The Mystical Mathematics and Geometry of the Torah — Adam
The Hebrew Gematria of Adam is 45, symbolic of the human being in relationship to the Creator.
Introduction
We have explored layers of meaning in the narratives of the Torah as a representation of the birth, descent, trials, purification and eventual return of the human soul to the Creator.
In this article, we examine specifically at the mathematics and geometry of Adam.
We have already explored and unpacked the narrative of the Books of the Torah using the multi-layered approach of the PaRDeS: literal, allegorical, symbolic and spiritual.
The below link takes you to the PaRDeS interpretation of the stories in the Book of Genesis.
You can find similar interpretations of the PaRDeS of the other books of the Torah in the below Medium list:
Interpretations
Here, let us delve into a sample of these numerical values and their potential symbolic meanings as applied to the character of Adam.
As already explained, this analysis is highly speculative and esoteric, blending traditional Jewish mysticism with a search for deeper, possibly mathematical and geometric, interpretations. This approach is not something to be found in most traditional interpretations of these stories in Judaism, Christianity and Islam. However, it is an approach followed by so-called “secret societies” such as Rosicrucianusm, Freemasonry, Kabbalah and Sufism.
Adam (אדם) — 45
The Gematria value of Adam is 45, which can be seen as symbolic of the human being (the microcosm) in relation to the divine (the macrocosm).
The isosceles triangle
In two-dimensional geometry, the number 45 is significant as an angle measure. In a right-angled triangle isosceles triangle with equal sides, the angles measure 45 degrees.
As shown in the diagram below, various “as above, so below” principles are expressed here. One of the approaches to Torah study in Jewish mysticism is to look for patterns in the mathematics, geometry and symbolism of Biblical scripture. Exegesis is the general term given to this type of approach.
As Above, So Below
We are told in the creation story of the Book of Genesis that Adam was created in the image of God. As God is above, so Adam is below. If Adam is represented by the number 45, we can intuit the following:
- God can see His reflection in Adam as opposite facing 45-degree angles
- God can see His reflection in Adam as opposite facing 45–45–90 triangles
In both these cases, there is a replication, balance and harmony of opposites. They both lead to a quality of unity in the resulting shape, that is in the equal sides of the isosceles triangle (meaning it has two sides of the same length). In addition, this equality meets in the perfection of a right angle.
Such a triangle and square, with sides of unity, provide a perfect “building block” for the universe. This is why Adam is often called the “perfect man”, principally because he was created in God’s image. If God is perfect, then Adam must also be. This has been interpreted to mean that Adam was created with a form of perfection, mirroring the divine qualities of God. This doesn’t necessarily imply physical perfection but rather spiritual or moral completeness.
There are some consequences of the construction of this geometry:
- the creation of a right-angle
- the creation of the square root of two, an irrational number
- the creation of half a square
- the natural consequence of two right angles in the internal angels
The creation of a right-angle
The right angle, a 90-degree angle, carries significant philosophical and spiritual symbolism in various cultural and intellectual traditions. As a fundamental element of geometry and a cornerstone in the construction and understanding of space, the right angle has been imbued with meanings that extend beyond its mathematical definition.
Symbol of Order and Rationality
In mathematics and geometry, the right angle is often associated with order, rationality, and predictability. It is a cornerstone of Euclidean geometry and represents a fundamental way in which space is measured and understood. Philosophically, this can symbolize the human capacity for reason and the ability to understand and organize the world. The right angle represents the logical structure underlying reality. Morally it represents the two ethically aligned individuals standing “shoulder-to-shoulder”.
Intersection of Two Realms
The right angle, formed by the intersection of two perpendicular lines or planes, can symbolize the meeting or crossing of two realms or dimensions. For instance, in religious or spiritual symbolism, it might represent the intersection of the divine and the earthly or the spiritual and the material. This is often seen in various religious architectures, such as churches and temples, where the vertical and horizontal dimensions intersect, symbolizing the connection between Heaven and Earth.
Stability and Foundation
The right angle is often associated with stability, strength, and groundedness. Right angles are essential for creating strong and stable structures in architecture and engineering. Spiritually, symbolizes a strong foundation for faith or belief or the grounding of spiritual practice in the physical world.
Masonic and Esoteric Symbolism
In Freemasonry and other esoteric traditions, the right angle symbolises virtue and a guide for moral conduct. The square, an instrument for creating right angles, is a Masonic emblem of truth, morality, and honesty. As part of the square, the right angle is used in Masonic rituals as a symbol for the proper regulation of life and actions.
