I'Oh'No What Your Prayer Circle Is Like, But This Is What I'm Talm'bout: La-ila ha-ill-allah !

wikipedia  |  The Tetris effect (also known as Tetris syndrome) occurs when people devote so much time and attention to an activity that it begins to pattern their thoughts, mental images, and dreams.^[1] It takes its name from the video game Tetris.^[1]

People who have played Tetris for a prolonged amount of time can find themselves thinking about ways different shapes in the real world can fit together, such as the boxes on a supermarket shelf or the buildings on a street.^[1] They may see colored images of pieces falling into place on an invisible layout at the edges of their visual fields or when they close their eyes.^[1] They may see such colored, moving images when they are falling asleep, a form of hypnagogic imagery.^[2]

Those experiencing the effect may feel they are unable to prevent the thoughts, images, or dreams from happening.^[3]

A more comprehensive understanding of the lingering effects of playing video games has been investigated empirically as game transfer phenomena (GTP).^[4]

The Tetris effect can occur with other video games.^[5] It has also been known to occur with non-video games, such as the illusion of curved lines after doing a jigsaw puzzle, the checker pattern of a chess board (or imagining chess pieces in unrelated objects or phenomena), or the involuntary mental visualisation of Rubik's Cube algorithms common among speedcubers.

The earliest example that relates to a computer game was created by the game Spacewar! As documented in Steven Levy's book Hackers: "Peter Samson, second only to Saunders in Spacewarring, realized this one night when he went home to Lowell. As he stepped out of the train, he stared upward into the crisp, clear sky. A meteor flew overhead. Where's the spaceship? Samson thought as he instantly swiveled back and grabbed the air for a control box that wasn’t there." (p. 52.)

Robert Stickgold reported on his own experiences of proprioceptive imagery from rock climbing.^[3] Another example, sea legs, are a kind of Tetris effect. A person newly on land after spending long periods at sea may sense illusory rocking motion, having become accustomed to the constant work of adjusting to the boat making such movements (see "Illusions of self-motion" and "Mal de debarquement"). The poem "Boots" by Rudyard Kipling describes the effect, resulting from repetitive visual experience during a route march:

'Tain't—so—bad—by—day because o' company,

But—night—brings—long—strings—o' forty thousand million
Boots—boots—boots—boots—movin' up an' down again.

There's no discharge in the war!

— Rudyard Kipling, Boots

Mathematicians have reported dreaming of numbers or equations; for example Srinivasa Ramanujan, or Friedrich Engel, who remarked "last week in a dream I gave a chap my shirt-buttons to differentiate, and he ran off with them".^[6]

wikipedia | Klüver's form constants have appeared in other drug-induced and naturally occurring hallucinations, suggesting a similar physiological process underlying hallucinations with different triggers. Klüver's form constants also appear in near-death experiences and sensory experiences of those with synesthesia. Other triggers include psychological stress, threshold consciousness (hypnagogia), insulin hypoglycemia, the delirium of fever, epilepsy, psychotic episodes, advanced syphilis, sensory deprivation, photostimulation, electrical stimulation, crystal gazing, migraine headaches, dizziness and a variety of drug-induced intoxications.^[1] These shapes may appear on their own or with eyes shut in the form of phosphenes, especially when exerting pressure against the closed eyelid.^[2]

It is believed that the reason why these form constants appear has to do with the way the visual system is organized, and in particular in the mapping between patterns on the retina and the columnar organization of the primary visual cortex. Concentric circles in the retina are mapped into parallel lines in the visual cortex. Spirals, tunnels, lattices and cobwebs map into lines in different directions. This means that if activation spreads in straight lines within the visual cortex, the experience is equivalent to looking at actual form constants.^[1]

Author Michael Moorcock once observed in print that the shapes he had seen during his migraine headaches resembled exactly the form of fractals. The diversity of conditions that provoke such patterns suggests that form constants reflect some fundamental property of visual perception.

Cultural significance

Form constants have a relationship to some forms of abstract art, especially the visual music tradition, as William Wees noted in his book Light Moving in Time about research done by German psychologist Heinrich Klüver on the form constants resulting from mescaline intoxication. The visual and synaesthetic hallucinations this drug produced resembles, as Wees noted, a listing of visual forms employed in visual music:

[Klüver’s] analysis of hallucinatory phenomena appearing chiefly during the first stages of mescaline intoxication yielded the following form constants: [emphasis original] (a) grating, lattice, fretwork, filigree, honeycomb, or chessboard; (b) cobweb; (c) tunnel, funnel, alley, cone or vessel; (d) spiral. Many phenomena are, on close examination, nothing but modifications and transformations of these basic forms. The tendency towards "geometrization," as expressed in these form constants, is also apparent in the following two ways: (a) the forms are frequently repeated, combined, or elaborated into ornamental designs and mosaics of various kinds; (b) the elements constituting these forms, such as squares in the chessboard design, often have boundaries consisting of geometric forms.^[3]

These form-constants provide links between abstraction, visual music and synaesthesia. The cultural significance of form constants, as Wees notes in Light Moving in Time is part of the history of abstract film and video.

The practice of the ancient art of divination may suggest a deliberate practice of cultivating form constant imagery and using intuition and/or imagination to derive some meaning from transient visual phenomena.

Psychedelic art, inspired at least in part by experiences with psychedelic substances, frequently includes repetitive abstract forms and patterns such as tessellation, Moiré patterns or patterns similar to those created by paper marbling, and, in later years, fractals. The op art genre of visual art created art using bold imagery very like that of form constants.

In electroacoustic music, Jon Weinel has explored the use of altered states of consciousness as a basis for the design of musical compositions. His work bases the design of sonic materials on typical features of hallucinatory states, and organises them according to hallucinatory narratives. As part of this work, form constants feature prominently as a basis for the design of psychedelic sonic and visual material.^[4]

New Model Of The Universe Chapter 2: The Fourth Dimension

avalonlibrary |  It will be possible to answer these questions definitely only when it is definitely known that the fourth dimension exists and when it is known what it really is. But so far it is possible to consider only what might be in the fourth dimension, and therefore there cannot be any final answers to these questions. Vision in the fourth dimension must be effected without the help of eyes. The limits of eyesight are known, and it is known that the human eye can never attain the perfection even of the microscope or telescope. But these instruments with all the increase of the power of vision which they afford do not bring us in the least nearer to the fourth dimension. So it may be concluded that vision in the fourth dimension must be something quite different from ordinary vision. But what can it actually be? Probably it will be something analogous to the " vision " by which a bird flying over Northern Russia " sees " Egypt, whither it migrates for the winter; or to the vision of a carrier pigeon which " sees ", hundreds of miles away, its loft, from which it has been taken in a closed basket; or to the vision of an engineer making the first calculations and first rough drawings of a bridge, who " sees " the bridge and the trains passing over it; or to the vision of a man who, consulting a time-table, " sees " himself arriving at the station of departure and his train arriving at its destination.

Now, having outlined certain features of the properties which vision in the fourth dimension should possess, we must endeavour to define more exactly what we know of the phenomena of that world.

Again making use of the experience of the two-dimensional being, we must put to ourselves the following question: are all the " phenomena " of our world explicable from the point of view of physical laws?

