DRAWING THE “JESUS TOMB” SYMBOL, PART 11

I was wondering how to rotate the tomb symbol angle so its ends would join up and make a star.

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

I have been making designs derived from the tomb symbol.  I am going by what I observe in my drawings; I am not attempting mathematical proofs.  As I go along I define whatever terms I need to, but might not repeat definitions in each post.  So this post should be read in conjunction with the previous ones:  Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, and Part 10.

Actually, once I figured out how to rotate the tomb symbol angle to make a 6-pointed starburst, I realized how simple it is.  When the angle opens outward, and the ends are anchored in two corners of an equilateral triangle, with the third corner anchored at the center of the standard circle which gives rise to the hexagram which gives rise to the equilateral triangle, and the angle is rotated in increments of 60 degrees, then you get a starburst, as shown in the following image.  The peripheral sides of the equilateral triangles now comprise the six sides of a hexagon.  The 6 tomb symbol circles are included with position relative to the 6 tomb symbol angles unchanged.

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I should mention here that some of my images are very wide and when shrunk down to fit in this column, they lose a lot of detail.  To view a full-size image in this series, click on “Full-size image” under the image, then click on the image to open or click “open.”  Then hover your cursor over the image to get a pop-up button in the lower right corner (or other feature depending on your browser – this will take a few moments), and click on that to get the actual full-size.

In the following image, I included a hexagram (navy) in the design and also increased the rotations to increments of 30 degrees, yielding a 12-point starburst constructed from the lines of the tomb symbol angle (pale green lines, lavender-filled).  The 12 tomb symbol circles are included with position relative to the 12 tomb symbol angles unchanged.  The tomb symbol’s position relative to its contextual hexagram is unchanged.

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The following image got rather busy as I added pentagrams (red), anchored on the center of my standard circle, and rotated in increments of 30 degrees, and added tomb symbols rotated in increments of 6 degrees.  Pentagram lines and hexagram lines (navy) scoot outwards from the center and pass between tomb symbol circles very close, but not tangential to them.  Some of the joined ends of tomb symbol angles (pale green) meet on pentagram lines.  Some tomb symbol circles intersect on pentagram lines.   Some tomb symbol circles intersect with hexagram lines at pentagram lines.

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In the following image, the 12-point starburst described earlier becomes a 24-point starburst (dark green) as the tomb symbol angle is rotated in increments of 15 degrees.  Tomb symbol angles opening outward are placed at several levels, each successive level adding one-fourth the diameter of the standard circle.  Level 1 (pale green) is anchored on the center.  Tomb symbol angle lines level 3 (purple) intersect at the apex of tomb symbol angle level 4 (pink).  Tomb symbol angle lines level 1 (pale green) end at or about tomb symbol angle lines level 3 (purple).

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In the following image, the tiers of tomb symbols are rotated in increments of 5 degrees, each successive level adding one-fourth the diameter of the standard circle.  Tomb symbol angle lines intersect at intersections among tomb symbol circles in tier 2.  Tomb symbol angle lines end at tomb symbol circles in tier 3.  Tomb symbol angle lines intersect at the interface between tier 3 and 4 circles.  In tier 4, the ends of tomb symbol angles join together.  Tomb symbol angle lines intersect at the centers (red, where visible) of tomb symbol circles in tier 5.    Tomb symbol angle lines intersect at or near the outermost points of tomb symbol circles in tier 6.  (See red arrows - click on "Full-size" below.)

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The tomb symbol, its circle and its angle, continue to be a font of inspiration and ever-evolving forms.  I am amazed.  Continued here.

-2008-

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

X Keywords:  symbol design how to draw math geometry MSN Windows Live Spaces X

 This post was updated on July 28, 2008.

DRAWING THE “JESUS TOMB” SYMBOL, PART 10

I got the urge to draw some more circles.  This time starting with a six-petal flower, six circles rotated about a central circle, all circles the same diameter.

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

I have been making designs derived from the tomb symbol.  I am going by what I observe in my drawings; I am not attempting mathematical proofs.  As I go along I define whatever terms I need to, but might not repeat definitions in each post.  So this post should be read in conjunction with the previous ones:  Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, and Part 9.

