Earth

https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVsohD4Sxlv_DRdoO-oPe86LWxKtDq4BkSl2d5fpkargXIyIdP7hUqkS5PhIitTswcgbYIy3-Fsf7zxlWbKqByiDh9hmkvVWxyRJP4gMfCwi1I-EVIQug8pHxDgaPluv-EuebseXT3Tnra/s1600-h/dodec+lines+on+earth+2.GIF

Plane-face dodecahedron (left) to spherical icosadodecahedron (center & right), great circles, small circles on pent faces may be ocean/air gyres, polar axis vs solar-lunar tides

http://www.progonos.com/furuti/MapProj/Normal/ProjPoly/Foldout/TIcosahedron/Img/ticGn-s128-z5.eos.png

A truncated icosahedron globe

amazing drops, plops & props

Drop Art
Corrie White, the artist behind Liquid Drop Art, has a talent for capturing the surreal impact of a water droplet. White’s photographs allow viewers to see something that would normally be “invisible to the human eye.” Most of the water droplets were created with a medicine dropper and food dyes. According to the White’s bio, the “forms of water and milk shapes are pure and unedited.”

link

The Line of the Archer, the Biologist & the Polymath

At Catalogue of Organisms biology blog, [http://coo.fieldofscience.com/2011/08/red-lined-wings-of-south-america.html?showComment=1312665778549#comment-c4532519180935840235 ] I made a comment regarding the original measure of the word "line", following his description : "A 'line' is a unit of measurement used by a number of 18th and 19th century biologists. The exact length of a line seems to have varied somewhat between countries (see this page for explanations), though it seems to have generally been a little more than 2 mm. Linnaeus apparently defined a line in the introduction to Philosophia Botanica as the length of a lunule (the white half-moon at the base of a fingernail) on any finger other than the thumb." (italics mine)

my comment: perhaps originally 'line' represented the diameter or thickness of a taut bowstring on an archer's bow? I'd think it fits in this way:

L-ine singlet, a-lign (ligament/tendon) (parallel fiber, straight or single coil)

Tw-ine duplet, div-ide, twisted lines -> X (double helix)

Tr-ine triplet, tri-plait, braided lines -> * (offset & interwoven)

See the picture in my earlier post here: http://the-arc-ddeden.blogspot.com/2010/05/archae-numeric.html

Note that in the 123 sequence, Roman numerals are vertical lines, Chinese numerals are horizontal lines and Indi-Arabic numerals are vertical cursively attached lines.

Per Bucky Fuller, there are no mathematically straight lines in nature, there are only progressively less non-straight lines as vector edges between and enclosing events.

http://www.rwgrayprojects.com/synergetics/synergetics.html

http://en.wikipedia.org/wiki/Synergetics_(Fuller)

Vertebrates "are" Invertebrates

I asked the following questions to Christopher at his blog Catalogue of Organisms, in his post on moths.

1. Are the pharyngeal arches in vertebrates homologous to the first pair of true legs in insects?





2. Are the abdomenal prolegs in holometabolous caterpillars homologous to the ventral mammae & milk line in mammals? (both involve fluid-dynamic flow rather than muscle movement, and woulld explain presence of most male mammals retaining vestigial nipples).

I suspect so, in both cases. Having just read The Secret Life of Lobsters by Trevor Corson, I see that female lobsters secrete protein glue (for egg attachment) from cement ducts on their caudalmost swimmerettes (homologous to caudalmost prolegs & mammae secreting casein glue-rich milk IMO). They fold their tails like crabs and deposit thousands of eggs within the folded area, protecting them from exposure. Marsupials seem to have retained this trait, except the marsupial embryo escapes the egg and womb and crawls by forelimbs to the mammae which are protected from exposure by a skin fold (pouch). The echidna, an egg laying primitive monotreme mammal with a pouch, has no external nipples, the hatched infant licks the abdomen to get milk. It appears to be a homology between these distinct taxa.

Aaron Filler's book on Vertebrae called The Upright Ape goes into detail on the spine & vertebrae as archetype, but does not mention this: Lobsters inside their eggs molt 35 times, changing their 'skin'. (After leaving the egg, lobsters eat their shed 'skin'.) The 35 molts produce the somites which form the vertebral column (in vertebrates), internally similar to the external rattles of the molting rattlesnake, I'd say. (Unlike lobsters, snakes never eat their shed skin AFAIK.) It is my contention that the 35 molts are, geometrically, 7 episodes of pentameric (5-way split) distribution, resulting in, for example, 7 cervical vertebrae in mammals, etc.

DDeden

PS. Insect wings and bird/dinosaur feathers appear to be homologous to lobster swimmerettes, (and more distantly to caterpillar prolegs and mammalian mammae). Imagine that! Nature Rules!

PPS. Insect wings appear to be homologs to a vertebrate rib "shell", that is, the delicate forewings of a butterfly are equivalent evolutionarily to the hyperdense ribcage of a dugong, the aftwings of a moth to a sauropod pelvis, the fly's vestigial flight knobs to a giant blue whales vestigial pelvis.

http://coo.fieldofscience.com/2011/06/colour-vs-crypsis.html#comments

http://www.uprightape.net/

http://www.amazon.com/Secret-Life-Lobsters-Scientists-Unraveling/dp/0060555580

Also interesting to compare human embryos and giant sauropod dinosaurs:

http://svpow.wordpress.com/2011/05/23/the-worlds-longest-cells-speculations-on-the-nervous-systems-of-sauropods/

and the tentacles of squid ((4 + 1) x 2) with the typical prolegs of a caterpillar ((4 + 1) x 2)...

=================================================================

Church forests of Lake Tana, Ethiopia 'Trees are the jewels of God"

http://blogs.plos.org/blog/2011/02/25/church-forest/

They function similarly to the European tradition of Royal Forest. Interesting the name of the island forests is Coptic Forest, similar to Coppice Forest.

steps

http://ngm.nationalgeographic.com/2011/06/gobekli-tepe/musi-photography
http://www.uprightape.net/Image_Pages/UA_Fig3-2_DjedDrawing.html

Note similarity of the T pillar at Gobleki Tepe 9ka and the Djed column in Ancient Egypt (fig. B), both have hands extended forward, both have bench (or ladder rungs) below and T (or multiple Ts) above.

Note similarity of vertebrae, mastaba (mammae + stepped pyramid), stupa/pagoda, stair, stele/tel/tepe...
cf Greek 'step' = "be'ma" (speakers stand or judgement seat at trial)

The first dwelling of humanity was the triangularly woven geodesic dome of branches with a waterproof external coil of inserted leaf shingles (cf modern BaMbuti mongolu dome hut constructed by Pygmy women from intertwined branches.), an inversion of the great ape nest (which had been naturally selected due to its effective mimicry of the raptors large canopy open nest, with internal leaves inserted for lining). The dome hut occurred after the #2 chromosome inversion/fusion in humans, when human ancestors (46 chromosomes) permanently separated from apes (48 chromosomes) and exchanged open-nest-tree-canopy dwelling for enclosed-dome-ground dwelling. From this, humans expanded from their forest origins outwards omnidirectionally, modifying their dome huts. This included changing from a coil of large leaves to a coil of grass or reed bundles (more insulating), clumps of clay-roots (first Jericho huts) or slate-slabs or rocks (more permanent, eg. Natufian) or even mammoth skulls & bones covered by animal furs or tree bark or grass bundles, depending on availability of leaves etc. and amount of rain and temperature changes. The partly buried sod dome (at first hand-pulled root-soil clumps, then serrated-blade-obsidian-knife-cut square clods and later sawn snowblocks for dome igloos (eg. Alaskan Eskimo Inuit) and sundried clay-straw bricks (eg. Sudan Nile huts, India Harappa) were derived gradually. (By this time the original all-branch geodesic frame was replaced by tied-stick frame, knots/lashings and glues more recent than weaving.) Nomads following herd seasonal migrations developed the cone (stick-hide Saami kota, Dakota tipi) in areas with few trees, and the stilted coned column (stick-lathe-felt yurt, stick-lather-manure-clay roundhouse hut) followed in seasonally semi-permanent villages. Then square base huts and longhouses formed due to population pressure, round huts became "squished" and straightened by permanent fences/walls/roads and more concentration, height became functional for growth, usable for open canopy-covered patios (stick stepladders), areas not flood-prone would allow subground cool storeroom cellars (stone stairs), houses above floodprone areas had shaded patios and animal pens below.

