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Archive for the ‘Unified Theory: Bringing Together Seemingly Paradoxical Elements’ Category

Those who fall in love with practice without science are like pilots who board a ship without rudders or compass. -Leonardo da Vinci

Q: Why do the Mona Lisa’s eyes appear to follow her viewers around the room?

A: Because Leonardo da Vinci was an expert at creating illusions…based on science and observation.

The development of perspective was hugely important in Renaissance art. Many artists of this time were obsessed with painting the world as it actually existed, rather than the way it appeared  to exist. The discovery of linear perspective allowed artists to create art that followed the laws of nature to create dimension, rather than merely using height and width to create the illusion of depth. Then they (the artists of the Renaissance) tossed in a few rockin’ shadows and created the most realistic two dimensional paintings made to date.

But back to Mona. I remember one time sitting on the couch eating dinner watching a television show. I saw something on the screen behind one of the actors and craned my neck to get a look behind him to see what it was. That was the moment that I truly understood the difference between two dimensions and three. No matter if I even stood up and walked across the room, I would never be able to see behind the fellow, unless he moved out of the way.  In a painting this limitation of two dimensions is even more prevalent because Mona Lisa will never acquiesce to a request to budge over so we can see whats going on behind her. She can never ever change what she’s doing. So if she is painted to be looking at the viewer, she will always be looking at the viewer, no matter where the viewer is standing. Once the perspective is set, it will remain forever.

Projective geometry, the mathematics underlying the rules of perspective, was born in the Renaissance and indeed may have ushered in the art of the High Renaissance. One-point perspective appeared first in the works of Masaccio and Masolino in the first half of the fifteenth century, coming to full fruition in the works of Leonardo da Vinci in the second half of the century. Although the scheme was firmly established with Leonardo, it saw further refinement in subsequent centuries with the introduction of two-point perspective a century later and three-point perspective much later–after cameras with tiltable lenses for architectural renditions were invented in the twentieth century. (Bülent Atalay, Math and the Mona Lisa)

(My other favorite artist, Albrecht Dürer)

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(Leonardo Da Vinci-self portrait circa 1512)

Leonarda da Vinci has long been my favorite artist. I thought about doing a blog posting on him several times over, but never could focus all the awesomeness into one idea succinct enough for a post. But, as will happen when the time is right, I scored a copy of a book entitled Math and the Mona Lisa: The Art and Science of Leonardo da Vinci by Bülent Atalay. From this score came the succinct thought that I needed. Leonardo da Vinci is known of as a renaissance man. Indeed, it was probably he as a subject, who first generated the term, because of his knowledge, curiosity and deep comprehension of so many varied, and seemingly polar opposite, subjects. Math and art. Science and religion. Circles and squares. These are all supposed opposites, and are also all ideas that Leonardo da Vinci was able to connect with his fabulous and inventive mind (a mind that is referred to as being seemingly superhuman, by some)

Since there are so many great ideas presented in Atalay’s book, I’ll just focus on a few and I’ll spread them out over a couple of postings. Too much goodness just goes to my head! I’ll start off with a quote:

For mathematicians and physicists it is undeniable that there exists inherent beauty in mathematics. This is the aesthetics of mathematics. Perspective, proportion, and symmetry in any context are quantifiable. Accordingly, art indeed possesses quantifiable aspects. There is the symmetry expressible in mathematical terms and then there are ‘nature’s numbers.’ These notations figure into the mathematics of aesthetics. The associated quantification  can be formulated at various levels of mathematical sophistication…The Fibonnaci series gives rise to the notion of dynamic symmetry, the golden section, or the ‘divine proportion,’ which Fibonacci himself could not have anticipated. Three hundred years after Fibonacci formulated the series Leonardo da Vinci illustrated a book called De divinia proportione. But the integration of science and art has many more strands than Fibonacci’s mathematics and Leonardo’s art: It also draws in elements of architecture, astronomy, biology, chemistry, geology, engineering, mathematics, philosophy, physics–encompassing the extraordinary range of Leonardo da Vinci’s interests. For him these were branches of the same tree, part of a grand unified structure, the universe. (Ataly, pg 14)

For those of you who skipped the quote, it basically said that beauty is often quantifiable through perspective, proportion, and symmetry and that for Leonardo da Vinci science, mathematics and art were all various parts of the same whole.

Up next…how is the Mona Lisa able to stare at you wherever you go? It’s beautiful…and it’s math.

(Leonardo Da Vinci-Flower of Life drawing)

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(The Rat Poison Peddler-Rembrandt, 1632)

I began this day in a tither, because I thought a good friend of mine had insulted me in a group email. I had checked my email from bed, because, of course, my cell phone is conveniently located within arms length of my pillow. That’s where the charger is. I got up and walked the dog to clear my mind, and I saw a woodpecker scouting out termites on the neighborhood trump (tree-stump), which was cool, but not cool enough to stop me from stewing.