In the following image, my six-petal flower became 12 petals when I copied/rotated/pasted the design 90 degrees.  The 12 circles are “green circles,” that is, the same diameter as the central circle (turquoise/regular blue, my standard circle), with centers on the standard circle, and intersecting the center of the standard circle.  I was a bit surprised to notice that each of the 12 circle centers lies on the intersection of a neighboring circle and the standard circle, until I remembered that in a six-sided hexagon the interval between corners is the radius of the enclosing circle.  The 12-pointed pale green-filled rosette is made from the “green circles.”  Notice how the borders of the tips of the rosette petals meet at the standard circle. 

The 12 indigo-filled circles are tomb symbol circles (one-fourth the diameter of my standard circle).  These 12 circles are likely not tangential to the “green circles,” but are nearly so, and each tomb symbol circle nestles closely within four “green circles.”  Each “green circle” passes close to four tomb symbol circles.  Each of 12 pink-filled half tomb symbol circles (one-eighth the diameter of my standard circle), is tangential to three “green circles.”  Each “green circle” is tangential to three half tomb symbol circles.

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In the following image, I stripped away the green circles, and added 12 “yellow circles” (gold-rimmed and partly yellow-filled, and three-fourths the diameter of my standard circle).   Each “yellow circle” is tangential to two tomb symbol circles (regular blue-filled) and two half tomb symbol circles (deep pink-filled).  After that, I added a central royal circle (royal blue rim, navy-filled, concentric with my standard circle (regular blue), and one-third the diameter of my standard circle).  This royal circle is tangential to the 12 “yellow circles.”  I added a wreath of 12 royal circles (royal blue rims, partly navy-filled, and one-third the diameter of my standard circle), each tangential to the standard circle and tangential to a tomb symbol circle.

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In the following image, the basic design is rotated at intervals of 6 degrees.  The outer coil is composed of 60 tomb symbol circles (black-green).  The inner rosette is also composed of 60 tomb symbol circles.  The pale green lines are tomb symbol angles; one anchored at the topmost point of the standard circle (regular blue) and opening downward (similar to the exercise in Part 2); the second anchored at the same point and opening upward. 

A pink circle, likely only visible in the full-size image, is inscribed through the innermost points of the outer coil of 60 tomb symbol circles.  Notice how the pale green tomb symbol angle lines intersect each other at that pink circle.  Wow!  When the circle is larger than the screen and the software won’t deliver a diameter sized one pixel smaller, then I have to improvise, which I did – this pink circle is derived from a section that fits at 9 and 12 o’clock, copied, rotated, and pasted into four quarters.

I couldn’t help but notice that a half royal circle (royal blue and one-sixth the diameter of my standard circle) will fit in the lattice made by the tomb symbol angles, fit so that the circle is tangential to four tomb symbol angle lines.  I couldn’t resist adding 20 such half royal circles.

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I should mention here that some of my images are very wide and when shrunk down to fit in this column, they lose a lot of detail.  To view a full-size image in this series, click on “Full-size image” under the image, then click on the image to open or click “open.”  Then hover your cursor over the image to get a pop-up button in the lower right corner (or other feature depending on your browser – this will take a few moments), and click on that to get the actual full-size.

In the following image, I used my 12 “green circles” flower.  I superimposed hexagons, both upward pointing and side-pointing (red), on each “green circle.”  I am awed that there is not a single point where “green circles” intersect that is not also an intersection point where red hexagon lines intersect.  Wow!  What a masterful design from the Great Designer!  Notice that some hexagon sides form perfect squares within the drawing.  I’ve added 48 tomb symbol circles (black-green) to the squares, each circle tangential to four sides of a square.  I guess I can catch a glimmer of why the circles fit the squares, but I still think it is marvelous.

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Since I started this series with a hexagon, I feel right at home here.  Continued here.

Slide show and music on my main page.

-2008-

X Keywords:  symbol design how to draw math geometry MSN Windows Live Spaces X

DRAWING THE “JESUS TOMB” SYMBOL, PART 9

Jacob had a dream of angels going up and down a ladder.  A ladder that reached to the door of heaven (Genesis, chapter 28 NIV).

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

I have been making designs derived from the tomb symbol.  I am going by what I observe in my drawings; I am not attempting mathematical proofs.  As I go along I define whatever terms I need to, but might not repeat definitions in each post.  So this post should be read in conjunction with the previous ones:  Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, and Part 8.

