Quick Wisdom with Bliss: Sacred Geometry

Namaste, welcome to Quick Wisdom with Bliss

My name is Bliss, meow, and this is my cute little furball friend Joy

Spirituality is everywhere, in the air we breathe, in nature all around us, and even written into our very DNA

We are energy, and together as energy, we're all connected, we're all one

United as one, we are here on the stage of life, to love and help each other live the best we can

Now I know you've come today to learn about a very special topic, so let's put on our fun caps and get started on this sacred exploration

This is Quick Wisdom with Bliss, Sacred Geometry

We live in a world of beautiful shapes, they're all around us, we can even make them with our body, isn't that right Joy? If you look at our tail, just right, it appears as if it's shaped like a question mark

That's fitting because you know how inquisitive kitties can be

Shapes can symbolize or represent just about anything, whether it be the building of beauty or the withering of decay

And between the two, you can find a land full of mysticism and wonder

One that is made up of something we call Sacred Geometry, and that can tie directly into the science of creation

Ready to go on a trip of wonder and enlightenment, Joy? Prrrrring! Awwww, what a big meow

Let's get to it! Sacred Geometry can assign symbolic and sacred meanings to different kinds of geometric shapes and even certain geometric sizes

It's often associated with the belief that a god is actually the greater geometer of the world

Geometry that is employed in the building and design of religious structures like temples, churches, mosques, altars, religious monuments, and tabernacles

As a result, this type of geometry has been considered by many to be sacred

This concept also applies to sacred spaces like sacred groves, teminoi, holy wells and village greens along with the creation of religious artwork

One belief that's been around since ancient times is that a god created the universe according to a geometric plan

A Greek biographer named Plutarch attributed this belief to Plato, who once wrote in one of his many essays that, Plato said god geometrizes continually

There are plenty of other beliefs too, isn't that right Joy? According to Australian author, editor, publisher and lecturer Stephen Skinner, research into sacred geometry has its origins in the study of nature and the mathematical theories that work within them

Many different things that can be easily found in nature can be related to geometry

Wow, isn't the world magical? It's always telling us something if we take the time to listen

Now listen to this

The chambered nautilus will continue to grow at a non-stop rate and so its shell forms a logarithmic spiral that can accommodate that type of constant growth without changing its shape

Cool, huh? Also honey bees will build hexagonal cells to store their honey

These and other accordances are often thought of in terms of being sacred geometry and are considered by many to be further proof of the natural importance of geometric forms

Symbolic figures and geometric ratios are often found in the designs of ancient Indian, ancient Egyptian, Roman and Greek architecture

Medieval European cathedrals also use symbolic geometry

Himalayan and Indian spiritual communities would often construct fortifications and temples on the design plans of mandala and yantra

Mandalas and yantras are super important in the usage of sacred geometry

Put down that yarn joy and let little miss Bliss teach you all about them

A mandala is a spiritual and or ritual geometric configuration of symbols or a map in the Indian religions of Buddhism, Hinduism, Jainism or Japanese lifestyle of Shintoism representing deities or in paradises the case of Shintoism, kami or actual shrines

Nowadays you can even find it almost everywhere including the United States

Typically, American use of mandala has become a generic term for any chart, diagram or geometric pattern that represents the cosmos symbolically or metaphysically, a time microcosm of the universe, originally meant to represent wholeness and a model for the organizational build of life itself

A cosmic diagram will show us our relation to the infinite and the world which extends within and beyond our minds and bodies

One of the most basic forms of most mandalas just happens to be a square with four gates that contains a circle within the center point

Mandalas often have a radial balance

The term appears in the Rig Veda as the name of the sections of the work and Vedic rituals use mandalas like the Navagraha mandala to this day

Mandalas can also be found being used in Buddhism

In many different spiritual traditions, mandalas may be used for focusing attention of adepts and practitioners as a spiritual guidance tool so that the user can establish a sacred space that will happen with meditation and trance induction

What do you think about that Joy? You're so cute Joy, I love you! Sorry, lost in cuteness, let's continue

Yantras are a mystical diagram that's mainly comprised from the tantric traditions of the Indian religions

They can be used to facilitate in the worshipping of deities in home or at temples

Essentially Yantras aid a person in meditation

They are also used because of the benefits given by their supposed powers which are based on tantric texts and Hindu astrology

