Saturday, February 15, 2014

In Defense of the Cognitive-Theoretic Model of the Universe (CTMU)

I will share some ideas, terms and a formula which helped me clarify a few of the basic concepts, and refer diligent researchers to the book, "Moonshine Beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics". For the right-hemisphere dominant I also rendered some concepts as metaphors.

Koinotely refers to the "common expressive medium", "synetic medium", or "diffeonic potential". It is produced by "unisection".

Isotelesis refers to the "diffeonic relands" or the "actualization" of diffeonic potential. It is produced by "reverse unisection".

If unisection is thought of as the fusion of parts, reverse unisection could be thought of as the fission of "wholes".

Koinotely refers to Conterminality and Isotelesis to Coextensivity, telesis being the common component, the former is concerned with connectivity and coherence while the latter with self-similarity and consistency. The self-similar motif is reminiscent of the flower of life, though with 19 non-overlapping "isotelic" circles (local telors) packed into 1 "koinotelic" circle (syntactic unisect or global telor) which covers them all, the circles and their constructive-filtrative layering can be thought of as spheres or hypersurfaces if you can see it as such, this relates logic with resources (as in the linear logic program uniting logic with linear algebra) or state-syntax duality with the packing-covering duality, where issues like optimization and the conservation of freedom (and information) become relevant. As far as self-determinacy is concerned, the diameter of the larger circle is defined in terms of the smaller circles, and the space for the smaller circles are defined in terms of the larger circle, with each circle being 5 sub-circles wide, and simultaneously/reflexively, the number of circles definable within 1 circle is 19. 19x5=95 represents "teleoplection" or the entanglement of local (isotelic) and global (koinotelic) utility functions, (what is globally optimal is automatically locally optimal due to a property of convex geometry). Teleoplection is a self-dual relation/process (as are Chu Spaces), and is involved in how complexity arises from simplicity from/through self-consistent entanglement (or coherent inner expansion/decoherent requantization of subjective/objective states in syntactic operators). The fractional multiplier 5/19 (koinotely/isotelesis) and/or conversely, 19/5 (isotelesis/koinotely) is representative of the scale invariance and the universality of conspansion. Visually, inscribed in each circle and sub-circle are 19 circles per 5-diameter circle, when/where circles overlap they create new inner expansive domains which add circles or constraints/subtract space or freedom while contracting/expanding as they divide diffeonetically/multiply synetically, with outward inductive and inward deductive processes mirroring each other. So each circle can be considered koinotelic within its own domain, while being isotelic to a higher and/or for a lower level domain. This can be formulated as koinotely(isotelesis)=isotelesis(koinotely). On the left side of the equation, koinotely distributes over isotelesis, acts as the "memory" or model of past/present domains topologically including the right side of the equation, where vice-versa, isotelesis distributes over koinotely, "anticipating" or modeling the "future" as a codomain of the "past/present", it descriptively includes the left side, where abstract potentialities are rescaled as they are actualized in situ.

Some preliminary ideas. Money (or abstractly, "utility" is a means for voluntary exchange which measures how much an "agent" is willing to give up in order to acquire some intrinsic/extrinsic motivator) is like a common denominator which allows for the exchange of values. If "spending/selection power" is thought of as a resource such as "freedom", then in order to be meaningful or useful, it could be subject to the laws of conservation (or global symmetry principles), such as energy, where one has to generate it in order to spend it (according to relative entropy). Although transformations among parts take place at varying scales of resolution, the self-consistency of the whole is maintained. As in the whole number "1", which as a resource may be divided and subdivided. The act of dividing resources is dually the process of multiplying functions, or similarly, the act of subtracting freedoms is dually the process of adding constructions. The whole is adjoined to its parts on all scales, while the parts are relatively disjoint from the whole. While some rules of exchange are reversible, others are not. The current monetary system can be thought of as "Abelian" which means that various dependencies among transactions are not relevant to the value of the outcome. However the paradigm of "non-Abelian money" is also worth considering for certain kinds of transactions (perhaps in triple-bottom line accounting, or mechanism design).

A brief sketch of an economy informed by "spiritual" concepts may be to consider these parts as instead, "letters" or "utils" of an alphabet which form "words" or "entangled utility functions".