What do I know about Jacob’s ladder?  That angels go up and down the ladder.  Well, assuming that “angels” are pentagrams, (and this has worked for me before, when I assumed Ezekiel’s “cherubim” were pentagrams (Part 2)), then the pentagrams should be pointed both up and down.  I am assuming the “ladder” is a repeating design that can be repeated endlessly, as far as “heaven.”

In the next image, I am starting my ladder with a hexagram (navy), an upward pointing pentagram (pink), and a downward pointing pentagram (green).  Notice the two horizontal lines of the hexagram and that each pentagram has a horizontal line – these will form the basis for my ladder.  Notice that the pink pentagram intersects the green pentagram at the horizontal line of the hexagram.  Wow!

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In the next image, I make my ladder by copying the image above and pasting it back on so that the top hexagram horizontal covers the nearest pentagram horizontal.  I do this a few times, repeatedly pasting the hexagram horizontal over the next pentagram horizontal, and notice that the circle centers are falling on points where pentagram lines crisscross the vertical diameter of the enclosing circle.  And as I continue, I notice that the lines of the green pentagram that crisscross the vertical diameter, cover (that is, coincide with) the lines of the pink pentagram that crisscross the vertical diameter – cover almost completely near this diameter!  Only a few pink pixels stick out.  My upward and downward “angels” overlap!!!  As I continue, the circle centers become covered by crisscrossing pentagram lines.  Circles intersect where some hexagram lines intersect.

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Broader view

I should mention here that some of my images are very wide and when shrunk down to fit in this column, they lose a lot of detail.  To view a full-size image in this series, click on “Full-size image” under the image, then click on the image to open or click “open.”  Then hover your cursor over the image to get a pop-up button in the lower right corner (or other feature depending on your browser – this will take a few moments), and click on that to get the actual full-size.

Here is a close-up of the pink pixels sticking out (8X magnification).

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Here I have re-colored my Jacob’s Ladder to emphasize the steps of the ladder:

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Have I discovered the real “Jacob’s ladder”?  I don’t know.  How could I possibly know?  I was so fascinated by it all, I was tempted to wrestle with it all night long, just like Jacob wrestled with an angel or divine messenger all night (Genesis, chapter 32 NIV). 

It seems to me there could be many different ways to draw a Jacob’s Ladder.  Think of the horizontal and vertical lines in a rotated hexagram (rotated 90 degrees to make a 12-point star).  Think of the horizontal and vertical lines made by pentagrams rotated 90 / 180 / 270 degrees.  These lines make rectangles and squares as shown in the following image.  These rectangles and squares can be assembled numerous ways to build fabulous designs.

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In fact I had been playing with my rectangles when I got the idea to build some stairs with them.  Then the idea of stairs reminded me of a ladder I had seen on a DVD in recent days.  A stone ladder sculpted on the exterior of a church in Bath, England, with winged angels going up and down – Jacob’s Ladder.  But nothing really worked for me until I examined the following design I made, placing pentagrams over the “Jesus Tomb” symbol to see how and what they would intersect. 

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Then I noticed that the upright and upside-down pentagrams meet at the hexagram’s horizontal.  Here’s a short list of interactions that can be found among the forms in this design:

1- Pentagram 1 (red-brown, downward pointing) meets the red line at the tomb symbol circle (black-green).

2- Pentagram 2 (purple, upward pointing) meets pentagram 1 at the hexagram’s horizontals,  meets pentagram 1 at the tomb symbol angle (pale green), and meets the yellow circle at the green circle.

3- Pentagram 3 (pink, right pointing) meets the red line at the hexagram, meets itself at the tomb symbol angle, meets pentagram 1 at about 3 o’clock on the tomb symbol circle, meets pentagram 1 at the green circle, and meets pentagram 2 at the green circle.

4- Pentagram 4 (gold, left pointing) meets pentagram 3 at the 12-point star’s verticals, meets itself at the tomb symbol angle, meets pentagram 1 at about 9 o’clock on the tomb symbol circle, meets pentagram 1 at the green circle, meets pentagram 2 at the green circle.

I’ll add a caveat here that I’m not convinced I have the perfect pentagram yet.  I’ve drawn pentagrams a number of different ways:  first with compass, protractor, and scanner; next by fitting lines around an inner concentric circle; and then by using software to rotate points around a circle.  If my pentagram is off by even one pixel, much of what I wrote above will be incorrect, will vaporize like morning dew in the sunlight.  (For instance, re-sizing the whole pentagram so its horizontal bar is one pixel closer to the circle center means no more ladder.)  Certainty awaits that perfect software.