Buddhism and Eastern Philosophy
In some Eastern philosophical systems, the concept of balance and the meeting of opposites can be symbolically represented by the right angle. It signifies the balance of yin and yang, or the middle path that avoids extremes. The right angle can also represent the idea of directness or straightforwardness in one’s spiritual journey or moral conduct.
Symbol of Equality
In a right-angled triangle, the two sides that form the right angle are often seen as equal contributors to the formation of the hypotenuse. This can symbolize the concept of equality, cooperation, and the idea that different elements or aspects can come together to create something greater. In Kabbalah this principle extends to any of the ways three Sefirot connect, creating the principles of thesis, antithesis and a resolving synthesis. For example, this is seen in the opposites of Chesed (mercy) and Guvurah (severity) and a synthesis in Tiferet (compassion).
The resulting irrational number, the square root of 2
The Pythagorean Theorem applies to this triangle, concluding that the hypotenuse is √2 times the length of either leg. This relationship is a cornerstone in understanding irrational numbers and Euclidean geometry. It is a basic building block for trigonometry, where sine, cosine, and tangent of 45 degrees have simple, easily memorable values (1/√2, 1/√2, and 1, respectively).
The irrationality of √2, discovered by the Pythagoreans, was particularly significant. It challenged their belief in the rationality of the universe (from the earlier mathematical discovery of the integers) and suggested a more complex, mystical aspect of numbers.
Thus, the interface between two 45–45–90 triangles is “irrational”, not definable (as where the integers), and infinitely long when expressed as a written number that has no end. This is reflected in the spiritual and mystical ideas that occur at the interface of God and man (in Adam). The square root of two represents the idea of infinity or the transcendence of human understanding.
The creation of half a square & the number 12
If the creation of man as a reflection of God creates a “half-square”, then to complete a square requires two such squares, and twelve to complete a cube.
The number twelve that comes from this construction has historically held significant symbolic and structural importance in various religious and spiritual traditions. This number often appears in religious texts, mythologies, and organizational structures, carrying with it connotations of completeness, authority, and cosmic order.
Let’s list a few:
Christianity: Perhaps the most well-known instance in Christianity is the 12 disciples or apostles of Jesus Christ. These twelve individuals were chosen by Jesus to spread his teachings and are central figures in the New Testament. The Book of Revelation also mentions 12 gates of the New Jerusalem, 12 angels at the gates, and the tree of life bearing 12 kinds of fruits.
Judaism: In Judaism, the number 12 holds significant importance with the 12 tribes of Israel. These tribes descend from the 12 sons of Jacob (renamed Israel). Each tribe held a specific role in the ancient society of Israelites. The High Priest's breastplate in the Temple of Jerusalem contained 12 stones representing the 12 tribes.
Greek Mythology: In ancient Greek religion and mythology, there were 12 Olympian gods. These included Zeus, Hera, Poseidon, Demeter, Athena, Apollo, Artemis, Ares, Aphrodite, Hephaestus, Hermes, and either Hestia or Dionysus. They were considered the principal deities of the Greek pantheon, residing atop Mount Olympus.
Hinduism: In Hinduism, the number 12 has various important references. There are 12 Jyotirlingas, which are sacred shrines dedicated to the god Shiva. The sun god Surya has 12 names, and there are also 12 Adityas, who are solar deities.
Buddhism: In Buddhism, particularly in Tibetan Buddhism, there are 12 Tenets, which are philosophical stances derived from the teachings of Buddha. The teaching of dependent origination, a Buddhist core concept, is often explained in a framework of 12 links.
Norse Mythology: In Norse mythology, the god Odin had 12 sons, each with their own distinct characteristics and realms of influence.
Roman Religion: Similar to Greek mythology, ancient Roman religion also revered 12 major deities, known as the Dii Consentes, who were equivalent to the 12 Olympians.
Astrology: While not a religion per se, astrology, which has been interwoven with various spiritual beliefs, is structured around 12 zodiac signs. This system is used in both Western astrology (based on the tropical zodiac) and Vedic astrology (based on the sidereal zodiac).
Shintoism: In Shinto, the native religion of Japan, there are mentions of 12 deities, which include both major gods and goddesses.
