The Science and Mysticism of Numbers - Ingrid young: transcript

The topic today for my talk is the Science and Mysticism of Numbers. And I hope you find it interesting, because whole books have been written on the subject of numbers and mathematics. I am not a math genius, so if you weren't good at math before, this doesn't mean that you will be better, but that you will perhaps learn some things that you didn't know before. Certainly, it was an enlightening experience for me to prepare this presentation. And the subtitle, of course, relates to our theme: Ancient Insight and Modern Understanding.

Numbers have meaning on the material and spiritual planes. Ancient wisdom has contributed to our knowledge and use of numbers today. The study of numbers is part of the Rosicrucian tradition. Our word "ritual" comes from the Indo-European root "ri," which means to count or to number. The use of "ri" for ritual comes from the use of rites, that is, formal ceremonies to mark seasons and cycles. The significance of ritual and its repetition is that it allows for the alignment of human consciousness with divine consciousness. That was a statement made by Iamblichus at the beginning of the Common Era.

He was a Neoplatonist. That means that he followed the teachings of Plato and additionally added some of his own ideas around that time that people were considering the importance of the divine as the monad. The Babylonians used finger counting up to 60 using joints in hands and feet. Ten is the basis for most human counting systems because people have ten fingers, ten toes, and three joints in each finger.

So if you've ever wondered why there are 60 seconds in a minute and 60 minutes in an hour, that goes all the way back to the Babylonian culture. Counting on your fingers is intuitive and makes you smarter, according to new research, and many of you have heard this expression: instead of counting your days, make your days count. The Sanskrit word for finger counting is closely related to mudra, the word for sacred hand gestures and dance in the Hindu religion and statuary. These are also related to the five elements. The first four you see there: earth, water, fire, air. Note that the fifth element is space—Akash. In mysticism, we often refer to the Akashic Records, or cosmic memory.

Recent physics uses the term Akashic field—the quantum actuality of energy and information underlying our reality. 50 years after an Indian astronomer and astrologer brought Indian reference works to Baghdad, al-Khwarizmi, a Persian polymath, published a book that was called simply Algebra. That was in 820 C.E. Algebra. Our word "arithmetic" comes from the word arithmos in Greek, meaning number.

And you see at the bottom a little bit of a footnote: Purnaka is gold in Sanskrit, and there is the proper pronunciation of al-Khwarizmi, and what the meaning of polymath is—someone who is a master of many domains. Al-Khwarizmi embraced the Indian number system and included zero as a placeholder, a novel idea. Algebra and other books by al-Khwarizmi were copied into Latin in the 12th century C.E. and hit the consciousness of Europe with their radical Arabic numerals 1 to 9 plus zero.

What were used in Europe before? Roman numerals, of course. Our terms "algebra" and "algorithm" come from the titles of his writings. During the 12th century, monk historian William of Malmesbury considered the new numbers Saracen magic, not to be trusted, because numbers, especially zero, were just scratchings on a page and not reliable like quantities you could see and touch: a handful of pebbles, a flock of sheep, or even a basket of fruit.

The use of an accounting board, the abacus, was a more reliable device as opposed to written calculations. Counting boards originated in Mesopotamia around 2300 BCE. They are the foundation of modern calculators over centuries, refined through ancient cultures from east to west. Children and adults today can improve their math skills by working with an abacus or counting frame. The Latin word calculus is used in medicine today—small stone or pebble. Calculator to count, and calculi counting boards. These words shape our language today, and you are all familiar with the term calculus.

This is an interesting image by Gregor Reisch from 1503. It's called Calculating Table, and we see two versions here. We also note that in its symbolism, arithmetic is here personified as a kind of goddess, Arithmetica. And she was one of the seven liberal arts studied during the Renaissance. She is instructing Boethius and Pythagoras, and they're shown as an algorist and an abacist, although Boethius was born certainly well before Arabic numerals or algebra were introduced into Europe. So you might wonder about why. In fact, also, the characters in this image are wearing Renaissance clothing.

That is in order to tell us how important mathematics and these philosophers were in the 1500s. So in the 16th century, we have an emphasis on the teachings of both Boethius and the Pythagoreans, who are shown here as contemporaries, and who are also not only mathematicians—they were also, although not shown here, music theorists. That brings us to the significance of numbers, ancient and modern.