I recently told another good friend, not the friend who’d electronically disappointed me so abhorrently, that I’m beginning to hate my cell phone, because I can’t stop checking it. Checking, checking, checking. He told me about a story he’d heard on NPR, about a scientist and some rats. The scientist put a few rats in a cage with a lever that dispensed food consistently when the rat pressed it. He put a few other rats in a cage with a lever that dispensed food occasionally when the rat pressed it. The rats is the consistent cage pushed the lever when they were hungry. The rats in the cage with the inconsistent food dispensation became obsessive lever pushers, whether they’d just gotten a pellet or not, they pushed the lever every time they were near it. The scientist likened this behavior to checking email. You never know when you’re going to get that pellet…

Anyway, I got home from my walk and started a witty and sarcastic email response. Having the attention span of a…geez, I can’t even think of a thing that has the same shortness of attention as me. I started to say a gnat, but then I thought, gnats are pretty damn persistent, which is why everybody finds them so annoying. Then I thought about a gerbil, but again, they pretty much do the same thing all day long: wiggling around in bark. So, pretty much, I have the attention span of myself, and so I checked facebook halfway through finishing said sarcastic email. There I saw a banner of a quote from Lao Tzu that said this:

When I let go of what I am, I become what I might be.

Hm. I always respond to insults with witty, sarcastic group email responses, I thought to myself. Perhaps today I should do something different.

So I did. I copied and pasted the offensive material onto an email directly to to offender and asked her if she meant it the way I was reading it. Then I checked my email obsessively, waiting for her response. Strangely enough, she just called me, rather than responding electronically. Well, I guess calling is electronic these days too. Probably has been since the days of Pony Express, but whatever. I called her back. She told me that she isn’t a sarcastic person and of course, she didn’t mean to be insulting to me. She said that her feelings were hurt that I would assume that she was capable of that. Email always makes people sound more blunt than it actually is. I apologized. I believed her. I felt better. I don’t know if she felt better, but I hope she did.

I’m sarcastic. I assume that others are too. I’m metaphoric in my language. I assume that others are too. I jump to conclusions. Sometimes I’m right.

I lost an hour today, but I gained something else. Thanks Lao Tzu (and whoever posted him on Facebook. I can’t remember who you are, but maybe sometime I’ll check back and see…well, I’ll be honest, I probably won’t because I’ve already moved on. But thanks anyway…you rock!)

And thanks, friend, who I now know wouldn’t insult me via email. I think I’ll move my phone charger to a different outlet.

(Confucius Lao-tzu and Buddhist Arhat, Ming Dynasty, painting is located in the Palace Museum, Beijing.)

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(Satan Sowing Tares–Félicien Joseph Victor Rops 1833-1898)

Sometimes I look at other people and think, it must be easier for them than it is for me, they’re always so happy. I’m really picky. I only like certain things, at certain times, in certain colors, and they have to smell good. When things go off and get a different color, or maybe they were softer yesterday, or maybe they weren’t smart enough to dazzle me, or they biffed whatever fine point of perfection I was looking for at that moment, I get disappointed. Then I act like a fool. I throw little fits that are blanketed in clouds of judgement and disappointment and blame. Because as long as it is somebody else’s fault, I don’t have to change.

I recently attended a life changing conference with Marianne Williamson, called Enchanted Love. I got really clear on what I need to do to change my life with my partner. Take 100% responsibility for my experiences and my perceptions, stop pointing fingers, stop being a crackpot. Then I came home from the conference and I was great for about 48 hours…and then I threw a doozy of a blame fest. I won’t get into the details, but it wasn’t pretty…”poor little me,” mixed up with “you’re so mean,” mixed up with “why do I bother?” I took a late night drive and relaxed for a few hours on the couch, letting how much un-fun I was having settle in.

We have repeatedly emphasized that the barrier of grievances is easily passed, and cannot stand between you and your salvation. The reason is very simple. Do you really want to be in hell? Do you really want to weep and suffer and die? (A Course in Miracles–lesson 73)

Being mean is not fun. Being angry and defensive isn’t either. I give up all three, starting yesterday. Satan, Get Thee Behind Me. Thank you God.

