A: From a crossing in the sky to a crossing on land . . .
Antonio Cassella (2018i) hypothesized that Sages from the Egyptian "House of Thoth" remained impressed in the 27th. century BCE (Before the Common Era) by the fact that the asterism known as the "Northern Cross" (now in the Cygnus Constellation) pointed at the crossing of two circles that contained more than three points each.
The Northern Circle is formed by Deneb, Sadr (or Gamma Cygni), Albireo, and the three stars of Orion's Belt; whereas the Southern Circle is made by Epsilon Cygni, Sadr, Delta Cygni, and Sirius.
The crossing of the two circles determines a west-to-east baseline, which parallels the look of Giza's Sphinx toward the rising sun.
Khufu, the second Pharaoh of the IV Dynasty, must have planned to replicate on Egyptian soil the disposition of the two astronomical circles . Indeed, three sons of his--Khafre, Djedefre, and Menkaure--followed his example of building massive pyramids in correspondence to the two celestial circles.
Cassella (2018i) hypothesized also that the two crossing circles and the 4 pyramids on them made a first-degree triangulation network that allowed Pharaohs to re-chart key landmarks after a prodigious Nile flooding was over.
B: . . . and to the nature of nature and the mind
Why ancient Egyptians valued Deneb and the Northern Cross
After aligning the 3 wing stars of the Cygnus constellation in the "Northern Cross" (and not Orion's belt) with the 3 pyramids of Giza, Cassella (2018i) corroborated (and anyone can do it) that:
- the wing stars of the Northern Cross (Delta Cygni, Sadr, and Epsilon Cygni) point at a circle of triangulation of ancient Egypt (in the 27th. century BCE) south of Giza;
- Deneb, Sadr, and Albireo (in the vertical line of the cross) point at a circle of triangulation north of Giza;
- on land, the two circles cross each other twice, on the tip of Khafre's Pyramid at the West and a few meters from the ruins of the temple of Isis/Sirius on the East, within the south-eastern part of modern Cairo;
- the common base of the two triangulation-circles is 14.1 miles;
- the two crossings make a metaphor for the principle of Ubiquity and Coincidence in quantum computing;
- the location of Khufu's, Khafre's, and Menkaure's pyramids, together with the temple of Isis/Sirio, reflect the land plotting of the southern triangulation-circle;
- the location of Djedefre's and Khafre's pyramids, of the top of the Gebel-Ghibli hill (the star Albireo), and of Orion's belt confirms the existence of the northern circle;
- the common base of the two circular triangulations is aligned with the look of the Sphinx toward the east;
- the two circles imply each four points or more, which goes beyond the theorem by which three points define a particular circle; and, finally,
- the diameter of the northern circle (about 23 miles) suggests that 47 centuries ago, some priests of the Egyptian "House of Thoth" knew of the curvature of the Earth and the length of its radius.
In the view of Cassella (2018i), the head of Giza's Sphinx and of the Lion Constellation represent the classical computing (or the 1st. attention) overdeveloped in high-functioning autistics; its feline body, the quantum coherence (or the 2nd. attention) impaired in autism; and the whole Sphinx represents the de-coherence of the 3rd. attention impaired in schizophrenia. (Cassella hypothesizes that the Sphinx was built about 10-11 millennia ago as a representation of a saber-toothed tiger and of the terrifying power of quantum computing).
By looking at the shared baseline of the two triangulation-circles, Giza's Sphinx (called "Father of terror" or "'Abu alhawl" in Arabic) sustains five hypotheses:
- The points inside the crossing of the two triangulation circles around Cairo validate the principle that "an object may exist simultaneously in two places (Ubiquity within the 2nd. attention); and the two circles validate the principle that 'two objects may share the same space at the same time (Coincidence at the end of the 2nd. attention or the beginning of the third attention);
- South of the eastern end of the baseline, should lie the ruins of a temple to Isis (Sirius, Sopdet, Venus) or the 2nd. attention;
- 1.8 miles up from the eastern end of the baseline, along the eastern side of the northern circle, three temples (buried now) would stand for the 3 stars of Orion's Belt;
- after a pharaoh of Dynasty IV died and his original ka returned home, his spirit (ba) and rigid body went from Orion-Osiris-Sah on land to Sopdet-Isis-Venus, before crossing the Nile toward the Sphinx;
- from the Sphinx, his mummy went to his pyramidal tomb, while his ba spirit went to the Lion asterism, before crossing the Milky Way in reaching the three stars of Orion's belt, his Third Point, and his resurrection.
Unveiling the secrets hidden in autistic minds, in Moses' "Ark of the Covenant," in Giza's monuments, and in Leonardo's artistic feats may help us transform into opportunities of growth the dangers of global warming, terrorism, and any major ill. As explained further on this page, the bad consequences of letting the temperature of the lower atmosphere of the Earth rise beyond 2 degrees Celsius (3.6 degrees Fahrenheit), within global warming, may surpass what the IPCC (Intergovernmental Panel on Climate Change) has envisioned so far.