I should tell you I started down this path, a detour really, a few months ago when I started re-drawing my forms with narrower lines.  Now I’ve learned that even a perceived setback can be a blessing if you find angels along the way.

I’m glad to have found my ladder with angels going up to heaven and down.  I’m so glad to have made this discovery on my own.  If this had been spoon-fed to me in a classroom setting, it might have been such a bore; but this way, on my own, I’m in drawing heaven, surrounded by angels.  Continued here.

Slide show and music on my main page.

-2008-

X Keywords:  symbol design how to draw math geometry MSN Windows Live Spaces X

DRAWING THE “JESUS TOMB” SYMBOL, PART 7

I looked some more for a “square,” playing with what I am calling my “orange lines.”  These are lines that are 45 degrees off the vertical, which can form diamond-shaped squares. 

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

I have been making designs derived from the tomb symbol.  I am going by what I observe in my drawings; I am not attempting mathematical proofs.  As I go along I define whatever terms I need to, but might not repeat definitions in each post.  So this post should be read in conjunction with the previous ones:  Part 1, Part 2, Part 3, Part 4, Part 5, and Part 6.

I was inspired in part by a design of “sails” carved in rock by ancient Polynesian seafarers shown in the National Geographic.  I still do not have a clue what the sails could signify or how to make them, but after many attempts at arranging circles and orange lines to make sails, I came up with the grid shown in the following image: 

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My orange line starts at the upper left corner of the hexagram (navy), meets a lower right corner of the 12-point star (gray), takes a sharp right (right angle) at that point and meets its mirror coming from the other way at a point directly under the center of the enclosing circle (circle 1, regular blue).  That point becomes the bottommost point of circle 2 (regular blue), and the center of circle 2 is where the orange line and its mirror intersect within circle 1.  The diameter of circle 2 is the same as circle 1.  With circle 2 established, I continued to work on the grid, extending the orange lines up to the sides of circle 2, taking a sharp right angle turn at the sides, making a perfect diamond square within circle 2. 

Take a look at how the orange lines intersect at the “green circle,” at the point where lines of the hexagram and 12-point star intersect (red arrows).  Amazing!!!  (The “green circle” is the top circle in the image, the same diameter as circle 1, and centered on the topmost point of circle 1.)  This is all amazing to me but maybe not to the real mathematicians among my readers.  How can this be happening?

I should mention here that the full-size image is 1800 pixels wide and when shrunk down to fit in this column, it loses a lot of detail.  To view a full-size image in this series, click on “Full-size image” under the image, then on the next page, click on the image to open or click “open.”  Then hover your cursor over the image to get a pop-up button in the lower right corner (this will take a few moments), and click on that to get the actual full-size. 

Something very interesting is shown in the next image.  I started putting horizontal lines through points where the orange lines intersect, still trying to find some “squares” as I mentioned in Part 1.  I found that the horizontal lines predict where a hexagram will appear in circle 2.  I’ve put in the hexagram, in red, to make it stand out.  The horizontal lines are marked with red markers.

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I copied my orange grid design, inverted, pasted, and copied, rotated 90 degrees, pasted, pivoting on the center of circle 1.  (I often manipulate designs just to see what they will do).  What a surprise!  The orange lines predict where 12-point stars will appear in the rotated green circles.  I’ve put in the 12-point stars, in red, to make them stand out.  Take a look at how the orange lines zoom through many of the points of the stars. 

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But where is the tomb symbol in all this?  Maybe I’ve drifted a bit, so I’ll bring back the “red line” derived directly from the tomb symbol in Part 1.  In the following image (shown at magnification 2X), I have many of the forms from Part 1, and thanks to my orange grid design, I could add an equilateral triangle (purple), with apex at the top point of the tomb symbol angle (pale green) and base coincident with the horizontal through the intersection of orange lines, and the base bounded by the verticals of the 12-point star.  The second equilateral triangle (“inner”) has its apex at an intersection of orange lines (inside apex of previous triangle) and its base bounded by the intersections of rotated circle 2’s.  Isn’t it neat that the triangles fit?  I also added verticals through the intersections of orange lines.  As the purple equilateral triangles and other forms are copied, flipped left/right, pasted, copied, inverted, pasted, and copied, rotated 90 degrees, pasted, they make an intricate design.  And by the way, I’ve found many equilateral triangles in my grid work here. 

