In its 6th assessment cycle, the IPCC (Intergovernmental Panel on Climate Change, 2021) reports that the temperature of our lower atmosphere has gone up 1.5 ° C (degrees Celsius) (from 1991). The IPPC does not emphasize the dangers (for example, changes in the monsoon season of India and Bangladesh) of letting that temperature go up more than 2 degrees Celsius from its normal value. In particular, the IPCC has reduced considerably the dangers of the thawing of the permafrost and of the release of methane from the sea bottom.
Cassella does not agree with such a conclusion, although many movies overstate the danger of methane marine hydrates. Besides keeping an interest in the integrity of the permafrost, this researcher emphasizes the sudden overarching of tipping points (e.g., the reduction of the Amazon rainforest and of nonhuman species at the right of Figure A) as a cause of abrupt climate changes, under an "avalanche" conception (left of Figure A), which includes atomic explosions.
Our best scientists have warned us since 1991 that we will face a social and environmental avalanche before the turn of the 21st century if our indifference to global warning continues unabated. Cassella has chosen the October 2022's article of Mc Key et al. to illustrate the consequences of forgetting the importance of tipping points. In any case, the thawing of the ice cap in the Arctic Ocean, Greenland, and West Antarctica would certainly occur if the temperature of the lower atmosphere went up by 3 ° C (a condition that occurred 125,000 years ago). In that case, sea levels could go up by 10 meters.
The sixth anthropogenic extinction of free nonhuman species (right of Figure A), which has been ongoing during at least two decades, also advises us to undo the tenfold population and economic growth of the last two hundred years. But we do not know how to do that.
There is more to our recklessness: If the permafrost and the oceans warm up by 3 degree Celsius, within an Earth that has become a powerful green house, the carbon dioxide that lies dormant in the permafrost and the methane frozen there and on the sediments of shallow seas might act as the drop that fills the glass, travel to the atmosphere, and boost the concentration of carbon dioxide there from 420 ppm (parts per million, at the end of 2022) to 1,300 ppm and more.
One needs to remember that, as a green-house gas, methane is a lot more powerful than carbon dioxide in a 20 years period. Neither can one forget the leaks from gas pipelines and methane deposits in the subsoil.
Under those conditions, the equilibrium between bacteria that rely on sulphur and bacteria that feed on oxygen (chemocline) in our oceans could be lost, causing the massive release of hydrogen sulfide, already surfacing in front of the shores of Angola and Namibia.
Our aim to multiply and live a longer and more comfortable life could destroy more than Earth's forests and nonhuman species. A social and environmental avalanche could take away the future, the hopes, and the smile of our children's children.
A repeat of the PETM (Paleocene-Eocene thermal maximum) of 56 million years ago (mya) and of the PTHT (Permian-Triassic Hyper-Thermal) of 252 mya cannot be discarded.
Our ancestors (Neanderthal and Homo sapiens) developed on a cold Earth. Inducing now an ice-free Earth with a high concentration of carbon dioxide (3500 ppm) that preceded the global cooling caused by the azolla might result very dangerous for us.
Perhaps the super-plant "Azolla," which grew and absorbed green gases during the Eocene in an isolated Arctic Sea, could reduce again the atmospheric concentration of carbone dioxide, nitrogen oxides and methane. However, if the Azolla escaped human control, damage from the decrease of green gases in the atmosphere of the Earth could be worse than their increase.
It is dangerous to go in a short time from a cold to a very hot Earth; and after that to a very cold Earth, the result of transforming important tipping points in domino pieces that fall on each other (the possible avalanche hypothesized by Cassella).
As reported in Cassella (2022b), instead of attempting to destroy each-other, perhaps Russia and Ucraine could ally with the USA, the EU, China, and other States the save human civilization.
The length of the average life span (73 years at the end of 2022) needs to be multiplied by the increase of global population (from 1 billion people in 1825 to 8 billons in October 2022); 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 1825 to 13.5 barrels at the end of 2021).
