ISSN: 1913-1917
IN THIS ISSUE
July 2008 Issue
Feature Article:
-- Mathematics and Dreaming
Cross Cultural Dreaming:
-- Scientists Learn to Program Human Dreams
Famous Dreams:
-- Friedrich Kekule and the Benzene Ring
Readers Dreams & Analysis:
--none this issue
Symbol of The Month:
-- Numbers
Reader Comments:
--None this issue
From The Editor:
-- Request for feedback
Submission Instructions:
--See bottom of newsletter
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Quote of the Month
The best reason for having dreams is that in dreams no reasons are necessary.
Ashleigh Brilliant
Ashleigh Brilliant
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Feature Article:
In all my attempts to understand the creative process I have discovered a fundamental similarity between the realm of mathematics and the real of dreaming . . .
Why dreams? I have been very aware of the irrational and mystical nature of the creative process in all my mathematical research. Several times dreams have given me hints for solutions of specific problems I was working on. This led me to ask, what is the creative process in mathematics like? Can the world of dreams and the irrational shed any light on this process?
What interests me most in both mathematics and dreams is the element of mystery. Mathematical proofs and symbols and formulas have always seemed deeply mysterious to me, even when I understood what they were about. When I get interested in a problem, it is the fundamental mystery about the problem that really attracts me: the fact that no one understands it or knows how to solve it, the beckoning images that it calls up in my mind when I meditate on it. Dream images have that same kind of mystery. They exert an irresistible pull, and I get drawn in like a moth. Then I get immersed in the problem or the idea to the extent that I feel as if I merge with it.
This sense of mystery is related to the feeling that underneath what I understand is a deeper meaning or a deeper structure waiting to be discovered. The problem a research mathematician tries to solve can be likened to a game, but a game in which the rules are not yet known. The real goal of a mathematical game is to determine, without having seen that particular game before, what its special rules are! The mathematician discovers these rules by playing with the game, experimenting, listening for its inner logic. Normally the rules of this kind of game are discovered out of order.
The truth is that the full application of logical principles usually comes relatively late in the process. In solving a problem that no one has solved before there is a weird mixture of the rational and irrational, of following hunches, meditating on images, performing calculations that lead nowhere, going on fishing expeditions, you might call it, and then suddenly seeing how everything fits together. It's only after you see how it all fits together that you can put it into a logical, rational order.
That's the last step.
Mathematics is logical, yes, but it's also symbolic and mysteriously coherent, so that it really requires both "left-brain" and "right-brain" approaches to comprehend it. It's a vast system of ideas, images, and symbols that all fit together beautifully to form a coherent, consistent whole. I like to think of it as a mosaic, a multidimensional network of ideas and interconnections, or a huge Lego set, with intricate, interweaving patterns and amazingly complex arrangements.
And mathematics exists primarily in our minds. You can't really see it anywhere in literal, physical form. Numbers don't exist as objects in the physical world; they are modes of perception. When you see two things you may think "two," but that "two" is just a name for the experience of seeing two things. You're really applying your imagination. Geometrical forms come the closest to being mathematical objects that actually appear in the physical world, but these forms are models of what we see in our imaginations. Mathematics is a symbolic language that refers to our imaginative modes of perception. Mathematics is really a mirror for the behavior of our own minds. That is a wild thought. What we calculate with and prove things about are our own imaginative modes of perception.
Looking for Patterns in Dreams
After having written down my own dreams for many years, I realized that an individual's dream life is the perfect analogy for the mathematical world: Each of our dream lives consists of images and symbols and ideas that live together in our imagination. These images and symbols fit together beautifully to give messages or encouragement or sometimes premonitions. Furthermore, if we start following the hints that our dreams give us, and keep track of where that takes us, we will start discovering new insights about ourselves and our lives. Just as in mathematics, where we can determine if something works by whether or not it fits with the rest of mathematics, whatever interpretation we find has to fit with the rest of our dreams–and with our life experience. It has to feel right to us, to resonate deeply with our experience, and it also has to change us in some way. That's the criterion for proof in this realm. A fresh dream not yet understood is like a mathematical problem, and the interpretations and insights gained in following the dream process and putting images and symbols together are like the theorems of mathematics. Each of our dream lives is also a multidimensional mosaic!