Notice how the “red lines” intersect where the inner purple equilateral triangles intersect, where the verticals and horizontals intersect making the four corners of the central square.  Wow.  There are at least 8 other corners where red lines intersect outer purple triangles.  Notice how the “red lines” intersect where the outer purple triangles intersect – on the design’s axes.  Notice how the outer purple equilateral triangles intersect where the half green circles (dark green) intersect, where the “orange lines” pass through.  There seems to be a meeting of red line, inner purple triangle, green circle, and turquoise circle.  There seems to be a meeting of inner and outer purple triangles and half green circle.  There seems to be a meeting of yellow circle, green circle, and red line.  There seems to be a meeting of tomb symbol circle, yellow circle, and outer purple triangle.  It’s all so colorful and pretty. 

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Broader view

I’m wondering if the rotated outer equilateral triangle also goes through the “A point” (where “red line,” tomb symbol angle, and green circle meet).  I think maybe it does.

Well, I’m sure there is more to discover.  Continued here.

Slide show and music on my main page.

-2008-  

X Keywords:  symbol design how to draw math geometry MSN Windows Live Spaces X

This page was updated on June 3, 2008.

DRAWING THE “JESUS TOMB” SYMBOL, PART 6

I was wondering what the tomb symbol circle did outside the environment of the circle it is derived from. 

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

I have been making designs derived from the tomb symbol.  I am going by what I observe in my drawings; I am not attempting mathematical proofs.  As I go along I define whatever terms I need to, but might not repeat definitions in each post.  So this post should be read in conjunction with the previous ones:  Part 1, Part 2, Part 3,  Part 4, and Part 5.

In the following image, I have 8 “yellow circles” (75 percent of the diameter of my standard circle).  The yellow circles (deep yellow) pass through the center of the standard circle (regular blue).  I added 8 tomb symbol circles (one-fourth the diameter of the standard circle).  Each tomb symbol circle (black-green) is tangential to the standard circle and a yellow circle.  Then I added 8 half green circles.  (Previously called the “dark green circle,” it is one-half the diameter of the standard circle and one-half the diameter of the “green circle.”)  Each half green circle (dark green) is tangential to two yellow circles and a tomb symbol circle.  Then I added a half green circle centered on the standard circle.  This half green circle is tangential to the other 8 half green circles.  A row of three half royal circles (one-sixth the diameter of the standard circle) fit across the central half green circle, and I’ve added 9 to make a rosette (royal blue).

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In the following image, I added 16 half tomb symbol circles (one-eighth the diameter of the standard circle).  Each half tomb symbol circle (pink) is framed by two yellow circles and a half green circle.  Next I added a royal circle (one-third the diameter of the standard circle) centered on the standard circle.  Of course, this royal circle (royal blue) passes through the centers of the half royal circles.

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In the following image, I added 8 green circles (same diameter as the standard circle) tangential to the 8 peripheral points where the yellow circles, tomb symbol circles, and half green circles meet.  Each green circle (deep turquoise) is also tangential to the central half green circle, and appears to pass through two additional points, where half green circles are tangential to a yellow circle.  Each green circle appears to cuddle two of the 16 half tomb symbol circles, and I added 8 more half tomb symbol circles, each framed by 4 green circles.  Now each green circle cuddles 6 half tomb symbol circles.

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Continuing on my journey to build this design, I added a yellow circle centered on the standard circle.  The central yellow circle is thicker, because it is pasted four times.  A one-pixel center won’t go symmetrically on a four-pixel center unless it is pasted four times, onto each of the four pixels – the software has such peculiarities.  Once I added that central yellow circle, I could add a rosette of 8 royal circles, each tangential to 3 yellow circles (including the central yellow circle just added).  With the addition of the royals, I found a way to add 8 half tomb symbol circles within the central royal circle.  Each of these is tangential to two royal circles and possibly two yellow circles.  See the following image.

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Does the tomb symbol circle keep on working even when outside the circle that spawned it?  Yes, indeed.  Isn’t it wonderful that all these circles fit together so nicely?  This particular design has 85 circles by my count.  Can you find them all?