See post on round basket craft, dome huts & round basket boats:
http://the-arc-ddeden.blogspot.com/2008/12/crescent.html

Le Tuc d'Audoubert cave, rotunda contains 2 clay sculted bison, outer chamber contains dripping stalactites (a poet referred to them as 'milky tits'), which links stalactite to galact to melt, molassis & Moses (drawn from water in a papyrus ark/teba coated in bitumen tar, as was the earlier Egyptian Horus) later getting water from stone in the land of milk (PIE melug, galact) & honey (mahdu, mead).

http://cd0901-2.blogspot.com/2009/01/birth-of-art-paleolithic-art.html

The holy sacred texts of ancient cultures speak of village squares, temples and 2 story buildings in towns & cities and fabricated tents of nomads, this dates them to long after the early human habitat of woven-branch dome shelters in small forest camps, rings of small huts (Saami kota, Malay mahakota = crown) around the central cooking/drying campfire (Mbuti apa = fire = camp, Malay api = fire, kampong = camp).

http://anthropology.net/2010/02/22/gobekli-tepe-temple-in-turkey-predates-the-pyramids-of-giza/#comment-25079

See beehive houses of Sanlurfia nearby:
http://images.travelpod.com/users/sallycousens/1.1244889872.bee-hive-houses.jpg

Compare to neolithic huts of Ban P'o site in 7ka China:
http://hilbertspaces.com/photos/china/xian/banpo/dscn1346.jpg
"Majority of them were semi subterranean, 3-5m (10-16ft) in diameter, and with floors almost a meter beneath the ground surface. Every house had timber beams that placed on stone bases, whereby they gave support to precipitously pitched roof. Moreover, the interior walls and floors were plastered with straw and clay". http://www.articlelisted.com/Art/41928/185/Neolithic-Village-Ban-po-ts-un.html

Basically a tied tipi top above ground and supported columnar bottom in or at ground level, typical for pre-brick neolithic small village settlements throughout Eurasia & Africa amongst transitional hunter-gatherer - permanent agriculturalists.

The igloo instead combined the coiled shingle unit (mongongo/pandanus leaf -> clay-straw clump (later brick) -> sod clod block -> snow block) and semi-subterranean depth with raised bed, but discarded the (scarce) wood branch geodesic framework, relying on the melt-freeze cycling of snow for rigid blocks similar to sun dried clay-straw bricks.
"Iglu is the Inuit word for a house or home built out of any material,[1] and is not restricted exclusively to snowhouses, but includes traditional tents, sod houses, homes constructed of driftwood and modern buildings.[2][3] The hole left in the snow where the blocks are cut from is usually used as the lower half of the shelter" (Similar to the semi-subterranean dome & cone structures elsewhere, inside was lower except in flood-prone areas where stilts were used.)Animal skins were used as door flaps to keep warm air in. Igloos used as winter shelters had beds made of snow, covered with twigs and caribou furs. (Furs were never used to cover the dome, only the doorway and bed.) Architecturally, the igloo is unique in that it is a dome that can be raised out of independent blocks leaning on each other and polished to fit without an additional supporting structure during construction. (Thus the wood frame was lost. In areas where snow was unreliable for blocks, huts of whale ribs and hides were built, surrounded by compacted snow for insulation.)
http://en.wikipedia.org/wiki/File:Igloo_spirale.svg (similar to leaf coiling of BaMbuti dome)
http://upload.wikimedia.org/wikipedia/commons/b/b3/EskimoIglooDrawing.jpeg

Earlier, I had speculated that the igloo had been derived from Lake Baikal seal air holes which are snow pile domes. In inuit these snowpiles are called aglu. But there is no coiled block construction, so I think the term aglu is derived from the igloo, which is surely derived from coiled sod clod domes derived from geodesic branch & coiled leaf domes (mongolu)

Where trees grew or driftwood was available, a pole & sod house was built:
http://pubs.aina.ucalgary.ca/arctic/Arctic45-2-199.pdf
Note that the ceiling was held up by either inverted forked roots or branch forks. [The T pillars of G. Tepe may have served a similar function, holding up a canopy, ceiling or dome above the central pair of Tees.] Some Siberian people had a tipi-like structure, but the smokehole was also the access hole, while a ladder was used for entry. In colder climates, the access hole was dug underground and covered. [Catal Hoyuk and other neolithic settlements also often used ceiling ladders rather than floor-level doorways or subterranean tunnels.]

Siberian yaranga (arctic yurt): http://en.wikipedia.org/wiki/Yaranga
Saami goahti*/kota/lavu: http://en.wikipedia.org/wiki/Goahti (peat & birch bark cover)
Siberian summer chum tipi tent: http://en.wikipedia.org/wiki/Chum_(tent)
Siberian winter pyramidal golomo uten**: http://www.grida.no/prog/polar/siberia2003/people/evenk/evenk.htm
nenet huts http://www.culturecenternorthernasia.org/housetypes.jpg
Siberian Koryak winter step hut: http://www.koryaks.net/history.html

* goahti (wide tipi) similar to: kota/cote/cottage/coat/hut/court
** golomo uten (wooden pyramid roof cabin) similar to: mongolu/igloo/harigolu/ma-gulu, uten similar to hut/wooden/hutan/(endu = interior of hut)/endura = forest interior)


DDeden

The arc of the universe

The Arc of the Universe Is Long But It Bends Towards Justice

On April 4, 2008, then-Senator Barack Hussein Obama, speaking on the 40th anniversary of the assassination of Dr. Martin Luther King, declared:

"Dr. King once said that the arc of the moral universe is long but it bends towards justice. It bends towards justice, but here is the thing: it does not bend on its own. It bends because each of us in our own ways put our hand on that arc and we bend it in the direction of justice...."

(My birthday is April 4th)

Archae-Numeric and origin of XYZ

[click pic to enlarge]

re. the numbers, seems to me that the last common numerical language was 1-12
_ (1 horiz line)
= (2 lines)
3 (3 horiz lines, cursive)
[=] square (4 lines, 2 vert 2 horiz)
_ above a square (5 lines)
= above a square (6 lines, 2 vert, 4 horiz)
3 above a square (7 lines)
square above a square (8 lines)
square above _ above a square (9 lines) (became % sign?)
square above = above a square (10 lines)
square above 3 above a square (11 lines)
square above a square above a square (12 lines)

12 might have been quickly drawn as a cube triface (a Y at center of angled cube)?
(A simple paint program or cad could show all this better.)

originally zero was a point or dot, not a circle, so 4 and 8 were curved.

Used probably 8,000 years ago, with local variations.
I'd wondered how 10, 11, 12 appeared before decimal notation.

Primitive numerical symbols used in early merchant/market trade, with local variations?

Numer = Sumer (symbol) name, used in Samar, Meroe, Meru, Samarkand, Somali, Sumatra... mer = merchant marine or port

> re. origin of XYZ in alphabet:
>
> XXXXXX if these letters all touched as a grid, they'd
> XXXXXX produce a bi axial weave of 90 deg. = squares
> XXXXXX add duplicate overlay & tilt = octagons
>
> YYYYYY if these letters all touched as a grid, they'd
> YYYYYY produce tri axial chicken wire weave = hexagons
> YYYYYY add duplicate overlay & tilt = rhombi (below)
>
> ZZZZZZ if these letters all touched as a grid, they'd
> ZZZZZZ produce bi axial 120,60 deg. weave = rhombi
> ZZZZZZ add duplicate overlay & tilt = 60 deg. triangles

add a duplicate overlay to get tetrahedral grid
add a duplicate overlay to get cube grid (?)