The havoc that might soon hit human civilization derives mainly from the accelerated exploitation of the carbon of biomass buried since the Devonian. As with all hydrocarbons, also the oil and gas under Greenland make the devil's excrement. Its eventual exploitation will deepen the autistic or schizophrenic trap that will frighten our descendants, before covering them with the mantle of a premature death. Knowledge of our autistic facet, opposed to our schizophrenic mind, however, could help us exit the trap of using fossil fuels.
The logos heuristics described here shows that autism is caused by the mental difficulty to . . .
- reach two or more places simultaneously and . . .
schizophrenia, by the difficulty to . . .
- share the same space at the same time with another object.
In other words, autism and schizophrenia are linked respectively to the mental deficiency of infinity and nothingness (transcendental zero), the two hinges of quantum computing in the human mind and the universe.
The journey through the infinite toward nothingness (or the coherence phase of quantum computing) in the funeral of the pharaohs of Dynasty IV suggests that the Sphinx represents the Third Attention, or the light at the end of the tunnel. As such, the Sphinx may be considered a metaphor for the reality of quantum decoherence, which favors the mental resurrection ascribed to the rise of the Third Point in individuals, their culture, and global civilization.
Although the previous hypotheses may seem sheer madness to some, they match ancient beliefs about the roots of nature and of the social organization behind Progress. Within a hypothetical example, after receiving from priests of the "House of Thoth" (perhaps following orders of the Queen-Pharaoh Hatshepsut) Egyptian teachings about the nature of the human mind and nature, Moses guarded his Wisdom in two crystals/stones (Thummim and Urim), which were left in the Ark of the Covenant that was inherited by King Solomon.
In the 10th. century BCE, the visiting Queen of Sheba saw the Solomonic tokens and seized their importance. Her sailors might have passed the meaning of the Egyptian/Israeli teachings to Sages in India and in the Mesoamerica inhabited by the Olmecs. From them, the secrets of the House of Thoth were passed to a few Sages among the Maya/Toltecs/Mexica-Aztecs; and finally to the Yaqui shaman don Juan, who showed them to the anthropologist Carlos Castaneda in the early 60s.
As in the Chinese game "Whispers" of accumulation of distortions, however, Castaneda understood too late the cognitive implications of the teachings of don Juan. As it seems, professors at UCLA (University of California at Los Angeles) and modern science have not absorb yet the importance of the infinity hurt in autism and of the nothingness impaired in schizophrenia.
Still, Cassella believes that autistics, schizophrenics, and especially the return of Quetzalcoatl will convince scientists unaware of the truths hidden in any Sacred Text and masterpiece of the arts. With the rise of the third point, anyone can pass from reading and reading, to reading; in the wake of a man- or a woman-of-knowledge.
Such was, for example, the path of Moses's and Leonardo da Vinci's hidden teachings; the aim of the next section.
C: The Ark of the Covenant and the Fight for the Standard
The logos heuristics, and the 'Ark of the Covenant'
The logos heuristics, and the 'Ark of the Covenant'
The logos heuristics, and the 'Ark of the Covenant'
If the "Ark of the Covenant" in Axum (Ethiopia) is not 'The Ark', it represents nonetheless (Cassella, 2019a) the 3 steps of our quantum capacity to solve serendipitously a problem by valuing three ideas:
- VALUE THE UNCHANGING INTEGRITY OF OUR MEMORY, Thummim, the Crook, the 1st. attention spared in high-functioning autism (or the classical computing in which 'yes' wins over 'no');
- IMAGINE NEW MEMORIES, Urim, the Flail, the union of 'yes' and 'no', the ambiguity of quantum coherence (or the 2nd. attention wronged in autism); and
- CHOOSE A 'PATH WITH HEART', with the Third Point that may follow the decoherence of the 3rd. Attention.
Moses sewed the Thummim and Urim crystals on the ephod of his brother Aaron; and placed that vestment in the Ark because Egyptian Sages had shown him the secret of the crossing of the Crook and the Flail on Osiris' chest. That secret is also hidden in the question placed by Medieval Scholastic philosophy, "How many angels (the infinite of Ubiquity) can dance on the tip (the nothingness of Coincidence) of a pin (Unity)?"
Decoherence completes the union of the Crook and the Flail, of the crystals Thummim and Urim, nature's nature, and the dance of unity with infinity and nothingness :
- 1/0 = ♾ = 1st. attention;
- 1/♾ = 0 = 2nd.attention/coherence/going; and
- ♾ x 0 = 1 = 3rd. attention/decoherence/returning.
Nothingness in decoherence may be viewed as the part of quantum computing (2) that escapes madness or as the beginning of the 3rd. attention.
The Dance of science, philosophy, art, and religion might help our escape from madness so as to unite infinity with nothingness, in the arms of the Third Attention and in the dream of Progress proposed about two centuries ago by the Blessed Roveretan priest Antonio Rosmini (the theme is developed in section E of this page).