There are so many inexplicable phenomena around us that merely by being too familiar with them we cease to notice their inexplicability, and, forgetting it, we begin to classify these phenomena, give them names, include them within different systems and, finally, even begin to deny their inexplicability.
Strictly speaking, all is equally inexplicable. But we are accustomed to regard some orders of phenomena as more explicable and other orders as less explicable. We put the less explicable into a special group, and create out of them a separate world, which is regarded as parallel to the " explicable ".

This refers first of all to the so-called " psychic world ", that is to the world of ideas, images and conceptions, which we regard as parallel to the physical world.
Our relation to the psychic, the difference which exists for us between the physical and the psychic, shows that psychic phenomena should be assigned to the domain of the fourth dimension.1 In the history of human thought the relation to the psychic is very similar to the relation of the plane-being to the third dimension. Psychic phenomena are inexplicable on the " physical plane ", therefore they are regarded as opposite to the physical. But their unity is vaguely felt, and attempts are constantly made to interpret psychic phenomena as a kind of physical phenomena, or physical phenomena as a kind of psychic phenomena. The division of concepts is recognised to be unsuccessful, but there are no means for their unification.

In the first place the psychic is regarded as quite separate from the body, as a function of the " soul ", unsubjected to any physical laws. The soul lives by itself, and the body by itself, and the one is incommensurable with the other. This is the theory of naive dualism or spiritualism. The first attempt at an equally naive monism regards the soul as a direct function of the body. It is then said that " thought is a motion of matter ". Such was the famous formula of Moleschott.
Both views lead into blind alleys. The first, because the obvious interdependence of physiological and psychic processes cannot be disregarded; the second, because motion still remains motion and thought remains thought.

The first view is analogous to the denial by the two-dimensional being of any physical reality in phenomena which happen outside his plane. The second view is analogous to the attempt to consider as happening on a plane phenomena which happen above it or outside it.
The next step is the hypothesis of a parallel plane on which all the inexplicable phenomena take place. But the theory of parallelism is a very dangerous thing.
The plane-being begins to understand the third dimension when he begins to see that what he considered parallel to his plane may actually be at different distances from it. The idea of relief and perspective will then appear in his mind, and the world and things will take for him the same form as they have for us.
We shall understand more correctly the relation between physical and psychic phenomena when we clearly understand that the psychic is not always parallel to the physical and may be quite independent of it. And parallels which are not always parallel are evidently subject to laws that are incomprehensible to us, to laws of the world of four dimensions.

1 The expression " psychic " phenomena is used here in its only possible sense of psychological or mental phenomena, that is, those which constitute the subject of
psychology. I mention this because in spiritualistic and theosophical literature the word psychic is used for the designation of supernormal or superphysical phenomena.
At the present day it is often said: we know nothing about the exact nature of the relations between physical and psychic phenomena; the only thing we can affirm and which is more or less established is that, for every psychic process, thought or sensation there is a corresponding physiological process, which manifests itself in at least a feeble vibration in nerves and brain fibre and in chemical changes in different tissues. Sensation is defined as the consciousness of a change in the organs of sense. This change is a certain motion which is transmitted into brain centres, but in what way the motion is transformed into a feeling or a thought is not known.

The question arises: is it not possible to suppose that the physical is separated from the psychic by four-dimensional space, i.e. that a physiological process, passing into the domain of the fourth dimension, produces there effects which we call feeling or thought?

On our plane, i.e. in the world of motion and vibrations accessible to our observations, we are unable to understand or to determine thought, exactly in the same way as the two-dimensional being on his plane is unable to understand or to determine the action of a lever or the motion of a pair of wheels on an axle.

At one time the ideas of E. Mach, expounded chiefly in his book Analysis of Sensations and Vitiations of the Physical to the Psychic; were in great vogue. Mach absolutely denies any difference between the physical and the psychic. In his opinion all the dualism of the usual view of the world resulted from the metaphysical conception of the " thing in itself " and from the conception (an erroneous one according to Mach) of the illusory character of our cognition of things. In Mach's opinion we can perceive nothing wrongly. Things are always exactly what they appear to be. The concept of illusion must disappear entirely. Elements of sensations are physical elements. What are called " bodies " are only complexes of elements of sensations: light sensations, sound sensations, sensations of pressure, etc. Mental images are similar complexes of sensations. There exists no difference between the physical and the psychic; both the one and the other are built up of the same elements (of sensations). The molecular structure of bodies and the atomic theory are accepted by Mach only as symbols, and he denies them all reality.
In this way, according to Mach's theory, our psychic apparatus builds the physical world. A " thing " is only a complex of sensations.

But in speaking of the theories of Mach it is necessary to remember that the psychic apparatus builds only the " forms " of the world (i.e. makes the world such as we perceive it) out of something else which we shall never attain. The blue of the sky is unreal, the green of the meadows is also unreal; these " colours " belong to the reflected rays. But evidently there is something in the " sky ", i.e. in the air of our atmosphere, which makes it appear blue, just as there is something in the grass of the meadow which makes it appear green.

Without this last addition a man might easily have said, on the basis of Mach's ideas: this apple is a complex of my sensations, therefore it only seems to exist, but does not exist in reality.

This would be wrong. The apple exists. And a man can, in a most real way, become convinced of it. But it is not what it appears to be in the three-dimensional world.
The psychic, as opposed to the physical or the three-dimensional, is very similar to what should exist in the fourth dimension, and we have every right to say that thought moves along the fourth dimension.

No obstacles or distances exist for it. It penetrates impenetrable objects, visualises the structure of atoms, calculates the chemical composition of stars, studies life on the bottom of the ocean, the customs and institutions of a race that disappeared tens of thousands of years ago. . . .

No walls, no physical conditions, restrain our fantasy, our imagination.

Physics Without Metaphysical Assumptions

quantumphysicslady |  Quantum physics also poses major challenges to realism. In 2017, Chinese physicists experimented with two photons, that is, bits of light. The specially-created photons were separated by 700 miles. The experiment showed that the photons were able to instantaneously coordinate their behavior. This phenomenon is called “quantum entanglement.”

According to Special Relativity, no signal can travel across a distance instantaneously. How can one photon instantaneously “know” what another photon over 700 miles away is doing? What kind of reality are we living in?

When people learn about quantum physics, they find out about specific oddities like quantum entanglement. But the most fundamental oddity is its most fundamental premise: Both matter and energy are mere vibrations in an invisible, undetectable medium called “fields.” How does our very impressive, very solid physical universe arise from vibrations in a kind of nothingness?

How does our reality arise from vibrations? [Image source: David Chalmers and Kelvin McQueen, “Consciousness and the Collapse of the Wave Function” (modified to omit a label) http://consc.net/slides/collapse.pdf]

But it gets worse. The vibrations represent a cornucopia of possible physical realities, only one of which becomes the solid reality that we perceive. (If this sentence is baffling to you, you are not alone. It condenses the heart of quantum physics, which is puzzling enough, into one sentence—which is a terrible idea. See the footnote below.**)

Do the oddities of quantum physics mean we must abandon realism? No. Many physicists have come up with interpretations of quantum physics that are based in realism. It’s also true that some of these interpretations describe very odd realities. For example, the Many Worlds Interpretation, perhaps the oddest, describes us as having infinite copies of ourselves in infinite numbers of universes. The desire to salvage realism may be an important reason that the Many Worlds Interpretation is gaining popularity among physicists. But there are other realistic interpretations of Special Relativity and quantum physics that are less mind-blowing.