Yantras are also used as an adornment of temple floors due mainly to their symmetric and aesthetic qualities

Tantric Yantras are almost always associated with specific deities

Various forms of the Yantra in India are believed to date back to 11,000 to 10,000 years B

P

And the Bhagavad Gita, which was found in an upper Paleolithic context in the Son river valley, is thought to be the earliest example by historian G

R

Sharma who was involved in the stone's excavation somewhere between 25,000 and 20,000 B

P

The Bhagavad Gita stone is a triangular shape and it has triangular engravings on one side, was found daubed in a natural clay earth pigment known as ochre

The stone was found in an area considered a site related to worship

Worship of goddesses in that region was practiced in a similar manner to the present day

Sacred Geometry can also be found used in the human body

Oh joy, calm down! I'm sure it's used somehow in kitties too

Did you know a lot of the sacred geometry principles of ancient architecture and the human body were organized into the Vitruvian man drawing by artist Leonardo da Vinci? Yup, the drawing itself was based on the ancient writings of the Roman architect Vitruvius

This translates to the proportions of the human body according to Vitruvius, or simply L'Uomo Vitruviano

The drawing was created around the year 1490

It is accompanied by notes that were based on the work of the Roman architect Vitruvius

The drawing and text are sometimes referred to as the Canon of Proportions or Proportions of Man

The drawing is kept in the Gabinetto dei disegni estampi of the Galleria dell'Academia in Venice, Italy

Because paper is so delicate, the Vitruvian man is displayed to the public only on occasion and it is not part of the normal exhibition of the museum

The drawing is based on the correlations of ideal human body proportions with the geometry described by the ancient Roman architect Vitruvius in Book III of his Treatise di Architettura

Vitruvius described the human figure as being the principal source of proportion among the classical orders of architecture

Vitruvius determined that the ideal body should be eight heads high

Leonardo's drawing is traditionally named in honor of the architect

The building of medieval European cathedrals was frequently based on geometries that were intended to make the onlookers see the world through mathematics

It was through this understanding that the viewer would gain a better understanding of the divine

Churches like these often featured a Latin cross floor plan

At the start of the Renaissance in Europe, perspectives changed to favor more simple and regular types of geometries

The circle became a central and symbolic shape for the base of buildings because it represented the perfection of nature and the centrality of man's place within the universe

The usage of the circle alongside other simple and symmetrical geometric shapes became a staple of Renaissance religious architecture in Leon Battista, Alberti's architectural treatise

In his work, Alberti described the ideal church in terms of spiritual geometry

See how joy sometimes runs around in a circle or maybe you spin yourself around and around while different types of circles play important roles in the world of sacred geometry

Joy, are you ready to learn more? That's what I thought! Here we go! Blessings of knowledge

Let these facts heal us with understanding

Let's talk about a magic circle for instance

These mystical ringlets of space have been marked out by practitioners of tons of branches of ritual magic

These practitioners are of the mindset that a magic circle can either contain energy and form a sacred space or even provide the users inside of the circle with a type of magical protection

Sometimes it can be both of the above possibilities at once

Cool, huh? A magic circle can be drawn in salt or chalk and can be marked physically or just simply visualized

The magic circle has a significance that is very similar to that of mandala and yantra in some eastern religions

These are also solomonic magic circles which have a triangle of conjuration in the east

These would be drawn on the ground and the conjurer would stand within the protection of the circle while a spirit was summoned into the triangle

Traditionally, circles were thought by ritual magicians to create a protective barrier between themselves and what they summoned

Modern practitioners now cast magic circles more to concentrate and contain the energy which they raise over a course of a ritual

There are tons of techniques for casting magic circles

Many groups and practitioners have developed their own unique methods

The one thing that all of these techniques have in common is that a boundary is traced around the working area

Some witchcraft traditions say that one must trace around the circle diocel three times

There is a variation over which direction one should start in

The four cardinal directions of a magic circle are often clearly marked by things such as four candles

During ceremonial magic, the four directions are almost always related to the four archangels – Gabriel, Michael, Uriel, who is also known as Ariel, and Raphael

Other ceremonial traditions will see the four candles between the quarters of the magic circle, meaning in the north-west, north-east, etc

, etc

, and cantations will usually be recited stating the purpose and nature of the circle