On my journey, I seem to be finding all sorts of interesting things.  Continued here.

Slide show and music on my main page.

-2008-

X Keywords:  symbol design how to draw math geometry MSN Windows Live Spaces X

PEOPLE WANT TO KNOW

Who are you?

People want to know. 

Some people define themselves by their age, their location, their gender.  “I am a woman of a certain age living in Timbuktu.”

Some people define themselves by what work they do.  “I am a J-O-B.”  Or “I am an O-C-C-U-P-A-T-I-O-N.” 

Some people define themselves by their illnesses and medical conditions.  “I am a pill-popping-person.”  “I am the one who is always visiting doctors.”  “I have this disease and that disease.  I am a disease.”

Some people define themselves by their family relationships or their friends and acquaintances.  “I am the one meeting with my friends, talking to my friends, my friends did this and that, and blah, blah, blah.”  Or “I am an appendage to this other person.” 

Some people define themselves by their possessions.  “I am my really neat car.”  “I am my house.”  “I am my new TV.”  “I possess XX number of children and pets and other assorted belongings and that is the sum total of my being.”

Some define themselves by their political views, their religion, or other “isms.”  “I am my opinion.”  Or “I am a fanatic.”

Some people define themselves by their pastimes and activities.  “I do this.  I do that.  I do, do, do, do.”  Or “I am my calendar.”

Some people define themselves by their physical characteristics.  “I am tall.”  “I am short.”  “I just got my hair done and it is me.”  Or “I am my bra size.”  And yes, there are some women who bring up the subject of their endowment – often.

While many seem to want to tell the world “I am sexy,” not many seem to define themselves as “kind.”  (Nevertheless, lots of people demonstrate kindness abundantly.)  Given the many Spaces with images of barely clothed female forms with exaggerated breasts and super-long legs – and it is women putting up this stuff – it seems clear there are many women who define themselves as “she who thinks about sex most of the time.”  Perhaps they are telling the world, “This glamorous image is who I am, a legend in my own mind.”

Some people define themselves with their clothing.  Clothes make a statement.  The woman dressed ultra-frilly or bizarrely “sexy” is saying, “I am not sure I am a woman.”

The woman wearing a miniskirt or short skirt and flashing her knees is maybe trying to re-live her youth when miniskirts were in (the 60’s), or maybe is a wannabe movie star.  Whenever she is sitting, everyone around her knows she is thinking, “I have to keep my knees together or else someone can peek up my skirt.”  How can anyone take her seriously knowing this?  Obviously she doesn’t take herself seriously.  “I am the woman who holds her legs together.”  A ridiculous fashion.  Sort of reminds me of the silly custom long ago of women trying to ride a horse while sitting in a sidesaddle (with both legs draped together demurely on one side of the horse).  Reminds me also of those silly hoop dresses women wore – imagine trying to sit in one of those and still be dignified.  Or imagine trying to sit with a bulky bustle in back.

It always seems to be the woman who doesn’t have much to reveal who wears a see-through blouse.  She is saying, “You didn’t think it possible, but yes, I am she who can wear a bra.”

The teen at the mall dressed like a hooker with spaghetti straps and belly button showing is saying, “I am powerful.”  She thinks she is.  After all, men are drooling.

You’ve seen those e-mail questionnaires that go around asking questions like:  “What is your favorite color?  What is your favorite TV show?  What are you wearing right now?”  You are supposed to answer all 20 questions and forward it to everyone you know so they can know who you are.  Supposedly.  Let’s see, uh, my favorite color is pink, or maybe red, or maybe purple.  I don’t watch programmed TV, so question 2 is out.  And I am wearing the sort of thing I always wear this time of day.  Now do you know me better?

Well, I certainly hope I am not my possessions, my relationships, my medical conditions, my clothing, or my favorite color.  Isn’t there something more to me?

Who am I?

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Aristotle supposedly said, “We are what we repeatedly do.  Excellence, then, is not an act, but a habit.”  Well, I hope I am not what I do habitually.  “I am she who does a tick-check once a day.” (essential in this neck of the woods).

Buddha supposedly said, “We are what we think.  All that we are arises with our thoughts.  With our thoughts, we make the world.”  (More quotes.)  Interesting.