Quantum physics undermines the solidity of the physical universe. When people learn that quantum physics is based on the proposition that matter and energy are, at bottom, vibrations of questionable reality which shake invisible, undetectable fields, the solidity of our universe loses some of its impressiveness. Thoughts pop up like: Could our physical universe have no more solidity than a dream?

To the dreamer, the houses, the cars, and the monsters all seem completely real. So, too do to the hallucinations of the psychotic and those of someone on LSD. Our minds are quite capable of creating solid reality without any necessity of an independent external world.

Quantum physics may also create wonderings about the mysterious invisible medium for the vibrations of matter and energy: Could the vibrations of matter and energy be vibrations in a new kind of energy that makes up consciousness?

In other words, some begin to entertain the notion of idealism.

More Thinking About The Fabric Of Reality

If you look at the graphic at the top of the article (Penrose tiling) you'll notice there are a bunch of points that are centers of rotational symmetry (you can rotate it 2pi/N and get the same thing) and lines of reflection symmetry (you can mirror it over that line and get the same thing) but there is no translational symmetry (you can't slide it over in any direction and overlap with the original), this is a "quasicrystal" (in 2d)

Compare this to a grid of squares that has reflection and rotation symmetry but also has translational symmetry, this is a true "crystal" (in 2d)

This article is treating a train of laser pulses as a "1d crystal" and if long/short pulses resemble a Fibonacci sequence treating it as a "1d quasicrystal". This seems to be noteworthy in that using such a structured pulse train provides some improvements in quantum computing when it's used to read/write (i.e. shine on) information (i.e. electron configuration) from atoms / small molecules (i.e. qubits)

The "2 time dimensions" thing is basically that a N-d "quasicrystal" is usually a pretty close approximation of an [N+M]-d "true crystal" projected down into N dimensions so the considering the higher dimension structure might make things easier by getting rid of transcendental numbers etc.

They could have just said "aperiodic laser pulses" are used. No need to introduce fantastical sounding terminology about multiple time dimensions, which seems to have been done quite deliberately.

The biggest and most important step is to make sure you drop any mysticism about what a "dimension" is. It's just a necessary component of identifying the location of something in some way. More than three "dimensions" is not just common but super common, to the point of mundanity. The location and orientation of a rigid object, a completely boring quantity, is six dimensional: three for space, three for the rotation. Add velocity in and it becomes 12 dimensional; the six previous and three each now for linear and rotational velocity. To understand "dimensions" you must purge ALL science fiction understanding and understand them not as exotic, but painfully mundane and boring. (They may measure something interesting, but that "interestingness" should be accounted to the thing being measured, not the "dimension". "Dimensions" are as boring as "inches" or "gallons".)

Next up, there is a very easy metaphor for us in the computing realm for the latest in QM and especially materials science. In our world, there is a certain way in which a "virtual machine" and a "machine" are hard to tell apart. A lot of things in the latest QM and materials science is building little virtual things that combine the existing simple QM primitives to build new systems. The simplest example of this sort of thing is a "hole". Holes do not "exist". They are where an electron is missing. But you can treat them as a virtual thing, and it can be difficult to tell whether or not that virtual thing is "real" or not, because it acts exactly like the "virtual" thing would if it were "real".

In this case, this system may mathematically behave like there is a second time dimension, and that's interesting, but it "just" "simulating" it. It creates a larger system out of smaller parts that happens to match that behavior, but it doesn't mean there's "really" a second time dimension.

The weird and whacky things you hear coming out of QM and materials science are composite things being assembled out of normal mundane components in ways that allow them to "simulate" being some other interesting system, except when you're "simulating" at this low, basic level it essentially is just the thing being "simulated". But there's not necessarily anything new going on; it's still electrons and protons and neutrons and such, just arranged in interesting ways, just as, in the end, Quake or Tetris is "just" an interesting arrangement of NAND gates. There's no upper limit to how "interestingly" things can be arranged, but there's less "new" than meets the eye.

Unfortunately, trying to understand this through science articles, which are still as addicted as ever to "woo woo" with the word dimensions and leaning in to the weirdness of QM and basically deliberately trying to instill mysticism at the incorrect level of the problem. (Personally, I still feel a lot of wonder about the world and enjoy learning more... but woo woo about what a "dimension" is is not the place for that.) 

The Universe As A Holographic Quasicrystalline Tensor Network

ncatlab |  The AdS-CFT correspondence at its heart is the observation (Witten 98, Section 2.4) that the classical action functionals for various fields coupled to Einstein gravity on anti de Sitter spacetime are, when expressed as functions of the asymptotic boundary-values of the fields, of the form of generating functions for correlators/n-point functions of a conformal field theory on that asymptotic boundary, in a large N limit.

This is traditionally interpreted as a concrete realization of a vague “holographic principle” according to which quantum gravity in bulk spacetimes is controlled, in one way or other, by “boundary field theories” on effective spacetime boundaries, such as event horizons. The original and main motivation for the holographic principle itself was the fact that the apparent black hole entropy in Einstein gravity scales with the area of the event horizon instead of the black hole’s bulk volume (which is not even well-defined), suggesting that gravity encodes or is encoded by some boundary field theory associated with horizons; an idea that, in turn, seems to find a concrete realization in open/closed string duality in the vicinity of, more generally, black branes. The original intuition about holographic black hole entropy has meanwhile found remarkably detailed reflection in (mathematically fairly rigorous) analysis of holographic entanglement entropy, specifically via holographic tensor networks, which turn out to embody key principles of the AdS/CFT correspondence in the guise of quantum information theory, with concrete applications such as to quantum error correcting codes.

quantumgravityresearch |  Recent advances in AdS/CFT holography have found an analogue in discrete tensor networks of qubits. The {5,4} hyperbolic tiling allows for topological error correction. We review a simple 32 x 32 Hamiltonian from five maximally entangled physical qubits on the boundary edges of a pentagon, whose two-fold degenerate ground state leads to an emergent logical qubit in the bulk. The inflation rule of a holographic conformal quasicrystal is found to encode the holographic code rate that determines the ratio of logical qubits to physical qubits. Generalizing SU(2) qubits to twistors as conformal spinors of SU(2,2), an H3-symmetric 5-compound of cuboctahedral A3 = D3 root polytopes is outlined. Motivated by error correction in the Hamming code, the E8 lattice is projected to the H4-symmetric quasicrystal. The 4-dimensional 600-cell is found to contain five 24-cells associated with the D4 root polytope associated with Spin(4,4). Intersection with Sp(8,R) phase space identifies three generations of conformal symmetry with an axial U(1) symmetry. A lightning review of E8(-24) phenomenology with Spin(12,4) is pursued for gravity and the standard model with a notion of CDT-inspired discretized membranes in mind. Warm dark matter beyond the standard model is briefly articulated to stem from intersecting worldvolumes related to the Leech lattice associated with the Golay code, hinting at a monstrously supersymmetric M-theory in D=26+1. A new D=27+3 superalgebra is shown to contain membranes that can give a worldvolume description of M-theory and F-theory.