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(the charming smirk of Count Cagliostro–Freemason, con man, alchemist, pimp, and saver of souls)

I’ve begun reading the book entitled The Last Alchemist: Count Cagliostro, Master of Magic in the Age of Reason. It’s a pretty good book. I just got to the part where the Count, who’s really just a regular-ish fellow named Giuseppe Balsamo, got initiated into the secret world of Strict Observance Freemasonry this evening. The author, Ian McCalman described his entry into the society thusly:

After he’d intoned his oath of absolute secrecy and obedience, several officials dressed in caps and aprons, blindfolded his eyes, tied a rope around his waist, and hauled him on creaking pulleys to the ceiling. Suddenly the rope gave way and he crashed to the floor. His complaints of a damaged hand did nothing to mitigate the ceremony’s next phase. Colonel Cagliostro watched uneasily while a pistol was loaded with powder and ball. His eyes were once again covered. He was handed the pistol and brusquely ordered to comply with the oath of obedience by blowing out his brains all over the tavern. He hesitated; he heard yells–coward, get on with it–and pulled the trigger. There was a detonation, he felt a blow on the side of his head and smelled acrid gunsmoke. By some miracle he was still alive; and as his panic gave way to clarity, he realized it had been a ruse: the lodge officials had given him an unloaded pistol and simulated the discharge (pg 40).

This passage reminded me of another book, The Secret Teachings of All Ages, by Manly P. Hall. Hall describes the tests a candidate had to survive in order to learn the Druidic Mysteries, to be “born again.” These folks had to get buried in a coffin and ride out to sea in an open boat. He also mentions the “strange machinery” found under a Greco-Egyptian temple of Serapis:

These machines indicate the severe tests of moral and physical courage undergone by the candidates. After passing through these torturous ways, the neophytes who survived the ordeals were ushered into the presence of Serapis, a noble and awe-inspiring figure illumined by unseen lights (pg. 25 and 27).

So. According to Manly P. Hall and other sources, there were two stories that Mystery School teachers came up with. One was simple, a moral code meant for Joe Everyman, which instructed him on the correct way to conduct himself in the world. The second story was deeper and secret, a story that had been passed down through the ages and only told to a very select few. These select were born into certain families and had passed the sorts of severe tests mentioned above. They starved themselves, broke bones jumping off cliffs, had limbs twisted into strange positions for long periods of time, etc., etc., in order to prove that they had overcome earthly limitations and were worthy of the truth (or perhaps to prove that they were willing to die in order to be included in the elite knowers of truth…)

There’s a lot of energy right now around these types of groupings, the elite v. Joe Everyman. A friend gave me a pin that says “99%” and I’ve been wearing it on my lapel. But, there’s something that’s been bugging me. What does being a part of the 99% mean, exactly? I wasn’t born into a fancy family. I have done a fast or two, but even just this morning in the shower I was vowing to never do one again. I hate being hungry. Am I a slave to my hedonistic nature? To be truthful, most of the work I’ve been doing with my counselor has been to help me feel ok with actually being who I am. Not trying to live up to some “moral code” written by some other dude who wore a wig and probably stole alms from the poor.

What does being a part of the 1% mean? Can the 1% be compared to the initiates of the past? What tests do they have to pass in order to get in? I can go to the library and read loads of words that tell me exactly what the different secrets of the ages were. It’s actually downright overwhelming all the secrets I’m privy to, and I didn’t even have to wander naked into the woods without any food or water. Does that make me a part of the 1%, now that I know the secret handshake? But then I remember that 2500 years ago Plato was splurging “secret” meeting minutes all over town after he was initiated into the elite.  Even then the secrets were available to anyone who was even slightly curious.

Do you think that God would put you on the earth without the tools possible for you to understand the secrets to sublime happiness? Are some people truly here without recourse from a life of misery, bound to the “simple moral code” of behave-now-and-you’ll-be-rewarded-later, forever doomed to 80 hours a week of assembling iPhones? Do the 1% still know some secret handshake that the 99% don’t? Is it possible that reading a book on a secret understanding won’t clue me in to the actual energy behind the words without the experience of pain and suffering that precede initiation? Why am I so lucky to be happy, when other people are suffering?  Is it because of what I’m doing? Or is it just because I’m lucky? To boil it all down, are there really secrets that you have to be born in the exact right time and place to understand? Or are these all figments, illusions, distractions?

More to come on this illustrious topic…Feel free to answer any of the above questions.