Saturday, June 30, 2012

Palintropos, Hylomorphism, Syndiffeonesis

Palintropos, Hylomorphism, and Syndiffeonesis The complementarity of potential and actualization, as discussed by Aristotle in his late metaphysics, could be interpreted as corresponding to freedom and constraint respectively in modern terms. Aristotle’s “Hylomorphism” may be found in several places, notably in the Baha’i Faith, which arose out of 19thcentury Persian Shia Islam. It may also understood as an earlier version of a concept described by Christopher M. Langan as “Syndiffeonesis” or “difference-in-sameness” which he states, “forms the basis of a new view of the relational structure of reality.” While Langan’s Cognitive-Theoretic Model of the Universe (CTMU) has been criticized for using jargon, as well as by those who think that when it comes to philosophy, there is nothing really new under the sun. Although there is much that one is left unable to fully understand regard the CTMU, this is no reason to not give it some consideration, especially since similarities and mutual support may be found between Ancient Greek philosophy, the CTMU, and Iranian philosophical theology.Thales was once asked “What is divinity?” to which he replied “That which has neither beginning or end.” While his student Anaximander did not agree that the fundamental element underlying all matter is water, he would develop the idea that the unbounded or aperion serves as the arche or ultimate reality and ground of all being. The aperion is described as unborn, immortal, formless, indeterminate, without origin and hence without limit and yet is the original sustainer of all things. That which derives form from it by necessity returns to formlessness, and thus existence emerges as a pair of opposites in a symmetric process of exchanges in reflexively balanced determinative tension. From his fragment it states, “For they give justice and make reparation to one another for their injustice, according to the arrangement of Time.” As his biographer Diogenes Laertius explains, “that the parts were susceptible of change, but that the whole was unchangeable.” In contrast, Parmenides held that forms could not emerge into existence and consequently submerge into formless non-existence, along with denying that being could be reconciled with becoming, he made a distinction between the mere appearance of multiplicity and the indivisible reality of unity. In response to this, Anaxagoras held than any part which is qualitatively the same as the whole is inseparable from it, and may be divided infinitely. “Nor is there a least of what is small, but there is always a smaller; for it cannot be that what is should cease to be by being cut. But there is also always something greater than what is great, and it is equal to the small in amount, and, compared with itself, each thing is both great and small.” Anaxagoras may have been the first to recognize this notion of self-scaling, in which a scale is not determined by an extrinsically fixed background or array, but is relative to an intrinsic, mutually commensurable relationship. Pythagoras would posit that numbers have a real existence and that all spatial objects are comparable to each other through harmonious proportions of whole numbers. While the Babylonians had calculated it up 6 decimal places, it was soon realized there was no exact common measure for a side of a square with its diagonal, since no multiple of a side of length 1 would ever meet with a multiple of its diagonal with a length of √2. This may have been the first confrontation between the relationship between the continuous and discrete in the form of geometry and number. Heraclitus may have been on the right track to this problem when he mentioned, “They do not understand how that which diverges converges on itself, for Harmony is opposite-tuning, like that of bow and lyre.” The Greek term “palintropos” is translated as “opposite-tuning”, however also been translated as “reflexive” or “turns back on itself”. He also mentions that all things are in flux and its ordering principle is the Logos is common to all, and that the one comes from the many and the many comes from the one, and that the road up and down is the same. Aristotle would describe the cryptic statements of Heraclitus as violation of the principle of non-contradiction. In Aristotle’s Metaphysics, he describes matter as the potential of some unrefined constituent to be actualized as some form. While the concepts of matter and form could be interpreted literally, such as uncarved wood and taking the shape of a bow, Aristotle also employs the concept for more abstract problems. For example, matter and form may correspond to the potential receptivity of the senses while objects of perception actively impress their forms upon them. In transactional form not mentioned by Aristotle, the matter and form can both be seen as in some respects active and receptive, such as a river bank shaping the flow of a river while inversely the river gives shape to the bank. In the CTMU, the concept of aperion bears a distant resemblance to the concept of unbound telesis which may be described as unrefined ontic potential without determinate form. In order for it do acquire a form it must to so in a self-determinate way, thus the origin of something would be -1 and its endpoint would be +1, such that they ultimately cancel out. This is also the justice or recompense which Anaximander describes. As a result, Langan seeks to avoids the dichotomy between an infinite open-ended causal regress or a prime mover without causal explanation itself, instead he adopts a “closed-cycle configuration” in which the active mover and the receptive moved are different yet through their complementarity the same. In terms of Heraclitus this relates to the identity of opposites and the bending-back of harmony. This concept is also found in Islamic theology, from the verse in the Koran which states, “all things are created in pairs.”To go into further depth, an overview of CTMU becomes necessary. It isn’t a theory, so much as it is a theory about theories generally. As Langan describes it, “The phrase “Cognitive-Theoretic Model of the Universe” contains three main ingredients: cognitive theory, model, and universe. Cognitive theory refers to a general language of cognition (the structural and transitional rules of cognition); universe refers to the content of that language, or that to which the language refers; and model refers to the mapping which carries the content into the language, thus creating information.” The question is: what is required formulate a theory of reality? Langan describes three components which together form what he calls a supertautology. The first principle is that reality must have closure or be self-contained. The leads to the Reality Principle which basically states that reality cannot be evaluated from the outside, because if it could then it wouldn’t be real, because reality contains only itself, therefore that any value given to it is internally scaled. This may be related to the views of Anaxogoras who said “all things partake in a portion of everything.” Second a theory of reality must be comprehensive enough, which is similar to but not as strong as completeness because not all statements which can be addressed can be proven. This leads to the Principle of Linguistic Reducibility, which states that anything which can be acquired as information conforms to the algebraic definition of a formal language consisting of strings (objects), structural rules (spatial relations) and grammatical rules (temporal transformations). Langan makes an allusion to Wittgenstein with the statement, ”whereof that which cannot be linguistically described, one cannot perceive or conceive.” Pythagoras thought that everything could be reduced to numbers, while Langan thinks that reality is reducible to the language of informational states and state-transitional syntax. Finally, a theory of reality must be consistent and coherent. The Principle of Syndiffeonesis states that reality is a relation between syntactic potential and actualized states. These states may be differentiated from