A tessellation or tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art of M. C. Escher. Tessellations are seen throughout art history, from ancient architecture to modern art.
M.C. Escher

Circle Limit III by M.C. Escher
Wednesday, April 13, 2011
Tessellations in the Garden
I think that this would be called an irregular, three dimensional, Euclidean space, tessellated natural structure, otherwise known as Sedum! And it is from my garden!
This is a salt water tessellation.
And this is a complex tessellation from nature., a tessellation on the water caused by the refraction of the light from the sun.
Monday, April 11, 2011
Letter to the Editors at Scientific American Magazine
I entreat the editors at Scientific American to please stick to science. When you do, I feel that I am getting my money's worth and am not wasting my time and energies wading through articles (and especially blogs and columns) that are not worth the effort. I do not need or desire anyone on your staff to suggest to me what I ought to think about non-scientific endeavors, i.e.; religion art, politics, etc.
I know this can be difficult when dealing with the soft sciences, but I think you can do better. And when dealing with more concrete disciplines, such as physics, astronomy, geology, etc., please do not get all gobbledygookish on your readers. I do not need to read all the things that science thinks dark matter is when in fact no one (yet) knows. I don't mind reading through theories or even flights of fancy, but so often it is presented as "wow, scientists now believe x,y,z" when in fact no science has actually been done, or no consensus exists because it is early days yet.
When science is done badly, or even presented badly, it makes it very difficult to discuss (for instance) global warming, where science HAS been done and there IS a consensus, with ones relatives who insist they have done the research and they are certain that global warming is a hoax. When you present science badly, and when you insist on publishing op eds and blogs on subjects that do not fall within the parameters of scientific inquiry, then you muddy the waters that you insist you are trying to clear. Then we are fishing blindly and no nourishment can be found
Meanwhile... I am getting so tired of all the religiosity of the anti-religious bloggers and columnists that you give ample space to in your otherwise wonderful magazine. The pursuit of science seems every bit as vulnerable as the pursuit of other disciplines to the fallibility of all human endeavor. I think that it would be a much more worthwhile endeavor, in the cause of advancing science, to first clean your own house, take the beam out of your own eye, etc. Science claims for itself things that the scientific method has not yet supported. It may yet, or it may not. But until it actually does, better to be careful how you report information. I LOVE science, good science. Good science does not include spending your time and space arguing about things that are outside the domain of science. So, give me well designed, constructed and implemented experiments, and keep me updated on the work of scientists. Please do not make science into another religion.
I know this can be difficult when dealing with the soft sciences, but I think you can do better. And when dealing with more concrete disciplines, such as physics, astronomy, geology, etc., please do not get all gobbledygookish on your readers. I do not need to read all the things that science thinks dark matter is when in fact no one (yet) knows. I don't mind reading through theories or even flights of fancy, but so often it is presented as "wow, scientists now believe x,y,z" when in fact no science has actually been done, or no consensus exists because it is early days yet.
When science is done badly, or even presented badly, it makes it very difficult to discuss (for instance) global warming, where science HAS been done and there IS a consensus, with ones relatives who insist they have done the research and they are certain that global warming is a hoax. When you present science badly, and when you insist on publishing op eds and blogs on subjects that do not fall within the parameters of scientific inquiry, then you muddy the waters that you insist you are trying to clear. Then we are fishing blindly and no nourishment can be found
Meanwhile... I am getting so tired of all the religiosity of the anti-religious bloggers and columnists that you give ample space to in your otherwise wonderful magazine. The pursuit of science seems every bit as vulnerable as the pursuit of other disciplines to the fallibility of all human endeavor. I think that it would be a much more worthwhile endeavor, in the cause of advancing science, to first clean your own house, take the beam out of your own eye, etc. Science claims for itself things that the scientific method has not yet supported. It may yet, or it may not. But until it actually does, better to be careful how you report information. I LOVE science, good science. Good science does not include spending your time and space arguing about things that are outside the domain of science. So, give me well designed, constructed and implemented experiments, and keep me updated on the work of scientists. Please do not make science into another religion.
Sunday, April 3, 2011
Response to Jamaica Plain Census
(For anyone interested in the actual data I am writing in response to you, can find it at
http://jamaicaplain.patch.com/articles/census-jamaica-plain-gets-whiter-and-less-brown)
This is a very murky set of statistics.
Exhibit A: I make it a point to never answer the question of “race” except with the obvious scientific answer of “homo sapiens sapiens”. A more accurate term when referring to various groups of peoples is “population”. Even “ethnicity” has become too murky a term to use in conversation if the goal is to actually communicate ideas.
Exhibit B: The statistics in the above article refer to those in the community who self-identify as only ONE of the choices. This is murky within murky. Self-identification is of no use for accurate data in this context. And these statistics do not take into account all those people who refuse to honor only one of the choices offered because they know that it would not accurately reflect who they are. Most people have very little idea about their origin past a few generations. The constructs they are holding onto are cultural constructs.