At first I took this as an amusing hypothesis, and started to play. I used a sequence of about sixty dreams that I had between 1978 and 1985. I decided not to rely at first on any of the traditional schools of interpretation, because I wanted to see what the dreams said on their own.1 As Rafael Lopez-Pedraza and James Hillman and others have stated,2 it is important in looking at dreams to stick closely to the images, and not lose one's way in a theory of dream interpretation. The same thing is true in mathematics. It's very important to try to understand the problem itself, on its own terms, and not assume that the answer is contained in someone else's theory.
In the beginning I tried understanding individual dreams in isolation. Then I started noticing patterns. Themes started to become apparent. After sifting through the dreams for a while, a couple of really important and deeply mysterious dreams stood out. They seemed to present the most difficult problems, so I focused on these. The more I played with the dreams, the more like mathematical work the whole process seemed.
I started putting different dreams together. Images in one dream would appear in several other dreams. This suggested using parts of one dream to interpret another. For example, I have had many dreams about women with a specific hair color. The hair color is always either red, blonde (yellow), white, or black, sometimes silvery. Other dreams would mention these colors in connection with certain compass directions. One dream was of a white tornado in the North. A whole sequence of dreams connected the element of water with the West. The yellow color seemed to refer to illumination and the East. I came to realize that the colors and directions were connected in my dreams with the specific elements, air, water, fire, and earth. I found that these colors match up with the colors that are emphasized in medieval texts on alchemy,3 and that they actually referred to certain states of consciousness, or modes of perception.
A Model of the Creative Process
Sometimes in mathematics you discover something extra without really trying. In the process of solving one problem, another whole avenue of investigation opens up and something beautiful falls into your lap. The same thing happened to me in this dream investigation. What emerged from putting together the hair-color dreams and the direction dreams was a model of the creative process. By taking the dream hints and placing them on a circle, and then filling in for the missing pieces, I came up with the diagram below.
The various areas of the circle represent different modes of perception, or different stages in our coming to consciousness related to a specific mathematical problem. The spiral path, taken clockwise, indicates that we can pass through each stage many times along the way to a "solution."
The South represents the stage of preparation, application, organization, and ritual. The West represents the introspective stage, the stage of stuckness, confusion, and darkness, where we learn to let go of preconceived ideas. The North is the stage in which we follow hunches and take the risk to see where subtle hints may be leading us. The East is the place of full illumination and realization, and simultaneously the place of desire.
What struck me about this was that I was using my dreams as a coherent, symbolic system to extract insights about the creative process itself. I remember how excited I was when I wrote all this down. I called one of my friends and told her about my circle, and she said, "Oh, that's a Native American medicine wheel!"4 So the above mandala isn't new, after all. But how interesting! My completely subjective process, which arose piecemeal over many years in my dreams, combined with the kinds of approaches I had used in mathematical work, had led to something that was known, and therefore, in a sense, objective. For me that's a verification that the creative process of dream interpretation can lead to insights in a shared reality, just the way different mathematicians' insights and images and proofs combine to form the shared reality of mathematics.
This feels important to me. Dreams, like mathematics, operate with and express themselves in terms of our imaginative modes of perception. In science we base our understanding of physical reality on mathematics. What would happen if we based our understanding of reality on our dreams instead? I suspect that working with our dreams in this way could lead us to a new, more comprehensive kind of mathematics, that includes psychic data and symbolism and uses our whole minds, intuitive, rational, and irrational, to learn more about the universe.
In working on a mathematical problem, I go around and around on the circle many times before I get anywhere. Some of this revolving leads me to a good question, which is an important insight in itself. I go around and around with different pieces of the problem, involving different levels of consciousness. When one piece gets clarified, the desire to know more is generated. This desire is also a form of illumination. More times around and the questions get clearer and sharper and more focused. Then I often get completely stuck. If I'm lucky, that state of stuckness makes me let go into following a new way of thinking. And, sometimes, I'm struck by a wonderful idea that hits like a bolt of lightning.
The diagram also gives a hint of how creativity is a multidimensional process. In solving a big problem, we solve smaller problems along the way, whether they are problems of sequence, language, or notation in the South, of realizing our stuckness in the West, or in knowing how to follow our hunches in the North. The skills of the four modes are required to solve problems associated with all four directions. We could represent this on the diagram by drawing a smaller directional circle attached to each of the original directions. But that is only the beginning of refining our model. Each of the four modes operates within all other modes at increasingly refined scales. Different levels of our consciousness move on different-sized wheels, with increasingly smaller circles inside bigger circles. With this understanding our mandala becomes a fractal, a mathematical object that is geometrically similar to itself at all scales. We have returned to our starting point! Creativity and dreams and mathematics are hopelessly entangled.