These incantations often repeat an assortment of angelic and divine names

When being used in the practice of Wicca, a magic circle is often about 9 feet in diameter, but its size can change depending on the purpose of the magic circle and of course the preferences of the caster

The barrier of a magic circle is thought of to be extremely fragile, so much so that merely passing through or leaving the circle could either weaken it or dispel it altogether

The act of doing so is called breaking the circle

It is generally believed that practitioners should only leave the circle if it is absolutely necessary

As a means to leave a circle and keep it intact, Wiccans are of the belief that a door must be cut into the energy of the circle

Usually this door is found on the east side

Whatever was used to conjure the circle is also used to cut the doorway

Tools to do so vary

A circle can be cut by a sword or knife

Once the doorway is in place, anything may pass through the door without harming the magic circle

However it's important that opening must be closed by reconnecting the lines of the circle afterwards

Yes, that's correct Joy

Overlapping circles have their very own meaning

An overlapping circle's grid is a geometric pattern of repeating

Overlapping circles of equal size in a two-dimensional space

Usually designs like these are based on circles which are centered on triangles with the simple two-circle form named Vesica Pisces or on the square lattice pattern of points

Patterns of seven overlapping circles have appeared in historical artifacts from the 7th century BC onwards

These patterns have become a frequently used ornament during the Roman Empire period

They have stood the test of time and have made their way into medieval artistic traditions both in Islamic art known as Ghira decorations and also in Gothic art

The name Flower of Life has been given to the overlapping circles pattern in a lot of New Age publications

One flower-like pattern of particular interest is the 6th Petal Rosette which was derived from the seven overlapping circles pattern

This very distinctive pattern is also known as the Sun of the Alps because of its frequent usage in Alpine folk art from the 17th and 18th centuries

The triangular lattice form with circle radii equal to their separation is called a seven overlapping circles grid

It contains six circles intersecting at a point with the seventh circle centered on that intersection

Overlapping circles that have a similar geometrical construction have been used infrequently in various forms of the decorative arts ever since ancient times

The pattern has enjoyed a wide range of use in fashion, jewelry, tattoos, popular culture and decorative products

The oldest known usage of the overlapping circles pattern has been dated back to the 17th or 6th century BCE and it was found on the threshold of the palace of a Syrian king, Asur Bani Apli and Dur Sarakin

It is currently on display in Paris at the Louvre

The design became even more widespread during the early centuries of the common era

One of the earliest examples are five patterns of 19 overlapping circles that were drawn on the granite columns at the Temple of Osiris in Abydos Egypt and there's even a further five located on a column at the opposite side of the building

They are drawn in red ochre and some are very faint and difficult to see

The patterns are a sort of graffiti and are not found natively on Egyptian ornaments

Most of them have been dated to the early centuries of the Christian era

But medieval or even modern early 20th century origins can't be entirely ruled out because the drawings aren't mentioned in the extensive listings of graffiti at the temple which was compiled by Egyptologist Margaret Murray in the year 1904

Patterns like these were sometimes used in England as an apotropac marks to keep nasty old witches from entering buildings

Consecration crosses which indicate points and churches which have also been anointed with holy water during a church's dedication have also taken the form of overlapping circles

There are tons of modern examples of this pattern around us all the time

You may not even realize it

This beautiful pattern has made its way into a wide range of uses

In quilting, the pattern has been called triangle wedding ring or diamond wedding ring as a means to contrast it from the traditional square pattern

You'll find the pattern occasionally in the fashion world

But it's also heavily used in the area of decorative arts

For example, Bring Me the Horizon's 2013 album SEMP INTERNAL uses the 61 overlapping circles grid as the main feature of its album cover

But that's not all either

The Sun of the Alps symbol has been used as the emblem of Padanian nationalism in northern Italy since the 1990s

It looks just like a pattern often found in that area on buildings

Nature is also the home of many different types of sacred geometry

For instance, an equilangular spiral, logarithmic spiral or growth spiral is a self-similar spiral curve that frequently appears in nature

The logarithmic spiral was first detailed by French philosopher Rene Descartes and then mathematician Jacob Bernoulli extensively investigated this pattern and called it Spira Mirabilis