each other, reality must balance out in a way so that it remains zero-sum, so new distinctions are allowed locally but are compensated for in time through global sameness. While there is much more to the CTMU, for the sake of simplicity and the scope of this essay, it suffices to bring us to the question of various parallels which may be found in Iranian philosophical theology. The nature of causality and composition are also central concerns in metaphysics. In the CTMU is described in terms of three categories: indeterminate, determinate, and self-determinate. In the Baha’i writings, it states that composition is of three kinds: accidental, involuntary, and voluntary. The concept of unity without uniformity and diversity without fragmentation is a key concept in the Baha’i writings, “No cell lives apart from the body, whether in contributing to its functioning or in deriving its share from the well-being of the whole.” Similar concepts may be found in Whitehead’s Metaphysics, “The ultimate metaphysical principle is the advance from disjunction to conjunction... The many become one, and are increased by one.” Langan also mentions a related notion, “Coherence flows from global syntax into local content by way of global topological containment, thereby enforcing unity across diverse locales, and back to global syntax in multiple entangled streams generated by cross-transduction of content.” The concept of purposiveness with respect to the whole has also been mentioned by Kant, “Everything in the world is good for something or other; nothing in it is gratuitous; everything is purposive in relation to the whole. It goes without saying that this principle [for judging nature teleologically] holds only for reflective but not for determinative judgement, that it is regulative and not constitutive.” The four modes of knowledge as described in the Baha’i writings, senses, reason, traditional interpretation and intuitive inspiration which in isolation are insufficient, but self-evident when in mutual accord. In the CTMU, the four components of the human cognitive syntax are described as the qualio-perceptual, logico-mathematical, space-time-object and emo-telic syntaxes. The Baha’i writings state that the essence of things are unknowable, and that it is only through attributes that they are knowable. A key concept in the CTMU is that information can only be known through an attributive syntax. The three ontological levels described in the Baha’i writings is that of absolute oneness (God), timeless creation or unity-multiplicity (Universal Mind or Primal Will), and creation in time. The CTMU describes three levels of “self-cognition”, which are global, agentive, and subordinate. The criticism of Paramenides on existence could be addressed in the Baha’I writings as follows, “If it be said that such a thing came into existence from nonexistence, this does not refer to absolute nonexistence, but means that its former condition in relation to its actual condition was nothingness.” Additionally a statement regarding how existence arises from relative non-existence is described, “The world of existence came into being through the heat generated from the interaction between the active force and that which is its recipient. These two are the same, yet they are different.” This implies that while God is the only uncomposed reality or absolute existence which has no specific purpose attached to it, all else comes into relative existence through complementary composition of the active and the receptive which together create the primal will. This bears a particular similarity with the concept of syndiffeonesis, which Langan describes the dual-aspect monism of “difference-in-sameness” . In the school of Islam which precedes the Baha’i Faith, it is believed that the whole of the Koran is contained in the first book, while the whole the the first book is contained in the first verse, and the whole of the first verse is contained in the first letter, and that first letter is contained in the dot underneath it, which became known as the primal point or primal will. In the CTMU, the grammatical “start symbol” or “seed” is called Multiplex Unity, which unfolds in a similar manner of fractal self-scaling. As a result, from the global perspective everything is contracting into itself, while from the local perspective everything is expanding away from itself. This leads to the concept of conspansive duality, in which outward expansion is conjoined with inward contraction. In the Baha’i writings, it also described how all plans come to fruition through the dual process of consolidation and expansion. They also state that human concepts involve such inverses, such as creator and created, however that each presupposes the other and that the attributes we give to the divine are simply reflections of our own state. In the CTMU, the universe consists of a series of nested state-syntax pairings in which each subsequent boundary is timeless relative to its contents. This is due to the fact that as a pair they are symmetric. However the boundaries relative to each other gives rise to the arrow of time in which the future is bound by the past, and each cause contains its effect. This leads to the notion the universe as a whole is atemporal, while the parts relative to each other aren’t. The Baha’i writings also state that a cause precedes every effect, and that the former have an independent existence while the latter are contingent. However they also state that both creator and created are without beginning or end, and that the physical world in one sense has limitations relative to the comprehension of the observer, but beyond that it is unbounded. The CTMU may be described as a dual-aspect monism between the observer and observed in which attributes are intrinsically scaled state-syntax pairings. The leads to the notion that the universe is a kind of self-simulation in which it simulates its contents while its contents simulate it, resulting in a “recursively inter-defining” relationship. The analogy used by in the Baha’i Faith of the relationship between creator and creation is that of the Sun whose rays of light are mirrored by its creation. In this sense, a reflection or attribute of the whole may be found reflected in all of its parts, which in turn mirror forth that light. In this sense, man is created in the image of its creator in reflecting its attributes. It also describes how the outward powers of the senses and in the inward powers of intellect, share a “common faculty” that mediates and unites the outward and inward, and from which both originate. This may relate to the modern question of whether the synthetic and analytic could be treated as separate. In the CTMU, the parts are like microcosms which mirror the macrocosmic system as a whole. Since the “conspansive dual” of geometric is logic, the increasing complexity of one is mirrored by the increase in the complexity of the other. Thus as local systems are “progressively exposed” a constant rate by global systems, they require better representations in order to operate effectively. The Baha’i writings also describe how as the horizon of mankind extends, there are new requirements that place and time, and that any religion which does not conform to science and reason must either adapt or no longer accepted as truth. In conclusion, philosophy and theology are quite intertwined, as ultimately the deal with metaphysical questions. Many ignore historical precedents, operating under the assumption that they have nothing in common with the past. Others tend to live in the past, without recognizing the needs of the present. This paper sought to lay the ground work for future investigations of cross-cultural and cross-historical metaphysics. One power which the Baha’i writings describe is that of humans to unite that past with the present and the present with the future, and thereby deducing laws and anticipating events so as to act in conformance with their intentions. It may be that the past is of little consequence to the future but as the CTMU describes, the future is never entirely independent from the past. - Hamid Y. Javanbakht