Maybe buy some cheap chickenwire, cut into 6 layers and overlay them, noting the cells (X-Y-Z-delta-tetra-cube?)
I'm sure someone has done this, but I don't recall seeing it anywhere, could be done with nets flat or on a sphere (notching where necessary.).
-

Polynesian contact with California?
here

Cybernetics, Synergetics, Synarctics

The top diagram is mine, entitled 'Trident Earth' (Earth as nuclear sphere surrounded by partially stellated duo-cuboctahedron with incidental owl imagery due to unfolding the top and bottom tets like flower petals opening), the next image is Bucky Fullers 'Cosmic Hierarchy' without the relative volume data.

http://en.wikipedia.org/wiki/Cybernetic#Overview
"The term cybernetics stems from the Greek (kybernetes, steersman, governor,
pilot, or rudder — the same root as government)."
Does that mean Trim-Tab?

http://en.wikipedia.org/wiki/Systems_theory
"Systems theory is an interdisciplinary theory about the nature of complex
systems in nature, society, and science, and is a framework by which one can
investigate and/or describe any group of objects that work together to produce
some result."
Is that Synergetics?
http://en.wikipedia.org/wiki/Synergetics

Synarctics: supplement to Synergetics by Bucky Fuller
-
Reciprocal relative volume calculation, conversion constant:: {via ku @ Synergeo}
XYZ -> IVM: sqrt (9/8)
IVM -> XYZ: sqrt (8/9)
-
Synergetics, tet cube

Fig. 986.210 Diagonal of Cube as Unity in Synergetic Geometry: In synergetic geometry mensural unity commences with the tetra edge as prime vector. Unity is taken not from the cube edge but from the edge of one of the two tetra that structure it. (Compare Fig. 463.01.) Proportionality exactly known to us is not required in nature's structuring. Parts have no existence independent of the polyhedra they constitute.

Synergetics, chefs' hat

fig 16
fig 17

416.02 If you next take two triangles, each made of three balls in closest packing, and twist one of the triangles 60 degrees around its center hole axis, the two triangular groups now may be nested into one another with the three spheres of one nesting in the three intersphere tangency valleys of the other. We now have six spheres in symmetrical closest packing, and they form the six vertexes of the octahedron. This twisting of one set to register it closepackedly with the other, is the first instance of two pairs internested to form the tetrahedron, and in the next case of the two triangles twisted to internestability as an octahedron, is called interprecessing of one set by its complementary set.
416.03 Two pairs of two-layer, seven-ball triangular sets of closestpacked spheres precess in a 60-degree twist to associate as the cube. (See Fig. A, illustration 416.01.) This 14-sphere cube is the minimum cube that may be stably produced by closest-packed spheres. While eight spheres temporarily may be tangentially glued into a cubical array with six square hole facades, they are not triangulated; ergo, are unstructured; ergo, as a cube are utterly unstable and will collapse; ergo, no eight-ball cube can be included in a structural hierarchy.
416.04 The two-frequency (three spheres to an edge), two-layer tetrahedron may also be formed into a cube through 90-degree interprecessional effect. (See Fig. A.)
417.00 Precession of Two Sets of 60 Closest-Packed Spheres

Fig. 417.01 417.01 Two identical sets of 60 spheres in closest packing precess in 90 degree action to form a seven-frequency, eight-ball-to-the-edge tetrahedron with a total of 120 spheres; exactly 100 spheres are on the outer shell, exactly 20 spheres are in theinner shell, and there is no sphere at the nucleus. This is the largest possible double-shelled tetrahedral aggregation of closest-packed spheres having no nuclear sphere. As long as it has the 20- sphere tetrahedron of the inner shell, it will never acquire a nucleus at any frequency.
417.02 The 120 spheres of this non-nuclear tetrahedron correspond to the 120 basic triangles that describe unity on a sphere. They correspond to the 120 identical right- spherical triangles that result from symmetrical subdividing of the 20 identical, equilateral, equiangular triangles of either the spherical or planar-faceted icosahedron accomplished by the most economical connectors from the icosahedron's 12 vertexes to the mid-edges of the opposite edges of their respective triangles, which connectors are inherently perpendicular to the edges and pass through one another at the equitriangles' center and divide each of the equilaterals into six similar right triangles. These 120 triangles constitute the highest common multiple of system surface division by a single module unit area, as these 30º , 60º , 90º triangles are not further divisible into identical parts.
417.03 When we first look at the two unprecessed 60-ball halves of the 120-sphere tetrahedron, our eyes tend to be deceived. We tend to look at them "three-dimensionally," i.e., in the terms of exclusively rectilinear and perpendicular symmetry of potential associability and closure upon one another. Thus we do not immediately see how we could bring two oblong quadrangular facets together with their long axes crossing one another at right angles.
417.04 Our sense of exclusively perpendicular approach to one another precludes our recognition that in 60-degree (versus 90-degree) coordination, these two sets precess in 60-degree angular convergence and not in parallel-edged congruence. This 60-degree convergence and divergence of mass-attracted associabilities is characteristic of the four- dimensional system.
418.00 Analogy of Closest Packing, Periodic Table, and Atomic Structure
418.01 The number of closest-packed spheres in any complete layer around any nuclear group of layers always terminates with the digit 2. First layer, 12; second, 42; third, 92 . . . 162, 252, 362, and so on. The digit 2 is always preceded by a number that corresponds to the second power of the number of layers surrounding the nucleus. The third layer's number of 92 is comprised of the 3 multiplied by itself (i.e., 3 to the second power), which is 9, with the digit 2 as a suffix.
418.02 This third layer is the outermost of the symmetrically unique, nuclear-system patterns and may be identified with the 92 unique, selfregenerative, chemical-element systems, and with the 92nd such element__ uranium.
418.03 The closest-sphere-packing system's first three layers of 12, 42, and 92 add to 146, which is the number of neutrons in uranium__which has the highest nucleon population of all the self-regenerative chemical elements; these 146 neutrons, plus the 92 unengaged mass-attracting protons of the outer layer, give the predominant uranium of 238 nucleons, from whose outer layer the excess two of each layer (which functions as a neutral axis of spin) can be disengaged without distorting the structural integrity of the symmetrical aggregate, which leaves the chain-reacting Uranium 236.
418.04 All the first 92 chemical elements are the finitely comprehensive set of purely abstract physical principles governing all the fundamental cases of dynamically symmetrical, vectorial geometries and their systematically self-knotting, i.e., precessionally self-interfered, regenerative, inwardly shunting events.
418.05 The chemical elements are each unique pattern integrities formed by their self-knotting, inwardly precessing, periodically synchronized selfinterferences. Unique pattern evolvement constitutes elementality. What is unique about each of the 92 self- regenerative chemical elements is their nonrepetitive pattern evolvement, which terminates with the third layer of 92.

Small duotet 1.5tv, small int octa .5tv, small cube 3tv
Large duotet 12tv, large int octa 4tv, large cube 24tv
Double Duo-tet = includes VE w/o 1/2-octas, in IVM and cubic matrix


4F tet (slightly offset)
Cubes ahoy!
1 F tet, volume 1, surface area 4 (triangle faces).
2 F tet, volume 8, surface area 16.
3 F tet, volume 27, surface area 36.
4 F tet, volume 64, surface area 64.
5 F tet, volume 125, surface area 100.
6 F tet, volume 216, surface area 144.

What about the oddball relative volumes of the icosa and vector edge cube? (cont'd)
18.51 + 8.49 = 27. 8 icosas in 2F cube pattern has central vector edge cube
27 = 3 x 3 x 3 (3 Freq small cube). 8 = 2 x 2 x 2 (2 Freq small cube)
3 layers of a cube of 9 spheres/cubes

01.02.03. + 04.05.06. + 07.08.09.
10.11.12. + 13.14.15. + 16.17.18.
19.20.21. + 22.23.24. + 25.26.27.