Maybe who I am is determined by how I react to adversity (there’s always plenty of that) . . . .  and by how I react to the little miracles that crop up in my life.

Maybe who I am is determined by my values and how well I express them in my day-to-day living.

Am I someone I’d like to meet?  An interesting question.

Do I know who I am?  Not really.  If you can read between the lines, if you are good at reading people, you might know me better than I know myself.

Here’s an interesting line from the November 30, 2007 Daily Word:  “I overflow with the joy of living from the sacredness of who I am and of recognizing the sacredness of all others.”  Wow.  Maybe I should add that to my Profile.

Who am I? 

If I knew, then I might have at least a chance of answering the question – why am I?  That’s a better question.

Slide show and music on my main page.

-2008-

X Keywords:  find yourself MSN Windows Live Spaces X

EDEN AND APOCALYPSE

The stories we tell ourselves make us what we are.

What about the story of Adam and Eve in the First Garden, the Garden of Eden in the Bible?  Some see this as myth; others as history. 

I see it as a story of our times. 

Here we are in the First Garden, our lovely Paradise, our Earth, and because we have misused the knowledge obtained from the “Tree of the Knowledge of Good and Evil,” we have almost completely destroyed our Paradise.  Everyday the headlines scream, “ice melting here,” or “glaciers melting there,” and my country, the “most powerful,” is on the sidelines, powerless to do anything, rudderless, under the thumb of corporations.  Evidently, the corporations that run our government have not yet decided to address global warming.  They’re too busy ripping off the Earth.  Soon we will have lost our Paradise – just like Adam and Eve.

The stories we tell ourselves motivate us, or not.  The biblical story of Apocalypse or Revelation is a good example.  Some see this story as coded references to happenings in the first century, that is, as history.  But others see it as a prediction of future events.  Many who take this stance become fatalistic, feel there is nothing they can do to affect the outcome, and adopt a passive wait-and-see attitude. 

But I have to ask myself – could Revelation be instead the kind of prophesy that is a warning of events that might be, if people don’t act?  Just as Jonah’s prophesy to the people of Nineveh was a warning?  Fortunately for that city, the people listened to the warning and acted in time.  They didn’t just sit around passively, waiting to see what would happen next (Luke 11:31-33).

We people of Earth have before us a challenge to stop the violence, the destruction, the chaos of our Apocalypse, and to start building the Earth.  On Earth Day, April 22, we need to think how we will take up the challenge.

Well, I wrote that, but that’s really too optimistic.  Do I think mankind is doomed to failure?  I think it’s likely.  The evidence is all around us.  Someone sent me a little booklet published by the Jehovah’s Witnesses, just FYI.  I was flipping through it and found a chapter on the last days.  We’ll know the Last Days are upon us, it says, by the huge amount of warfare and by the huge numbers of hungry people:  “more than 100 million people have died as a result of wars since 1914 . . . . well over a billion people have to live on an income of a dollar or less a day.  The majority of these suffer from chronic hunger.”

I can pick up the phone and order some trinket that will arrive on my doorstep in a matter of days or even hours, maybe even manufactured on the other side of the globe.  But do these marvelous systems of transportation, banking, infrastructure, etc. deliver decent lives to the millions and billions who are exploited and suffering?  Hardly.

Just think how easy it was for a tiny group of obscenely wealthy men to redirect the energies and resources of an entire nation (and drain the Treasury) for their own selfish goals.  Think how quickly the nation turned to war, as if there were not any number of better ways to achieve our goals, unless of course, the goal is trashing another country.  War is the ultimate management failure.  How ironic that the very people who should have stood with Jesus, the Prince of Peace, followed after politicians with the word “Jesus” on their lips, followed like so many children dancing after the Pied Piper.

Just think that there are still those who think our country is “superior” because it has nuclear weapons, weapons-of-mass-destruction, aimed at cities across the globe.  Those people equate brutishness with superiority.  Those are the people who think that having enough nuclear weapons to destroy the entire Planet ten times over is a good survival strategy.  The detonation of even one nuclear weapon in a city would be an indescribably evil act.  Aren’t we smart enough to manage our enemies without killing tens or hundreds of thousands or even millions of innocents?