Exhibit C: is a challenge. Send a cheek swab to the National Geographic Human DNA Project and learn about your more ancient past. It can be illuminating. This is how a Mexican priest learns that he carries the “Aaron” gene on his Y chromosome, or how a dark skinned man from the American south learns that his mtDNA (from mother to mother) is predominantly European.
Exhibit D: Jamaica Plain abounds with people who have married outside of their population (“race”) and produced children that continue to produce children with others outside of each population circle. How is this multitude reflected in the quoted set of statistics? And how do these people react to a set of statistics that utterly excludes them, and yet is used to make points about the community they belong to?
There is (currently) only one human race. It is homo sapiens sapiens. Within this race, there are multitudes of ever shifting populations. I believe that the statistics quoted above refer to the respondents understanding of what culture they identify with. And that is useful. But you must not say that it is something else. It is not even a bad approximation of the diversity that is Jamaica Plain. As a census of “race” it is poorly devised and utterly useless.
A new paradigm needs to be created to be able to actually study the population of Jamaica Plain and the rest of America as well. It cannot include terms like “race” and “ethnicity”. It cannot use peoples own self-identification regarding which population they see themselves belonging to.
While hair texture, eye shape and color and the amount of melanin we have are obvious identifiers, they are, after all, only skin deep.
Thursday, March 31, 2011
Fern Hill in Winter - February 2011
Went to Fern Hill last night to see Orion hanging low in the night sky. Visited Kitchell Snow's eagle along the way. Lay in the deep untouched snow on Fern Hill and imagined that I could see the star formerly know as "Orion RA6h6m57.45s D17 10'11.32", which is now known as Hunter Pope. Made a snow angel in the virgin snow. Thought how I could not see Hunter's star, but still, it is there whether I see it or not. Lay for a long time enveloped in the cold snow until I was calm enough to return home.
Hunter riding Kitchell Snow's eagle.
At The Thunder of Thy Cataracts (Psalm 42:7) - February 2011
When deepness calls, I have longed to go,
When clarity and calm quiet the heart
And when ravaged by the mind's fierce fires.
A soft command, - not from hell's depths below...
Deep, from deep, to deep calling, to part
The soul from flesh, impels, me inspires
Toward the breath of mute and mystic death.
- Alexandra Pope
No Balm In Gilead - January 2011
She longs in light and dark
For the pleasures of his presence.
In sun - or moon and stars -
Her heart grows wild with yearning
As longing moves on reminiscence.
The past, in partial pictures,
Flares, with sudden light, to mind.
Where once the slow, soft grief
(her silent loneliness)
Was calm in caverns deep and blind
Now voices cry and cries
Ring out the pain of his going.
They shatter the treaty of silence.
They call out his name in vain,
And crumble the air with their moaning.
- Alexandra Pope
Stillness is Screaming - December 2010
It came to me in a flash today; “This isn’t over at all, surviving this, - I may not survive it yet.” It’s harder and harder to think. I can act outwardly with grace, but inwardly there is such horror and screaming. I don’t want to be here without him. The pull is stronger, the call more compelling. The moment I am still the storm begins. There is no center, no point of clarity and vision, - only this swirl of screaming. I keep moving, always moving; through space, through time, my mind always moving, because stillness is screaming.
It is harder and harder. And I have become desperate for distraction. I am starving for the lack of Hunter. Better not to exist than to continue without him, or better to fight my way to him, wherever he is. I don’t think I’ve allowed even myself to know how far gone I am. This separation is dangerous for me. The cost of functioning is this split: “To be here, I must not know myself.” So I am disintegrated, disintegrating. I am no longer whole. “Integritas, consonantia, claritas”: wholeness, harmony, radiance.
I am split, not whole. My sound is a scream. My radiance is a mask, not revealing, but concealing myself, - even from myself.
I am drowning in this fire
The flaming out of fierce desire
Born of grief and loss and love
This Phoenix will not rise above
The ashes of her own demise
I am not safe, to others or to myself. I am in flames. Why does it not consume me? I am willing…. – speak the word only.
Hunter, my Seeker, I seek you.
It is harder and harder. And I have become desperate for distraction. I am starving for the lack of Hunter. Better not to exist than to continue without him, or better to fight my way to him, wherever he is. I don’t think I’ve allowed even myself to know how far gone I am. This separation is dangerous for me. The cost of functioning is this split: “To be here, I must not know myself.” So I am disintegrated, disintegrating. I am no longer whole. “Integritas, consonantia, claritas”: wholeness, harmony, radiance.
I am split, not whole. My sound is a scream. My radiance is a mask, not revealing, but concealing myself, - even from myself.
I am drowning in this fire
The flaming out of fierce desire
Born of grief and loss and love
This Phoenix will not rise above
The ashes of her own demise
I am not safe, to others or to myself. I am in flames. Why does it not consume me? I am willing…. – speak the word only.
Hunter, my Seeker, I seek you.
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