Too many of us consume too much. Although a lethal and very infectious virus (e.g., Covid 19) could change all that, terrorism united to the use of weapons of mass destruction (WMDs) and a global warming above 3 ° C would suffice to take away social Progress; and to increase the sufferings of our grandchildren.
That said, few people might believe on the possibility of a climatic and social avalanche in the 21st century. But Figure B above shows two important points:
The concentration of carbon dioxide in Earth's atmosphere, for example, has increased from an average 240 ppm (part per million) in 800 thousand years to 420 ppm in 2022. The other two green gases have followed suit. Obviously, the temperature of the lower atmosphere and the level of the sea will go up. It is impossible to burn without consequences in a geological instant the coal, oil, and gas that have been trapped in Earth's crust during million years.
The climatic avalanche on the horizon might induce more than the PETM (+ 6 degrees Celsius in the lower atmosphere) of the Superior Eocene 56 mya, which brought horses. It might match, instead, the disaster associated to the PTHT of 252 mya, in which the lower atmosphere reached a 14 degrees Celsius temperature. At that time, the degradation of the ozone shield, caused by emanations of hydrogen sulfide from Earth's oceans, accompanied by its characteristic odor of rotten eggs, annihilated almost all the species on Earth (Ward, 2006; Benton, 2018). Thus, will we laugh (by reason of breathing laughing gas) while our children and grandchildren die poisoned?
If the climate change of 252 mya initiated with the local burning of carbon by the magma that erupted from the Siberian Traps, could there be similar consequences with the human exploitation on a global basis of gas, oil, and coal? The hypothesis of a world without riders should be discarded only after a deep analysis.
If the super-plant "Azolla" thrived in the Eocene and became later hydrocarbons, there could be huge oil and gas deposits under Arctic ice. But searching for and exploiting the oil and gas under the ice of the North Pole could be lethal. Perhaps going back to the Earth-greenhouse of the Eocene would favor new species. It is doubtful, though, that humans and the nonhuman species that developed in a cold Earth may not reach a favorable return.
Conversely, any reader of any Sacred Text will reach his or her Third Point, within the charity that wins with others.
Every Sacred Text points indirectly to the cognitive roots of the integration of the coherence damaged in autism with the decoherence hurt in schizophrenia:
Science alone cannot dispel the extreme dangers that loom upon our descendants. Only by integrating our scientific muscle with the dreams and the social values cherished by our Paleolithic ancestors, by all schools of philosophy and by all Sacred Texts can we transform any danger in new opportunities of growth. Cassella continues showing the evolution of his "logos heuristics" as a Vision that could elicit the repentance of important leaders and thus bring many people to change the bearing of their lives toward winning with their enemies.
Uncovering the mural "Fight for the Standard" (the central piece of the "Battle of Anghiari") by Leonardo da Vinci in the Hall of the 500 of the "Palazzo Vecchio" of Florence could prove very valuable in saving our grandchildren. Cassella''s logos heuristics, based on autistics' performance in cognitive tests agrees with complex numbers. The logos heuristics suggests that the center of the "Fight for the Standard" lies hidden in that Hall at 7.035 meters under the center of Vasari's "Battle of Marciano."
(Pressing the associated button will lead to Cassella's book on global warming and the hidden remains of Leonardo's mural Battle of Anghiari)
The next section stresses the fact that behind the visible and measurable reality searched by René Descartes in the 17th century hide infinity, nothingness, complex numbers (z) and the dance that animates the cosmos and the human brain (Cassella, 2018a, 2019b, 2022a, 2022b).
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).
Around 1625, Descartes might have thought that his location in a Roman hotel was the center of a Cartesian Plane and of a circle with radius one; also, that the Colosseum was somewhere on that circle and 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 axis of the cosines of the angle theta) and then north (by tracing an ordinate parallel to the "y" axis, of the sines of theta). Had he had wings, he could have flown to the Colosseum over the specific unitary radius of the involved circle.