000+000+000
000+000+000
000+000+000

000+000+000x000+000+000x000+000+000

27 + 27 = 54 (2 cubes)
54 - 42 = 12 (2 cubes - 2nd freq VE vertices = 1st freq VE 12 vertices)
54 - 12 = 42 (2 cubes - 1st freq icosa vertices = 2nd freq icosa vertices)

92 = 90 + 2 where 2 is suffix, 90 is 9 x 10, 9 is the full set.

Wonky watercube: foam has 14 sided cells of minimal surface area
here

involution, revolution, evolution A geodesic hemispheric dome of aluminium tubing and fabric with congruent torus with central funnel column as supporting mast, wind turbine, tracking solar collector, chimney, water spout reservoir, air conditioning.


. In single symmetrical systems, all the vertexes are equidistant radially from their common volumetric centers, and the centers of area of all their triangular facets are also equidistant from the system's common volumetric center.
400.41 The minimum single symmetrical system is the regular tetrahedron, which contains the least volume with the most surface as compared to all other symmetrical single systems. There are only three single symmetrical systems: the regular tetrahedron, with a "unit" volume-to-skin ratio of 1 to l; the regular octahedron, with a volume-to- surface ratio of 2 to 1; and the regular icosahedron, with a volume-to-surface ratio of 3.7 to 1. Single asymmetrical systems contain less volume per surface area of containment than do symmetrical or regular tetrahedra. The more asymmetrical, the less the volume-to- surface ratio. Since the structural strength is expressed by the vector edges, the more asymmetrical, the greater is the containment strength per unit of volumetric content.

VE to octa showing icosa phases
Flexible polyhedra, VE, golden icosa/tetra, the Arc: red curve at upper left at page 12 includes the Synergetics jitterbug transformation from VE cuboctahedron through the various icosahedral phases to the octahedron. The Synarctics full jitterbug actually continues through to the tetrahedron and triangle without stopping, though it can reverse at any click-stop phase.

The Synarctic version of structural dimensionality of the jitterbug transformation, with decrease in bond distribution:

Dimension	Single Jitterbug	Dual Jitterbugs	Int plane polygons
6th Dimension	VE non-nuclear cuboctahedron	Dual non-nuc cuboctahedra	hexagon
5th Dimension	fluid icosahedra	rigid icosahedron	pentagon
4th Dimension	octahedron	cube faced w/ 6 octamids	square
3rd Dimension	tetrahedron	tri prism w/ 3 octamids & 2 tetramids	triangle
2nd Dimension	2 Freq triangle	"winged" octahedron	triangle
1st Dimension	equil triangle 8 layer non-Z "prism"	octa? tet? SoD? triangle? non-Z "anti-prism"	triangle

internal flat planar polygon defines dimension:

cuboctahedron = 6 dimension, hexagon, dynamic cycle
icosahedron = 5 dimension, pentagon, static shell
octahedron/cube/triprism = 4 dimension, square, matrix
tetrahedron = 3 dimension, triangle, structure, crystal
2 Freq triangle = 2 dimension, triangle, system, tile
1 Freq triangle = 1 dimension, triangle, unit, cell



Note on Synarctic Jitterbug:
VE vertex single bond pin hinged, (compress able)
octa double bond edge hinged, (torque able)
tetra tri bond cirumferentially hinged (squish able)
triangle 8 plane full face hinged (coplanar polar layerable)
SoD nuclear plane face hinged (noncoplanar neutral layerable)

12, 42, 92
12 = 6 x 2, 3 x 4
42 = 6 x 7, 6 is non-nuc hexagon, 7 is nuc hexagon
42 = 3 x 14, 3 is prime triangle, 14 is VE & foam faces
92 = 90 degrees/surface spheres + polarity suffix

am: A regular octahedron can be cumulated so that it is either a rhombic
dodecahedron or a stella octangula.
http://mathworld.wolfram.com/Cumulation.html
Math World won't admit this, but if you cumulate an octahedron, then
you can get the rhombic dodecahedron, just as if you cumulate the cube.

A stella octangula and rhombic dodecahedron are identical on a spherical surface AFAICT.
-

VE as 5tv
VE**5 = 160tv

Table: Initial Frequencies of Vector Equilibrium
Close-packed
Spheres Freq Tetravolumes
Radius 1 VE0/2 2 1/2
Radius 1 VE0 5
Radius 2 VE1 20
Radius 4 VE2 160



patern(pattern/path/pith/pathos) matern(matrix/matter/material/math/method)

Monogamy in humans, hominoids and tree frogs
here

Air sac in a puddle frog species used for visual gesture more than vocalization, probably due to a 'tuned-in' aural predator abundance similar to Hawaiian crickets which lost their song due to predation:
here

Some frogs lack vocal sacs, such as those from the genera Heleioporus and Neobatrachus, but these species can still produce a loud call. Their buccal cavity is enlarged and dome-shaped, acting as a resonance chamber that amplifies their call. The noise of flowing water overpowers any call, so some river frogs communicate by other means.

The main reason for calling is to allow males to attract a mate. Males call either individually or in a group called a chorus. Females of many frog species, for example Polypedates leucomystax, produce calls reciprocal to the males', which act as the catalyst for the enhancement of reproductive activity in a breeding colony.[39] A male frog emits a release call when mounted by another male. Tropical species also have a rain call that they make on the basis of humidity cues prior to a rain shower. Many species also have a territorial call that is used to chase away other males. All of these calls are emitted with the mouth of the frog closed.

A distress call, emitted by some frogs when they are in danger, is produced with the mouth open, resulting in a higher-pitched call. The effectiveness of the call is unknown; however, it is suspected the call intrigues the predator until another animal is attracted, distracting them enough for its escape.

Many species of frog have deep calls, or croaks. The English onomatopoeic spelling is "ribbit". wikipedia

Nature by number: spatial geometry in natural growth patterns

here

New apith skeletons found

Monday, March 22, 2010

Algebra in Wonderland?

Brief moment of math:

"The word “algebra,” De Morgan said in one of his footnotes, comes from an Arabic phrase he transliterated as “al jebr e al mokabala,” meaning restoration and reduction".

Was Lewis Carrols' Alice in Wonderland a satire of the new math of the time period?

NY Times article

Donald Duck in Mathmagic land: Disney cartoon movie from 1959
http://en.wikipedia.org/wiki/Donald_in_Mathmagic_Land

video short of film
http://www.kheper.net/topics/theoryofeverything/Reflexive.htm
h/t Kirby U @ synergeo
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Synergetics

646.18 Atoms dislodged from the outer layer of the omniintermagnetized ball bearings would always roll around on one another to relocate themselves in some closest- packing array, with any two mass-interattracted atoms being at least in tangency. When another dynamic-spherical-domain atom comes into closest-packing tangency with the first two, the mutual interattractiveness interrolls the three to form a triangle. Three in a triangle produce a "planar" pattern of closest packing. When a fourth ball bearing lodges in the nest formed between and atop the first three, each of the four balls then touches three others simultaneously and produces a tetrahedron having a concave-faceted void within it. In this tetrahedral position, with four-dimensional symmetry of association, they are in circumferential closest packing. Having no mutual sphere, they are only intercircumferentially mass-interattracted and cohered: i.e., gravity alone coheres them, but gravity is hereby seen experimentally to be exclusively circumferential in interbonding.
646.19 With further spherical atom additions to the initial tetrahedral aggregate, the outermost balls tend to roll coherently around into asymmetrical closest-packing collections, until they are once more symmetrically stabilized with 12 closest packing around one and as yet exercising their exclusively intercircumferential interattractiveness, bound circumferentially together by four symmetrically interacting circular bands, whereby each of the 12 surrounding spheres has four immediately adjacent circumferential shell spheres interattracting them circumferentially, while there is only one central nuclear ball inwardly__i.e., radially attracting each of them. In this configuration they form the vector equilibrium.