Something Else Ordered Yet Non-Repeating...,

ibn Khaldun |  Mystical ⁴⁶⁹ exertion, retirement, ⁴⁷⁰ and dhikr exercises ⁴⁷¹ are as a rule followed by the removal of the veil (kashf) of sensual perception. The Sufi beholds divine worlds which a person subject to the senses cannot perceive at all. The spirit belongs to those worlds. The reason for the removal of (the veil) is the following. When the spirit turns from external sense perception to inner (perception), the senses weaken, and the spirit grows strong. It gains predominance and a new growth. The dhikr exercise helps to bring that about. It is like food to make the spirit grow. The spirit continues to grow and to increase. It had been knowledge. Now, it becomes vision. The veil of sensual perception is removed, and the soul realizes its essential existence. This is identical with perception. (The spirit) now is ready for the holy gifts, for the sciences of the divine presence, and for the outpourings of the Deity. Its essence realizes its own true character and draws close to the highest sphere, the sphere of the angels. The removal of (the veil) often happens to people who exert themselves (in mystical exercise). They perceive the realities of existence as no one else (does).

They also perceive many (future) happenings in advance. With the help of their minds and psychic powers they are active among the lower existentia, which thus become obedient to their will. The great Sufis do not think much of the removal (of the veil) and of activity (among the low exis­tentia). They give no information about the reality of any­thing they have not been ordered to discuss. They consider it a tribulation, when things of that sort happen to them, and try to escape them whenever they afflict them.⁴⁷²

The men around Muhammad practiced that kind of (mystical) exertion. They had a very abundant share in the acts of divine grace, but they did not bother with them. (The description of) the virtues of Abu Bakr, Umar, ⁴⁷³ and Ali contain much (information) to this effect. They were followed in this respect by the Sufis who are mentioned in the Risalah of al-Qushayri, ⁴⁷⁴ and their later successors.

Recent mystics, then, have turned their attention to the removal of the veil and the discussion of perceptions beyond (sensual perception). Their ways of mystical exercise in this respect differ. They have taught different methods of mortifying the powers of sensual perception and nourishing the reasoning spirit with dhikr exercises, so that the soul might fully grow and attain its own essential perception. When this happens, they believe that the whole of existence is encompassed by the perceptions of the soul, that the essences of existence are revealed to them, and that they perceive the reality of all the essences from the (divine) throne to light rain. ⁴⁷⁵ This was said by al-Ghazzali in the Kitab al-Ihya', after he had mentioned the forms of mystical exercise.

The ⁴⁷⁶ (Sufis) do not consider removal (of the veil) sound, unless it originates in straightforwardness.⁴⁷⁷ People who do not eat and who retire (from the world), such as sorcerers, Christians, and other ascetics, may obtain removal (of the veil) without the existence of straightforwardness. However, we mean only that removal (of the veil) which originates in straightforwardness. It may be compared with (the reflections of) a mirror. If it is convex or concave, the object reflected by it appears in a distorted form different from the actual form of the object, but if the mirror is flat, the object appears in its correct form. As far as the "states" impressed upon the soul are concerned, straightforwardness means to the soul what flatness means in a mirror.

The recent (Sufis) who have occupied themselves with this kind of removal (of the veil) talk about the real character of the higher and lower existentia and about the real character of the (divine) kingdom, the spirit, the (divine) throne, the (divine) seat, and similar things. Those who did not share their approach were not able to understand their mystical and ecstatic experiences in this respect. The muftis partly disapprove of these Sufis and partly accept them. Arguments and proofs are of no use in deciding whether the Sufi approach should be rejected or accepted, since it belongs to intuitive ⁴⁷⁸ experience.

 Some ⁴⁷⁹ details in explanation:

Hadith scholars and jurists who discuss the articles of faith often mention that God is separate from His creatures. The speculative theologians say that He is neither separate nor connected. The philosophers say that He is neither in the world nor outside it. The recent Sufis say that He is one with the creatures, in the sense that He is incarnate in them, or in the sense that He is identical with them and there exists nothing but Himself either (in the) whole or (in) any part (of it).

Let us explain in detail these dogmatic opinions and the real meaning of each of them, so that their significance will be clarified. We say:

Separateness has two meanings. It may mean "separateness in space and direction." ^479a The opposite, then, would be connectedness. In this sense, the statement of (separation) ⁴⁸⁰ implies (that God is in some) place, either directly - which would be direct anthropomorphism (tajsim) or in directly - which would be indirect anthropomorphism (tashbih) ⁴⁸¹ in the way in which one speaks about (God's having) direction. It has been reported that an early Muslim scholar similarly professed the separateness of God, but a different interpretation is possible.

The speculative theologians, therefore, did not acknowledge this (kind of) separateness. They said: It cannot be said that the Creator is separate from His creatures, and it cannot be said that He is connected with them, because such a statement can be made only about things in space. The statement that a particular thing ⁴⁸² can be described as devoid of one concept and at the same time of the opposite of that concept depends upon whether the description is sound in the first place (or not). If it is impossible, (the statement is) not (correct). It is, in fact, permissible to describe (a certain thing) as devoid of one concept and at the same time of the opposite of that concept. Thus, a solid substance may be described as not wise and not ignorant, not powerful and not weak, not causing harm [?] and not being harmed. ⁴⁸³ Now, the correctness of describing God as separate in the way mentioned is predicated upon the possibility of ascribing direction to Him in the proper meaning of the word, but this cannot be done with the Creator, who is free from (such a description).

This was mentioned by Ibn at-Tilimsani ⁴⁸⁴ in his commentary on the Luma' of the Imam al-Haramayn. He said: The Creator can neither be said to be separate from the world, nor to be connected with it. He is not in it and not outside it. That is what is meant by the philosophers when they say that He is neither in the world nor outside it. They base themselves (on the assumption) that there exist substances (atoms) that exist not in space. The speculative theologians did not acknowledge their (existence), because they would have to be considered equal to the Creator in the most specific qualities. That is fully dealt with in the science of speculative theology.

The other meaning of separateness is "being distinct and different." The Creator is called separate from His creatures in His essence, identity, existence, and attributes. The opposite is being one, mingled, and merged (with something else).

(God's) separateness in this sense is assumed in the dogmas of all orthodox people, such as the great mass of early Muslims, the religious scholars, the speculative theologians, and the ancient Sufis, such as the men mentioned in (al­Qushayri's) Risalah, and those who follow them.

A number of recent Sufis who consider intuitive ⁴⁸⁵ perceptions to be scientific and logical, hold the opinion that the Creator is one with His creatures in His identity, His existence, and His attributes. They often assume that this was the opinion of the philosophers before Aristotle, such as Plato and Socrates.

That is what the speculative theologians mean when they speak about the (oneness of God with His creatures) in theology and try to refute it. They do not ⁴⁸⁶ mean that there could be a question of two essences, one of which must be negated or comprised (in the other) as a part (in the whole). That would be clear distinctness, and they do not maintain that to be the case.

The oneness (assumed by the Sufis) is identical with the incarnation the Christians claim for the Messiah. It is even stranger, in that it is the incarnation of something primeval in something created and the oneness of the former with the latter.