Platonic Solids: The dodecahedron has 12 sides of pentagons, corresponding to the ancient element of “spirit”, known as the “fifth element” or quintessence. It is said to represent the underlying structure of the universe. For example, in Islamic mysticism, it is known as the “Cosmic Mosque”.
The internal angles of a triangle add up to two right angles
The fact that the internal angles of a triangle add up to 180 degrees, or two right angles, has been a subject of interest not only in mathematics but also in various philosophical, religious, and spiritual contexts. This geometric principle reflects a deeper search for order, harmony, and understanding in the universe. Here are some ways in which this aspect of a triangle connects with broader philosophical and spiritual ideas:
Symbol of Cosmic Harmony
In many philosophical and spiritual traditions, geometric shapes are seen as representations of cosmic truths. The triangle, with its angles summing to a stable and predictable 180 degrees, can symbolize the order and harmony inherent in the cosmos. This reflects a belief in a universe governed by understandable and consistent laws.
Trinity and Unity
The triangle is often used to symbolize the concept of the Trinity in various religions. In Christianity, for instance, the triangle represents the Holy Trinity (Father, Son, Holy Spirit). The fact that three distinct angles (or entities) combine to form a complete and unified whole (180 degrees) can be seen as a metaphor for the unity of the Trinity.
Balance and Completeness
The idea that the sum of the angles of a triangle is always constant (180 degrees) symbolizes balance and completeness. In spiritual terms, this represents the idea that different aspects of existence (physical, spiritual, intellectual) must be in balance to achieve a complete and harmonious life.
Buddhist Symbolism
In Buddhism, the triangle is often used in mandalas and represents stability. In the Tibetan Buddhist tradition, the triangle pointing downward symbolizes the female principle, and pointing upward, the male principle. The sum of angles being a constant can represent the balance of these principles.
Pythagorean Philosophy
For Pythagoras and his followers, geometry was more than just mathematics; it was a way to understand the universe and its underlying principles. The triangle, and the fact that the sum of its angles to 180 degrees, was a key part of this understanding, symbolizing harmony and the interrelation of parts to a whole.
Hindu and Vedic Traditions
In Hinduism, the triangle is a powerful symbol used in Yantras and represents various trinities like creation, preservation, and destruction. The stability of the triangle’s internal angles can be seen as the universe's stability maintained by these three forces.
Philosophical Symbolism
Philosophically, the triangle’s properties can be seen as a metaphor for the idea that different elements or perspectives can come together to form a complete and coherent truth (thesis — antithesis — synthesis). This can be related to dialectical methods in philosophy, where thesis, antithesis, and synthesis combine to form a complete understanding.
Other Aspects of the Number 45
- In some Kabbalistic interpretations, 45 could be broken down into 4 and 5, whose sum is 9, a number often associated with completeness or finality.
- Mathematically, 45 is the sum of the first nine positive integers (1+2+3+4+5+6+7+8+9=45), which can be visually represented in a triangular pattern, known as a triangular number.
- 45, is also a composite number, divisible by 1, 3, 5, 9, 15, and 45.
- The four could symbolise the square and the 5 the pentagon. These shapes come up time and again in geometry and in particular the Platonic solids.
Famous quotes revering the triangle
Plato: “The triangle is the building block of the universe.”
Pythagoras: “The triangle is the harmony of the world.”
Hermes Trismegistus: “In the triangle, the beginning, middle, and end are united.”
Manly P. Hall: “The triangle is a symbol of the divine expressing itself in creation.”
Rudolf Steiner: “The triangle — it is the point of departure for all that exists.”
Sri Aurobindo: “The triangle stands as a symbol for the path from the earthly to the divine.”
Ancient Hindu Scripture: “The triangle is the sacred geometry of the Vedas.”
Kabbalistic Teaching: “As the triangle weaves together the heavens, so it binds the soul to its destiny.”
Mystical Alchemy: “In the triangle, matter and spirit find their confluence.”
Native American Wisdom: “The triangle teaches us the balance of earth, sky, and spirit.”
The Law of the Square
A final consequence of the 45–45–90 degree square is the concept of the “law of the square”, a fundamental mathematical, geometric, philosophical and spiritual principle. In a later article, we will look at the law of the square as it pertains to:
- Nature
- Architecture
- Morality
- The point within a circle
- The square in a cross
In addition, we unpack other elements of the Book of Genesis in a similar way.