What Bucky didn't address there is that any spherical configuration (with any number of spheres) produces a geometrical nucleus, but the surface area (number of surface facets) determines if the nucleus is vertexial like the VE (sometimes defined as a small rhombic dodeca) or skeletal polyhedral like the star tetra, star octa, star icosa core polyhedra.

interim

"Every physical body has four basic sides, or four comers: two points alone are only collinear, and three are only coplanar; not until there are four comers can the property of spatial existence be recognized. As a result, any physical body must be held at four noncoplanar points (triangulated distally), with three torque restraints at each point (triangulated locally), in order to be stabilized.
There are four fundamental corners in every system, and each must be triangulated: 4 × 3 = 12. Thus there are twelve degrees of freedom, tetrahedrally organized." Amy Edmondson, A Fuller Explanation, Re. R. Buckminster Fuller, vector equilibrium





Relative Volume Table: (tetra volumes) | (cube volumes)

form	= tv|cv	form	= tv | cv
tetra/coupler	= 1 | 1/3	star octa	= 12 | 4
double tetra	= 2 | 2/3	star rh dodeca	= 12 | 4
duo-tet cube	= 3 | 1	cmpd cubocta ext	= 20 | ~7
reg octa	= 4 | 4/3	reg icosa int	:~18 | ~6
star tetra	= 5 | 5/3	star icosa ext	= 20 | ~7
rhom dodeca	= 6 | 2	cubocta int	= 20 | ~7
2F coupler	= 8 | 8/3	2F cube	= 24 | 8

Icosa = 18.51 tv +
Vector edge Cube = 8.49 tv =
Icosa + Vector edge Cube = 27 tv -
Vector diagonal Cube = 3 tv (2 small duotets) =
2F lattice Cube = 24 tv (2 big duotets) -
Octa = 4 tv =
Star Icosa ext = 20 tv or
Cubocta = 20 tv + 8 ext tetra =
Star Cubocta Cube = 28 tv + 6 ext sq pyramids =
Cmpd Cubocta = 40 tv - 8 ext tetra =
Superocta = 6 octa & 8 tetra = 32 tv

compound of (1st stellation of) cube & octahedron (not star cubocta)


Cumulation: tet, octa, cube, icosa, dodeca can be cumulated 4 times
CUMULATION
(Cube & tet can't be stellated but both can be cumulated)
tetra, triakis tetra, cube, 12-faced star deltahedron (star tetra)
cube, tetrakis hexahedron, rhomb dodeca, 24 face star deltahedron (star cube)
octa, sm triakis octa, stella octangula/duotet (star octa)

star tetra, star octa (domain net of cubocta), star icosa




Now excluding the nucleic polyhedron volume:
View of surface tets as skeletal structure, equi length struts
Star Tet: nuc tet void, 4 tets, 6 circ + 12 ext struts = 18
Star Octa: nuc octa void, 8 tets, 12 circ + 24 ext struts = 36
Star Icosa: nuc icosa void, 20 tets, 30 circ + 60 ext struts = 90

I think the star tetra, star octa and star icosa qualify as 'VE', if the central polyhedra (reg tet, reg octa, reg icosa) is considered to be the nucleus. All the connecting vectors are same length AFAICT. Eg. the star icosa has all equal length vectors and has no centroid vectors (which would be a different length). So you need to specify which VE:

VE cubocta
VE star tetra
VE star octa
VE star icosa

The star tetra has 12 face planes
Multiplication by division: http://synergeticists.org/synergetics/plates/figs/plate03.html

Noting Kirby's & Alan's relative volume tables here:
math
Eschers solid

A 1F cube has 3 tv. First stellation of a cube is a rhombic dodeca of 6 tv.
First stellation of a rhombic dodeca is Escher's Solid, of 12 tv,
half the volume of the 2F cube, same as the star octa.

The volume of the cuboctahedron is 5/6 of that of the enclosing cube and 5/8 of that of the enclosing octahedron. The cuboctahedron shares its edges and vertex arrangement with two nonconvex uniform polyhedra: the cubohemioctahedron (having the square faces in common) and the octahemioctahedron (having the triangular faces in common).



I suggest adding one more, some star polyhedra with identical regular tetrahedra, the internal central polyhedron is a void*, since the external tetras produce the structure, so no additional struts required:

star tetra: 4 tetras (star tet - tet nucleus)
star octa: 8 tetras (duotet - octa nucleus)
star cubocta: 8 tetras (cube - cubocta nucleus)
=====================
star icosa: 20 tetras (4 + 8 + 8) * jitterbug transformation

*These exclude the nuclear polyhedron, since it is a void built by the exoskeleton of structural tets and overlapped struts are unnecessary.

I haven't checked if the orientation of the 20 tets of the star icosa match with those of the others, or if they need to be rotated or jitterbugged to fit the icosa.

compound cubocta & 120 cell

What can fit into an icosa? a tet. an octa. a star tet? a star octa?
unknown.

rhombic dodeca (cube with pyramidal faces combine coplanar pairs of triangles into rhombi) rhomdodeca from cube+6pyramid (differs from star cube with noncoplanar pairs of triangles)

star rhombic dodeca & star octa:
star vol



C60 Carbon buckyball fullerene: 60 vertices divided into 12 pentagon sets; 32 faces of 12 pentas and 20 hexas, 90 edges of 60 pentagonal edges (single bonds)and 30 hexagonal edges (double bonds), each hexagon has alternating single and double bonds. Dual of truncated icosahedron C60 with 32 faces and 60 vertices is the pentakis dodecahedron (triangulated C60) of 60 faces and 32 vertices.

syn

1033.53 The vector equilibrium jitterbug provides the articulative model for demonstrating the always omnisymmetrical, divergently expanding or convergently contracting intertransformability of the entire primitive polyhedral hierarchy, structuring as you go in an omnitriangularly oriented evolution.
1033.54 As we explore the interbonding (valencing) of the evolving structural components, we soon discover that the universal interjointing of systems__and their foldability__permit their angularly hinged convergence into congruence of vertexes (single bonding), vectors (double bonding), faces (triple bonding), and volumetric congruence (quadri-bonding). Each of these multicongruences appears only as one vertex or one edge or one face aspect. The Eulerean topological accounting as presently practiced__innocent of the inherent synergetical hierarchy of intertransformability__accounts each of these multicongruent topological aspects as consisting of only one of such aspects. This misaccounting has prevented the physicists and chemists from conceptual identification of their data with synergetics' disclosure of nature's comprehensively rational, intercoordinate mathematical system.
1033.55 Only the topological analysis of synergetics can account for all the multicongruent__doubled, tripled, fourfolded__topological aspects by accounting for the initial tetravolume inventories of the comprehensive rhombic dodecahedron and vector equilibrium. The comprehensive rhombic dodecahedron has an initial tetravolume of 48; the vector equilibrium has an inherent tetravolume of 20; their respective initial or primitive inventories of vertexes, vectors, and faces are always present__though often imperceptibly so__at all stages in nature's comprehensive convergence transformation.

2 fold: triangle octavalent
3 fold: tetra quadruvalent
4 fold: cube, octa, apparent cubocta, rhom dodeca
5 fold: icosa, penta dodeca
6 fold: actual cubocta in motion when surface squares collapse
7 axes of symmetry, 14 faces of bubbles & cells: 14faces
Carbon C60 buckyball: truncated icosahedron C60
Boron B80 buckyball: truncated rhombic triacontahedron B80
Tetrakaidecahedron: 14 sided polyhedra includes VE, truncated octahedra (space filler) and hexagonal truncated trapezohedron (14 sided soap foam)
http://en.wikipedia.org/wiki/Tetrakaidecahedron

The more regular honeycombs dualise neatly:
* The cubic honeycomb is self-dual.
* That of octahedra and tetrahedra is dual to that of rhombic dodecahedra.

