhere, and the astonishing depth and breadth of Wikipedia  it seems this undertaking begins to be feasible.
We see the potential  and we see the value of the effort. We think this is feasible  and very likely essential to human welfare over the long term. Yes, this is hard, and mindblowing and very overloading and difficult to the point of impossible to hold together in one mere puny human brain.
But take it one step at a time  one item at a time, one facet of the large fuzzy vision at a time  and the project begins to look more likely.
And that's what we are doing,
Yes, we bounce around in a kind of random freeassociation way, finding things that seem interesting and helpful and illuminating, and tacking them into the project somewhere.
But a picture is forming. We are beginning to see the outlines. Yes, it is overwhelming and iffy at best, but the core principles are getting simpler and clearer, and we are beginning to trust the guidance of the Closed Loop idea.
So as the project grows, we ask "how does this particular idea fit in?" "How does this idea serve the project?"
 How does this idea serve the clarification or simplification of science?
 How does this idea sere our broad humanitarian ideals?
 How is this idea an "essential piece of the puzzle"?
Our database framework vastly expands our "cognitive bandwidth"  Cognitive bandwidth
 Simultaneity  "everything at once"
Sun, May 9, 2021

A few hundred elements
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This project runs on an SQL database, and supposedly presents something like a hierarchical word processor, of a very basic sort. We are gathering elements to the database, generally organized in terms of "theme groups"  major topic areas  and "themes"  subject areas that are aligned somewhere with that theme group. We are also developing a basic vocabulary  like a glossary of basic concepts and terms, generally concerned with epistemology. What is a dimension, what is a unit, what is an interval, what is a metaphor, what is equivalence or identity or equality? What does it mean when we say "two things are equal"  when clearly they are not the exact same thing  but are "equal" in some sense that we have to clarify. We are looking at 100 issues like this.
Today, at this early stage, our database system is starting to work fairly well, and we are starting to slowly load in data  ideas, content, specific statements and interpretations, graphics and diagrams  all of which is intended to illustrate the broad thesis that "in significant ways, the Closed Loop contains philosophy and science and mathematics."
This is a big deal, and a very broad reach. What are the historical precedents?
You are putting together 100+ definitions, and this project is a house of cards  it could collapse at any of 100 failure points, true.
As far as I can tell, from my limited research, "nobody has done anything quite like this"  but maybe this project could be described as inspired by Leibnitz or Ramon Lull  and who knows how many medieval visionary philosophers who drew complex ontological diagrams as explanations of the universe.
This project is almost a cosmology  a theory of the universe  a proposition that we might defend by insisting that we mere humans only know reality  and/or have mapped reality  in terms of our concepts.
What we think we know are our concepts and the empirical experience that we believe we have correlated and organized within or by those concepts.
Is it true that "all science is conceptual"? That even mathematical explanations are "mere maps" of an inexplicable territory?
What we do know  is that mathematics works. Our rockets do reach the moon  or mars.
But one other thing we know  is that we mere humans do not always understand one another very well, and in an era of accelerating complexity, this can be dangerous. Maybe Closed Loop is a step towards a collective human awakening that can get us through this crisis.
Thu, May 6, 2021

This project and database
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I am a database developer, working with MS SQL and the ColdFusion programming language  a bit oldfashioned, true, but employing simple principles that are consistent with this overall vision for ontology, in a traditional "rows and columns" form that enables a strong global/local consistency and connection.
The core architecture of the project runs on three categories or classes of logical objects:
 Theme groups  broad general categories like topic headings, under which a lot of subjects can be organized
 Themes  semiindependent subjects which can be grouped together under theme groups and displayed in any order. Themes can appear in multiple theme groups as appropriate
 Terms  words or simple basic concepts that tend to form a core vocabulary, supposed including all the basic concepts from cognitive psychology, semantics and epistemology and the foundations of mathematics
The actual programming mechanics of this project are simple and unsophisticated, but very adaptable and fluent. My framework is just simple "serverside" programming. Click something on a webpage, that click sends a signal to the ColdFusion and database servers, which then send a response. By today's standards that is primitive. But I don't want to learn sophisticated programming. I want to develop sophisticated applications of simple technology that I can handle.
The rows and columns model is basic to this entire structure. Our intuition is that this model preserves global/local connections through basic and linear forms of recursive nesting. Our model of the world involves recognizing that the global is constituted from the local, and that the local is a reprisal of the global in much more detailed specific form.
We are presuming that this framework may be the optimal way to organize a form of democracymediated global homeostasis running on basic principles of cybernetics. This idea is a reprisal of the ancient cybernetic idea of "governor" as defined by James Watt in the steam engine. It is a traditional formula for stability across the world at all levels, consistent with the notion of homeostasis as it occurs in the human body an in all living things.
Mon, Apr 12, 2021