"An author of a system, once he succeeds in persuading others that his work is indeed significant, will be lacking neither in admirers nor disciples, who will study his teachings in the light of history and appropriate their master's manners with words and ideas as much as possible. Thus a doctrine comes to be perpetuated and popularized by the educated classes. It may even rise to such exalted heights of prominence that anybody audacious enough to voice reservations, or doubts, is charged with insolence. Only after much time has passed will such a holy of holies be called into question, common sense vindicated, and the fog of illusory , and often noxious ideology, scattered.
Yet it is not enough to point out dangers and issue warnings. One has to find and give examples. In the first part of this essay, I criticized attempts to prove the veracity of a theory by simply relying on the unmediated results of empirical experiments. This criticism carried the implication that mediation may be indispensable in the advancement of science. Since this essay's goal is simply to state the case on behalf of mediation, I will enlarge on this point: Whatever happens in and by nature is inter-connected. Though experiments furnish facts about phenomena isolated from their matrix, they do not thereby prove that the matrix does not exist, or can be simply disregarded. We saw already that theories drawn directly from empirical data derived from various experiments are often mistaken, while research that stays with one object as the subject of experimentation, exploring with thoroughness all possible modifications, achieves solid results. A separate study is called for on how far reason's role and rule extend in experimental investigation. Here a brief sketch will have to suffice. Since all things in nature partake in her dynamic power, one can observe throughout the rhythms, as well as spasms, of countervailing forces. It follows that each phenomenon is connected to numberless others, reminiscent of a star seen as a point of light, dispersing single rays in all directions. Scientific investigations occur within spaces of contending forces, and adequate research has to allow for patterns where analysis and synthesis are working in a mutually challenging complementary partnership." - The Experiment as Mediator between Subject and Object
By Johann Wolfgang von Goethe
http://www.satworld.cn/user1/doctorzhang/archives/2011/4409.html