The dance among unity, infinity, and nothingness feeds our perception of beauty. We may find beauty in a masterpiece, in reading a Sacred Text, and in the opportunity to win with the angels of Ubiquity and Coincidence--placed by Moses on the top of the Ark of the Covenant.
Leonardo's 'Natività' and 'Fight for the Standard'
The logos heuristics, and the 'Ark of the Covenant'
The logos heuristics, and the 'Ark of the Covenant'
Because he knew about infinity and nothingness, Leonardo da Vinci placed the two corresponding angels at the top of his vanished 'Nativity' painting.
The 'Natività' ('Nativity scene', at the left) is kept in the church of 'Santa Maria dei Canali' at Tortona (AL, Italy):
Without the cloud, the angels of Ubiquity and Coincidence would stay inside the stable; and without the angels, the cloud would stay outside. Together, the angels and the cloud stay inside and outside at once (Ubiquity) and share the same space at the same time (Coincidence).
In the unrecognized Nativity, . . .
- Joseph makes the 1st. attention, or the Crook;
- Mary, the 2nd. attention, or the Flail; and
- Jesus, the 3rd. Attention, or the fruit of the virtual union of the Crook and the Flail in people that follow the Will of their Third Point.
Leonardo placed the three modes of attention of nature and the human mind in all his works. For example, in his vanished mural 'Lotta per lo Stendardo' ('Fight for the Standard'), the center piece of the ruined 'Battaglia di Anghiari' ('Battle of Anghiari'), the confrontation (1st. attention) depicted by Leonardo's Third Attention exalts the losers-to-be (the Milanese) and the winners-to-be (the Florentines) simultaneously (2nd. attention): a silent and elegant trick, which Vasari would not destroy (Vasari, 1550).
Giorgio Vasari hid the center of the "Fight for the Standard" at 7.035 meters below the center of his own "Battaglia di Marciano" in the Hall of the 500, at Florence's Palazzo Vecchio (Cassella, 2017c).
Cassella (2017c) found that drilling a hole at 0.915 meters from the floor, on the vertical that comes down from the throat of the warrior dying on the ground of the Battle of Marciano, will uncover the throat of the warrior dying on the ground of the Fight for the Standard.
The crossing of two primary triangulations in 26th century BCE Egypt, the Ark of the Covenant, and Leonardo's "Nativity" suggest that the legend of Quetzalcoatl's and the Love of the Goddess Mother reflect the distributed hierarchy of the human brain. The next section shows Quetzalcoatl's voyage from our autistic to our schizophrenic and back to a renovated autistic facet.
D: Tonantzin Guadalupe hugs winners and losers
THE LEGEND OF THE GOING AND RETURNING VOYAGE OF QUETZALCOATL
Although he goes as 'Coatl-quetzal' from the perception of shared spacetime (on the earth that supports the serpent-coatl) to the sky of madness that welcomes the bird-quetzal, 'Quetzalcoatl' will escape madness. As a metaphor for Progress, he (or she) will return from the meeting of infinity and nothingness in the superior conjunction toward a spacetime renewed in the inferior conjunction.
We should also consider the degeneration of our ability to think (quantum computing, learning, Moses' Urim, Zechariah's No'am, or the Aztecs' Nagual) between autistic need (Thummim, classical computing) and schizophrenic chance. There is more to nature and the human mind than the less-than-perfect relationship between perfect need and imperfect chance proposed by Charles Darwin. As with the mad, we have become blind to the distributed hierarchy that readjusts reality.
The research of Antonio Cassella aims at more than preventing the increase of autistic order in babies and psychotic disorder in adults. Grasping the roots of autism and of the schizophrenia at the center of psychosis will allow us to offset the destruction brought by the Four Horsemen of Apocalypse:
- terrorism;
- global warming;
- autism; and
- schizophrenia.
The two last riders could help us control the first two horsemen. Besides avoiding the destruction of human civilization, the comprehension of the cause of autism and schizophrenia may allow us to seek and find a new horizon of social problem-solving, learning, and progress for our grandchildren.
Wise ones, among Mesoamerican Olmecs, Maya, and Toltecs/Aztecs believed that the 'bird-serpent' "Quetzal-coatl" (at the left in the figure above) had the capacity to leave behind the memory of classical reality (or spacetime), go toward madness, into mutually exclusive imaginary worlds (quantum hyperspace), and return (right) through the hyperspace of quantum computing into a renewed spacetime.
The cognitive ability of nonautistic children to go with quantum coherence and to return with quantum decoherence is innate.
Because any person has an innate endowment, any person can deepen the implications of the 5 wounds of Christ, a fact shown to us by the blessed Antonio Rosmini about two centuries ago.
E: THE FIVE WOUNDS OF CHRIST
THERE IS NO RESURRECTION WITHOUT CONFRONTATION
The figure above mentions the sensible thief called "Dimas," who was crucified to the right of Christ, and the crazy thief called "Gestas," crucified at Christ's left. Luke (23-43) does not mention names. He implied, however, that Gestas remained impenitent.