A Sacred Process
Creativity is a complex, spiralling process that looks like itself at every level and then returns to itself. It is about mystery and illumination, about being divinely inspired by the Muses and about hard work and attention to detail. Yes, each of my dreams was a divine gift, but I had to work hard to get the whole picture the Muses were hinting at. In every situation creativity happens differently, yet it is also mysteriously familiar.
This suggests to me that creativity is a deeply spiritual endeavour, and that to be creative in the middle of a challenging situation calls forth from us our deepest humanity, our deepest resources, our greatest longings to experience oneness with the world around us. When we commit ourselves to being creative in answer to a real need, I believe we are helped by divine agencies that are simultaneously a larger part of ourselves. Put another way, each of us lives inside and outside time, and in creativity the part of us living outside time pours itself through the part of us living inside time. Socrates called this greater being our daimon, the guiding principle of our lives, which seems to exist prior to the living out of our lives.
Creativity combines the person and the process: In letting this principle work through us, we are changed and our consciousness is transformed.
Ultimately, that may be the real goal of the creative process, to change our own consciousness, and to become more aware of the larger mosaic of which we are all part.
NOETIC SCIENCES REVIEW # 49, PAGE 44
AUGUST -NOVEMBER 1999
Patrick Morton
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Cross-Cultural, Cross Platform Dreaming:
Research Adds to Links Between Dreams and Learning, Creativity
Boston--October 12, 2000--
A team of Harvard Medical School scientists has achieved what researchers since Freud's day have sought: a way to control -- at least in part -- the content of a person's dreams. They are using their dream-provoking method to explore age-old questions, such as: Where do dreams come from? What do they mean? What is their role in memory, learning, and creativity? What is their link to the unconscious?
For years, scientists have been stymied in their quest to understand these associations because dreams are unique events that cannot be replicated. Until now. Robert Stickgold, HMS assistant professor of psychiatry, and his colleagues report in the Oct.13 Sciencethat they were able to get 17 different people to see the same dream images as they drifted off to sleep.
Stickgold and his colleagues elicited the carbon-copy images using the computer game Tetris, training 27 subjects -- 12 novices, 10 experts and 5 amnesiacs -- to play the game over the course of three days -- a two-hour morning and one-hour evening session the first day and an hour-long morning and evening session each of the following two days. They then monitored the subjects' dreams as they were drifting to sleep on the first two evenings.
Seventeen of the subjects, over 60 percent of the total, reported dreaming at least once in the hour after they fell asleep, and all reported the exact same dream images -- falling Tetris pieces. And intriguingly, the majority of dream reports occurred on the second rather than the first night of training. This lag between first training and most intensive dreaming is interesting for
the light it may shed on the link between learning and dreams. It appears that the need to learn may actually prod the brain to dream. "It's as if the brain needs more time or more play before it decides, 'Okay, this is something that I really need to deal with at sleep onset,'" Stickgold said.
Perhaps the most surprising findings of all came from the amnesiacs in the study. Co-author David Roddenberry found that when the five amnesiacs -- who had no short-term memory due to hippocampal damage -- were exposed to the computer
game protocol, three of them experienced the same hypnagogic dreams as the normal subjects.
"I was just stunned when David called me and said they're getting them," Stickgold said. Though amnesiacs were known to dream, their dreams were thought to have little to do with the day's events, since those events are not remembered.
Stickgold had assumed that this would be especially true of the early, or "hypnagogic," stages of dreaming explored in their studies. Compared to later stages of dreaming, such as those occurring during deep sleep or REM sleep, hypnagogic dreams were thought to be more tightly linked to conscious, or episodic, memory. "We thought if there's one part of sleep that depends on episodic memories, which amnesiacs lack, it's sleep onset," he said.
The fact that some of the amnesiacs saw the falling Tetris pieces points to the powerful role played by the unconscious in dreams. In fact, Stickgold believes that the amnesiac's unconscious Tetris memories may have affected not only their dreams but also their waking behaviour. Unlike the normal subjects in their study -- who improved in their computer games over the course of the three days -- the amnesiacs showed marginal improvement. Most had to be taught the game all over again each day. But Roddenberry, an undergraduate at Harvard University, observed that at the start of a session, one of the amnesiacs placed her fingers on the exact three keys used in playing Tetris.
