Let's face it, humanity has a lousy definition, accompanying practice, and analysis of peace.
As mentioned on the previous page, we shall provide some examples of remarks to Wigner's paper, keeping in mind that the topic of the present series is directed towards an analysis of the "Peace" concept, which necessarily invites inclusions of the "War" concept, and the very many analogical considerations such as a discussion involving mathematics, since there very often is cited a reference to dichotomies and triplicities, even if the author or commentators to an author's article are not aware of such. They may not be focused on making a connection on basic levels of formulaic design since many researchers and analysts prefer to use some method of conservation in the materials being applied. The present series is taking a much broader adventurous view because current types of analysis which utilized conventionalized constraints have not yielded anything but references to results already found; and may want to suggest the repetition in findings means the analytical algorithm being used is the correct one, instead of that this means the answer being derived is due to the constraints being applied. In other words, the same answer is achieved because it is the only answer which can be obtained from the material and the way the material is being reviewed.
Analogously, the writer of this page in the series had the personal experience of having taken a chemistry test in which five answers were provided for a given equation. Yet, no matter how often I did the equation, and attempted to use the experimental materials at hand, I could not get one of the supplied answers. Dumbfounded, I went to the instructor and queried about the absence of the answer which was obtained by using both the experimental and mathematical methods. He said I wasn't getting the right answer because I was doing the the problem wrong. In other words, he had supplied the right answer... or at least the result which he wanted the class to "discover" as well. So I made a guess and got the correct answer... or at least the one he wanted. Yet, I wasn't satisfied. So I enlisted the help of some other students to do the same problem without providing any of the answers which were provided on the test. All of them got what I had gotten and were surprised to find that it was not on the original test. Several of them began to question their answer and began "fudging the numbers" to get one of the answers. Interestingly, all of them "fudged" numbers in the same direction so as to get the "correct" test answer. No doubt this same sort of "rationalized adjustment" takes place so that we coincide with expectations in order to maintain some level of social equalibrium. And no doubt we all make such adjustments to changes in the environment as it continues to deteriorate. I'll leave a further exploration into the experience for another time because of its obvious ramifications in our present analysis.
Now let's move on to remarks made about the previous article.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences" is the title of an article published in 1960 by the physicist Eugene Wigner. In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.
The miracle of mathematics in the natural sciences
Wigner begins his paper with the belief, common among those familiar with mathematics, that mathematical concepts have applicability far beyond the context in which they were originally developed. Based on his experience, he says "it is important to point out that the mathematical formulation of the physicist's often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena." He then invokes the fundamental law of gravitation as an example. Originally used to model freely falling bodies on the surface of the earth, this law was extended on the basis of what Wigner terms "very scanty observations" to describe the motion of the planets, where it "has proved accurate beyond all reasonable expectations".
Another oft-cited example is Maxwell's equations, derived to model the elementary electrical and magnetic phenomena known as of the mid 19th century. These equations also describe radio waves, discovered by David Edward Hughes in 1879, around the time of James Clerk Maxwell's death. Wigner sums up his argument by saying that "the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it". He concludes his paper with the same question with which he began:
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
The deep connection between science and mathematics
Wigner's work provided a fresh insight into both physics and the philosophy of mathematics, and has been fairly often cited in the academic literature on the philosophy of physics and of mathematics. Wigner speculated on the relationship between the philosophy of science and the foundations of mathematics as follows:
It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of laws of nature and of the human mind's capacity to divine them.
Later, Hilary Putnam (1975) explained these "two miracles" as being necessary consequences of a realist (but not Platonist) view of the philosophy of mathematics. However, in a passage discussing cognitive bias Wigner cautiously labeled as "not reliable", he went further:
The writer is convinced that it is useful, in epistemological discussions, to abandon the idealization that the level of human intelligence has a singular position on an absolute scale. In some cases it may even be useful to consider the attainment which is possible at the level of the intelligence of some other species.
Whether humans checking the results of humans can be considered an objective basis for observation of the known (to humans) universe is an interesting question, one followed up in both cosmology and the philosophy of mathematics.