The same figure also shows Cassella's quantum and mystical interpretation of that account:
- The beam of the confrontation between the good thief and the bad thief carries in its center the arithmetical zero of nothingness in the first attention.
- Behind that zero stands the imaginary zero at the center of the vertical pole of the second attention, deep-set in the Golgotha Mount.
- And behind both zeroes stands the zero that drives the third attention in any complex number and in any abrupt change in the life of the universe and the anti-universe.
Confrontation between goodness and what opposes it drives two armies to challenge each other in the Baghavad Gita, in front of the undecided Arjuna (the 2nd. attention, empowered with the Gandiva bow [quantum computing])--who has friends and relatives among both contenders--and Krishna, Arjuna's master and the 3rd. Attention.
Only true confrontations lead to a true resurrection (for example, in a democracy). By the same token, the 5 wounds of Christ may represent the union of the principles of quantum computing with the principles of classical computing.
In a similar manner, Israel returned to Canaan after 20 years of absence by trusting the possibility that his brother Esau might understand that he had acquired the Will to help others grow before dying. Before meeting Esau, prudence invited Israel to leave women and children in the rearguard. He remained with his faith, hope, and charity. And Esau understood!
The figure above enriches our view of autism and the logos heuristics by exalting three metaphors for the cognitive and social understanding associated to the arrival of the Third Attention and the Third Point:
- MEIDUM PYRAMID and the GREAT PYRAMID, in which the perimeter of the base over the height is equal to 6.28, or Tau;
- GIZA's SPHINX, in which the head represents the real "+a, -a" axis, and the body, the imaginary "+ib, -ib" axis; and
- the TAU IDENTITY presented in section "I" below
The Tau Identity may convey a Vision of the metaphorical meaning of the 5 wounds of Christ, implied in the writings of Antonio Rosmini.
Cassella agrees with Rosmini that the the wounds in the two hands of Christ and the wounds in the two feet of Christ may ally in the mind of any human being as they do in nature. The 5th wound, caused by the spear of a Roman soldier (see the figure above), proved once the oncoming of death.
However, the 5th wound proves also the possibility of resurrection in whoever perceives the Vision of the Third Attention, the reality of the Way to the Third Point, and the fact that fear of death did not stop Israel from returning to Canaan; Moses, from leaving slavery behind; and Esther, from seeking and finding justice.
In the same way, Quetzalcoatl will return to Earth; Jesus to kind words; Muhammad, to the heart of every Hajji; Laozi, to the Great Wall; the Thatagata, to the abandoned; and Brahma, to Shiva and Vishnu.
Going with coherence and returning with decoherence makes quantum computing and the root of social values.
F: Social Values cross the 1st., 2nd., and 3rd. attention
SOCIAL VALUES
Both classical and quantum computing are innate in nature and in nonautistic human beings. This hypothesis agrees with the genetic consequence that there are four times more autistic males than females, who are endowed in general with better chromosomes and values than are their power-hungry companions.
High-functioning autistics keep intact at birth the cognitive domain (bottom left in the figure above) that Cassella matches to the crystal Thummim, stitched by Moses with the crystal Urim into the ephod that his brother Aaron kept in the Ark of the Covenant.
The Thummim crystal can also be equated with the Egyptian Crook worn by the god Osiris and by all pharaohs, up to the suicide of Cleopatra VII. The Crook and the Thummim also make the staff Hovalim, faith, order (or the truth that opposes disorderly chaos/falsity), the Tonal cherished by the Olmecs/Maya/Toltecs/Aztecs, measurable unity, and the classical computing that guards the "invariant" schemata stored in the cerebral cortex of humans.
Without the classical computing imposed by the Aztec Tonal, the world of shared repetitiveness in a healthy self would vanish. After all, the quantum computing inherent in the Aztec Nagual needs a platform from which to fly into the infinity that surrounds any explorer surrounded by doubt.
By way of illustration, after stealing from his father Isaac the blessing that belonged to his twin brother Esau, "Jacob" (or "the deceiver") left his classical Crook-home, on the road of the Egyptian Flail, Urim (or Zechariah's No'am). He was driven by fear of Esau's anger, or perhaps by his own courage, curiosity, dreams, hopes, and the advice of his keen mother Rebecca.
Before vanquishing madness, Jacob dreamt in Bethel of a ramp (quantum computing) that went from the earth (classical computing) to the sky (the unilateral unreality of the mad). The image of God's angels going up and down the ramp is an allusion to the creativity of the nonautistic person. Within the competing options dreamt by quantum coherence, the 2nd. attention goes up the ramp toward schizophrenia; and within de-coherence, the 3rd Attention returns, from schizophrenia to a renewed autistic facet.
In Bethel, Jacob understood through the Archangel Gabriel, that there is something worse than material poverty: a) the cognitive poverty of the person whom the devil and the angels of God have abandoned in the visible world; and even worse than that, b) the quantum spirit of leaders who have been enslaved by devilish cohorts, and condemned to roam the very edge of madness before falling in its depths.