 

Za'irajah

A branch of the science of letter magic, (practiced) among the (authorities on letter magic), is (the technique of) finding out answers from questions by means of connections existing between the letters of the expressions (used in the question). They imagine that these (connections) can form the basis for knowing the future happenings they want to know. Here we have something like puzzles and trick problems.⁸³⁵ There are many discussions of the subject by them. The most comprehensive and most remarkable discussion of it is as-Sabti's Za'irajah of the World. It has been mentioned before. Here, we shall explain what has been said about how to operate it. We shall quote the poem that, it is thought, as-Sabti wrote on the subject.⁸³⁶ Then, we shall give a description of the Za'irajah with its circle and the table written on the verso.^836a Finally, we shall reveal the truth about it. It is nothing supernatural; (the indications derived from it) result from an agreement in the wording of question and answer. It is (just) one interesting way among others, and a curious one, for finding out the answer from the question with the help of the technique called the technique of "breaking down."

From the Science of Letter Magic THE MUQADDIMAH Abd Ar Rahman bin Muhammed ibn Khaldun Very few people share the (self-scrutiny) of the Sufis, for negligence in this respect is almost universal. Pious people who do not get that far perform, at best, acts of obedience 464 freed from the juridical study of how to be satisfactory 465 and conforming (in the execution of the acts of divine worship). The (Sufis), however, investigate the results of (acts of obedience) with the help of mystical and ecstatic experience, in order to learn whether they are free from deficiency or not. Thus, it is evident that the Sufis' path in its entirety depends upon self-scrutiny with regard to what they do or do not do, and upon discussion of the various kinds of mystical and ecstatic experience that result from their exertions. This, then, crystallizes for the Sufi novice in a "station." From that station, he can progress to another, higher one. From the Science of Sufism THE MUQADDIMAH Abd Ar Rahman bin Muhammed ibn Khaldun

Why UFO Research Has Always Been Clustered With "Paranormal" Research - It's A People Filter

9:04 that's the only explanation I can get is that that if they if people are here 9:10 from another civilization then they if they've understood the the 9:15 higher the higher the finer points of quantum of quantum physics and how to 9:20 couple that from particles into beings that can do what quantum what particles 

The best way to understand their approach is by considering something else ordered yet non-repeating: "quasicrystals." A typical crystal has a regular, repeating structure, like the hexagons in a honeycomb. A quasicrystal still has order, but its patterns never repeat. (Penrose tiling is one example of this.) Even more mind-boggling is that quasicrystals are crystals from higher dimensions projected, or squished down, into lower dimensions. Those higher dimensions can even be beyond physical space's three dimensions: A 2D Penrose tiling, for instance, is a projected slice of a 5-D lattice.

9:25 can do now when I was at wright-patterson we had the flying saucers it went up I think they covered the distance from 9:32 Columbus to Detroit in something like equivalent of about 20,000 miles an hour 9:39 I don't think anyone in the canoe in the ordinary aerospace business would have 9:46 had any knowledge of what they were even talking about if you mentioned quantum 9:51 physics or or wormholes are the type of things we know now because if you went 9:59 to CERN and talked to the particle physicists they would tell you certainly some of this was possible because they 10:06 see it all the time where they think they see mass they really see they 10:12 really see energy frozen in it in a time quantum and what they're seeing is not 10:18 is this is really a frozen bundle of energy and it moves back and forth 10:25 almost without any restriction 

I thought there were enough credible stories that I may not be able to 10:32 explain them but they weren't phenomenon that were people's imagination whatever 10:41 they saw was real but I couldn't explain how it how it was real what made it real but I think what they I think they saw 10:48 what they saw near st. Louis there was a fairly large triangular object seen and 10:54 it covered the distance down to south st. Louis in some in some of its 11:00 sightings it was moving relatively benign Lee but then it it literally jumped about 20 miles in a sec couple of 11:07 seconds and I've received a lot of phone calls from the local newspapers and TV 11:13 stations is how can that be and 

I said I don't know how it can be except if you 11:18 explain it through something like a quantum physics explanation of time and 11:24 space relationships it gave you time and space travel but other than that I don't 11:30 there's no way I know that I can put the biggest rocket engine I could think of 11:36 on it it still couldn't get there at that speed and the noise and the sounds 11:42 you would make doing something like that would wake everybody up for 10 miles and 11:47 it made no sound at all it's see it starts out at hover and it literally almost disappears and pops 11:53 over here so it's not like it's not like a cartoon where it goes whoosh it's 12:00 almost like it disappears and comes up over here at least that the descriptions 12:06 that some of the police officers gave to it a lot of combat pilots routinely go 12:13 up to 7 and 8 GS but that's a very specific direction that's from your head 12:19 downward along the axis of your spine if you were to take that what's called 12:24 eyeballs in which is when you accelerate the forces this way you literally would 12:32 have your eyeballs and compressed out of their sockets and you have brain damage so that the G's the do that might be in 12:40 the level of order of so no that's not physically possible for any even even insects to take that level 12:48 of acceleration even over a short period of time you might get in an automobile 12:53 accident you might get a hundred two hundred and fifty G's and that's when the car is completely crushed so that's 13:00 what happened would happen to a human being if that were a conventional force accelerator so it's not a conventional 13:06 force accelerator because if there's people in human beings in them or something being in them that isn't 13:13 crushed then it has to be a different way of doing it the hard part is to find 13:19 a way to physically do that 

you know there are people who have been experimenting with zero-point energy or 13:25 try to tap zero-point energy for years every once in a while someone will do it 13:30 accidentally they'll call it cold fusion but I don't think it's cold fusion I just think it's a zero-point energy tap 13:36 except for three people that I know no 13:41 one has been able to control it when it happens it happens for a short period of time 13:47 and it's almost always destructive it's like drilling a hole into the base of Grand Coulee Dam and all of a sudden 13:54 this jet of water comes out that literally has enough pressure to cut you in half without a valve on it you can't 14:02 shut it off does one guy that that that 14:07 a friend of mine actually visited in Ann Arbor Michigan that was I consider a mathematical genius that actually 14:14 figured out a way to control it he was so paranoid he divorced his wife 14:20 left his wife and children and went in hiding because he was terrified that someone 14:26 would would kill him for the knowledge that he had the ability to tap this whenever he chose to and control it we 14:33 don't know worried we haven't seen him in five years I don't worry is you know right now today you've got an energy 

14:39 problem with the price of oil what do you think would happen if you introduced 14:45 an ability to attempt zero-point energy represents about 40 to 50 megawatts of 14:53 power per cubic inch of space that's a lot of power 15:00 that's 4600 million watts of power and 15:07 if you could tap it at will then no one 15:12 would have to sell gasoline or oil anymore you would just tap into it it would be it would be like taking and 15:20 going out to the Great Lakes and taking out one drop and using it it would you'd 15:25 hardly miss it and since it permeates the whole universe and it continually 15:31 fluctuates as it as as that as the matter and antimatter interact it's not 15:40 like it's a steady lake it's um you see it's a pool the size of the universe so 15:45 you'd never for what we've used before you never even miss it the only thing this one guy claimed that happened is if 15:52 you bottle it and move it to another location and release it he sounded 16:00 exactly like mr. Spock he said you create a tear in the in the time time 16:07 domain of the of local space and actually caused a problem which he 16:13 claims he did and he will never do it again which is bottle and move it the other part is that you're knock it 16:19 doesn't work on conventional jet engines one has to create an actual zero point 16:25 energy engine to do that this one guy in Ann Arbor Mich Michigan had one running in his basement 16:30 not connected to any power source whatsoever sitting in the middle of a table and it had been running for a year 

Trust Neither Your Senses Or Your Ordinary Waking State

Consciousness Come After Language?

