DRAWING THE “JESUS TOMB” SYMBOL

What a wonder the symbol is!

The large symbol on the Talpiot tomb in Israel (aka “The Lost Tomb of Jesus”) is a stone relief sculpture of a small circle within an upside-down Y-shape.  (More on the tomb here.)  

I’ve found this symbol is easy to draw exactly and is easily reproduced to make proportional copies.

In the following image of the Talpiot tomb symbol, my turquoise overlay is derived from a hexagon, and has certain proportions which are consistently reproducible when using a hexagon as a template. 

Full-size image

In the image, the tomb symbol appears to share three points (the top of the Y stem and the two ends of the arms of the Y) with the corners of a hexagon, with other relationships as follows:  The diameter of the rim of the small circle is one-half the radius of the circle enclosing the hexagon.  The rim of the smaller circle intersects both the center of the larger circle and the midpoint of the radius of the larger circle.  My turquoise overlay defines this rim and also the angle under the arms of the upside-down Y.  The lines forming this angle intersect at the midpoint of the horizontal line connecting two remaining corners of the hexagon.  That intersection point is also a midpoint of the radius.  The sixth and bottom-most corner of the hexagon would be barely above the center of the top of the entryway to the tomb.

My hexagonal design is easy to construct with simple tools.  You need only a string and piece of chalk.  This is how: 

First attach your chalk to one end of your string.  Anchor the other end of the string or have someone hold it in place at your designated center.  Move your chalk-on-string to draw a circle with every part of the circle equidistant from the center.  In a hexagon, each side of the hexagon is equal to the radius of the circle enclosing the hexagon.  Therefore, you can mark off the corners, where the hexagon meets its enclosing circle, by using the same length of string you used for the radius of your circle.  To find the point where the two arms of the upside-down “Y” intersect, draw lines as indicated in the image (or in the text above).   Draw straight lines using a taunt string as a guide.  To make the radius of the smaller circle fold your string in half twice (to make it one-fourth the length of the radius of the larger circle).

Is this the way the sculptor made the original tomb symbol?  With chalk, string, chisel, and a hexagon?  Who knows?  It’s possible.

While my hexagon overlay fits the photo well, the fit could be better.  One explanation – distortion could have been introduced in a number of ways:  during my pencil/compass drawing of the hexagon, by my scanner, or by my drawing software while working with the hexagon or sizing the photo of the tomb symbol.  Distortion might be inherent in the original photograph of the tomb symbol or the sculpture itself may lack absolute symmetry.

A hexagon yields other very pleasing designs, formed within it by making connecting lines.  For example, the three hexagonal corners, where the “Y” shape meets the hexagon, correspond to the three points of an equilateral triangle.  Also, two equal interlocking equilateral triangles form a six-pointed star (called a “hexagram”) within a hexagon.

Here is something that occurred to me as I played with my hexagon:  The Talpiot tomb symbol shares at least 5 points (the 3 ends of the Y and the 2 midpoints of radii discussed above) with a six-pointed star (hexagram); 6 points, if the placement of the top of the entryway quite near the bottom-most point of the hexagon is not mere coincidence but is actually part of the design of the facade.  The hexagram is often called the sign of King David.  If the tomb symbol means “birth” as I hypothesized in an earlier post, and if it is linked conceptually to the hexagram by its shared points and its hexagonal derivation, then perhaps the tomb symbol means “of the lineage of David” or Son of David.  I definitely was intrigued and pleased to discover hexagonal geometry in the symbol carved on what might be the Tomb of Jesus.

Of course, maybe I’m reading too much into this.  Maybe the hexagon is just a ubiquitous artist’s tool, or maybe there is no hexagon at all – maybe the sculptor just drew freehand.

Drawing hint:  To draw a hexagram onscreen, begin by dividing the vertical diameter of a circle into four equal quarters.  This yields the two points where the horizontal lines of the hexagram cross.  Onscreen, a perfect circle begins with a perfect square.

I took another look at the Talpiot tomb symbol in the context of a hexagon and hexagram.  I discovered five amazing phenomena – see the next image.  (Now these are merely my observations based on my drawings, and I have not attempted mathematical proofs.  There are significant changes in this update, as I improve my drawing techniques.)  As you read the following, think about the relationships that are defined, and how these tie together the forms of circle-under-angle, that angle, and the hexagram. 

Full-size image

Broader view

(1)  Red line:  I was wondering how far the tomb symbol’s small circle was from its overarching angle.  So I made a line from the circle’s center perpendicular to the side of the angle (the shortest distance between them).  That line is approximately the same as the diameter of the circle.  A pleasing design.   On a whim I extended the line and found that it intersects one peripheral point of the hexagram and also intersects a point where the interlocking equilateral triangles of the hexagram intersect.  Why do all these points line up?  I don’t know!