And we're going to talk about the meaning of numbers from 1 to 10—I mean one, sorry, to ten. The monad or one is central to human observation and represents timelessness, infinity, the circle of life, and the cosmic egg itself. It is said there is one universal soul, diffused through all things, eternal, invisible, unchangeable—in essence, like truth; in substance, like light.

Two. And here is a quotation from the Kybalion: "Everything is dual; everything has poles; everything has its pair of opposites; like and unlike are the same; opposites are identical in nature, but different in degree." And I know you understand now that temperature is one of these good examples, if you're not sure how things can be identical in nature, but different in degree. Hot and cold are certainly extremes in the one thing: temperature. According to Carl Jung, embracing the opposite brings balance and wholeness. He said, "The conjunction of opposites is necessary to create the self."

All 2D surfaces have length and width, like a painting. Its higher-dimensional aspect is its meaning beyond measure. Two interlaced circles form the vesica piscis. That's Late Latin, that pronunciation, piscis. The Italian mandorla, meaning almond or almond-shaped, is contained in the vesica piscis. And we see it here, where the two circles interlace at their midpoint. The shape in the center is the vesica piscis, also called the mandorla.

What's interesting about this image is that it's so pleasing that many companies have used it in their ad campaigns or in their logos: MasterCard, for example, has two interlaced circles; Coco Chanel, the two C's interlaced in that cosmetic company. The proportions of the mandorla were described by Pythagoras. And those proportions—it's a ratio—come out to the square root of three. The square root of three is a number that also defines three-dimensional space. Symbolically, the mandorla represents the heart, the mouth of Ra, the yoni, the doorway of life, the mirror, and the moon—also the doorway to manifestation. Two then leads to three. Empedocles described human beings as triple with a body (soma), a soul (psyche), and a spirit (nous).

We use similar terms today in Rosicrucian ontology with slightly different meanings, and if you're studying with us, it would be a good idea to go back to the neophyte monographs and have a look at those definitions, because they're very important. Many of you understand that the tria prima—the three principles in alchemy—the tria prima is salt (body), sulfur (soul), and mercury (spirit). The Law of the Triangle is also called the Law of Manifestation in Rosicrucian ontology, and functions on both the material and spiritual planes. And here within the circle, also, there's a very important symbol, often which represents the Philosopher's Stone. We see two triangles: we see the triangle on the material plane, and the one with the point downward on the spiritual plane.

This is a very significant law. Just like the law of duality and opposites, we have the Law of the Triangle, and notice how it functions: thesis and antithesis appear to be opposites or opposing forces. They combine to create a third condition, a synthesis of the two, and this is studied at length, especially in the early monographs of our study system. Three leads to four. And you will notice against the right-angle triangle here that we have three squares—four-sided squares. This is the Pythagorean theorem: area A plus area B equals area C. The ten dots arranged as a triangle had multi-level meanings for the Pythagoreans; they were mathematical, philosophical, and metaphysical.

We have the monad (1), the dyad (2), triad (3), and tetrad (4), and these were aligned with the classical elements: earth, fire, water, and air. Four also has mystic significance. And one thing I really wanted to share with you, because I find this fascinating, is that in 2016, physicists created a hologram of a single light particle—what we call a photon, a holographic image. What's amazing about it is that it looks like a Maltese cross, and crosses are symbols of cosmic unity. You see also...

The cross and the circle—it's used today as the astronomical symbol of Earth. The two together suggest the harmonious binding of the spiritual and material worlds. In Pythagorean philosophy, the tetrad (4) represented the completion of space and the physical manifestation of the material world, Earth, and nature. Four in the West symbolically represents justice, balance, foundation, strength, and stability, both earthly and cosmic.

And you see here the pyramid resting on the base of a square. Asian pop culture considers four unlucky since it sounds like the word for death, and actually in several languages—in Chinese, and Japanese, and in Korean. This superstitious belief is called tetraphobia, even though four is important in Chinese design and seasonal celebrations—lots of pop cultural things. Here is another interesting quotation by Iamblichus from the beginning of the Common Era: "The tetrad comprehends the principle of the soul as well as that of corporeality," that means of the body. "For they say that a living creature is ensouled in the same way that the whole universe is arranged according to harmony."