Wigner also laid out the challenge of a cognitive approach to integrating the sciences:
A much more difficult and confusing situation would arise if we could, some day, establish a theory of the phenomena of consciousness, or of biology, which would be as coherent and convincing as our present theories of the inanimate world.
He further proposed that arguments could be found that might:
put a heavy strain on our faith in our theories and on our belief in the reality of the concepts which we form. It would give us a deep sense of frustration in our search for what I called 'the ultimate truth'. The reason that such a situation is conceivable is that, fundamentally, we do not know why our theories work so well. Hence, their accuracy may not prove their truth and consistency. Indeed, it is this writer's belief that something rather akin to the situation which was described above exists if the present laws of heredity and of physics are confronted.
Peter Woit, a theoretical physicist, believes that this conflict exists in string theory, where very abstract models may be impossible to test in any foreseeable experiment. If this is the case, the "string" must be thought of either as real but untestable, or simply as an illusion or artifact of either mathematics or cognition.
Responses to Wigner's original paper
Wigner's original paper has provoked and inspired many responses across a wide range of disciplines. These include Richard Hamming  in computer science, Arthur Lesk in molecular biology , Peter Norvig in data mining , Max Tegmark in physics , Ivor Grattan-Guinness in mathematics  and Vela Velupillai in economics .
Richard Hamming, an applied mathematician and a founder of computer science, reflected on and extended Wigner's Unreasonable Effectiveness in 1980, mulling over four "partial explanations" for it.  Hamming concluded that the four explanations he gave were unsatisfactory. They were:
1. Humans see what they look for. The belief that science is experimentally grounded is only partially true. Rather, our intellectual apparatus is such that much of what we see comes from the glasses we put on. Eddington went so far as to claim that a sufficiently wise mind could deduce all of physics, illustrating his point with the following joke: "Some men went fishing in the sea with a net, and upon examining what they caught they concluded that there was a minimum size to the fish in the sea."
Hamming gives four examples of nontrivial physical phenomena he believes arose from the mathematical tools employed and not from the intrinsic properties of physical reality.
Suppose that a falling body broke into two pieces. Of course the two pieces would immediately slow down to their appropriate speeds. But suppose further that one piece happened to touch the other one. Would they now be one piece and both speed up? Suppose I tie the two pieces together. How tightly must I do it to make them one piece? A light string? A rope? Glue? When are two pieces one?
There is simply no way a falling body can "answer" such hypothetical "questions." Hence Galileo would have concluded that "falling bodies need not know anything if they all fall with the same velocity, unless interfered with by another force." After coming up with this argument, Hamming found a related discussion in Pólya (1963: 83-85). Hamming's account does not reveal an awareness of the 20th century scholarly debate over just what Galileo did.
The inverse square law of universal gravitation necessarily follows from the conservation of energy and of space having three dimensions. Measuring the exponent in the law of universal gravitation is more a test of whether space is Euclidean than a test of the properties of the gravitational field.
The inequality at the heart of the uncertainty principle of quantum mechanics follows from the properties of Fourier integrals and from assuming time invariance.
Hamming argues that Albert Einstein's pioneering work on special relativity was largely "scholastic" in its approach. He knew from the outset what the theory should look like (although he only knew this because of the Michelson–Morley experiment), and explored candidate theories with mathematical tools, not actual experiments. Hamming alleges that Einstein was so confident that his relativity theories were correct that the outcomes of observations designed to test them did not much interest him. If the observations were inconsistent with his theories, it would be the observations that were at fault.
2. Humans create and select the mathematics that fit a situation. The mathematics at hand does not always work. For example, when mere scalars proved awkward for understanding forces, first vectors, then tensors, were invented.
3. Mathematics addresses only a part of human experience. Much of human experience does not fall under science or mathematics but under the philosophy of value, including ethics, aesthetics, and political philosophy. To assert that the world can be explained via mathematics amounts to an act of faith.
4. Evolution has primed humans to think mathematically. The earliest life-forms must have contained the seeds of the human ability to create and follow long chains of close reasoning. Hamming, whose expertise is far from biology, otherwise says little to flesh out this contention.