Numbers, alphabets, symbolic structures
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Numbers and alphabets are finitestate digital objects defined in a finite set that can be fully ordered (numerical order, alphabetical order).
We are presenting the argument that "anything in the world" that can be described can be described by a limited set of finitestate variables.
Modesl are always defined for specific purposes.
Sun, Mar 14, 2021

What is a universal container?
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Set of all sets  Universal Set
We might be exploring the possibility that the "twist" in the Closed Loop is a way to overcome the challenges of universal sets and of Russell's paradox.
Sun, Mar 14, 2021
Reference
In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, the conception of a universal set leads to Russell's paradox and is consequently not allowed. However, some nonstandard variants of set theory include a universal set.
Notation
There is no standard notation for the universal set of a given set theory. Common symbols include V, U and ?.[citation needed]
Reasons for nonexistence Many set theories do not allow for the existence of a universal set. For example, it is directly contradicted by the axioms such as the axiom of regularity and its existence would imply inconsistencies. The standard Zermelo–Fraenkel set theory is instead based on the cumulative hierarchy.
Russell's paradox
Main article: Russell's paradox
Theories of universality
The difficulties associated with a universal set can be avoided either by using a variant of set theory in which the axiom of comprehension is restricted in some way, or by using a universal object that is not considered to be a set.
Restricted comprehension
There are set theories known to be consistent (if the usual set theory is consistent) in which the universal set V does exist (and {\displaystyle V\in V}V\in V is true). In these theories, Zermelo's axiom of comprehension does not hold in general, and the axiom of comprehension of naive set theory is restricted in a different way. A set theory containing a universal set is necessarily a nonwellfounded set theory. The most widely studied set theory with a universal set is Willard Van Orman Quine's New Foundations. Alonzo Church and Arnold Oberschelp also published work on such set theories. Church speculated that his theory might be extended in a manner consistent with Quine's,but this is not possible for Oberschelp's, since in it the singleton function is provably a set,[4] which leads immediately to paradox in New Foundations.
Another example is positive set theory, where the axiom of comprehension is restricted to hold only for the positive formulas (formulas that do not contain negations). Such set theories are motivated by notions of closure in topology.
Universal objects that are not sets
Main article: Universe (mathematics)
The idea of a universal set seems intuitively desirable in the Zermelo–Fraenkel set theory, particularly because most versions of this theory do allow the use of quantifiers over all sets (see universal quantifier). One way of allowing an object that behaves similarly to a universal set, without creating paradoxes, is to describe V and similar large collections as proper classes rather than as sets. One difference between a universal set and a universal class is that the universal class does not contain itself, because proper classes cannot be elements of other classes.[citation needed] Russell's paradox does not apply in these theories because the axiom of comprehension operates on sets, not on classes.
The category of sets can also be considered to be a universal object that is, again, not itself a set. It has all sets as elements, and also includes arrows for all functions from one set to another. Again, it does not contain itself, because it is not itself a set.
URL
https://en.wikipedia.org/wiki/Universal_set