In sum, artistic freedom to sin is better than autistic innocence, and autistics' link to reality is better than the link to unreality adored by the mad. Diabolical tyrants emphasize their capacity to impose order; however, what good would lie in sterile and undemocratic order if it will lead in the end to maddening chaos?
Jacob understood at Bethel that he could use his capacity for tackling the infinity of quantum computing to shorten the growth of others, as tyrants do, or to grow with others, in the pursuit of win-win outcomes. Undemocratic tyrants lack the vision that leads to the solution of a problem. After Bethel, the Force of freedom led Jacob to a sober learning and to his redemption in Penuel.
In Penuel, Jacob fought a whole night with the Archangel Michael , a metaphor for firming up his realization that he had to explore God's Will before exercising his will.
Michael saw there and then that Jacob had left behind his quantum devil, his twisted mind, and his egoism after acquiring his Third Point. Consequently, the Face of God twisted one of his legs and changed forever his first name from "Jacob" (or 'the deceiver') to "Israel," or 'he who fights with and is saved by God'. After all, a twisted leg accompanies the repented self better than a twisted mind.
After Penuel, Israel embraced a patient will that sought to grow with and to win with others. He had left Bethel in poverty, and Penuel in richness. Still, neither poverty nor richness would influence his will to 'walk with God'.
The oral tradition behind Genesis and the story of Jacob were devised by Moses. The Prince of prophets hid in the Pentateuch (the first five books of the Bible) the social values needed to turn the dangers introduced by crucial problems into a new horizon of Progress.
Similarly, the Toltec/Mexica Eagle is a metaphor for the return of Quetzalcoatl, which will lead our children's children into saving the cycle of water on Earth before reaching the aqueous planet that turns around Proxima Centauri (the nearest star to the Sun); or before changing Venus into the ancient Earth that hosted saber-toothed tigers.
Understanding the autistic facet, and the artistic facet of our minds will lead to:
- a new Ramayana, in which Rama will not send Sita away;
- a new encounter between Kong Fuzi and Laozi;
- an understanding of Muhammad's night journey;
- an understanding of the mystery of transubstantiation in the Eucharist;
- the return of Quetzalcoatl;
- an understanding of the alliance between autism and psychosis;
- an alliance among powerful nations;
- our stopping the death of nonhuman species;
- a lessened consumption of hydrocarbons and energy;
- the education of the leaders that wash the brains of terrorists;
- the lowering of the temperature of the lower atmosphere;
- the cleaning of our oceans; and
- the smile of future children.
As did Gilgamesh (Andrew, 1999) ,the king of the Sumerian Uruk in the 27th century BCE and a metaphor for classical computing), and Enkidu (a man-beast and the corrupted quantum computing that befriended Gilgamesh) when they killed Gugalanna (or the monster sent by the mother goddess Ishtar to empty the streets of Uruk), in the end we will get rid of any temporary nuisance (for example, the pandemic caused by a virus that can be stopped).
According to the 4,000-year-old writing The Epic of Gilgamesh (Andrew, 1999), Enkidu died after the fight with Gugalanna, out of a mix of hubris and madness. Although he had lost Enkidu, a repented Gilgamesh found the plant of immortality, through the advice of the immortal Sage Utnapishtim, but lost it on the way back to Uruk, out of his scarse sobriety.
In other words, should we lose the creativity of our artistic side (Enkidu), our autistic side (Gilgamesh) alone will not be able to take advantage of the secret of the Third Attention (the plant of immortality) brought by the return of Quetzalcoatl. In that case, we will succumb to terrorism and the million-years permanence of the after-effects of global warming.
The next section will deepen the analysis of global warming.
G: Global warming may obliterate us in the 21st. century
AUTISM, LOGOS, AND GLOBAL WARMING
As explained in the workshop on climate change (8th), in an article (Cassella, 2017b), and in a book on the subject (Cassella, 2018j), the IPCC (Intergovernmental Panel on Climate Change, 2007, 2014) has not considered yet the extreme danger inherent in letting our lower atmosphere heat up more than 2 degrees Celsius.
If the permafrost and the oceans warm up now (within an Earth that could become the most powerful green house in 250-million years), the methane clathrates that lie dormant on the sediments of the continental rise in shallow seas might break their cage of crystal, travel to the atmosphere, and cause indirectly the fast rise of the concentration of carbon dioxide in the atmosphere from 410 ppm (at the end of 2019) to 1,300 ppm and more. One needs to remember that, as a green-house gas, methane is about 25 times more powerful than carbon dioxide.
Under those conditions, the equilibrium (chemocline) between bacteria that rely on sulphur and bacteria that feed on oxygen in our oceans could be lost; and an environmental avalanche could cause the massive release of hydrogen sulfide, already surfacing in front of the shore of Angola and Namibia. Our aim to live a longer and more comfortable life could destroy more than Earth's forests and nonhuman species: It could take away the future, the hopes, and the smile of our children's children.