(2)  Green circle:  I wanted to discover more about the tomb symbol’s angle, and about the point where the “red line” perpendicularly intersects the symbol’s angle and also, the corresponding mirror-image point on the other side of the angle.  I’ll call these points the “A points.”  I got out my compass and it told me that each “A point” is at a distance from the topmost point of the hexagram equal to the radius of the circle enclosing the hexagram.  Cool!  A circle passing through the two “A points” also passes through the circumference of the symbol’s small circle and two peripheral points of the hexagram.  This “green circle” is the same diameter as the hexagram’s enclosing circle.

(3)  Yellow circle:  What next?  Well, I couldn’t resist making a test circle with the center at the top of the tomb symbol’s angle and with the circumference passing through the center of the tomb symbol’s circle.  It appears to be tangential to two sides of the hexagram.  Amazing! 

(4)  Turquoise circle:  Is there more?  Oh help, I found another circle.  This one centered where the “red line” intersects the side of the upright equilateral triangle within the hexagram.  The circumference of the circle passes through a peripheral point of the hexagram and also passes through the center of the circle enclosing the hexagram (and that latter center is also the top point on the circumference of the tomb symbol’s small circle).  Gasp!

(5)  Dark green circle: 

This “dark green circle” is half the diameter of the hexagram’s enclosing circle, has its center at a midpoint of the side of the upright equilateral triangle within the hexagram, and passes through the center of the enclosing circle and a lateral point of the hexagram.  The “dark green circle” intersects many other interesting points, but most importantly, it intersects the top point of the tomb symbol angle.  Far out!  Maybe that’s enough for now.

The enigmatic Mason symbol with its compass and square base had inspired me to get out my compass, and when I looked for a “square,” I found that there are many lines that are 45 degrees off the vertical, which intersect two or more interesting points, and which could form diamond-shaped squares.  Just which one is the most important?  This is something I am contemplating.  (Other than the clues in the Mason symbol, I have no idea what Masons think about geometry.)

So the tomb symbol with circle and angle appears to be linked to a hexagram in many different ways.  These relationships seem almost magical.  I can well understand the pleasure and excitement that the first person who discovered this must have felt.

Long before the time of Jesus, Ezekiel reported he saw four “wheels” in a vision of angels.  Could these “wheels” be my green, yellow, turquoise, and dark green circles?  In Ezekiel 1:15-18, he says “Each appeared to be made like a wheel intersecting a wheel,” (New International Version).  Did each of his four wheels intersect the same wheel just like my four colored circles intersect the tomb symbol’s small circle?  “Their rims were high and awesome,” he says.  Yeah, some of my rims are very high.  Fascinating.  Perhaps this math is very ancient; and perhaps it was mystical, even sacred, to those who first discovered it.

And where the New Living Translation says in Ezekiel 10:10, that “each wheel had a second wheel turning crosswise within it,” and the NIV renders that as “each was like a wheel intersecting a wheel,” could the original really mean that each wheel intersected “two” others, as is the case with my circles?  (Each colored circle intersects at least two other colored circles.)  Where the NIV says in Ezekiel 1:16, that “. . . . all four looked alike. Each appeared to be made like a wheel intersecting a wheel,” could the original really mean that all four were alike in that each wheel intersected the same wheel?    But maybe Ezekiel was just writing about angels, not angles.

And while we’re visiting the Bible, let me ask you – in John 8:6-8, what was Jesus writing in the dirt?  He could have conveyed words orally – so was he drawing?  Was he drawing circles?  Was he into sacred geometry?

One more image:  I had to ask myself if a five-pointed star (pentagram) can be derived from the tomb symbol and its companion hexagram.  It would seem that the lines of the pentagram intersect or are very close to the points where the “yellow circle” meets the “green circle,” and where the “yellow circle” meets the “dark green circle.”  Using these points, you can draw a fairly decent pentagram.

Full-size image

My conclusion is that the relative proportions and relative arrangement of the circle and angle in the tomb symbol may be a shorthand way of signifying a broad array of geometrical wonders.

Maybe the symbol on the Talpiot tomb is there to remind us of the Eternal One who is the Great Designer of all those wonderful, and sometimes inexplicable, geometrical relationships; and to remind us that if there is such geometric beauty and order inherent in the Universe, then maybe, despite everything, there is hope.  Continued here.

 Index

Slide show, music, and folders on my main page.

-2008-

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This post was updated on May 19, 2009.

THOSE MERCURY LIGHT BULBS

I almost bought one of those compact fluorescent light bulbs. 

That had been my intention – to buy one of those new-fangled compact fluorescent light bulbs.  You know – the new energy-saving light bulbs we are all supposed to buy to save energy, save the environment, slow global warming, save money, etc., etc.  We are all supposed to jump on the bandwagon.  Media and environmental groups urge us to buy the new-fangled light bulbs that are “equivalent” to a 100-watt incandescent bulb but use less electricity.  We are supposed to go for this like a bunch of lemmings rushing to the sea.