Spira Mirabilis is Latin for Miraculous Spiral

Franco-American mathematician Benoit Medelbrot delved deeper into this pattern in his 1982 book, The Fractal Geometry of Nature, which is a revised and enlarged version of his 1977 book entitled Fractals, Form, Chance and Dimension, which in turn was a revised, enlarged and translated version of his 1975 French book Les Objets Fractals, Form, Hazard et Dimension

As technology has improved mathematically accurate, computer-drawn fractals have become more detailed

Early drawings were low resolution black and white

Later drawings were higher resolution and in color

Many examples were created by programmers working with Mandelbrot, primarily at IBM Research

These visualizations have added to persuasiveness of the books and their impact on the scientific community

The number 108 also plays an important part in the world of the sacred geometry as it's considered sacred by the dharmic religions such as Buddhism, Hinduism and Jainism

In Hindu tradition, the Mukhya Sivaganas, the attendant of Shiva, are 108 in number and hence Shaiva religions, particularly Lingayats, use malas of 108 beads for prayer and meditation

Similarly in Guadia Vaishnavism, Lord Krishna in Vrindavan had 108 followers known as gopis

Recital of their names often accompanied by the counting of 108 beaded mala is often done during religious ceremonies

The Sri Vaishnavite tradition has 108 Divya Desams, the temples of Vishnu that are revered by the 12 Alvars in the Divya Pradabandha, a collection of 4,000 Tamil verses

In Jainism, the total number of ways of karma influx known as Asarav, four kashes, anger, pride, conceit, greed, times three karmas, mind, speech, bodily, actions, times three stages of planning, planning, procurement, commencement, times three ways of execution, own action, getting it done, supporting or approval of action

In Buddhism, according to Bhante Gunarthana, this number is reached by multiplying the senses smell, touch, taste, hearing, sight and consciousness by whether they are painful, pleasant or neutral, and then again by whether these are internally generated or externally occurring and yet again by past, present and future, finally we get 108 feelings

Tibetan Buddhist malas or rosaries are usually 108 beads, sometimes 111 including the Guru bead, reflecting the words of the Buddha called Tibetan the Kangyur in 108 volumes

Zen priests wear Juzhu, a ring of prayer beads around their wrists, which consists of 108 beads

Japa mala or japa beads made from thulasi wood, consisting of 108 beads plus the head bead

The Lankavatara Sutra has a section where Bodhisattva Mahatmi asks Buddha 108 questions and another section where Buddha lists 108 statements of negation in the form of, a statement concerning X is not a statement concerning X

In a footnote, D

T

Suzuki explains that the Sanskrit word translated as statement is pada, which can also mean footstep or a position

This confusion over the word pada explains why some have mistakenly held that the reference to 108 statements in the Lankavatara refer to the 108 steps that many temples have

In Japan at the end of the year, a bell is chimed 108 times in Buddhist temples to finish the old year and welcome the new one

Each ring represents one of 108 earthly temptations known as the bono, a person must overcome to achieve nirvana

In the neognostic teachings of Samayal Aon we are, an individual has 108 chances or lifetimes to eliminate his egos and transcend the material world before devolving and having the egos forcefully removed in the infrared dimensions

These fun facts fill my heart with happiness

I love learning, don't you? I hope these spiritual concepts are becoming clear

Let's keep learning

I get what you're doing, you clever kitty

This is your way of reminding me to tell everyone about how sacred geometry has even made its way into music

The musica universalis, which literally translates to universal music, is also called music of the spheres or harmony of the spheres

Musica universalis is an ancient philosophical concept that regards proportions in the movements of celestial bodies, the sun, moon and planets, as a form of music

This music is not thought of to be audible but rather a harmonic, mathematical or religious concept

The idea continued to appeal to scholars until the end of the Renaissance, influencing many kinds of scholars, including humanists

Further scientific exploration discovered orbital resonance and specific proportions in some orbitable motion

The discovery of the precise relation between the pitch of the musical note and the length of the string that produces it is attributed to Pythagoras

The music of the spheres incorporates the metaphysical principle that mathematical relationships express qualities or tones of energy which manifest in numbers, visual angles, shapes and sounds, all connected within a pattern of proportion

Pythagoras first identified that the pitch of a musical note is in inverse proportion to the length of the string that produces it and the intervals between harmonious sound frequencies from simple numerical ratios