"The Quine thesis breaks down into two related theses.  The first says that there is no distinction between analytic statements (e.g. definitions) and synthetic statements (e.g. empirical claims), and thus that the Duhem thesis applies equally to the so-called a priori disciplines.  To make sense of this, we need to know the difference between analytic and synthetic statements.  Analytic statements are supposed to be true by their meanings alone, matters of empirical fact notwithstanding, while synthetic statements amount to empirical facts themselves.  Since analytic statements are necessarily true statements of the kind found in logic and mathematics, while synthetic statements are contingently true statements of the kind found in science, Quine’s first thesis posits a kind of equivalence between mathematics and science.  In particular, it says that epistemological claims about the sciences should apply to mathematics as well, and that Duhem’s thesis should thus apply to both."
http://www.megafoundation.org/CTMU/Articles/Theory.html

"Reality is a relation, and every relation is a syndiffeonic relation exhibiting syndiffeonesis or “difference-in-sameness”. Therefore, reality is a syndiffeonic relation. Syndiffeonesis implies that any assertion to the effect that two things are different implies that they are reductively the same; if their difference is real, then they both reduce to a common reality and are to that extent similar. Syndiffeonesis, the most general of all reductive principles, forms the basis of a new view of the relational structure of reality. ... Every syndiffeonic relation has synetic and diffeonic phases respectively exhibiting synesis and diffeonesis (sameness and difference, or distributivity and parametric locality), and displays two forms of containment, topological and descriptive. The medium is associated with the synetic phase, while the difference relation is associated with the diffeonic phase (because the rules of state and transformation of the medium are distributed over it, the medium is homogeneous, intrinsically possessing only relative extension by virtue of the difference relationships it contains). Because diffeonic relands are related to their common expressive medium and its distributive syntax in a way that combines aspects of union and intersection, the operation producing the medium from the relands is called unisection (un). The synetic medium represents diffeonic potential of which the difference relationship is an actualization." http://www.iscid.org/papers/Langan_CTMU_092902.pdf

“The universe can be described as a cybernetic system in which freedom and constraint are counterbalanced. The constraints function as structure; thus, the laws of physics are constraints which define the structure of spacetime, whereas freedom is that which is bound or logically quantified by the constraints in question. Now, since there is no real time scale external to reality, there is no extrinsic point in time at which the moment of creation can be located, and this invalidates phrases like "before reality existed" and "when reality created itself". So rather than asking "when" the universe came to be, or what existed "before" the universe was born, we must instead ask "what would remain if the structural constraints defining the real universe were regressively suspended?" First, time would gradually disappear, eliminating the "when" question entirely. And once time disappears completely, what remains is the answer to the "what" question: a realm of boundless potential characterized by a total lack of real constraint. In other words, the real universe timelessly emerges from a background of logically unquantified potential to which the concepts of space and time simply do not apply.  Now let's attend to your "how" question. Within a realm of unbound potential like the one from which the universe emerges, everything is possible, and this implies that "everything exists" in the sense of possibility. Some possibilities are self-inconsistent and therefore ontological dead ends; they extinguish themselves in the very attempt to emerge into actuality. But other possibilities are self-consistent and potentially self-configuring by internally defined evolutionary processes. That is, they predicate their own emergence according to their own internal logics, providing their own means and answering their own "hows". These possibilities, which are completely self-contained not only with respect to how, what, and when, but why, have a common structure called SCSPL (Self-Configuring Self-Processing Language). An SCSPL answers its own "why?" question with something called teleology; where SCSPL is "God" to whatever exists within it, teleology amounts to the "Will of God".” – C.M. Langan, Q&A http://www.megafoundation.org/CTMU/Q&A/Archive.html