The length of any life span (73 years at the end of 2019) needs to be multiplied by the increase of global population (from 1 billion people in 1750 to 7.8 billon at the beginning of 2020); and a comfortable life can be multiplied by the increase in the per-capita energy consumption (from 1.8 barrels of equivalent oil per year before the Industrial Revolution to 13.5 barrels at the end of 2019).
- Uniting our increased number with our increased per-capita energy consumption results in an impact factor of 1 million. That is,
- we are using Earth's resources 1 million times more than our Neanderthal cousins did about 40,000 years ago.
Too many of us consume too much. A lethal and very infectious virus could change all that. But in the end terrorism and global warming will bring to zero any possibility of social Progress.
The climatic avalanche on our horizon might induce more than the thermal maximum (+ 6 degrees Celsius in the lower atmosphere) reached in the Superior Eocene 56 million years ago; which brought horses and riders. It might match, instead, the disaster associated to the late Permian age (or initial Triassic), about 250 million years ago in which the lower atmosphere reached a 14 degrees Celsius temperature. At that point in time, the degradation of the ozone shield, caused by emanations of hydrogen sulfide accompanied by its characteristic odor of rotten eggs, annihilated almost all the species on Earth (Ward, 2006).
The advice by some scientists to exploit the oil and gas under Greenland's ice could be lethal. Conversely, the counsel of our preferred Sacred Text will lead any reader to his or her Third Point.
Every Sacred Text points to the cognitive roots of the integration of the coherence damaged in autism with the decoherence hurt in schizophrenia:
- The apostle Thomas passed from doubt to certainty when he understood that the combination of Ubiquity and Coincidence had allowed Christ to enter the house of the apostles through a locked door;
- the pilgrims of Hajj cross seven times in time and against time the infinite number of rays in a circle, pointing at its center; and
- in Penuel, Gabriel changed the name of Jacob to Israel.
Science alone cannot dispel the extreme dangers that loom upon us. Only by integrating our scientific muscle with the dreams and the social values cherished by our Paleolithic ancestors can we transform any danger in new opportunities of growth.
(Pressing the associated button will lead to Cassella's book on global warming and the remains of Leonardo's mural Battle of Anghiari)
The next section deals with some implications of autistics' lack of quantum computing in relation to real numbers, complex numbers, and the existence of the anti-universe (Cassella, 2018a, 2019b). The short explanation provided there might increase the disdain of mathematicians, quantum physicists, and cosmologists; besides removing the fright of readers who wish to reach their Third Point.
H: From real numbers in the Cartesian Plane . . .
FROM DESCARTES TO THE ANTI-UNIVERSE
In the first half of the 17th century, the mathematician, philosopher, and scientist René Descartes ("Renatus Cartesius" in Latin) discovered the Cartesian Plane and analytic geometry (Gaukroger, 1995).
About four centuries ago, Descartes might have thought that his location in Rome was the center of a Cartesian Plane and of a circle with radius one; also, that the Colosseum was somewhere to the north-east. In order to reach that monument, he could have followed his genius to go east (by tracing an abscissa along the "x" axis, or the cosines of the angle theta) and then north (by tracing and ordinate parallel to the "y" axis, or the sines of theta). Had he had wings, he could have flown to the Colosseum over a specific unitary radius of the involved circle.
As figure A shows, we may suppose that Descartes realized that the equation of the unitary circle centered in his location and passing through the Colosseum was: x^2 + y^2 = 1
Suppose also that Descartes were tired and did not have wings; but he had the magical capacity to induce the Colosseum to move where he was. In that case, the radius of the unitary circle would become zero, producing the equation x^2 + y^2 = 0. The roots, or solutions, of that equation would be the numbers "x "and "-x" multiplied by the square root of "-1."
Descartes wrote that the square root of "-1" could not be placed among real numbers. He called such a number "imaginary"; a qualification shortened today in "i" or "1i," the imaginary unit. In the 17th century, no one imagined that an unreal number would relate two exceptional numbers of the Cartesian Plane: Euler's number and Greek Pi.
- Euler's number ("e," or 2.718 . . .) represents an irrational and transcendental reality. (Unlike algebraic numbers, transcendental numbers cannot be counted.) That reality may stand for an infinite expansion into nothingness, as in the equation y = 1/x (Figure A), in which "y" becomes infinite when "x" becomes nothing.
- Also Greek Pi (3.141 . . .), or the relationship of the circumference of any circle to its diameter, can be placed among irrational and transcendental numbers. The fact the Pi is transcendental explains why no one has squared, or will ever square, a circle with a compas and straightedge.
The relationship between Euler's number and Greek Pi is dealt with in the next section.
I: . . . to complex numbers, the Tau Identity, . . .