As figure C above 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 the imaginary unit could relate two exceptional numbers of the Cartesian Plane: Euler's number and Greek Pi.
The hidden relationship between Euler's number and Greek Pi is dealt with in the next section.
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 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 same way, the first attention is a particular case of the Third Attention.
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, given by z = cos (theta in radians) + i sin (theta) in polar coordinates, is equal to Euler's number (e) with the exponent (^) "i by theta."
The exploratory journey of Euler (1748) was 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 in section B); in the Complex Plane (Figure in section C), however, Euler's number is equivalent to a side kick that turns us 90 degrees in undertaking a circular motion. As in the Mexican song "y volver, volver, volver" ("and to return, return, return"), "e^itheta," or the Aztec demigod Quetzalcoatl, must return with the angle 2 x Greek Pi--a full circle in radians.
Someone near Euler saw that if the angle theta equalled Greek pi, his formula would become 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 left side. (See the upper right angle of the Figure in section D above.)
Cassella (2018a) tried to upset the general adoration for Euler's Identity, which in his view is equivalent to a pact with the devil under the temptations introduced by a second attention in which the devil and the Virgin of Guadalupe coincide.
Cassella considered in the first place that . . .
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 C 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 C starting from -1 and going down counterclockwise toward the right, before going up and to the left in returning to -1. In a way, +1 and -1 join in provoking the rise of the central circle of Figure D.
The Tau Identity would correspond thus to Euler's number ^ "i by Tau," equated to zero after the subtraction of unity (lower right angle of Figure D). 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.
Cassella also envisioned that Euler's Identity is also a mathematical metaphor for Muhammad's going journey to the Farthest Mosque; while the Tau Identity can be taken also as a metaphor for Israel's struggle with the Archangel Michael in Penuel, for Muhammad's return to the Black Stone in Mecca, and the confrontation with the Archangel Raphael who opens the door of Progress into a new familiar world.
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, a compendium of the kindness of the Archangel Gabriel, the strength of Michael, and the compassion of Raphael.
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 emphasized the alleged beauty of Euler's Identity.
The Figure above shows that the Tau Identity beats Euler's Identity in defeating the temptations brought by the devil, but beats it deeply, as does the Virgin of Guadalupe although her power feeds on the same principles (of hyperspace).
As it was said before, the Virgin of Guadalupe may replace the grace of Gabriel, the courage of Michael and the compassion of Raphael. She prays that before dying, we may blush in realizing that we are only humble sinners who may personally help God if Divinity helps us repent as might do the universe and the anti-universe.
Will Volodymyr and Vladimir repent in time? or will those two liars fall in the arms of the devil before becoming crazy?
The human mind and the revelation contained in any Sacred Text go by the union of hyperspace and spacetime in the Tau Identity. This consideration led Cassella (2019b) to explore the evolution of the universe and of the anti-universe, which makes the aim of the next section.
The right pair of cymbals in figure D 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 C) that hosts the circular completion of the Tau Identity in its two possibilities:
The universe and the anti-universe chase each other as in a dog that tries to bite its tail. After a half-turn of 180 degrees, the universe will occupy the place of the anti-universe and vice versa. Both the universe and the anti-universe are opposite point in the periphery of a same circle, turning counter-clockwise.
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.
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.
Following 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 counter-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, at the completion of the Tau Identity.
Figure e suggests that every counterclockwise turn of the universe and anti-universe would take 35.2 billion years, before their renaissance into a new and 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.
That problem refers to 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), adding the measured (almost zero) to the calculated values would result in the density of the universe; and of its opposite in the anti-universe.
As in the complex plane, the two universes depicted in Figure E 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 respective 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.
The logos heuristics and figure E 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 E 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 transform alpha into 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.