OCBBM | The Features of Consciousness - I. Spatialization. The first and most primitive aspect of consciousness is what we already have had occasion to refer to, the paraphrand of almost every mental metaphor we can make, the mental space which we take over as the very habitat of it all. If I ask you to think of your head, then your feet, then the breakfast you had this morning, and then the Tower of London, and then the constellation of Orion, these things have the quality of being spatially separated; and it is this quality I am here referring to. When we introspect (a metaphor of seeing into something), it is upon this metaphorical mind-space which we are constantly renewing and 'enlarging' with each new thing or relation consciousized. In Chapter 1, we spoke of how we invent mind-space inside our own heads as well as the heads of others. The word invent is perhaps too strong except in the ontological sense. We rather assume these 'spaces' without question. They are a part of what it is to be conscious and what it is to assume consciousness in others. Moreover, things that in the physical-behavioral world do not have a spatial quality are made to have such in consciousness. Otherwise we cannot be conscious of them. This we shall call spatialization. Time is an obvious example. If I ask you to think of the last hundred years, you may have a tendency to excerpt the matter in such a way that the succession of years is spread out, probably from left to right. But of course there is no left or right in time. There is only before and after, and these do not have any spatial properties whatever — except by analog. You cannot, absolutely cannot think of time except by spatializing it. Consciousness is always a spatialization in which the diachronic is turned into the synchronic, in which what has happened in time is excerpted and seen in side-by-sideness. (leading to other problems and limitations previously noted (Bearden's 4th Law of Logic)) This spatialization is characteristic of all conscious thought. If you are now thinking of where in all the theories of mind my particular theory fits, you are first habitually 'turning' to your mind-space where abstract things can be 'separated out' and 'put beside' each other to be 'looked at' — as could never happen physically or in actuality. You then make the metaphor of theories as concrete objects, then the metaphor of a temporal succession of such objects as a synchronic array, and thirdly, the metaphor of the characteristics of theories as physical characteristics, all of some degree so they can be 'arranged' in a kind of order. And you then make the further expressive metaphor of 'fit'. The actual behavior of fitting, of which 'fit' here is the analog in consciousness, may vary from person to person or from culture to culture, depending on personal experience of arranging things in some kind of order, or of fitting objects into their receptacles, etc. The metaphorical substrate of thought is thus sometimes very complicated, and difficult to unravel. But every conscious thought that you are having in reading this book can by such an analysis be traced back to concrete actions in a concrete world. 2. Excerption. In consciousness, we are never 'seeing' anything in its entirety. This is because such 'seeing' is an analog of actual behavior j and in actual behavior we can only see or pay attention to a part of a thing at any one moment. And so in consciousness. We excerpt from the collection of possible attentions to a thing which comprises our knowledge of it. And this is all that it is possible to do since consciousness is a metaphor of our actual behavior. Thus, if I ask you to think of a circus, for example, you will first have a fleeting moment of slight fuzziness, followed perhaps by a picturing of trapeze artists or possibly a clown in the center ring. Or, if you think of the city which you are now in, you will excerpt some feature, such as a particular building or tower or crossroads. Or if I ask you to think of yourself, you will make some kind of excerpts from your recent past, believing you are then thinking of yourself. In all these instances, we find no difficulty or particular paradox in the fact that these excerpts are not the things themselves, although we talk as if they were. Actually we are never conscious of things in their true nature, only of the excerpts we make of them. The variables controlling excerption are deserving of much more thought and study. For on them the person's whole consciousness of the world and the persons with whom he is interacting depend. Your excerptions of someone you know well are heavily associated with your affect toward him. If you like him, the excerpts will be the pleasant things; if not, the unpleasant. The causation may be in either direction. How we excerpt other people largely determines the kind of world we feel we are living in. Take for example one's relatives when one was a child. If we excerpt them as their failures, their hidden conflicts, their delusions, well, that is one thing. But if we excerpt them at their happiest, in their idiosyncratic delights, it is quite another world. Writers and artists are doing in a controlled way what happens 'in' consciousness more haphazardly. Excerption is distinct from memory. An excerpt of a thing is in consciousness the representative of the thing or event to which memories adhere, and by which we can retrieve memories. If I wish to remember what I was doing last summer, I first have an excerption of the time concerned, which may be a fleeting image of a couple of months on the calendar, until I rest in an excerption of a particular event, such as walking along a particular riverside. And from there I associate around it and retrieve mem-ories about last summer. This is what we mean by reminiscence, and it is a particular conscious process which no animal is capable of. Reminiscence is a succession of excerptions. Each so-called association in consciousness is an excerption, an aspect or image, if you will, something frozen in time, excerpted from the experience on the basis of personality and changing situational factors. 3. The Analog 'I'. A most important 'feature' of this metaphor 'world' is the metaphor we have of ourselves, the analog 'I', which can 'move about' vicarially in our 'imagination', 'doing'things that we are not actually doing. There are of course many uses for such an analog 'I'. We imagine 'ourselves' 'doing' this or that, and thus 'make' decisions on the basis of imagined 'outcomes' that would be impossible if we did not have an imagined 'self' behaving in an imagined 'world'. In the example in the section on spatialization, it was not your physical behavioral self that was trying to 'see' where my theory 'fits' into the array of alternative theories. It was your analog 'I'. If we are out walking, and two roads diverge in a wood, and we know that one of them comes back to our destination after a much more circuitous route, we can 'traverse' that longer route with our analog 'I' to see if its vistas and ponds are worth the longer time it will take. Without consciousness with its vicarial analog 'I', we could not do this. 4. The Metaphor 'Me'. The analog 'I' is, however, not simply that. It is also a metaphor 'me'. As we imagine ourselves strolling down the longer path we indeed catch 'glimpses' of 'ourselves', as we did in the exercises of Chapter 1, where we called them autoscopic images. We can both look out from within the imagined self at the imagined vistas, or we can step back a bit and see ourselves perhaps kneeling down for a drink of water at a particular brook. There are of course quite profound problems here, particularly in the relationship of the 'I' to the 'me'. But that is another treatise. And I am only indicating the nature of the problem. 5. Narratization. In consciousness, we are always seeing our vicarial selves as the main figures in the stories of our lives. In the above illustration, the narratization is obvious, namely, walk-ing along a wooded path. But it is not so obvious that we are constantly doing this whenever we are being conscious, and this I call narratization. Seated where I am, I am writing a book and this fact is imbedded more or less in the center of the story of my life, time being spatialized into a journey of my days and years. New situations are selectively perceived as part of this ongoing story, perceptions that do not fit into it being unnoticed or at least unremembered. More important, situations are chosen which are congruent to this ongoing story, until the picture I have of myself in my life story determines how I am to act and choose in novel situations as they arise. The assigning of causes to our behavior or saying why we did a particular thing is all a part of narratization. Such causes as reasons may be true or false, neutral or ideal. Consciousness is ever ready to explain anything we happen to find ourselves doing. The thief narratizes his act as due to poverty, the poet his as due to beauty, and the scientist his as due to truth, purpose and cause inextricably woven into the spatialization of behavior in consciousness. But it is not just our own analog 'I' that we are narratizing; it is everything else in consciousness. A stray fact is narratized to fit with some other stray fact. A child cries in the street and we narratize the event into a mental picture of a lost child and a parent searching for it. A cat is up in a tree and we narratize the event into a picture of a dog chasing it there. Or the facts of mind as we can understand them into a theory of consciousness. 6. Conciliation. A final aspect of consciousness I wish to mention here is modeled upon a behavioral process common to most mammals. It really springs from simple recognition, where a slightly ambiguous perceived object is made to conform to some previously learned schema, an automatic process sometimes called assimilation. We assimilate a new stimulus into our conception, or schema about it, even though it is slightly different. Since we never from moment to moment see or hear or touch things in exactly the same way, this process of assimilation into previous experience is going on all the time as we perceive our world. We are putting things together into recognizable objects on the basis of the previously learned schemes we have of them. Now assimilation consciousized is conciliation. A better term for it might be compatibilization, but that seems something too rococo. What I am designating by conciliation is essentially doing in mind-space what narratization does in mindtime or spatialized time. It brings things together as conscious objects just as narra-tization brings things together as a story. And this fitting together into a consistency or probability is done according to rules built up in experience. In conciliation we are making excerpts or narratizations compatible with each other, just as in external perception the new stimulus and the internal conception are made to agree. If we are narratizing ourselves as walking along a wooded path, the succession of excerpts is automatically made compatible with such a journey. Or if in daydreaming two excerpts or narratizations happen to begin occurring at the same time, they are fused or conciliated. If I ask you to think of a mountain meadow and a tower at the same time, you automatically conciliate them by having the tower rising from the meadow. But if I ask you to think of the mountain meadow and an ocean at the same time, conciliation tends not to occur and you are likely to think of one and then the other. You can only bring them together by a narratization. Thus there are principles of compatibility that govern this process, and such principles are learned and are based on the structure of the world. Let me summarize as a way of 'seeing' where we are and the direction in which our discussion is going. We have said that consciousness is an operation rather than a thing, a repository, or a function. It operates by way of analogy, by way of constructing an analog space with an analog 'I' that can observe that space, and move metaphorically in it. It operates on any reactivity, excerpts relevant aspects, narratizes and conciliates them together in a metaphorical space where such meanings can be manipulated like things in space. Conscious mind is a spatial analog of the world and mental acts are analogs of bodily acts. Consciousness operates only on objectively observable things. Or, to say it another way with echoes of John Locke, there is nothing in consciousness that is not an analog of something that was in behavior first. This has been a difficult chapter. But I hope I have sketched out with some plausibility that the notion of consciousness as a metaphor-generated model of the world leads to some quite definite deductions, and that these deductions are testable in our own everyday conscious experience. It is only, of course, a beginning, a somewhat rough-hewn beginning, which I hope to develop in a future work. But it is enough to return now to our major inquiry of the origin of it all, saving further amplification of the nature of consciousness itself for later chapters. If consciousness is this invention of an analog world on the basis of language, paralleling the behavioral world even as the world of mathematics parallels the world of quantities of things, what then can we say about its origin? We have arrived at a very interesting point in our discussion, and one that is completely contradictory to all of the alternative solutions to the problem of the origin of consciousness which we discussed in the introductory chapter. For if consciousness is based on language, then it follows that it is of a much more recent origin than has heretofore been supposed. Consciousness come after language! The implications of such a position are extremely serious.