"As the foregoing passages make clear, the Writings and Aristotle284 agree on hylomorphism, that is, the belief that everything in creation is made of both matter and form, though we must bear in mind that ‘matter’ is a relative term in Aristotle insofar as it can refer to physical ‘stuff’ sometimes called “elemental”285 by Abdu’l-Baha. Most fundamental to Aristotle is the doctrine that matter is the potential to receive form. In Aristotle, the form is the active principle while matter is receptive, passive or patient, an idea Baha’u’llah expresses when He writes: The world of existence came into being through the heat generated from the interaction between the active force and that which is its recipient. These two are the same, yet they are different.286 Two comments are in order. First, the statement that these two are the “same” 287 refers to their origin and nature as created entities while their differences refer to their action in the phenomenal world of creation. This statement should no more be read as a reductionism to spirit than as a reductionism to matter. The Baha’i Writings, like Aristotle’s thought, are examples of hylomorphism, the belief that existence is made of matter and form; therefore, neither of them can be reduced to a spiritual-idealistic or material monism. Second, in the foregoing passage, the “heat generated”288 by the imposition of form onto matter is the tension that inevitably exists between form and matter, since form is the active principle of perfection while matter is the principle of receptivity but also of inertia. This tension is part of what constitutes and most especially living things since the quest for perfection, that is, highest possible self-expression, is an integral part of their existence. Although Aristotle does not explicitly refer to such tension, it is implicit in his characterization of matter and form. The distinction between matter and form also brings us back to our resolution of the apparent self-contradiction between creationism and emanationism and the associated doctrines of time. ‘Creation’ refers to the notion that God made the world like an artisan, a concept implying that the world was made at some point in time. On the other hand, emanationism suggests that the universe is eternal – which, by the way, is another point of agreement between Aristotle and the Baha’i Writings – and, consequently, there is no creation in time. On the basis of Aristotle289, we may conclude that ‘creation’ refers to the specific creation of a concrete thing such as the earth or this universe whereas ‘emanation’ refers to the formal principle, essence which has always existed as a potential available for actualization. After all, a Creator requires a creation but nothing says this creation must be material. In short, there is no contradiction between the two Teachings because one refers to the order of specific matter and time, whereas the other refers to the order of potential and form." http://www.bahaiphilosophystudies.com/articles/?p=7

"The active force" and "its recipient" are, again, a reference to the pairing of matter and form. This helps explain why they are the same, yet different. If you look at an object, you can see how its matter is different from its form, and yet these two things cannot be separated and are, in a sense, the same thing. Baha'u'llah goes on to say that "Such as communicate the generating influence and such as receive its impact are indeed created through the irresistible Word of God...", which shows the line-up with the B and E: the generating influence is the B and the recipient is the E, for these are also created through the Word." http://meditationsonbahaullah.blogspot.com/2010/11/being-throbbing-artery.html