THE COMPLEX PLANE, EULER'S IDENTITY, AND THE TAU IDENTITY (Figure B)
At the turn of the 18th century, about 150 years after the death of Descartes, the Danish-Norwegian mathematician and cartographer Caspar Wessel realized that he if he replaced the vertical "y" axis of the Cartesian Plane with an axis that contained positive and negative multiples of imaginary units, he could represent as points numbers that had a real abscissa (parallel to the axis "+a" and "-a") and an imaginary ordinate (parallel to the axis+"ib" and "-ib").
Wessel's idea introduced a practical use of the complex plane and complex numbers, given by the formula z = a + ib. Real numbers on the horizontal axis ("a" and "-a"), then, are particular cases of complex numbers (z).
In the 19th century, also Jean Robert Argand and Carl Friedrich Gauss stressed the importance of complex numbers. Still, in 1748 the Swiss mathematician Leonhard Euler had already established a formula (upper left) in which any complex number z = cos (theta in radians) + i sin (theta in radians) was also equal to Euler's number (e) with the exponent (^) "i by theta" in polar coordinates.
- Euler understood that, the equation of a circle, cos[theta])^2 +(sen[theta])^2 = 1" in the Cartesian Plane, in the Complex Plane would become (cos[theta] + isen[theta]) x (cos[theta] - isen[theta]) = 1 .
- This expression is equivalent to cos[theta] + isen[theta] = 1/(cos[theta] - isen[theta]) = 1/e^(-i[theta]) = e^(i[theta]).
The exploratory journey of Euler (1748) was considerably more complex, since he did not know initially that the meaning of e^i[theta] is forcing a complex number to trace the unitary complex circle corresponding to the angle twice Greek Pi in radians (as shown by the blu quadrants A, B, C, and D).
In other words, Euler's number is a metaphor for infinite expansion in the Cartesian Plane (Figure A); but in the Complex Plane, Euler's number is equivalent to a side kick that turns us 90 degrees in becoming a metaphor for circular motion. As in the Mexican song "Y volver, volver, volver" ("and to return, return, return"), "e"^itheta, or Quetzalcoatl, must return.
Someone near Euler saw that if the angle theta equalled Greek pi, his formula would become an equation (known today as Euler's Identity) in which his Euler number "e" ^ to " i by pi" could be added to the number 1 before equalling to zero the whole left side. (See the upper right angle of Figure B.)
Cassella (2018a) tried to upset the general adoration for Euler's Identity, which in his view is equivalent to a pact with the devil. Cassella considered in the first place that . . .
- the horizontal axis of the complex plane can be associated to the 1st. attention of the logos heuristics;
- the vertical axis, to the 2nd. attention; and
- complex numbers, to the Third Attention.
In the second place, he considered that Euler's Identity reflects the quantum coherence that reaches schizophrenia (-1) in two quadrants (blue A and B); and, in the third place, that if we were to return to the sanity of mental spacetime in the real axis, the angle to be adopted would have to be twice Greek Pi, or Tau.
By replacing Euler's Greek Pi with Tau in Euler's Formula, Cassella obtained an identity he called Tau, since he found no name for it in the literature.
The Tau identity can be equated with the true return of Quetzalcoatl, since it contains both the going movement of that Mesoamerican demigod (quantum coherence in the upper half-circle seized by Euler's Identity and the blue A and B half circles) and his return movement (quantum decoherence in the lower half-circle of Figure B and the quadrants blue C and D).
In any case, one should not forget that the Tau Identity has the same beginning of Euler's Identity in the autistic +1 of real numbers. Neither should we forget that if we centered the needle of a compass in the zero of the complex plane, we could also trace the central circle of Figure B starting from -1 and going clockwise toward the right, before going down and to the left to return to -1.
The Tau Identity would correspond thus to Euler's number ^ "i by Tau" and equated to zero after the subtraction of unity (lower right angle of Figure B). If one changed Tau by twice Greek Pi, the resulting Tau Identity would also include plurality (the number 2), besides including unity, zero, Euler's number and Greek Pi.
Euler's Identity, then, might be taken as a metaphor for using quantum computing to satisfy the needs and the desires of the self, whereas the Tau Identity becomes a metaphor for serving the self and the other.
Cassella also envisioned that . . .
- Euler's Identity is a mathematical metaphor for Muhammad's going journey to the Farthest Mosque;
- the point in which Euler's identity seems to change into the Tau Identity can be taken as a metaphor of Jacob' dream in Bethel induced by the Archangel Gabriel; and
- the Tau Identity, a metaphor for Israel's struggle with the Archangel Michael in Penuel and for Muhammad's return to the Black Stone in Mecca.
In the case of the Tau Identity, both coherence and decoherence, or the angle twice Greek Pi, could be equated also with the grace of the Virgin of Guadalupe, the kindness of the Archangel Gabriel, the beauty of Venus, and the strength of Michael; all of them seen as the quantum computing that joins the beginning of coherence and the end of decoherence.
Richard Feynman, the father of QED (the quantum electro-dynamics that studies the relationship between light and matter) called Euler's Formula the most remarkable formula in mathematics. He provided a base for the alleged beauty of Euler's Identity and for seeing the Tau Identity as the most gracious, kind, and beautiful formula in mathematics.