Russell's Paradox
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Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction.
Russell’s paradox
Bertrand Russell (18721970) was involved in an ambitious project to rewrite all the truths of mathematics in the language of sets. In fact, what he was trying to do was show that all of mathematics could be derived as the logical consequences of some basic principles using sets. At this time (around 1900), it was generally believed that any property of objects could define a set. For example, the property “x is a natural number between four and seven” defines the set {4, 5, 6, 7}. We could also write this set as {x x is a natural number between 4 and 7}. What was believed was precisely that for any property “P” that you can think of, it made sense to talk about the set {x x has property P}. Certainly, sets that consist of numbers make sense this way. But when you allow any objects in your sets, you can run into trouble.
Russell was the first one to notice this.
Russell’s insight was the following. First, it is possible for a set to be an element of itself. (Remember that elements are the objects which make up the set, e.g. the number 4 is an element of the set {4, 5, 6, 7}). An example of a set which is an element of itself is {x x is a set and x has at least one element}.
This set contains itself, because it is a set with at least one element. Using this knowledge, Russell defined a special set, which we’ll call “R”. R is the set {x x is a set and x is not an element of itself}.
Russell then asked: is R an element of the set R? Let’s think about this question.
If R is an element of R, that exactly means that it is an element of itself.
Which means that it can’t possibly be in R  by definition R is the collection of all sets which are not elements of themselves.
Since this option is impossible, we must agree that R is not an element of R.
But in that case, R is not an element of itself, so by definition it belongs to the collection of sets which are not elements of themselves. Uhoh! [It is worth pausing a minute here and reassessing the situation on your own. Do you believe that R is an element of R or not? Neither? What’s the problem?]
Mathematicians and logicians thought for a while that the problem with the set R was going to undermine their whole project to do all mathematics in terms of set theory. Fortunately, they eventually came up with a technical solution that changes the way sets are constructed (slightly) and prevents R from being considered a set (whew!). This technical solution is why you sometimes see a set being described in the form {x ? X x has property P}, where “X” is supposed to denote some other set, or “the universe” (whatever that means!) We won’t worry about that issue in our class, as most of our sets will be sets of numbers and these are always safe.
So did Russell succeed? Yes and no. The program to do all mathematics in terms of set theory was the birth of modern day logic, a rich and exciting area of mathematics. But ultimately, the logician Kurt G¨odel showed that the original goal of the project – to deduce all mathematics from some axioms (rules) concerning sets – was itself mathematically impossible!
For more details on this story, I recommend the excellent book Logicomix by Doxiades and Papadimitriou. You may be delighted to know that a) it’s a graphic novel and b) the Reg library has a copy.
Sun, Mar 28, 2021
Reference
In the foundations of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901,[1][2] showed that some attempted formalizations of the naive set theory created by Georg Cantor led to a contradiction. The same paradox had been discovered in 1899 by Ernst Zermelo[3] but he did not publish the idea, which remained known only to David Hilbert, Edmund Husserl, and other members of the University of Göttingen. At the end of the 1890s Cantor himself had already realized that his definition would lead to a contradiction, which he told Hilbert and Richard Dedekind by letter.[4]
According to naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves. If R is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set of all sets that are not members of themselves. This contradiction is Russell's paradox. Symbolically:
{\displaystyle {\text{Let }}R=\{x\mid x\not \in x\}{\text{, then }}R\in R\iff R\not \in R}{\text{Let }}R=\{x\mid x\not \in x\}{\text{, then }}R\in R\iff R\not \in R In 1908, two ways of avoiding the paradox were proposed: Russell's type theory and the Zermelo set theory. Zermelo's axioms went well beyond Gottlob Frege's axioms of extensionality and unlimited set abstraction; as the first constructed axiomatic set theory, it evolved into the nowstandard Zermelo–Fraenkel set theory (ZFC). The essential difference between Russell's and Zermelo's solution to the paradox is that Zermelo altered the axioms of set theory while preserving the logical language in which they are expressed, while Russell altered the logical language itself. The language of ZFC, with the help of Thoralf Skolem, turned out to be firstorder logic.[5]
URL
https://en.wikipedia.org/wiki/Russell%27s_paradox