In a theory known as the Harmony of the Spheres, Greek philosopher Pythagoras proposed that the sun, moon and planets all emit their own unique hum based on their orbital revolution and that the quality of life on Earth reflects the tenor of celestial sounds which are physically imperceptible to the human ear

Subsequently, Plato described astronomy and music as twin studies of sensual recognition, astronomy for the eyes, music for the ears and both requiring knowledge of numerical proportions

Greek philosopher Aristotle criticized the notion that celestial bodies make a sound and moving in the context of his own cosmological model

From all this, it is clear that the theory that the movement of the stars produces a harmony i

e

that the sounds they make are concordant in spite of the grace and originality with which it has been stated is nevertheless untrue

Some thinkers suppose that the motion of bodies of that size must produce a noise since on our Earth, the motion of bodies far inferior in size and in speed of movement has that effect

Also when the sun and the moon, they say, and all the stars, so great in number and in size are moving with so rapid of a motion, how should they not produce a sound immensely great? Starting from this argument and from observations that their speeds, as measured by their distances, are in the same ratios as musical concordances, they assert that the sound given forth by the circular movement of the stars is a harmony

Since however it appears unaccountable that we should not hear this music, they explain this by saying that the sound is in our ears from the very moment of birth and is thus indistinguishable from its contrary silence, since sound and silence are discriminated by mutual contrast

What happens to men then is just what happens to coppersmiths, who are so accustomed to the noise of the smithy that it makes no difference to them

But as we said before, melodious and poetical as the theory is, it could not be a true account of the facts

There is not only the absurdity of our hearing nothing, the ground of which they try to remove, but also the fact that no effect other than sensitive is produced upon us

Excessive noises we know shatter the solid bodies even of inanimate things

The noise of thunder, for instance, splits rocks and the strongest of bodies

But if the moving bodies are so great and the sound which penetrates to us is proportionate to their size, that sound must need to reach us in an intensity many times that of thunder and the force of its action must be immense

The three branches of the medieval concept of Musica were presented by Boethius in his book De Musica

Musica Mondana, sometimes referred to as Musica Universalis

Musica Humana, the internal music of the human body

Musica que in qui bustam constituta est instrumentis, sounds made by singers and instrumentalists

According to Max Heindl's Rosicrucian writings, the heavenly music of the spheres is heard in the region of concrete thought, the lower region of the mental plane which is an ocean of harmony

Musica Universalis which had existed since the Greeks as a metaphysical concept was often taught in quadrivium

And this connection between music and astronomy intrigued German astronomer Johannes Kepler and he devoted so much of his time after publishing the Mystery of the Cosmos, also known as the Mysterium Cosmographicum, looking over tables and trying to fit the data to what he believed to be the true nature of the cosmos

In 1619 Kepler published Harmonices Mundi, which literally translates to the Harmony of the Worlds, expanding on the concepts he introduced in Mysterium and positing that musical intervals and harmonies describe the motions of the six known planets of the time

He believed that this harmony, while inaudible, could be heard by the soul, and that it gave a very agreeable feeling of bliss afforded him by this music in the imitation of God

In Harmonices Kepler laid out an argument for a creator who had made an explicit connection between geometry, astronomy, and music, and that the planets were arranged intelligently

Wow, I can feel my spirit evolving as we learn all this new and important information

And there's more! Harmonices is split into five books, or chapters

The first and second books give a brief discussion on regular polyhedron and their congruences, reiterating the idea he introduced in Mysterium that the five regular solids known about since antiquity define the orbits of the planets and their distances from the sun

Book three focuses on defining musical harmonies, including consonance and dissonance, intervals, including the problems of just tuning, their relations to string length, and what makes music pleasurable to listen to

In the fourth book, Kepler presents a metaphysical basis for this system, along with arguments for why the harmony of the world appeals to the intellectual soul in the same manner as the harmony of music appeals to the human soul

Here he also uses the naturalness of this harmony as an argument for heliocentricism

In book five, Kepler describes in detail the orbitable motion of the planets and how this motion nearly perfectly matches musical harmonies

Finally, after discussion on astrology in book five, Kepler ends harmonises by describing his third law, which states that for any planet, the cube of the semi-major axis of its elliptical orbit is proportional to the square of its orbital period

In the final book of harmonises, Kepler explains how the ratio of the maximum and minimum angular speeds of each planet, its speeds and the perihelion and aphelion, is nearly equivalent to a consonant musical interval