 

Vision Neither Directly Or Accurately Reports Reality

frontiersin |  Sensory perception is often the most striking proof of something factual—when we perceive something, we interpret it and take it as “objective”, “real”. Most obviously, you can experience this with eyewitness testimonies: If an eyewitness has “seen it with the naked eye”, judges, jury members and attendees take the reports of these percepts not only as strong evidence, but usually as fact—despite the active and biasing processes on basis of perception and memory. Indeed, it seems that there is no better, no more “proof” of something being factual knowledge than having perceived it. The assumed link between perception and physical reality is particularly strong for the visual sense—in fact, we scrutinize it only when sight conditions have been unfortunate, when people have bad vision or when we know that the eyewitness was under stress or was lacking in cognitive faculties. When people need even more proof of reality than via the naked eye, they intuitively try to touch the to-be-analyzed entity (if at all possible) in order to investigate it haptically. Feeling something by touch seems to be the ultimate perceptual experience in order for humans to speak of physical proof (Carbon and Jakesch, 2013).

We can analyze the quality of our perceptual experiences by standard methodological criteria. By doing so we can regularly find out that our perception is indeed mostly very reliable and also objective (Gregory and Gombrich, 1973)—but only if we employ standard definitions of “objective” as being consensual among different beholders. Still, even by meeting these methodological criteria, we cannot give something in evidence about physical reality. It seems that knowledge about the physical properties of objects cannot be gained by perception, so perception is neither “veridical” nor “valid” in the strict sense of the words—the properties of the “thing in itself” remain indeterminate in any empirical sense (Kant, 1787/1998). We “reliably” and “objectively” might perceive the sun going up in the morning and down in the evening; the physical relations are definitely different, as we have known at least since Nicolaus Copernicus’s proposed heliocentricism—it might also be common sense that the Earth is a spheroid for most people, still the majority of people have neither perceived the Earth as spherical nor represented it like that; one reason for this is that in everyday life contexts the illusion of a plane works perfectly well to guide us in the planning and execution of our actions (Carbon, 2010b).

Limitations of the Possibility of Objective Perception

The limitations of perception are even more far reaching: our perception is not only limited when we do not have access to the thing in itself, it is very practically limited to the quality of processing and the general specifications of our perceptual system. For instance, our acoustic sense can only register and process a very narrow band of frequencies ranging from about 16 Hz–20 kHz as a young adult—this band gets narrower and narrower with increasing age. Typically, infrasonic and ultrasonic bands are just not perceivable despite being essential for other species such as elephants and bats, respectively. The perception of the environment and, consequently, the perception and representation of the world as such, is different for these species—what would be the favorite music of an elephant, which preference would a bat indicate if “honestly asked”? What does infrasonic acoustics sound and feel like? Note: infrasonic frequencies can also be perceived by humans; not acoustically in a strict sense but via vibrations—still, the resulting experiences are very different (cf. Nagel, 1974). To make such information accessible we need transformation techniques; for instance, a Geiger-Müller tube for making ionizing radiation perceivable as we have not developed any sensory system for detecting and feeling this band of extremely high frequency electromagnetic radiation.

But even if we have access to given information from the environmental world, it would be an illusion to think of “objective perception” of it—differences in perception across different individuals seem to be obvious: this is one reason for different persons having different tastes, but it is even more extreme: even within a lifetime of one person, the perceptual qualities and quantities which we can process change. Elderly people, for instance, often have yellowish corneas yielding biased color perception reducing the ability to detect and differentiate bluish color spectra. So even objectivity of perceptions in the sense of consensual experience is hardly achievable, even within one species, even within one individual—just think of fashion phenomena (Carbon, 2011a), of changes in taste (Martindale, 1990) or the so-called cycle of preferences (Carbon, 2010a)! Clearly, so-called objective perception is impossible, it is an illusion.