"She did not quite know what she was doing and yet she did know what she was doing," said Stickgold. "In a way, this is Freud's unconscious -- things activated in our brain, that are in fact memories that guide our behaviour but are not conscious," he said.
The notion that dreaming is prompted by a need to learn was supported by other findings as well. The researchers found that novices who reported seeing falling Tetris pieces did not perform as well in their initial two hour Tetris training session as those who did not see the images. "It's as if the more work you have to do, the more likely you are to get the imagery," said Stickgold.
Those who needed to do the least work were the experts in the study, each of whom had previously logged at least 50 and as much as 500 hours of Tetris playing, mostly on Nintendo sets. Half of them reported dreams of Tetris pieces falling before their eyes, but the last two experts reported an intriguing twist. Rather than seeing the Tetris pieces in black and white, as they were shown in the experimental protocol, they saw them as they appeared in their earlier Nintendo Tetris-playing days -- in color and accompanied by music. This substitution of old images for new ones strikes at the most distinctive quality of dreams -- their often astounding creativity. In dreaming, the brain does not merely replay memories but transforms them by associating them with old images and memories. "It's actually hunting around and finding other relevant information to connect to, which is the integrative process -- which over time, I would argue, is a critical function of sleep," said Stickgold.
"What we're really looking at here is the age-old mind-body problem: the mind-brain connection," said Stickgold. "We think of our mind as being ours. But there are real ways in which the brain has a set of rules of its own. We're getting an idea of what the brain uses as its rules for picking out cortical memory traces to reactivate and bring into our conscious mind, and, we're trying to see across wake-sleep cycles how that process happens."
Support for this research was provided by the National Institutes of Health and The Network on Mind-Body Interactions, a multidisciplinary research network sponsored by the John D. and Catherine T. MacArthur Foundation. Begun a decade
ago, the Mind-Body Network has been committed to discovering the biological mechanisms by which the social world and mental processes affect physical health.
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Famous Dreams:
He was not a brilliant chemist nor was he an exceptional teacher, yet Friedreick Kekule is credited with making one of the more amazing chemical discoveries of the time. How did he do it? Through what he called 'a waking dream.'
Kekule was originally a student of architecture but in 1850 he, along with the famous chemist Justus von Liebig, testified at the murder trial of a young maid accused of killing her mistress by setting her body afire. Initially, it was thought that the death of the woman was caused by 'spontaneous combustion' which occurred by the victim drinking too much alcohol. Liebig testified that the woman would have died of alcohol poisoning well before she could have drank enough to make her flammable.
Kekule then testified, positively identifying a distinctive ring found in the maid's possession as being the same ring which belonged to the dead woman. What was so distinctive about this ring? It was an unusual design: one of two snakes biting their own tails.
This design would, years later, show up in Kekule's own life. At Kekule's time, scientists believed that the structure of atoms was 'unknowable' as they believed that anything which acted with atoms created a reaction thereby keeping the atomic structure in constant flux. Kekule, however, doubted this hypothesis and spent years studying chemical structure. The exact nature of the structure eluded him until one evening when he let his conscious mind go and allowed his unconscious to take over.
Kekule claims that he stopped writing and dozed off to sleep. He saw atoms whirling and dancing before his eyes. The atoms then began to reassemble themselves into long rows that seemed to move about in a snake-like motion. As he watched the snake dance, the vision progressed until the snake formed itself into an image he had seen years before at the 1850 murder trial: the snake devouring its own tail.
Kekule states that he awoke as if struck by lightning. He realized in a flash that the problem he had worked on for years had been solved not by studying, but by the serendipitous intervention of a dream.
The snake biting its tail is an ancient symbol of alchemy known as the 'ouroboros'. An image of it as well as an image of the chemical structure of benzene can be found about mid-page of the site listed here: http://www.fortunecity.com/emachines/e11/86/l-hand13.html
Kekule is not the only person to have found the answer to a vexing question in his dream. Writers and artists often speak of dreaming lyric, plots, and images while sleeping. You too can use the unconscious for problem solving. Think of the unconscious as a vast library filled not only with forgotten personal memories, such as Kekule's memory of the ouroboros ring, but with forgotten bit of wisdom from humanity as a whole. To access this library, simple program your thoughts before you go to sleep. Think of the problem you need solved and tell yourself: "I will dream of the answer to this tonight."
