GLOBAL WARMING, CARTESIAN PLANE, THE TAU IDENTITY, THE ANTI-UNIVERSE, AND THE 5 WOUNDS OF CHRIST

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.

• Euler's number ("e," or 2.718 . . . with an infinite number of decimals) represents an irrational and transcendental reality. (Unlike algebraic numbers, transcendental numbers cannot be counted.) Euler's number may stand for an infinite expansion into nothingness, as in the equation y = 1/x (Figure B), in which "y" becomes infinite when "x" becomes nothing.

• Also Greek Pi (3.141 . . .), or the relationship of any circumference 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 in a finite number of steps, a circle with a compass and a straightedge.

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."

• 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 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 . . .

1. the horizontal axis of the complex plane can be associated to classical computing in the 1st. attention of the logos heuristics;
2.  the vertical axis, to quantum computing in the 2nd. attention; and 
3. complex numbers (z), to the 3rd. attention, within the crossing of classical and quantum computing.

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. 

• 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 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: 

• starting from +1 and going up and left, before returning; and 
•  starting from -1 and going down and right, before returning. 

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:

1. The axis of the confrontation between the good thief and the bad thief (or the axis of bread blessed in the Last Supper) carries in its center the arithmetical zero of nothingness in the first attention (the first two wounds in the hands of Christ).
2. Behind that zero stands the imaginary zero at the center of the vertical pole of the second attention, deep-set in the Golgotha Mount (the third and fourth wounds in the feet of Christ).
3. And behind both zeroes stands the zero that drives the  third attention, or the union of the rigidity of bread and the flexibility of wine, in any complex number  (the 5th wound on a side of Christ).

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 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 autistic "+a, -a" axis; or the bread that Christ offered his Apostles, while the body represents the artistic axis, the wine blessed in the Last Supper, or the imaginary "+ib, -ib" axis of the second attention; and, 
• the whole monument, the TAU IDENTITY that unites the second to the first attention in the growth of any natural system.

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.