Universal hierarchy of symbolic representation
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The grand scheme 
Objective  to build a single hierarchical structure that follows basic/generic computer design from a bitstructure level through a process of assembling data structures composed of bits and bytes, building every type of standard computer data structure, and in those terms, interpreting every element of semantics and mathematics
Find a good graphic on the hierarchical structure of computer operating systems
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This is a masterfeature of this project. In some ways, it is the grand container for the entire project.
Maybe what we want to do is to offer a single framework that defines all aspects of "the construction of a semantic object"
This task involves several layers
 Hardware  the mechanism that support the definition
 The interpretation of the "state" of the hardware  in terms of bits, binary off/on 0/1 twostate logic from which everything grows, and within which, from which, everything is constructed
 The definition of language built on top of this mechanistic framework
 Pixel grid (matrix) of on/off state "in a medium"  like a computer screen or a sheet of paper
 The creation of fonts and alphabets, so that symbolic representation can be "actual" and not merely "mental" or in the mind
 The construction of numbers
 The construction of "words" from this alphabet
 The assignment of "meaning" to this "symbolic state of a medium"
 The construction of mathematics and logic from this process
 The construction of abstraction and generalization from this process
Definition of the continuum as a digital discrete/state object, from which all distinctions and complex structures are created
Sat, May 8, 2021
URL
https://en.wikipedia.org/wiki/Computer_science

The digital integration of conceptual form
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This project combines the insights of philosophy, cognitive psychology and semantics with the language and analytic methods of computer science.
Our argument is
 There are many ways to discuss these subjects  and this plethora of descriptions and approaches and disciplines can become confusing, overwhelming, and inconsistent
 The methods and language of computer science, when generalized into mathematical descriptions, are capable of describing most cognitive phenomena
All semantics and code structures are constructed using digital mathematics  which is made consistent with strong theories from cognitive psychology, semantics, ontology and philosophy
Digital models have a strong ontology grounded in realworld engineering and constructivist definitions
All semantic elements can be constructed from digital elements
words, meanings, alphabets, numbers, arithmetic and algebraic processes
this includes basic concepts and principles from epistemology, such as metaphor and other forms of comparison
it includes everything needed in a theory of classification
The digital approximation of continuous reality
Fri, Apr 2, 2021
Reference
Digital data, in information theory and information systems, is the discrete, discontinuous representation of information or works. Numbers and letters are commonly used representations.
Digital data can be contrasted with analog signals which behave in a continuous manner, and with continuous functions such as sounds, images, and other measurements.
The word digital comes from the same source as the words digit and digitus (the Latin word for finger), as fingers are often used for counting. Mathematician George Stibitz of Bell Telephone Laboratories used the word digital in reference to the fast electric pulses emitted by a device designed to aim and fire antiaircraft guns in 1942.[1] The term is most commonly used in computing and electronics, especially where realworld information is converted to binary numeric form as in digital audio and digital photography.
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Since symbols (for example, alphanumeric characters) are not continuous, representing symbols digitally is rather simpler than conversion of continuous or analog information to digital. Instead of sampling and quantization as in analogtodigital conversion, such techniques as polling and encoding are used.
A symbol input device usually consists of a group of switches that are polled at regular intervals to see which switches are switched. Data will be lost if, within a single polling interval, two switches are pressed, or a switch is pressed, released, and pressed again. This polling can be done by a specialized processor in the device to prevent burdening the main CPU. When a new symbol has been entered, the device typically sends an interrupt, in a specialized format, so that the CPU can read it.
For devices with only a few switches (such as the buttons on a joystick), the status of each can be encoded as bits (usually 0 for released and 1 for pressed) in a single word. This is useful when combinations of key presses are meaningful, and is sometimes used for passing the status of modifier keys on a keyboard (such as shift and control). But it does not scale to support more keys than the number of bits in a single byte or word.
Devices with many switches (such as a computer keyboard) usually arrange these switches in a scan matrix, with the individual switches on the intersections of x and y lines. When a switch is pressed, it connects the corresponding x and y lines together. Polling (often called scanning in this case) is done by activating each x line in sequence and detecting which y lines then have a signal, thus which keys are pressed. When the keyboard processor detects that a key has changed state, it sends a signal to the CPU indicating the scan code of the key and its new state. The symbol is then encoded or converted into a number based on the status of modifier keys and the desired character encoding.
A custom encoding can be used for a specific application with no loss of data. However, using a standard encoding such as ASCII is problematic if a symbol such as 'ß' needs to be converted but is not in the standard.
It is estimated that in the year 1986 less than 1% of the world's technological capacity to store information was digital and in 2007 it was already 94%.[2] The year 2002 is assumed to be the year when humankind was able to store more information in digital than in analog format (the "beginning of the digital age").[3][4]
URL
https://en.wikipedia.org/wiki/Digital_data