Check: quasicrystal matrix composed of icosa & star tetra, where the icosa contain nuclei of star tetra.
Da Vincis' star tetrahedron & icosahedron: star tet

Jitterbug transformation: from 4 fold VE through 5 fold icosa to 3 fold tetra VV
The nucleated cubocta is a unique 3D system in Vector Equilibrium, where all 24 circumferential vectors (edges) are the same length as the 12 nuclear radiating vectors (rays). The non-nucleated VE is not structurally rigid with rubber joints (unlike the tetra, octa and icosa of 60 degrees) due to the 6 collapsable square faces of 90 degrees, but with polarised kinetic energy applied (compressed, extended or torqued at opposing triangle or square faces) will transform as follows:

Compressing polar triangles inward: spins through an incomplete icosa to an octa.
Extending polar triangles outward: unstable convex-concave tri-prism, which if equatorially compressed (at evertices or invertices) or polarly torqued forms a webbed pin-hinged double tetra hourglass.
Torqueing polar triangles laterally: 2f (nuc) triangle, folds to tetra.

Compressing polar squares inward: star square, folds to 1/2-octa to 1f triangle.
Extending polar squares outward produces stretched cube, which if equatorially compressed or polarly torqued forms a pin-hinged double 1/2-octa hourglass, folds to a single 1/2-octa to 1f triangle.
Torqueing polar squares laterally: incomplete 2f tetra, folds to saddle form or hexagon or 2f (nuc) triangle to tetra.

Jitterbug collapse to tetra: http://www.rwgrayprojects.com/synergetics/s04/figs/f6108.html
Jitterbug collapse to octa:
6 loops circumscribe a spherical VE: 6 loop VE

Relative Volumes at Grunch: http://grunch.net/archives/47
Concentric hierarchy: here
Quintet dodeca: http://www.newciv.org/Synergetic_Geometry/Quintet_Dodeca.JPEG
http://www.newciv.org/Synergetic_Geometry/amoeba.htm
xkcd symmetree
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Octet truss IVM virtual space frame allows tourists to see ancient artifacts without disturbing them at Java, Indonesia.
Time & Space Perspective
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On spherical gravity "attraction" & EM radial wave "repulsion" relationships

2 round objects have more surface area than 1, so they are "attracted" to each other, collision reduces total surface area. Energy has no surface area so is independent of gravity, (it 'curves' around bodies due to reflection pressure?) it radiates outwardly in periodic (tidal) waves linearly from sphere center.

circumferential vectors & great circles: icosa edge vectors 30, icosa great circles 31; cubocta edge vectors 24, cubocta great circles 25

1052.21 Isaac Newton discovered the celestial gravitation interrelationship and expressed it in terms of the second power of the relative distance between the different masses as determined by reference to the radius of one of the interattracted masses. The gravitational relationship is also synergetically statable in terms of the second power of relative frequency of volumetric quanta concentrations of the respectively interattracted masses. Newton's gravitational constant is a radially (frequency) measured rate of spherical surface contraction, while Einstein's radiational constant is a radial (frequency) rate of spherical expansion. (See Secs. 960.12, 1009.31 and 1052.44.)
1052.30 Gravitational Constant: Excess of One Great Circle over Edge Vectors in Vector Equilibrium and Icosahedron: Pondering on Einstein's last problem of the Unified Field Theory, in which he sought to identify and explain the mathematical differentiations between electromagnetics and gravity__the two prime attractive forces of Universe__and recalling in that connection the conclusion of synergetics that gravity operates in spherical embracement, not by direct radial vectors, and recalling that electromagnetics follows the high-tension convex surfaces, possibly the great-circle trunk system of railroad tracks (see Secs. 452 and 458); led to pondering, in surprise, over the fact that the vector equilibrium, which identifies the gravitational behaviors, discloses 25 great circles for the vector equilibrium in respect to its 24 external vector edges, and the icosahedron, which identifies the electron behaviors of electromagnetics, discloses 31 great circles in respect to its 30 external vector edges.
1052.31 In each case, there is an excess of one great circle over the edge vectors. Recalling that the circumferential vector edges of the vector equilibrium exactly equal the radial explosive/implosive forces, while the icosahedron's 30 external edges are longer and more powerful than its 30 radial vectors [What 30 radial vectors?? A star icosa has external equilength pentalateral-bond tets, a cubocta has equilength quadrilateral-bond & equilength mono-radial vectors.], yet each has an excess of one great circle, which great circles must have two polar axes of spin, we encounter once more the excess two polar vertexes characterizing all topological systems, and witness the excess of embracingly cohering forces in contradistinction to the explosively disintegrative forces of Universe.
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A star tetra, a star octa, and a star icosa each contain a nuclear void (empty space tet, octa, icosa) polyhedron surrounded and structured by reg ext tets. A star cubocta does not contain a void nucleus. A star rh dodeca and star non-nucleated cubocta contain void polyhedron nuclei, but lacking full tet surfaces are not structured. Empty stars can be nucleated by structures: star icosa accepts a nuclear star tetra (free spinning? quasicrystal matrix), star cubocta accepts a nuclear star octa (IVM crystal matrix).

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domed dive mask
I'd like to get this dive mask, great vision underwater for those who are nearsighted (myopic) like me, and lack sufficient visual accomodation for clear dark adapted acuity.

Vortices in dragonfly flight animation:
http://www.news.cornell.edu/releases/March00/APS_Wang.hrs.html

Spiral column foldable origami: spiral

Fish bones, fermented fish vs cooked fish, calcium carbonate in sea water, sleep

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=921452
Fish-bone peptides (FBP) with a high affinity to Ca were isolated using hydroxyapatite affinity chromatography, and FBP II with a high ratio of phosphopeptide was fractionated in the range of molecular weight 5·0–1·0kDa by ultramembrane filtration. In vitro study elucidated that FBP II could inhibit the formation of insoluble Ca salts in neutral pH. In vivo effects of FBP II on Ca bioavailability were further examined in the ovariectomised rat. During the experimental period, Ca retention was increased and loss of bone mineral was decreased by FBP II supplementation in ovariectomised rats. After the low-Ca diet, the FBP II diet, including both normal level of Ca and vitamin D, significantly decreased Ca loss in faeces and increased Ca retention compared with the control diet. The levels of femoral total Ca, bone mineral density, and strength were also significantly increased by the FBP II diet to levels similar to those of the casein phosphopeptide diet group (no difference; P>0·05). In the present study, the results proved the beneficial effects of fish-meal in preventing Ca deficiency due to increased Ca bioavailability by FBP intake

ocean alkalinity & fish
New research reveals the major influence of fish on maintaining the delicate pH balance of our oceans, vital for the health of coral reefs and other marine life.
The discovery, made by a team of scientists from the UK, US and Canada, could help solve a mystery that has puzzled marine chemists for decades. Published 16 January 2009 in Science, the study provides new insights into the marine carbon cycle, which is undergoing rapid change as a result of global CO2 emissions.

Until now, scientists have believed that the oceans' calcium carbonate, which dissolves to make seawater alkaline, came from the external 'skeletons' of microscopic marine plankton. This study estimates that three to 15 per cent of marine calcium carbonate is in fact produced by fish in their intestines and then excreted. This is a conservative estimate and the team believes it has the potential to be three times higher.

Fish are therefore responsible for contributing a major but previously unrecognised portion of the inorganic carbon that maintains the ocean's acidity balance. The researchers predict that future increases in sea temperature and rising CO2 will cause fish to produce even more calcium carbonate.

To reach these results, the team created two independent computer models which for the first time estimated the total mass of fish in the ocean. They found there are between 812 and 2050 million tonnes (between 812 billion and 2050 billion kilos) of bony fish in the ocean. They then used lab research to establish that these fish produce around 110 million tonnes (110 billion kilos) of calcium carbonate per year.

Calcium carbonate is a white, chalky material that helps control the delicate acidity balance, or pH, of sea water. pH balance is vital for the health of marine ecosystems, including coral reefs, and important in controlling how easily the ocean will absorb and buffer future increases in atmospheric CO2.