A different response, advocated by physicist Max Tegmark, is that physics is so successfully described by mathematics because the physical world is completely mathematical, isomorphic to a mathematical structure, and that we are simply uncovering this bit by bit. The same interpretation had been advanced some years previously by Peter Atkins. In this interpretation, the various approximations that constitute our current physics theories are successful because simple mathematical structures can provide good approximations of certain aspects of more complex mathematical structures. In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics.
Ivor Grattan-Guinness finds the effectiveness in question eminently reasonable and explicable in terms of concepts such as analogy, generalisation and metaphor.
[W]ir auch, gleich als ob es ein glücklicher unsre Absicht begünstigender Zufall wäre, erfreuet (eigentlich eines Bedü;rfnisses entledigt) werden, wenn wir eine solche systematische Einheit unter bloß empirischen Gesetzen antreffen. [We rejoice (actually we are relieved of a need) when, just as if it were a lucky chance favoring our aim, we do find such systematic unity among merely empirical laws.]. — Immanuel Kant
The most incomprehensible thing about the universe is that it is comprehensible. —Albert Einstein 
How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? [...] In my opinion the answer to this question is, briefly, this: As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. — Albert Einstein 
Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover. — Bertrand Russell 
There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology. — Israel Gelfand 
Sciences reach a point where they become mathematized..the central issues in the field become sufficiently understood that they can be thought about mathematically..[by the early 1990s] biology was no longer the science of things that smelled funny in refrigerators (my view from undergraduate days in the 1960s)..The field was undergoing a revolution and was rapidly acquiring the depth and power previously associated exclusively with the physical sciences. Biology was now the study of information stored in DNA — strings of four letters: A, T, G, and C..and the transformations that information undergoes in the cell. There was mathematics here! — Leonard Adleman, a theoretical computer scientist who pioneered the field of DNA computing 
(References for numerical indicators can be found at the site source for the above information:)
We should stop acting as if our goal is to author extremely elegant theories, and instead embrace complexity and make use of the best ally we have: the unreasonable effectiveness of data. — Peter Norvig 
Despite all the above commentary, the problem still remains to be discussed. This relates to whether mathematics is simply part of the architecture of human biology, like the construction of a web by a spider. Irrespective of the different techniques used in the construction of a web, do spider actually engage in some sort of geometry-like "thinking"? Do they have different types of names for different types of spider webs or different types of spider strategies which detail the difference or similarity? Do birds need mathematics? Can humans live without mathematics that we assume primates in zoos do? Do ants routinely conduct a census on their populations? And what of this human (brain) architecture which may or may not acknowledge its uses of two, three, or other-patterned configurations? Is there a preponderance of two-patterned references to be made as used by Wigner, or is a three-based formula of greater relevance as suggested by Wilson's paper? Is there a 1, 2, 3 maturational development sequence due to some unrecognized environmental influence which makes us view the world according to the dominant pattern in our personal psychological makeup, or does reality actually exist in such patterns?
However, though we recognize three Murray Gelman red, green, blue varieties, three quarks and anti-quarks, three fundamental particles (protons- neutrons- electons), three families of particles (stable, unstable, highly unstable), four charges (-1 -2/3 -1/3) 0 (1/3 2/3 1) and three forces... there are numerous two-patterns such as strong/weak, up/down, particle/anti-particle, positive/negative, hyper-charge/weak charge, two charges corresponding to gravitational force, clockwise/counter-clockwise (spin), etc... do such patterns actually exist or we only think they do because this is how our brains are wired due to a physiology subjected to an incrementally deteriorating environment? Does the architecture of our brain developed in a deteriorating environment construct the world according to the limitations of its parameters... like the world view of an insect with a given (short) life span?
No less, can't particles spin in three directions like the movement of chess or checker pieces (horizontal, diagonal, vertical)? Or are our brains limited (at this present time in our evolutionary development) towards seeing the world in patterns-of-two where patterns-of-three can exist if our brains were thus configured? Are we so used to viewing in a left and right or up and down direction due to the orientation of our bodies in the present environment, we view a two-patterned spin as both natural and therefore universal? Does direction of spin add a third component to a two-patterned uni-direction, such as the image a spiraling screw evokes, such as one might also visualize the spinning Earth's movement in an expanding universe or a spinning DNA molecule or the left and right spins of molecules?