What is the digital integration of conceptual form?
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 What is a concept?
 What is a digital structure?
 How can a concept be a digital structure?
 Why is it advantageous for the science of concepts to understand concepts as digital structures?
 What is the integration of conceptual form?
 What is the digital integration of conceptual form?
 How is this consistent with the cognitive psychology of concepts?
 How is a concept a formal structure?
 How can a concept be a digital structure?
 How can "all concepts" not only be "integrated", but integrated as a "digital structure"?
Mon, Apr 5, 2021

The integral vision
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This idea is grounded in and led by a classical metaphysics of spirit, in a form consistent with the vision of great prophets and mystics and saints and religious teachers since the beginning of history. We speak of "the beginning" and where ideas come from, and what they are made out of.
And yes, of course, ideas in "the real world as it actually is" are a spontaneous overwhelming jumble coming from everywhere, in endless and very complex combinations. But the instinct here is that these combinations are formed by simple common underlying principles, that we can know in mathematical and scientific terms. Every human being is different, every moment of human experience is different, every culture is different. But the incremental elements from which ideas are created can be understood as common to all of them.
Yes, this project is like a vast jigsaw puzzle, where we can identify hundreds of pieces and explore how they fit together to form a whole  under the intuitive conviction that they DO "form a whole"
But there are other analogies. This project is like a child's construction set  like "Leggos", like "Erector Sets", like "Tinker Toys", like "Lincoln Logs". Or it's like an adult construction project, like assembling a building or (build an entire neighborhood) an entire housing development.
Wold civilization today is passing though an intense crisis of complexity and fragmentation. Cultures which have arisen independently throughout history are now converging into one another in a common global melting pot. And our most urgent problems are global and our conflicts are increasing dangerous complex.
We need a common ethic of the whole. We need new guiding principles for governance. We need "homeostatic cybernetic democracy". We need cooperation and convergence into a common human mesh, where all things are guided by common boundary values on ecology and economic and individual personal behaviour.
And we need to see how to do this. We need to see that it is possible  despite very great reasons for skepticism and doubt, despite despair over the human track record of rage and cruelty and selfishness. In the context of all this, this project starts at the beginning  from the bottom up as the analysis of the continuum as a structure composed of bits, and from the top down, as an analysis of the whole, the one, with all of reality  all of human ideas and all of culture  caught in the spectrum between those two polarities. We are proposing to show how this makes sense, is feasible, and how this form can be sealed into unity, into a sealed Oneness that contains it all in an inviolate stability, into a form that honors and embraces all of human creative history, forming a kind of guiding compass for a world that must converge toward The Whole.
We need a core common vision, towards which the world can incrementally transition. This vision must contain science and it must contain spirit and it must contain governance. We can conceive of a global homeostasis mediated in its particulars through electronic networks, and guided from the deeply human level by handshaking agreements between cultures as we confront the tremendous stresses prompted by global evolution and global transition and deepseated human foibles.
This project is both synthetic and analytic. It creates and compiles and assembles its solutions. Yet it is also empirical, because it proposes to connects to the world as it is, starting from now.
It is a spiritual or humanistic vision, expressed in the language of engineering. As such, it spans the great gulf between cultures and traditional departments of knowledge.
Mon, Apr 12, 2021

The power of analogy
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It could be argued that this project emerges from poetry  from a deep instinct for metaphor and analogic comparison  "this thing is very much like that thing, in these regards". Maybe we push it and say "this thing IS that thing".
Our "unit spectrum" is the core idea of the project  rendered amazing through the dimensional twist.
But the design flows from analogy. So many forms in mathematics and semantics and visionary philosophy take approximately the same form. We re trip over the differences and announce them as unreconcilable. Or we can follow an instinct for simplification and trust the instinct for comparison.
This project tend to the latter option.
Sat, May 8, 2021