This calcium carbonate is being produced by bony fish, a group that includes 90% of marine fish species but not sharks or rays. These fish continuously drink seawater to avoid dehydration. This exposes them to an excess of ingested calcium, which they precipitate into calcium carbonate crystals in the gut. The fish then simply excrete these unwanted chalky solids, sometimes called 'gut rocks', in a process that is separate from digestion and production of faeces.

The study reveals that carbonates excreted by fish are chemically quite different from those produced by plankton. This helps explain a phenomenon that has perplexed oceanographers: the sea becomes more alkaline at much shallower depths than expected. The carbonates produced by microscopic plankton should not be responsible for this alkalinity change, because they sink to much deeper depths intact, often becoming locked up in sediments and rocks for millions of years. In contrast, fish excrete more soluble forms of calcium carbonate that are likely to completely dissolve at much shallower depths (e.g. 500 to 1,000 metres).

Lead author Dr Rod Wilson of the University of Exeter (UK) said: "Our most conservative estimates suggest three to 15 per cent of the oceans' carbonates come from fish, but this range could be up to three times higher. We also know that fish carbonates differ considerably from those produced by plankton"

toads, fish, sharks, CaCO3, etc.
reefs
Photic Sneeze
Photic sneeze: vestige of past tropical lagoon diving ancestors? Aqua-photic Respiratory Cycle forage divers, fast dark-adapted sunlight exhalations...

Y DNA Haplogroup T: Salt trade, boiling brine to trade via dugout for inland goods?
coastal transit/trade 30ka

Upper Rift seasonal fishing camp 770ka: carp, acorn, olive pit, raisin, bark
carp fishing with acorn bait & crabbing 770ka at Lake Hula
23ka bedding, salt and freshwater springs at Sea of Galillee
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC409895/
http://www.ncbi.nlm.nih.gov/pubmed/19125919?ordinalpos=1&itool=PPMCLayout.PPMCAppController.PPMCArticlePage.PPMCPubmedRA&linkpos=2

Similarities between Hs & Pt: proteins, DNA, chromosome
http://academic.reed.edu/biology/professors/srenn/pages/teaching/431S05/431S05_readings/431s05_examples/king_wilson_1975(classic).pdf

numeric sequences

197th post: Hey, Its Ant-a Claws !!

South of Spain: Mar Menor Lagoon

Ant-a Claws
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In honor of Darwins' anniversary of On the Origin of Species.
New Papyrus: Darwin

it takes 20 000 genes to make a nematode and 25 000 to make a human

http://www.livescience.com/technology/technovelgy_eyes_041104.html
Charles Darwin recognized that the eye would be a real test of the theory of evolution. He suggested that it might be possible to evolve an eye from "imperfect and simple" forms:

"To suppose that the eye, with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest possible degree.

"Yet reason tells me, that if numerous gradations from a perfect and complex eye to one very imperfect and simple, each grade being useful to its possessor, can be shown to exist; if further, the eye does vary ever so slightly, and the variations be inherited, which is certainly the case; and if variation or modification in the organ be ever useful to an animal under changing conditions of life, then the difficulty of believing that a perfect and complex eye could be formed by natural selection, though insuperable by our imagination, can hardly be considered real."

Scientists today believe that the eye could evolve from a single light-sensing cell. Scientists disagree over whether it evolved just once, or many times.

It turns out that Nature is both creative and generous with her gifts. Recent research has shown that the tiny marine worm Platynereis dumerilii has two types of light-sensing cells. The eyes of the worm have rhabdomeric photoreceptors, a compound lens formation that is seen almost exclusively in insect eyes. Rhabdomeric photoreceptors are covered in little finger-like protrusions. In its brain, however, it has a different kind of light-sensing cells - ciliary cells that are seen in vertebrate animals. Ciliary cells have hair-like cilia that extend outward and branch out like tiny umbrellas. Two different ways of sensing light in a single organism! images
http://scienceblogs.com/pharyngula/2006/09/rhabdomeric_and_ciliary_eyes.php

Researcher Joachim Wittbrodt of the European Molecular Biology Laboratory in Heidelberg, Germany speculates that the ciliary cells may regulate the worm's daily activity cycle, saying "We think they are related to circadian rhythms. We have found that there is a direct connection to the area used for locomotion... In the beginning we had a toolbox... what was in the brain in the worm ends up in our eye." If the animal had two copies of the genes needed to make one kind of photoreceptor, speculates Wittbrodt, then the extra set would have been free to evolve into the other photoreceptor. Different animals would subsequently evolve to use the two options in different ways.
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Genome: Ramen noodle folding form (no knots) is fractal globule based on icosa-dodecahedron.
"perfect" genome code
empirical genome code
"perfect" periodic table
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I have speculated earlier here and elsewhere, that the human thumb's missing bone and associated muscle evolutionarily moved to become the fused mandible (lower jaw) and tongue.
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I posted this comment at a biology website (RDF), in response to why flies have 6 legs and most vertebrates have only 4 [clue - beetles have 4 wings/jaws, reptiles have 4 legs]:

bilateral pentadactyle digits (insect legs/"hands"/wings/"jaws")*
bilateral pentadactyle digits (invertebrate squid tentacles)*
bilateral pentadactyle digits (vertebrate fingers/toes)*
(larval bilateral) pentadactyle digits (starfish or sand dollar)*
icosahedral/pentameric (eg. virus) symmetry (12 oral/anal sets of five cilia)

*digits can be asexually replicated (due to incomplete meiosis?) or mutatively lost, body segments also, so bilateral millipedes simply have axial multiple copies of their earlier rear set, while bilateral vertebrates have axial duplicated the pelvis from the forelimb carriage or axial duplicated the rear limbs on a rear part of the primitive forelimb carriage which eventually moved caudally.

Flies have 6 legs, 2 wings, 2 wing knobs = 10 digits (no jaws just sharp tubes, larval jaws are forelimbs)
Spiders/crabs have 8 legs, 2 pedipalps ("jawclaws") = 10 digits (no wings)
Squid have 8 regular tentacles, 2 long "thumb" tentacles = 10 digits
Reptiles, fish, mammals (primitive) have 10 digits (forelimbs), 10 digits (rear limbs)

Evo-devo, human mandible/tongue associates with the missing thumb bone and muscle, while the maxillae associates with the four fingers (before mandibular separation, all five fingers).

Probably, due to the developmental order, a fly would be more likely born without wing knobs or wings than to be born without legs, since legs seem to be more ancient. One born without a leg pair probably also has other more severe genetic mutations, especially in internal segmental replication. While a reptile with 6 legs must oxygenate them with lungs, sufficient oxygenation is critical (dolphins lost their legs as oxygen conservation became more significant) while small insects' spiracles provide enough O2 for many legs, and wings help gain more O2. Perhaps.
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There is an invertebrate (marine proto-crustacean?) which cannot eat unless it locomotes all limbs, its jaws can't chew unless its digits are moving. This would seem very primitive, since lobster claws and fish jaws operate independently from the legs or fins. Note that while larval caterpillars chew using their 4 forelegs/jaws, adult butterflies only suck nectar while still.

Caterpillars chew with forelimbs modified into jaws, during pupation these jaws reform into webbed wings, so butterflies can fly but can't chew. Grasshoppers do not pupate, they go through stages of enlargement and add wings at a certain instar stage (they can't eat at this stage). The adult grasshopper can both leap and fly. Humans have webbing between thumb and forefinger and between maxillae and mandible (cheeks), in flying insects the same genes form webbed wings associated with jaws; initially (ancestrally) this webbing assisted in filter feeding in early marine invertebrate, moving food particles closer to the mouth orifice.

The primitive invertebrate ancestor had an oral-GI-anal pore/tube with 5 mobile cilia, with variable degrees of rigidity (tentacle vs tendon/bone) and inter-digital webbing, depending on whether the food drifted by current (river) or was static and required cilia pulsation and attachment.