Five is humanity incarnated, and notice that the five points of the pentagram here are interlaced. The rose in mystical tradition is the Rosa canina, the wild or dog rose. It consists of an open center and five heart-shaped petals. In tarot, the tarot deck card five is the Hierophant, the wise one; and when reduced, card 14—in classical numerology, we add the numbers together. For example, the number 14 becomes one plus four, which is also five. That card is Temperance, and there are correspondences in the tarot between their cards and their numerological equivalents.

So this is interesting, because temperance is something that wise persons should exhibit—that is a kind of wise moderation in all things. There are five elements in the traditional Chinese system: wood, earth, fire, metal, and water. In Japan, the pentagram symbolizes the yin-yang master, Abe no Seimei, and Onmyōdō—a master of earthly and cosmic energies. And today you can buy little—like even keychains with pentagrams on them, because they're considered to be good luck charms. But the Order does not subscribe to superstitious beliefs. We are grounded really in science and in metaphysics, that is, going beyond physics to the mystical elements or spiritual elements of all things.

The quintessence, or fifth element, is the final stage of the alchemical process. So there is the—call it the fifth element beyond the four, and it is a result of the divine marriage of spirit and soul of the tria prima. Five is important when we talk about sacred geometry because of the five Platonic solids. There are five polyhedra, and they were originally equated with the five elements. And again, you see five elements: fire, air, earth, water, but notice that the fifth element is ether, space, or the Akashic field, which is not so empty after all, as we are discovering.

So in centuries past, and actually for a very long time up until about the 20th century, people talked about the cosmic void as the ether. What is the Pentacle of Venus? It is an astronomical five-pointed star traced repeatedly and on a near-perfect schedule, taking approximately eight years to complete. The ancients knew of the Venus Pentacle—the Mayans, the Pre-Aztecs, the Sumerians, the Egyptians, and the Greeks, the Knights Templar too. The next transit of Venus across the sun won't occur again until December 2117. Earth and Venus will then be in perfect alignment again with the sun.

The last transit of Venus looked like this, and it occurred in 2012. So we see here the disk of Venus, which is closer to the sun than we are—it's one of the inner planets. We see it crossing the face of the sun. These other black spots are actually on the surface of the sun; they're cooler spots called sunspots. Now, what's interesting about understanding how this works: that five times over eight years Earth and Venus align, but they're not in identical or perfect—on the perfect plane of alignment.

They're slightly on different planes, so we don't always have a transit of Venus, just like we don't always have a total solar eclipse of the sun at the same spot on the Earth. Six is often represented as two interlaced triangles, or the hexagram. It represents balance: the above and the below. It is significant in the Martinist tradition. 666 is a sacred number in the secret symbols of the Rosicrucians of the 16th and 17th centuries. Again, Western pop culture falsely misreads 666 as something to fear. The magic square of the sun totals 666. It was also a number sacred to Apollo as well.

It is the foot measurement of the cathedral labyrinth, and here we have the 666: six points, six triangles, six sides. And we have quotations from the biblical texts, from Revelation, especially down here at the bottom where we see the two interlaced triangles: "Blessed is he who can name the number of the beast, 666. The beast was, and is not, and shall ascend and be in eternity."

And here is the magic square of the sun. It's considered magic—squares are considered magical because they sum to the same numbers. And here we have 36 numbers, and this is called the magic square of the sun. These correspondences were linked astrologically with the main six planets, the magic squares, again, from the 15th and 16th centuries onward. So notice that each row sums to 111, and six rows times 111 is 666.

Not only do the rows sum to 111, but the columns do as well, as well as the diagonals. So that's why the magic squares are seemingly magical. We see also here the labyrinth of the cathedral and its central point. The still point at the center is a rose, and it represents an internal journey, and it was often used as a meditation mandala. Seven is the ideal cycle on the material and spiritual planes. In Martinism, the temple designation of heptad is based on the Greek word for the number seven, valued by the Pythagoreans.

All dates divisible by seven were considered important, like 7, 14, 21, 28. There are seven generations which are valued by First Nations people in planning the future; seven rungs in the ladder to enlightenment in the alchemical tradition; the seven notes of the diatonic scale, the sacred notes of Guido d'Arezzo: do, re, mi, fa, sol, la, ti; and of course, the seven color wavelengths of white light, Roy G. Biv, as we learn in school: red, orange, yellow, green, blue, indigo, and violet.