Illusory Construction of the World

The problem with the idea of veridical perception of the world is further intensified when taking additional perceptual phenomena, which demonstrate highly constructive qualities of our perceptual system, into account. A very prominent example of this kind is the perceptual effect which arises when any visual information which we want to process falls on the area of the retina where the so-called blind spot is located 

Interestingly, visual information that is mapped on the blind spot is not just dropped—this would be the easiest solution for the visual apparatus. It is also not rigidly interpolated, for instance, by just doubling neighbor information, but intelligently complemented by analysing the meaning and Gestalt of the context. If we, for example, are exposed to a couple of lines, the perceptual system would complement the physically non-existing information of the blind spot by a best guess heuristic how the lines are interconnected in each case, mostly yielding a very close approximation to “reality” as it uses most probable solutions. Finally, we experience clear visual information, seemingly in the same quality as the one which mirrors physical perception—in the end, the “physical perception” and the “constructed perception”, are of the same quality, also because the “physical perception” is neither a depiction of physical reality, but is also constructed by top-down processes based on best guess heuristic as a kind of hypothesis testing or problem solving (Gregory, 1970).

Binaural Beats Exist Solely As A Consequence Of The Interaction Of Perceptions Within The Brain

amadeux  |  If two tuning forks of slightly different pitch are struck simultaneously, the resulting sound waves and wanes periodically. The modulations are referred to as beats; their frequency is equal to the difference between the frequencies of the original tones. For example, a tuning fork with a characteristic pitch of 440 hertz, if struck at the same time, will produce beats with a frequency of six hertz.

In modern investigations tuning forks are replaced by electronic oscillators, which can supply tones of precisely controlled pitch, purity, and intensity. Beats are produced when the outputs of two oscillators tuned to slightly different frequencies are combined electrically and applied to a loudspeaker. Alternatively, the signals can be applied individually to separate speakers and the beats will still be heard. The result is the same whether the tones are combined electrically and then converted into sound, or converted into sound separately and then combined.

A quite different phenomenon results when stereophonic earphones are used and the signals are applied separately to each ear. Under the right circumstances beats can be perceived, but they are of an entirely different character. They are called binaural beats, and in many ways they are more interesting than ordinary beats, which in this discussion will be called monaural.

Monaural beats can be heard with both ears, but one ear is sufficient to perceive them. Binaural beats require the combined action of both ears. They exist as a consequence of the interaction of perceptions within the brain, and they can be used to investigate some of the brain’s processes.

The physical mechanism of monaural beats is a special case of wave interference. At any instant the amplitude of the resulting sound is equal to the algebraic sum of the amplitudes of the original tones. The signals are reinforced when they are in phase, that is, when the peaks and nulls of their waves coincide. Destructive interference diminishes the net amplitude when the waves are in opposition. The pure tones used in these experiments are described by sine waves’ the resulting beats are slowly varying functions similar to, but not precisely conforming to, a sine wave.

A beat frequency of about six hertz, as in the example given above, would sound something like vibrato in music (although vibrato is frequency modulation rather than amplitude modulation). If the interval between frequencies is made smaller, very slow beats can be produced, down to about on per second, to perceive. Rapid beats, up to about 30 hertz, are heard as roughness superimposed on the sound, rather like a Scotsman’s burr. With still greater intervals beats are not heard; the two tones are perceived separately.

Beats are rarely encountered in nature because in nature sustained pure tones are rare. They abound, however, in mechanical devices. In an airplane, jet engines operating at slightly different speeds may produce a very strong-beat, often recognized only as a feeling “in the pit of the stomach.” Acoustical engineers can filter out the whine of the engines, but the slow vibrations are difficult to suppress. Occupants of apartment houses may be annoyed by beats produced by machinery, such as two blowers running at different speeds, but they will have a hard time finding the source.

On the other hand, beats are used to advantage where frequencies must be determined precisely. Electrical engineers compare the output of a test oscillator with that of a standard oscillator by detecting the beats produced when their signals are combined. The tuning of pianos is another process that depends on beats. Typically the piano tuner will first listen for the beats produced by a tuning fork of 440 hertz and the A above middle C, and tighten or loosen the A wire until the beats slow to zero. He then strikes the A key and the D key below it and tunes the latter wire until 10 beats per second are heard. That frequency is produced by the interaction of the A string’s second harmonic, or second multiple (2 x 44 0 = 180), and the D string’s third harmonic (3 x 290 = 870). In this fashion, key by key, the piano is tuned; in theory it could be done even by someone who is tone-deaf.

Binaural beats were discovered in 1839 by a German experimenter named H. W. Dove, but as late as 1915 they were considered a trivial special case of monaural beats. It was argued that each ear was hearing sounds intended for the other. This extraneous result could be eliminated by placing the tuning forks in separate rooms, with the subject in a third room between them, and guiding the sounds through tubes to each ear. It was necessary to carefully seal each tube to the head, however, and another objection was raised; that sound presentation to one ear could be conducted through the skull to the other.

Bone conduction is well established, and indeed some hearing aids operate on this principle, although sound is attenuated a thousandfold from ear to ear. The possible contribution of bone conduction to the perception of binaural beats is eliminated, however, by the use of modern stereophonic earphones. Such earphones have padding, often liquid filled, to insulate the head from the sound source, and are designed explicitly to prevent conduction effects. Indeed, stereophonic recordings played through earphones can sound unnatural because the instruments seem too isolated.

The difference most immediately apparent between monaural and binaural beats is that binaural beats can be heard only when the tones used to produce them are of low pitch. Binaural beats are best perceived when the carrier frequency is about 440 hertz; above that frequency they become less distinct and above about 1,000 hertz they vanish altogether. No person I have tested reports hearing beats for frequencies above 900 hertz. Experimental conditions, particularly the intensity of the sounds and the type of earphones used can affect the results, however, and other investigators report detecting beats produced by tones up to almost 1,500 hertz. At the other end of the scale beats also become elusive. Below about 90 hertz the subject may confuse the beats with the tones used to produce them.

J. C. R. Licklider of the Massachusetts Institute of Technology developed a technique when he was working at Harvard University to measure a spectrum of binaural beats [see upper illustration on page 102]. He adopted the frequency of one oscillator until the interval was large enough so that the beats seemed “rough”; then he noted the frequency of the unchanged reference oscillator. Next he changed the setting of the reference oscillator and repeated the procedure. In this way the range of perception of each subject was recorded.

Another distinguishing characteristic of binaural beats is their muffled sound. Monaural beats produced with sounds of equal intensity pulse from loudness to silence, as their wave form would suggest. Binaural beats, on the other hand, are only a slight modulation of a loud background. I have tried to estimate the depth of the modulation, and it seems to be about three decibels, or about a tenth of the loudness of a whisper. In order to help subjects recognize these relatively faint effects I usually present signals with monaural beats and then suddenly change to the binaural mode. With tones of about 440 hertz it usually takes two or three seconds for the subject to recognize the binaural beats.
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