In the same way, the human mind and the story of the cosmos rely on our capacity to open the door of our Third Point before dying. The Saint-to-be Antonio Rosmini wrote on the goodness of that route about two centuries ago through a metaphorical re-interpretation of the 5 wounds that Christ received before dying and then resuscitating.
The figure above shows 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 opposition between Dimas and Gestas, matter and antimatter pervades de cosmos outside and inside the human mind.
Figure E also shows Cassella's quantum and mystical interpretation of that account, inspired by Antonio Rosmini's philosophical reasoning:
Confrontation between goodness and badness 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 (the wine) with the principles of classical computing (the bread.)
In a similar manner, Israel returned to Canaan after 20 years of absence by hoping in the possibility that his brother Esau might understand that he had acquired the Will (or the Third Point) to help others grow before dying, instead of deceiving them. And Esaù did understand!
Figure F above exalts three metaphors for the cognitive and social understanding associated to the arrival of the Third Point, which will remain inaccessible to leaders that are not sensitive to forgiving or repenting:
The Tau Identity conveys 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 (the Centurion Longinus) (see Figure F above), proved once the oncoming of death.
However, the 5th wound proves also the possibility of resurrection in whoever perceives 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, the demigod Quetzalcoatl will return to Earth; Jesus to kind words towards his assassins; Muhammad, to the heart of every Hajji; Laozi, to the Great Wall; the Thatagata Buddha, to the abandoned; and Brahma, to Shiva and Vishnu.
Going with coherence is impaired in autism and returning with decoherence is impaired in schizophrenia. The two illnesses are dealt with in the next page.
For references about articles and books by Antonio Cassella, please look at the list provided in the Biography.
Andrew, G. (1999). The epic of Gilgamesh. London: Penguin Books.
Benton, M.J. (2018). Hyperthermal-driven mass extinctions: killing models during the Permian-Triassic mass extinction. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 376(2130), https://doi.org/10.1098/rsta.2017.0076
Castaneda, C. (1968). The teachings of Don Juan: A Yaqui way of knowledge. New York: Simon and Schuster.
Castaneda, C. (1972). Journey to Ixtlán: The lessons of Don Juan. New York: Simon and Schuster.
Castaneda, C. (1987). The power of silence: Further lessons from Don Juan. New York: Simon and Schuster.
Castaneda, C. (1991). The Eagle’s gift. New York: Simon and Schuster.
Euler, L. (1748). Introductio in analysin infinitorum. Bosquet: Lausanne. Feynman, R. P. (1985). The strange theory of light and matter. Princeton, N.J.: Princeton University Press.
Gaukroger, S. (1995). Descartes: An intellectual biography. Oxford: Clarendon Press.
IPCC-WG1. (2007) Intergovernmental Panel on Climate Change. Fourth Assessment Report. Summary for Policymakers: A Report of Working Group I. IPCC-WMO.
IPCC. (2014). Intergovernmental Panel on Climate Change. Fifth Assessment Report. Summary for Policymakers: A Report of Working Group I. IPCC-WMO.
Jozuel et al. (August 2007) Orbital and Millennial Antarctic Climate Variability over the past 800,000 years. Science, 317, 793-796.
IPCC (2021). Sixth Assessment Report.
Jozuel et al. (August 2007) Orbital and Millennial Antarctic Climate Variability over the past 800,000 years. Science, 317, 793-796.
Rosmini, A. (1848). Delle cinque piaghe della Chiesa: Trattato dedicato al clero cattolico. Bruxelles: Société Typographique.
Vasari, G. (1550). (1986). Le vite de’ più eccellenti architetti, pittori, et scultori italiani, da Cimabue insino a’ tempi nostri. Torino: Einaudi.
Ward, P. D. (October, 2006). “Impact from the Deep.” Scientific American, 295, 64-71.
Voigt, W. (1887). Ueber das Doppler'sche. Princip. Nachr. Ges. Wiss. Gottingen 8, 41-51.
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