Furthermore the ratios between these extreme speeds of the planets compared against each other create even more mathematical harmonies

These speeds explain the eccentricity of the orbits of the planet in a natural way that appealed to Kepler's religious beliefs in a heavenly creator

While Kepler did believe that the harmony of the worlds was inaudible, he related the motions of the planets to musical concepts in book four of harmonises

He makes an analogy between comparing the extreme speeds of one planet and the extreme speeds of multiple planets with the difference between monophonic and polyphonic music

Because planets with larger eccentricities have a greater variation in speed, they produce more notes

Earth's maximum and minimum speeds, for example, are in ratio of roughly 16 to 15, or that of a semi-tone, whereas Venus's orbit is nearly circular and therefore only produces a singular note

Mercury, which has the largest eccentricity, has the largest interval, a minor tenth, or a ratio of 12 to 5

This range, as well as the relative speeds between the planets, led Kepler to conclude that the solar system was composed of two bases, Saturn and Jupiter, a tenor, Mars, two altos, Venus and Earth and a soprano, Mercury, which had sung in perfect concord at the beginning of time and could potentially arrange themselves to do so again

He was certain of the length between musical harmonies and the harmonies of the heavens and believed that man, the imitator of the creator, had emulated the polyphony of the heavens so as to enjoy the continuous duration of the time of the world in a fraction of an hour

Kepler was so convinced in a creator that he was convinced of the existence of this harmony despite a number of inaccuracies present in harmonesis

Many of the ratios differed by an error greater than simple measurement errors from the true value for the interval and the ratio between Mars' and Jupiter's angular velocities does not create a consonant interval, though every other combination of planets does

Kepler brushed aside this problem by making the argument, with the math to support it, that because these elliptical paths had to fit into the regular solids described in Mysterium, the values for both the dimensions of the solids and the angular speeds would have to differ from the ideal values to compensate

This change also had the benefit of helping Kepler retroactively explain why the regular solids encompassing each planet were slightly imperfect

Kepler was convinced that the geometrical things have provided the creator with the model for decorating the whole world and wanted to further explore the aspects of the natural world specifically being involved with astronomical and astrological concepts of music

When Kepler published Harmonesis Mundi, Kepler was held liable in a dispute with physician Robert Flood, who also published his own harmonic theory at the time

To Kepler, the celestial physics of the spheres were seen as geometrically spatial regions that consisted of each planetary orbit rather than its physical form

The connection between music, mathematics, and astronomy had a profound impact on history

It resulted in music's inclusion in the quadrivium

The medieval curriculum that included arithmetic, geometry, music, and astronomy, and along with the trivium, grammar, logic, and rhetoric, made up the seven liberal arts, which are still the basis for higher education today

A small number of recent compositions either make reference to or are based on the concepts of Musica Universalis or Harmony of the Spheres

Among these are Music of the Spheres by Mike Oldfield, owned by the Moody Blues, The Earth Sings Me, Follow Me album by the Receiving End of Sirens, Music of the Spheres by Ian Brown, and Björk's single Cosmogyny, included in her 2011 album, Biophilia

Earlier in the 1910s, Danish composer Rued Langart composed a pioneering orchestral work titled Music of the Spheres

Music of the Spheres was also the title chosen for the musical foundation of the video game Destiny and was composed by Martin O'Donnell, Michael Salvatore, and Paul McCartney

Paul Hindemith wrote a 1957s opera and a symphony using the same music called Die Harmony der Welt, based upon the life of the astronomer Johannes Kepler

The next time you find yourself listening to music, observing nature and your surroundings or just solving a simple mathematical equation, take a moment to reflect on the patterns around you

They have so many exciting things to tell you

Okay Joy, I know it's time to eat, I get what you're telling me

Okay so before we're out of here, remember whether the microcosm or the macrocosm, sacred geometry is written into the fabric of life itself

Now that's Quick Wisdom with Bless and that wraps up our learning for today's fascinating subject

I hope your spirit has grown as much as mine has

Please come see me anytime to discuss more spiritual ideas and heart-fulfilling concepts

What was that Joy? You don't want them to leave? Neither do I

Well they can stay if they want to

Now let's meditate on our next adventure

Let's begin

You