And even though some may look upon the creation of a mathematics or chemistry formula with the same level of awe another does when observing the creation of a painting, sculpture, computer program, architectural blueprint, birds nest, antlion burrow, pyramid, mandala, etc., do all of them actually represent simplistic diagrams that are convoluted into proposed complexities merely because of the type of repetition employed to overlay the simple illustration? Do they actually represent what humans say they do, or are our labels and definitions merely fairy-tales of a different kind? Are we telling stories that others come to believe and we create social structures around such beliefs... but such beliefs are false and this is why a civilization comes to fail? Are peace and war made up activities used as attempts to describe some underlying schematic that we have not yet grasped... and so we make up excuses around which we institutionalize into an activity called socialization or civilization?
In Hindu and Buddhist Tantrism, (the mandala is) a symbolic diagram used in the performance of sacred rites and as an instrument of meditation. The mandala is basically a representation of the universe, a consecrated area that serves as a receptacle for the gods and as a collection point of universal forces. Man (the microcosm), by mentally "entering" the mandala and "proceeding" toward its centre, is by analogy guided through the cosmic processes of disintegration and reintegration.
Mandalas in China, Japan, and Tibet are basically of two types, representing different aspects of the universe: the garbha-dhatu (Sanskrit: "womb world”; Japanese taizo--kai), in which the movement is from the one to the many; and the vajra-dhatu (Sanskrit: "diamond [or thunderbolt] world"; Japanese kongo--kai), from the many into one. Mandalas may be painted on paper or cloth, drawn on a carefully prepared ground with white and coloured threads or with rice powders (as for Buddhist Tantric ceremonies of initiation), fashioned in bronze, or built in stone, as at Borobudur, in central Java. There the circumambulation of the stupa (a commemorative monument) is tantamount to the ritual approach to the centre.
The mandala of a Tibetan tanka (cloth scroll painting) characteristically consists of an outer enclosure around one or more concentric circles, which in turn surround a square transversed by lines from the centre to the four corners. In the centre and the middle of each triangle are five circles containing symbols or images of divinities, most commonly the five "self-born" buddhas. Of the borders surrounding the mandala, the first is a ring of fire, which both bars entry to the uninitiated and symbolizes the burning of ignorance; next comes a girdle of diamonds, which stands for illumination; then a circle of eight graveyards, symbolizing the eight aspects of individuating cognition; next a girdle of lotus leaves, signifying spiritual rebirth; and, finally, at the centre, the mandala itself, where the images are set.
Similar ritual drawings have been found in cultures other than Hindu and Buddhist—for example, in the sand paintings of the North American Indians. The Swiss psychologist Carl Jung published studies of mandala-like drawings executed by his patients. In his view, the spontaneous production of a mandala is a step in the individuation process—a central concept in Jung's psychological theory—and represents an attempt by the conscious self to integrate hitherto unconscious material.Source: "Mandala." Encyclopædia Britannica Ultimate Reference Suite, 2013.
Note: one must distinguish between a "true" mandala and those claiming a similar identity but do not illustrate traditional symbolism.
Is the usage of the term "man-dala" a chauvinistic term? Why is there no "Ms-dala"? Don't females create mandalas? Also, the "from the many into one" phrase in the above reference to mandalas in China, Japan, and Tibet may be an unrecognized insight into the eventuality of the Sun's three "moments" (dawn, noon, dusk) "fusing" (from its perspective and effects on Earth), as it expands along a course of its incremental decay.
Would a greater universal truth be possible if we were some other species not confined to an environment whose deteriorating effects forced us into accepting various "conservations" such as a conservation of energy, of thinking in certain numerically based mental patterns, in imagination... all for the purpose of maintaining some measure of equilibrium in a deteriorating environment?
If we add examples of Native American Dream Catcher designs to the foregoing examples of intricate designs, what are they illustrating other than a commonality of a type of mentality? Just because a human has created ("uncovered") a design doesn't mean it has some vast universal significance beyond the human application. Why does one seek to capture the kaleidoscopic events of a dream as if they represented a greater message than the events of a presumed waking state? Is the phenomena of Peace and War best described as dreams, fragments of dreams, or illusions created by dreams?
We will pursue a selection on dreams in the next section.