Well, I was standing there in the grocery store.  I read the front of the packaging.  I read the back of the packaging.  I read the warning in very, very small print that says, “Contains mercury.  Dispose of in accordance with local, state or federal laws.”  Contains mercury???!!!!

Mercury?  As in mercury the hazardous chemical?  As in mercury in my tuna fish, so I can only eat one serving of tuna a week? (calculate your dose here).  Mercury?  As in pollution causing horrible health effects? 

Am I afraid to bring mercury into my home?  Well, no.  I’m sure they have it figured out so the mercury would stay in the light bulb and not leak out into my home and into the air I breathe.  (Almost sure.)

As I stood there in the store, I looked down and saw a little warning notice on the shelf telling me I should phone the local county office for instructions on how to dispose of mercury light bulbs.  I definitely had second thoughts about buying one.  How would I dispose of it?  I couldn’t just throw it into the trash can.  Wouldn’t that be a violation of some law? 

I rather doubted I could even find out when the hazardous waste day is in this county.  I’ve tried before.  I call up and they say, “We haven’t decided yet when the day is; just watch the newspaper.”  Well, I don’t get the paper every day.

I suspect that most people who buy the new-fangled light bulbs won’t even bother to read the back of the packaging and won’t know about the mercury in the bulbs.  Even if they read it, will they remember to “dispose of it in accordance with the law” when the bulb finally burns out?  Will they know how to do it?  Or will the bulb just get tossed in the regular trash?

If your average consumer can’t or won’t deal with proper disposal, aren’t these light bulbs just creating another environmental problem?

I wonder where the mercury comes from.  Does the light bulb manufacturer in China (where this is outsourced, according to the packaging) actually spend money to refine mercury for the express purpose of putting it into the bulbs, or does the manufacturer process a waste stream containing mercury pollution and funnel that mercury into bulb manufacturing?  Does the manufacturer solve an industrial hazardous waste pollution problem by creating a municipal hazardous waste pollution problem?  Now this mercury pollution problem is in the laps of every county and every municipality in the US!

What happens to the light bulbs when they get into a municipal landfill by mistake?  (And I have to believe that most of these bulbs will not get disposed of properly.)  Do the bulldozers plowing the garbage in the landfill crush the light bulbs, and when they break, is the mercury released, contaminating the environment?  In an incinerator, does the mercury go straight up the smoke stack into the atmosphere?

Can these mercury light bulbs actually be safely disposed of and isolated indefinitely from the environment or is that just a fiction?  Should we be creating thousands of hazardous waste garbage piles like so many pimples spread across the face of our Planet, or should we avoid creating hazardous waste in the first place?  Should any company even be manufacturing these hazardous mercury light bulbs that are obviously harmful to the environment in the aggregate.  Shouldn’t we be trying to live simply and live in harmony with our Planet instead? 

As for recycling these mercury light bulbs – I have no idea if people will be motivated to do that.  Where are the incentives?  And how much mercury is released to the environment during the recycling process?  I’ve looked for information online on recycling.  Here’s the recycling Web site for the dozen or more companies involved in manufacture of these bulbs – I can’t say it helped me much.

I do wonder about the incredible cynicism that would allow a company to produce light bulbs with mercury inside, and pass this off as the solution to the problem of global warming. 

What’s my solution?  Well, I don’t need to have 100-watt bulbs or 100-watt equivalents in my house.  In fact, I prefer softer light.  I don’t like glare.  Also, I don’t need to see every wrinkle when I look in the mirror (heh, heh).  So I don’t buy high wattage bulbs – I haven’t in years.  I’ll save energy by buying regular 40-watt incandescent light bulbs.  Furthermore, I’m smart enough to turn off lights when I’m not using them.  I use one or two lights at a time.  I don’t pay the electric company any more than I need to.  I’m quite capable of practicing conservation without some new-fangled mercury light bulb.

I’m not like my neighbors who have their whole house lit up with powerful outdoor floodlights, and each and every window blazing with light from within, bright enough to light up the surrounding countryside for hundreds of feet in every direction. 

It occurred to me that if enough people are sucked into this new-fangled light bulb thing, manufacturers might just stop making the regular incandescent light bulbs.  Greenpeace would like to ban incandescents.  So I did a quick calculation and figured out how many light bulbs I would need to keep my hallway lit for the remainder of my life.  Then I bought 32 of the regular 40-watt incandescent light bulbs.  Am I hoarding regular light bulbs?  Yes.

The world may be ending from climate change but I am not about to be stampeded into buying mercury light bulbs.

Slide show and music on my main page.

-2008-

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