Since the publication of my
book The End of Economic Science, The Beginning of the Golden Age, many
of you have asked me to deepen the chapter devoted to sacred mathematics and
especially the identity cos²x + sin²x = 1, which escapes the simple scholastic
framework. This formula is one of the secret pillars of the universal
tradition, a key to reading reality, an exact mirror of the unity that sustains
all manifestation.
For this equality is not an
abstract construction: it is the beating heart of living geometry. Imagine a
point traveling around the circle of radius 1: its horizontal projection, the
cosine, is water, receptivity, the feminine horizontality evoked by Sleeping
Beauty or Snow White lying down. Its vertical projection, the sine, is fire,
the ascending energy of the masculine, that force which rises toward the sky,
symbolized by the Olympic flame.
Thus is revealed the
fundamental truth that the sages of all traditions have transmitted in a
thousand forms: existence rests on two complementary polarities, one
horizontal, the other vertical, one feminine, the other masculine, and it is
their harmonious union that gives birth to the One. The unit circle does not
merely represent a geometric figure; it is the perfect illustration of
totality, of the union of opposites, of the balance that sustains creation. And
the trigonometric identity that governs it is nothing less than the
mathematical signature of this unity.
This chapter, which I develop
here, reveals why cos²x + sin²x = 1 is not a simple calculation tool: it is a
matrix formula, a schema of the world, a forgotten spiritual key—and yet indispensable
for understanding what must collapse and what must be reborn in our
civilization.
THE CIRCLE AND THE CROSS
The cross is not an accessory
religious image: it is the geometry of living together. To fix the horizontal
and the vertical is to show that unity is not the negation of opposites but
their harmonic relationship. Jesus on the cross embodies this junction:
horizontality of love and verticality of transformative energy, culminating in
unity. The central point, the axis mundi, is the place of passage where the
multiple becomes One again.
THE SACRED LETTERS: JUDAISM,
CHRISTIANITY AND ISLAM
The Tetragrammaton YHWH is the
architecture of a becoming. Yod (principle), Heh (manifestation), Vav (link)
and Heh (return) form a structure where the double Heh signifies squaring,
stabilization of a potential. Reading YHWH through trigonometry enlightens us
in more ways than one: Y (Yod) corresponds to horizontality (cos x), Vav to
verticality (sin x), and the repetition of the letter H is the squaring, the
affirmation of a totality that cannot be reduced.
Yeshua (יֵשׁוּעַ) reveals the
same mechanics: Yod-Shin-Vav (Ayin, the vowel disappears in written Aramaic).
Shin is the flame, the active purification of the Word; Vav is the nail that
connects high and low; Yeshua is therefore the divine seed traversing fire and
connecting heaven and earth. The two-triangle star (ISIS + RA = EL, ISRAEL)
visually manifests the reunion of polarities: two triangles that interpenetrate
and form a perfect unity. The bain-marie—a foundational image—unites water and
fire, proof that transformation is the conjunction of elements, not
annihilation.
IBN ARABI AND THE UNITY OF
BEING
Sufism affirms without detour:
the world, with its multiplicity, is the language through which the Unique
reveals itself. Letters are not simple signs; they are creative forces.
Complete humanity is that which reunites within itself the different letters
and names, becoming the receptacle of the Word. He explains that letters are
the bodies of the Divine Names and the very substance of creation. Each letter
is a degree of this divine manifestation. "Know that the letters are, in
their essence, the bodies of the Divine Names... All existence is a word
uttered by God, and the letters are the roots of all manifested things, for it
is through them that the divine word has diversified and unfolded in the
universe." The perfect human being (al-insān al-kāmil) is one who
understands and reunites all these letters, thus becoming the totality of the
divine Word and the receptacle of all Names. This is the meaning of the
Perfection and Unity sought (Tawhid). Islam possesses an unsuspected spiritual
depth, far from the image of the evil bearded throat-slitter they want to sell
us...
The formula cos²x + sin²x = 1
is the formal demonstration that this plurality holds within the perfect unity
of the circle. He maintains that Tawḥīd is Wihdat al-Wujūd (the Unity of
Being): there is only one true reality, which is God. The world, in its
apparent duality and multiplicity cos²x + sin²x, is only the manifestation (the
expression) of this single divine Essence.
CONSEQUENCE FOR ECONOMICS
The collapse of systems that
forget unity is inevitable. Our financial and political systems have ignored
sacred geometry. Linear accumulation—the flight toward infinity on a finite
Earth—is a logic of implosion. We must stop thinking GDP and replace it with
GNH, Gross National Happiness, as Bhutan has done. Where traditional wisdom
proposes encounter and balance of polarities, our ideologies have institutionalized
polarization, transformation through violence, disunion, war of all against
all. The result is visible: cycles of crises, ideological skirmishes, moral
collapses and finally, world wars.
The irrational constants (√2,
π, φ, e) are not abstract curiosities: they testify to the infinite inscribed
in form—the irrational order that sustains creation. The quest for unity is
indeed the common chorus of traditions. It does not require uniformization, but
the recognition and respect of diverse paths leading to the same center. To
refuse this is to transform spirituality into totalitarian ideology; to accept
this is to restore the plural richness of traditions while affirming the same
central truth.
CLARIFICATION AGAINST
DISTORTIONS
The great unity at the heart
of religions is not synonymous with uniformity. True spiritual work consists in
defending and preserving singularities, respecting rites and forms, preventing
a great globalist synthesis from becoming an empty "mixture" that
will fail anyway. My purpose has always been to show that the convergence of
religious roots does not lead to a global dogma, but to mutual recognition and
common responsibility toward the sacred.
CONCLUSION: RECONQUERING
BALANCE
The formula cos²x + sin²x = 1
is a simple and energetic rule: the sum of polarities is unity. Any science,
any social practice that deviates from it exposes itself to rupture. This is
not about replacing economics with a mystical creed, but about integrating
geometric and symbolic wisdom at the heart of collective choices.
After
the great massacres to come (generalized hatred), we will finally be able to
relearn to love one another. This is the message of Yeshua/Jesus/'Îsâ,
and it is the only one that matters.
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