Figure B shows that the Tau Identity beats Euler's Identity in defeating the devil since the beginning of time with the Big Bang. Indeed, the Tau Identity may guide our exploration of the dance of light, matter, and anti-matter in the universe and the anti-universe.
The consideration that the human mind and the revelation contained in any Sacred Text go by the union of hyperspace and spacetime in the Tau Identity led Cassella (2019b) to explore the evolution of the universe and the anti-universe--which makes the aim of the next section.
J: . . . the universe (right), and the anti-universe (left)
THE EVOLUTION OF THE UNIVERSE AND THE ANTI-UNIVERSE (Figure C)
The right pair of cymbals in figure C reflects the expansion and contraction of our universe toward the right/east, whereas the left pair of cymbals reflects the expansion and contraction of the anti-universe toward the left/west. Because 13.8 billion years have passed by since the initial Big Bang shared by matter and anti-matter, Cassella (2019b) proposed that in 3.8 billion years (17.6 - 13.8 = 3.8) an accelerated contraction will start in both our universe and the anti-universe.
The 4 divisions of 8.8 billion years each, to the right for the universe and to the left for the anti-universe, reflect the 4 quadrants of the Complex Plane (Figure B) that hosts the circular completion of the Tau Identity in its two possibilities:
- from right to left, when one starts from +1, before returning to this value; and
- from left to right, when one start from -1, and returns to this value.
The change from coasting to accelerated expansion, 8.8 billion years after the Big Bang--and, especially, the change from accelerated expansion to accelerated contraction in 3.8 billion years--may seem revolutionary; but from the geometrical point of view of the two Tau Identities involved, the circular change cannot be seen.
Beyond the Tau Identity, there is no way to prove the hypotheses made in Cassella's (2019b).
The accelerated contraction would last 8.8 billion years, until a coasting contraction in both matter and anti-matter during an additional period of 8.8 billion years would end in two Big Crunches, two White Holes, and a new Big Bang.
As with the Tau identity in our universe, pilgrims of the Islamic Hajj turn 7 times counter-clockwise around the Black Stone in Mecca. Similarly, anti-pilgrims would turn clockwise around the anti-Black Stone of the anti-universe. Islamic pilgrims and anti-pilgrims involved in the Hajj do not realize that they are retracing metaphorically Muhammad's journey to the Farthest Mosque in the first half of their circular walk and back to Mecca in the second half, although at the end of every circle they feel that something raises inside their spirit.
Figure C suggests that every counterclockwise turn of the universe would take 35.2 billion years; and the same time would correspond to a clockwise turn of the anti-universe, before their renaissance into a shared Big Bang.
Positing the existence of an anti-universe made of anti-matter and subject to anti-gravity might solve hypothetically the "vacuum catastrophe" problem of cosmology, or the disparity between the measured density of the universal vacuum (near zero) and the value 50 times (or more) orders of magnitudes of the same parameter when it is calculated through quantum physics. According to Cassella (2019b), if we add the measured and the calculated values, we would obtain the density of the anti-universe.
As in the complex plane, the two universes depicted in figure C would be joined by an infinite speed associated to a Dark Energy rooted in the principles of the second attention (centered in Ubiquity), whereas positive Dark Matter in our universe and negative Dark Matter in the anti-universe would respond to the Coincidence of the Third Attention in their support of gravity and anti-gravity. According to the logos heuristics, all Dark Energy will become Dark Matter before the next two Big Crunches will mix in the next Big Bang. Hence, Dark Energy and Dark Matter seem to be part of the Tau Identity behind the return of Muhammad to the Black Stone in Mecca, the immortality linked to the Sacred Graal of Medieval Christian hagiography, and the resurrection of Hunahpu and Xbalanque in the Popol Vuh.
From a scientific point of view, the logos heuristics and figure C imply that the complex field "z" would correspond to Higgs's field, as long as the latter were uniplural in its capacity to feed both an infinite speed within Ubiquity, the transformation of Ubiquity into the nothingness of Coincidence, and the transformation of the latter into the principles of spacetime.
The fact that an electron of matter and a positron of anti-matter hide behind a matter-empty photon and come to light near an atomic nucleus seems to agree with the ideas sketched in figure C and the nonlocal phenomenon of quantum entanglement.
In fact, Paul Dirac's mathematical discovery of the positron in 1928, the infinite speed of quantum entanglement, and their relationship to complex numbers are contained indirectly in a paper by Woldemar Voigt in 1887. That paper involves the inverse of Lorentz factor, today's alpha, or the square root of 1 less v^2/c^2 (where "c" is the speed of light and "v" is any speed.) Indeed, v = c would take to nothingness the denominator of alpha, and to infinite the whole fraction; and v > c would make alpha a complex number.
It might be worth noticing that the Big Bang at the center of the Complex Plane contains arithmetical zero, imaginary zero, and transcendental zero, since everything begins there and, after connecting coherence with decoherence, ends there.