Don't be discouraged if the dream you have doesn't appear to answer your question. You may need more time or you may need to look more carefully at the dream. Remember, dreams speak the language of symbols. The structure of benzene is not literally an ouroboros as you can see from the images cited above. However, the ouroboros does symbolically represent the structure of benzene rather nicely--at least it did to Kekule.
This brings us to another important point. Symbols have universal meanings and personal meanings. Dreams are messages from you to you so they will use a symbol in a manner that is consistent with your association with it. When looking for the meaning to your dream, always start with the personal--like Kekule did.
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Reader’s Dream & Analysis:
None this issue.
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Symbol of the Month:
Numerology –the study of numbers and their significance—is based on the belief that each number has its own distinct energy or vibration, which is attuned to the rhythm of the universe. Numerology is an ancient practice going back thousands of years to Pythagoras and not a new new-age development. Thus, numbers and their meanings have been studied and recorded for centuries and their meanings and vibrations well established.
When numbers appear in your dreams, it may be either because they hold some special significance for you or because your mind is trying to tell you something that you have not consciously recognized. Because your dreams work on so many different levels, it’s important to remember that they may not only be repeating factual information, but that a symbolic inference can also be drawn.
A number will sometimes flash into your head, but more usually you’ll take note of a certain number of chairs in a room, or lights on a street, and then wonder why the information is so important to you.
Unfortunately these days, you can read five different books on numerology or the meaning of numbers and get five different meanings for the numbers. The best resource for numerology, in my opinion is a system based on the Jewish Caballah.
Zero
Zero, although many people don’t think of it as a number, is a very significant symbol. It represents timelessness, limitlessness, perfection, no beginning and no end, the absence of quality, quantity and mass. Zero is the absolute freedom from limitation. It’s the sign of infinite and eternal conscious energy, superconsciousness, and a symbol for God (or the Universe) or eternity if it’s seen by itself. When zero is behind another number, it gives added importance, emphasis and power to the preceding number.
One
The meaning of one is somewhat obvious, it represents the first, the beginning, the origin or original. In a dream it can represent a pioneer, leader or the first experience, such as a first love, a first trophy, a first kiss, etc.
Two
Here we are seeing double; double weakness, double strength, double meaning. The number two, in general, represents the soul, but in dreams in more often represents the subconscious mind, duality, division or receptivity.
Three
This is the number of the Trinity. Three also represents completion, creativity –or your ability to create- and strength. In dreams it may signify the physical, mental and spiritual aspects of your self as well.
Four
The most common associations to the number four are the four corners of the earth –north, south, east and west- and the seasons. Numerologically, however, four represents material matters, the physical world; doing things in a material (non-spiritual) manner. In a dream it can imply hard, physical work, or doing things the hard way. On the other hand it could be implying balance and sturdiness.
Five
Five usually means change in whatever area or matter it’s associated with in the dream; finances, love, work, and so on. However, it can represent freedom or sensitivity, common sense or perception, because five is associated with our five senses.
Six
Perfection, beauty, strength, harmony, completion, or the cycle of creation can all be implied by the number six. You’ll need to examine the number in context and in relation to the other symbols in your dream.
Seven
The number seven is associated with the seven days of creation, the seven days of the week and the seven centres (or chakras) of the body. In dreams it demonstrated completion, perfection, balanced spiritual forces and victory. Seven’s a very fortunate number to have in your dreams.
Eight
This number represents the power to do or be, the potential for success, wealth, material gain and money.
Nine
Nine is the number of completion, termination, the end of one cycle (thus, the beginning of the next cycle).
There are several other numbers which are significant in numerology, but since this article isn’t about numerology, per se, I won’t delve into their meanings. If numerology is something you’re interested in, you can find all kinds of information on the web.
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Readers Comments:
No comments this issue
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From The Editor:
Okay ladies and gentlemen, I am asking for some feedback. You don’t have to submit a dream, I’d even appreciate a comment, good or bad, in general, a suggestion for a topic or opinions on past articles. Anything.
I’d like to know what readers think of the newsletter, of the articles, the format, etc. If I can improve this newsletter for readers, I’d like to hear about it. After all, I am writing and publishing this for you, the reader.
Talk to you next month,
Dream Well,
Terry
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