(Mystical Seven–a secret society at Wesleyan University of Connecticut)

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(mid-sagittal brain fibers that connect the two hemispheres through the corpus callosum, photographed by Thomas Schultz–2006)

In my last post, which you can read here, I noted that it is important for me to take some quiet moments to listen to what my emotional body is telling me. If I’m able to do that I can make proactive choices about things that I’m feeling yucky about and make them better, thusly living a happier and more authentic life. Here’s an example:

I have a weird and possibly obsessive hatred of dry things touching other dry things. As a school teacher, this is an unfortunate hatred, because chalk and chalk boards are both very, very dry. Very dry. I’ve managed to survive by using this particular type of “dust free” chalk that comes in a green box. It’s denser than most chalk. I tell myself that it’s denser because it has more water in it, which allows me to use it without all of my teeth falling out. But that’s just an aside. The real story/pain comes in wiping the chalk off the board. All that bone dry power wafting into the air, dusty eraser fibers scratching along the slated board…I feel faint just thinking about it.  I try to have the students do it most of the time (even then sometimes I have to stand at the back of the room and not watch) and in the winter time, when it’s raining outside, I can handle it. But in August, hot and dry, sun burning down outside the window…oops! My bicuspid fell out! Dang.

Anyway, I’ve been cleaning my room in preparation for the first day. The boards have been on my list for days. I kept avoiding them, ignoring them, doing other jobs that don’t need to be done, without ever noticing or questioning why. Yesterday I stopped myself and said, Self, why are you avoiding the chalkboards? Then I answered Because the dryness is too much. If I have to, I will, but only with hatred in my heart. So then I asked myself, How can I make the job better for you/me? and then I answered Go and buy a giant sponge and fill up a bucket of water and use the giant sponge and the wet water on the dry, dry board.

So then that’s what I did. Well, actually I found a giant sponge and used that instead of buying one, but it came to the same end. The boards are clean and ready and I enjoyed the task.

I could have ignored myself. I could have powered through and wiped the boards with the dusty eraser and rubbed them black with the cloth that I keep for the job. But I would have had hatred in my heart, and now all I have is love. Love, moistened with the 98% water that’s in my body.

The point of this little story is to illuminate the dual nature of individual humans. How can there be a part of me that I ignore unless I have parts to me? How can I talk to myself and answer myself unless there are multiple sides to my nature? There are loads and loads of informative websites and books and research projects that have proven that the left and right hemispheres of the brain serve different functions. The left brain hemisphere controls literal language (grammar and vocabulary) while the right brain hemisphere controls the understanding of non-literal language (reading between the lines, intonation, sarcasm, contextual meanings). The left brain deals in facts–decoding the rational, linear, and objective–while the right brain deals in intuition–focusing on patterns, connections between experiences and things, and with a subjective understanding of the world. In other words, the right brain is all about feelings and the left brain is all about facts. The two hemispheres are connected by a band of nerve fibers called the corpus callosum, which allows the two sides to communicate with each other.

While we use both sides of our brain constantly throughout the day, most people tend to show a preference for one type of thinking over the other. (Here’s a fun test to see what your brain preference is.) Don’t worry, my point is still coming. Most people are left brain dominant, meaning that most people will believe facts coming from an external authority above their own feelings and intuitions, even when the facts are at odds with their own experiences. Over time, we begin to lose touch with our own feelings, choosing instead to focus on what is happening outside our actual experience. This leads to, at best, a superficial and un-authentic  life littered with depression and prescription drugs. At worst, it leads to illness and violence. Feelings that are pushed aside and ignored do not go away, they find alternate paths to the surface.

Fortunately, with a little conscious action, I can cut through that big bossy mouthed left hemisphere that always wants the facts. I can kneel down and put my ear on the track of that gentle, soft spoken feely, feely right hemisphere and give a good listen. It’s not that hard, once I remember to do it, and wow, I’m so much happier (and whole-er and more balanced) when I do.

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All neurosis is a substitute for legitimate suffering.– Carl Jung

I passed a bumper sticker the other day. It said “Dare to Feel.” I’ve been thinking a lot about that. A few years back I went to a massage therapist who does a massage technique called Rosen bodywork. She’d be working on me and then she’d ask, often right in the middle of the massage, “How do you feel?” At first I answered, “fine” but she would continue on asking me questions. “Do you have any pain? Any anxiety anywhere? Where is it? How does it feel?” At first I found it mildly irritating, because I go to massage to relax, not to think about how I feel, but when I finally stopped to think about how I felt, really think about it, I realized how seldom I paid attention to what is really happening inside me.

Maybe I have a little stomach ache.  I can think to myself (when I remember to anyway) Why does your stomach hurt? Maybe it’s because I dread something that’s going to happen later. If I know about it, I can make a plan on how to make it better for myself. Maybe I can cancel it. Maybe I can eat some ice cream and it might be better. The point is, when I locate my feelings and put words to them, I can actually be proactive on working through the feeling, rather than ignoring it and creating an alternate and altogether unreal existence.

It’s a lot harder, for sure. But it makes me happier in the long run. Up next, what does all this have to do with the right and left brain hemispheres? (I just now thought of the connection while I was writing this…yahoo for therablogging!)

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