I do tend to believe that mankind will never succeed in building a better world, but to do nothing is to be complicit in the prevailing misery of our times.  I feel fatalistic, but I still try to make a point of being kind, when I think of it.  I still try to make a small donation to charity now and then.  I still try to reduce my carbon footprint.  I am grateful to those who volunteer, those who struggle for fairness, peace, justice, and environmental sanity; those who take jobs that are noble and contribute to the betterment of the whole.

When will peace come?

Full-size image

Are we about to be rescued by a man from first century Palestine who will rule as our King?  A man who will rule better than all the inadequate men who have ruled to date, better because this rescuer is more than just a man?  I do like the idea of being rescued from mankind, and here I am referring to their tendency to form hierarchies, a tendency that leads to gangs, militias, wars, power-crazed and rampaging governments, gouging corporations, devastated environments, starving people, and the like, as distinct from beneficial networking among equals.  I would like to be rescued from the possibility of nuclear winter, from our looming global warming summer, and from the continuing saga of one disaster after another after another.  It is interesting to contemplate the spirit of Jesus (love-compassion-inclusiveness-good stewardship-caring) pouring forth as a balm healing our weary, wayward, war-torn world.

The End of Times is when Good finally triumphs over Evil, when the Wheat is separated from the Weeds, when all become a unified One manifesting a Divine Christ-like essence, when humanity evolves to its Teilhardian Omega Point, or whatever.  Could it be that the end of times cannot arrive until we at least take a few collective steps in the direction of that goodness, oneness, divine-beingness, etc.?  If we don’t, we may be stuck in the constant turmoil which is our ongoing Apocalypse – forever.  Maybe the Kingdom will not be finally realized until our ways are His Way.

Some think the Kingdom can be established by destroying every evil person.  But since the boundary between good and evil runs through the middle of each and every soul, such a Kingdom would be largely uninhabited.  Oh, I forgot, except for those who are forgiven.  And who is God incapable of forgiving?  No one?  So the Kingdom includes everyone?  OK.  When does the Kingdom begin?  It is here within us, among us, and growing.  OK.  So if it includes everyone and is here and now, then how do we move beyond our apocalyptic times?    

Why not take a few collective steps towards caring, understanding, and thoughtfulness, recognizing the oneness of all people and all things; for example, we can recognize that if we dump toxic pollution into a river, that someone downstream drinking the water could be harmed, so we refrain from destroying the environment.  That’s genuine morality and caring for one’s neighbor.  That’s growing the Kingdom.

Here’s a neat formula for growing the Kingdom:  “Above all, clothe yourselves with love, which binds us all together in perfect harmony.  And let the peace that comes from Christ rule in your hearts.” (Colossians 3:14-15 NLT).  Words nearly two thousand years old, yet perfect for today.

Our vision of the future is important because it determines how we act in the present.  What’s your vision?

Slide show and music on my main page.

-2008-

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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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POEM:  THIS WAR HAS GOT TO STOP

I always knew the war was wrong.

I’m glad I knew it all along.

In boardrooms, planned in secrecy,

It’s now a disaster for all to see.

The oil they seek to liberate

Will make them rich and make them great.

The bill for this venture will be paid

By the taxpayers that they raid.

Think of the soldiers maimed and killed.

Think of their dreams now unfulfilled.

Our soldiers’ safety needs to be

Our number one priority.

The public was so unaware –

They didn’t know and didn’t care.

“Weapons of mass destruction” they feared.

They went along like sheep to be sheared.

They trusted in their Uncle Sam.

They didn’t learn from Vietnam.

I find it really hard to accept,

That this all happened while Congress slept.

But grabbing oil is still the game.

This tragedy will be their fame.

Your private life’s an open book.

Big Brother now can take a look.

To torture suspects is so vile,

Yet our nation slumbers all the while.

And who will mourn uncounted dead,

Or feed the refugees who’ve fled?

Apocalypse has come at last,

As factions feud with hate so vast.

The Prince of Peace will come to reign

When we are just; free of this stain.

When we have leaders who don’t mislead,

But reflect our values in word and deed.

Don’t you know this war’s in error –

An injustice that breeds more terror!

*******

There is a marvelous op-ed article by Walter Cronkite (the former long-time anchor for CBS Evening News) and David Krieger, December 4, 2007, that you might like to read, “Our Troops Must Leave Iraq.”  I like it because they say we should “turn Iraqi oil over to Iraqis.” 

Slide show and music on my main page.

-2007-

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