And here we have Rosicrucian Isaac Newton's color wheel, which equated musical pitches with the spectrum of light in his publication Opticks from 1704. And we do the same thing when we use vowel sounds in our Order. The Sanskrit ashta, or eight, is like aster, Greek for star, and we see the eight-pointed star as a symbol of Inanna or Ishtar. Ishtar—she was an ancient goddess of war and love, interesting opposites. The eight-pointed star of the compass rose of navigation—and it's called the compass rose. It has eight points. Light, heat, sound, and color move in waves of vibration and frequency in octaves, that is, repeating scales of seven plus one. In the manifest universe, the lemniscate, or sideways eight, represents infinity.

Also, the analemma, or endless loop of the sun as it seemingly moves across the Earth between the Tropics of Cancer and Capricorn. The number nine symbolizes completion, perfection, fulfillment, gestation, experience, and self-awareness. Multiples of nine sum to nine in classical numerology. So try this with 18, 27, 36, and 45: nine times two is 18, which is one plus eight (9); nine times three, 27 (two plus seven is 9); nine times four, 36 (three plus six, 9); nine times five, 45 (four plus five is 9).

It also works as we go higher: nine times six is 54, that's 45 backwards. So as a list, multiples of nine create a palindrome—you can read it the same backwards and forwards. So again: 9, 18, 27, 36, 45; and at 45 the numbers flip backwards—54 and 45 are the reverse of each other, 36 and 63, 72 and 27, 81 and 18, and 90 and 09, in other words.

And 11 times nine is 99. Now I want to talk to you about creating the basic magic square, and we start with three times three: 1, 2, 3, 4, 5, 6, 7, 8, 9. That itself is not the magic square. I'm going to tell you first the story of the Luoshu. It's considered the oldest magic square, although that may not be precisely true, but it involves the story of the sacred turtle.

Legend states that about 3000 BCE, Emperor Yu the Great discovered a so-called magic turtle on the Luo River and took it back to his palace to study. The number sequence itself became the Luoshu, mentioned in Chinese mathematical texts circa 2200 BCE and onward. I Ching and Feng Shui all descended from this sacred creature. It had odd-numbered white dots and even-numbered black dots on its shell.

And here's the final result of the Luoshu square: we see five at the center, nine at the top surrounded by four and two, five surrounded by three and seven, one at the bottom surrounded by eight and six. So what makes this square so-called magical? Well, and how do you make one? This is quite easy. First, tip the box on its side to create a diamond of 45 degrees.

Notice how one is at the top, seven and three here on each side. Next, reverse one and nine, and then three and seven. So nine goes to the top, one at the bottom, three over to the left, and seven to the right, and you have this. So notice how you flipped one and nine, three and seven; the other numbers remain the same. Nine would be surrounded by four and two—see how that works? One will be at the bottom surrounded by eight and six, and three and seven are reversed, and five stays at the center. So why is this an interesting creation? Numerology—it's considered also—it's called the square of Saturn, and it sums to 15 diagonally, across, and down.

And the total of the numbers in the magic square is 45, and that is the numerological value of the planet Saturn in Arabic: Zuhal. Notice that this has been known for centuries. In the 1500s we have the German penny, German pfennig, and the words in German are "Schlag von Gerold." So Gerold was the king of Germany and he was also the pope, and he transitioned in 1500. So this is in a way a kind of emblem of power, but also of good luck. It means timely wholeness or well-being. That brings us finally to ten and its mystical significance. Ten rungs on the DNA chain form a protective tenfold rosette. So physically, this is quite interesting about DNA—it has ten rungs, and when it's folded, the rosette shape protects it from being damaged.

We don't want to have damage in DNA. The Pythagorean tetractys is shown here surrounded by the ouroboros, the snake biting its tail. Here again, as a triangle, it is one plus two plus three plus four is ten. The tetractys is from the Pythagoreans, and we have ten sephirot in the Tree of Life in the study of Kabbalah or Kabbalah. Finally, Plato felt that ten contained all numbers, and in a sense we understand that it too represents the monad, the beginning and the end. Ten symbolizes both a return to unity and divine omnipresence in all things. To conclude: now and in the ancient past, numbers express principles of order, harmony, and beauty. Just as in music and other art forms, numbers have mundane use in measurement, counting, and relationships of time and space.

More profoundly, they represent the fundamental correspondence between outer and inner worlds, as in an inner psychic order, and thus our underlying unity with the divine or absolute. Thank you.