""This passage has been explained by ‘Abdu’l-Bahá. In regard to the first sentence, he says: “From this blessed verse it is clear and evident that the universe is evolving. In the opinion of the philosophers and the wise this fact of the development and evolution of the world of existence is also established. That is to say, it is progressively transferred from one state to another.” In regard to the next two sentences, he states:  “The substance and primary matter of contingent beings is the ethereal power, which is invisible and known only through its effects, such as electricity, heat, and light—these are vibrations of that power, and this is established and proven in natural philosophy and is known as the ethereal matter. This ethereal matter is itself both the active force and its recipient” (Má’idiy-i-Ásmání, vol. 2, p. 69). Now, first we have Bahá’u’lláh affirming that the active force is the “lord of the species,” in other words, the Platonic Forms or realities of things. But ‘Abdu’l-Bahá states that ethereal matter is meant. This seeming contradiction is easily resolved, because what is being referred to is simultaneously two things, neither of which can be realized without the other. These two are matter and form, or in other terms, existence and essence. This ontological polarity principle is also a cornerstone of the philosophy of Shaykh Aḥmad, who proposed that matter and form logically require each other in order to exist. Hence, matter, which receives God’s action, becomes active in relation to the form it takes on, which, in turn, is active in relation to that which it acts upon. These two together are the inseparable common ground of all creatures, whether they be eternal and intelligible or perishable and material. As Idris Hamid expresses it: “Every created, contingent thing is a complex of acting (fi‘l) and becoming-in-yielding-to-acting (infi‘ál)” (“Metaphysics and Cosmology of Process,” p., 136). The Báb confirms this essential duality at the basis of contingent existence. He explains: “With the exception of God, nothing can subsist through itself. All things are composite. Once this duality is established, connection is also established, for a thing cannot be a thing except through its existence, which is the aspect of manifestation (tajallí) in it, through its essence, which is the aspect of receiving (qubúl), and through connection (rabṭ), which is realized after the union [of the first two]” (INBA, vol. 14, p. 268)." http://users.sisqtel.net/kevenbrown/creation.html


"This work continues the development of relational biology and its characteristic association with the study of causality.
Specifically, it re-­‐interprets and integrates the four Aristotelean causalities (or modes of natural
explanation) – material, efficient, formal, and final – using the framework of modeling relations.
...
The relationship between actual (realized)and contextual (potential) aspects of nature described here
is very much entailment of existence. We are learning that complexity is the coincidence of four causes that were introduced by Aristotle but inadequately understood and only partly adopted since then.
The mathematical integration of these causes into a recursive, hierarchical framework, as proposed here, provides a new and deeper understanding of causality."
http://relationalscience.org/wp-content/uploads/2011/06/R-theory-Synthesis.pdf


"O Pen of the Most High! Recount unto him who hath turned unto Thy Lord, the All-Glorious, that which shall enable him to dispense with the sayings of men. Say: Spirit, mind, soul, and the powers of sight and hearing are but one single reality which hath manifold expressions owing to the diversity of its instruments. As thou dost observe, man’s power to comprehend, move, speak, hear, and see all derive from this sign of his Lord within him. It is single in its essence, yet manifold through the diversity of its instruments. This, verily, is a certain truth. For example, if it directeth its attention to the means of hearing, then hearing and its attributes become manifest. Likewise, if it directeth itself to the means of vision, a different effect and attribute appear. Reflect upon this subject that thou mayest comprehend the true meaning of what hath been intended, find thyself independent of the sayings of the people, and be of them that are well assured. In like manner, when this sign of God turneth towards the brain, the head, and such means, the powers of the mind and the soul are manifested. Thy Lord, verily, is potent to do whatsoever He pleaseth." - Bahá’u’lláh
 http://reference.bahai.org/en/t/b/SLH/slh-10.html

Wednesday, February 22, 2012

Covering-Packing and State-Syntax Duality

N. J. A. Sloane: Papers on Sphere Packings, Lattices and Quadratic Forms (see also Spherical Codes and Designs)
http://www2.research.att.com/~njas/doc/sp.html

"In combinatorics and computer science, covering problems are computational problems that ask whether a certain combinatorial structure 'covers' another, or how large the structure has to be to do that. Covering problems are minimization problems and usually linear programs, whose dual problems are called packing problems.

The most prominent examples of covering problems are the set cover problem, which is equivalent to the hitting set problem, and its special cases, the vertex cover problem and the edge cover problem."
http://en.wikipedia.org/wiki/Covering_problem

"Packing problems are a class of optimization problems in mathematics which involve attempting to pack objects together (often inside a container), as densely as possible. Many of these problems can be related to real life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap.

In a packing problem, you are given:

'containers' (usually a single two- or three-dimensional convex region, or an infinite space)
'goods' (usually a single type of shape), some or all of which must be packed into this container

Usually the packing must be without overlaps between goods and other goods or the container walls. The aim is to find the configuration with the maximal density. In some variants the overlapping (of goods with each other and/or with the boundary of the container) is allowed but should be minimized."
http://en.wikipedia.org/wiki/Packing_problem