Interesting news confirms earlier speculations
link
Public release date: 20-Apr-2007
[ Print Article | E-mail Article | Close Window ]

Contact: Anna-Lynn Wegener
wegener@embl.de
49-622-138-7452
European Molecular Biology Laboratory

Researchers discover that the centralised nervous system of
vertebrates is much older than expected

The rise of the central nervous system (CNS) in animal evolution has
puzzled scientists for centuries. Vertebrates, insects and worms
evolved from the same ancestor, but their CNSs are different and were
thought to have evolved only after their lineages had split during
evolution. Researchers from the European Molecular Biology Laboratory
(EMBL) in Heidelberg now reveal that the vertebrate nervous system is
probably much older than expected. The study, which is published in
the current issue of Cell, suggests that the last common ancestor of
vertebrates, insects and worms already had a centralised nervous
system resembling that of vertebrates today.

Many animals have evolved complex nervous systems throughout the
course of evolution, but their architectures can differ substantially
between species. ...all these species descend from a common ancestor
called Urbilateria. If this ancestor already possessed a nervous
system, what it might have looked like and how it gave rise to the
diversity of nervous systems seen in animals today is what Detlev
Arendt and his group study at EMBL. To do so, they investigate the
nervous system of a marine annelid worm called Platynereis dumerilii.

"Platynereis can be considered a living fossil," says Arendt, "it
still lives in the same environment as the last common ancestors used
to and has preserved many ancestral features, including a prototype
invertebrate CNS. Comparing the molecular fingerpint of Platynereis
nerve cells with what is known about vertebrates revealed surprising
similarities.

"Our findings were overwhelming," says Alexandru Denes, who carried
out the research in Arendt's lab. "The molecular anatomy of the
developing CNS turned out to be virtually the same in vertebrates and
Platynereis. Corresponding regions give rise to neuron types with
similar molecular fingerprints and these neurons also go on to form
the same neural structures in annelid worm and vertebrate."...

The findings provide strong evidence for a theory that was first put
forward by zoologist Anton Dohrn in 1875. It states that vertebrate
and annelid CNS are of common descent and vertebrates have turned
themselves upside down throughout the course of evolution.

"This explains perfectly why we find the same centralised CNS on the
backside of vertebrates and the bellyside of Platynereis," Arendt
says. "How the inversion occurred and how other invertebrates have
modified the ancestral CNS throughout evolution are the next exciting
questions for evolutionary biologists."

http://chancenecessity.blogspot.com/2009/02/geoffroys-lobster-and-animal-common.html
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urbilateria
A similar study involving Platynereis dumerlii comes to much the same conclusion. PZ Meyers has a explanation of this bit of research. This result, that humans are evolutionarily slow has been portrayed as a bit of a surprise, but is something that has been in the works for awhile. For example, as early as 1992 it was known that insulin genes in humans and apes evolved at a slower rate than in monkeys. The phenomena, called the “Hominid-rate-slowdown hypothesis”. was first suggested by Goodman in a 1961 paper entitled “The Role of Immunochemical Differences in the Phyletic Development of Human Behavior” (published in Human Biology) and led to papers being published on the subject up to the present (here and here for example).
http://www.hoxfulmonsters.com/2008/12/living-fossil-platynereis-dumerilii-unraveling-the-first-steps-of-eye-evolution
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updated from earlier post (Vertebrates are inverted invertebrates).
To continue, with slight clarification, if interested:

See Neil Shubins slideshow, especially page 6 slide 5, to compare Hox gene positions in human and fruit fly.
http://tiktaalik.uchicago.edu/book-tools.html

My earlier explanation of primitive pentadactylity (5 digits) didn't well cover the duplication of reptile/mammal rear limbs from the forelimb carriage, this duplication is actually the same as the duplication of (beetle) 4 wings / 4 jaw mouthparts from the primitive frontal digits.
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(I've briefed the text)
Dragonflies & damselflies (Odonates) can chew but they can't walk, their 6 legs are for perching and grabbing.
http://theatavism.blogspot.com/2009/11/sunday-spinelessness-damselflies.html
"You can tell a damselfly from a dragonfly thanks to the way they hold their wings - damselflies fold them up over their body when they land (butterfly-like) while dragonflies hold them open (moth-like)..." Interesting, butterflies or moths can walk a bit but can't chew, beetles & grasshoppers can walk and chew but their flight is not so well controlled.

wiki lacewings/netwings/antlions
The insect order Neuroptera, or net-winged insects, includes the lacewings, mantidflies, antlions, and their relatives. The adults of this order possess four membranous wings, with the forewings and hindwings about the same size, and with many veins. They have chewing mouthparts, and undergo complete metamorphosis. Neuropterans are soft-bodied insects with relatively few specialised features. They have large lateral compound eyes, and may or may not also have ocelli. Their mouthparts have strong mandibles suitable for chewing, and lack the various adaptations found in most other endopterygote insect groups.

They have four wings, which are usually similar in size and shape, have a generalised pattern of veins. Some Neuropterans have specialised sense organs in their wings, or have bristles or other structures to link their wings together during flight.[4]

The larvae are specialised predators, with elongated mandibles adapted for piercing and sucking. The larval body form varies between different families, depending on the nature of their prey. In general, however, they have three pairs of thoracic legs, each ending in two claws. The abdomen often has adhesive discs on the last two segments.[4] ...ant lions, which bury themselves completely out of sight and ambush prey from "pits" in the soil. Larvae of some Ithonidae are root feeders, and larvae of Sisyridae are aquatic, and feed on freshwater sponges. A few mantispids are parasites of spider egg sacs.

As in other holometabolic orders, there is a pupal stage, generally enclosed in some form of cocoon composed of silk and soil or other debris. The pupa eventually cuts its way out of the cocoon with its mandibles, and may even move about for a short while before undergoing the moult to the adult form.[4] Adults of many groups are also predatory, but some do not feed, or consume only nectar. They are delicate or cumbersome flyers, the spoon wings have rear wings like birds of paradise. Nemoptera
Nemoptera larvae



http://theatavism.blogspot.com/search/label/sci-blogs
It's a springtail (Collembola) - a member of a group of arthropods closely related to (but distinct from insects). They get their common name from a long forked organ, the furcula, that usually sits folded up under the abdomen. The earliest fossil hexapod, and one of the first terrestrial animals, Rhyniella praecursor, is a springtail...'Gomph's live in Antarctic mainland, springtails importantly make soil. Tail derived from crab/crayfish folded tail?

Orobophana pacifica: They are tiny, live on coral rubble on Cook Islands. Even though they live on land they aren't closely related to the "true" landsnails in the order Stylommatophora. To see the difference you need to look into their eyes. If you click on the image above to get a high resolution version you might just be able to see the eye - it's a black dot just underneath the tentacles ("feelers"). In true landsnails like the ones you find in you garden the eyes sit on the ommatophores, a second set of tentacles which are retractable.

bird feet, talons, webbing



Can you walk and talk and chew gum at the same time ?

The mechanics of being Human: a self-balancing, 28-jointed adaptor-based biped; an electro-chemical reduction plant, integral with segregated stowages of special energy extracts in storage batteries, for subsequent actuation of thousands of hydraulic and pneumatic pumps, with motors attached; 62,000 miles of capillaries.... R. Buckminster Fuller-
Bucky: Dictators never create their own opportunities.

A neat series of articles on human facial expressions (non-verbal communication), especially interesting after having read that human cheeks are merely muscular/fatty webbing connecting the mandible to maxilla like butterfly wings. Makes me wonder about the link of the smile to the crinkling of the eyelids or the tightening of the eyebrows, all these facial muscles which communicate internal feelings instantly which are usually masked by reflexive social gestures. They must have evolved in deep time, and gradually fine tuned in humans, a super-social species.

facing others

Human social traits: anonymous, cooperative, infants
Hrdy sociality hypothesis

Corneal blink reflex: trigeminal nerve senses, facial nerve motors to blink at bright light or loud sound or irritating particle in eye.
Corneal reflex
Accomodation reflex
Pupillary light reflex

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Pigmentation in desert lizards
white lizards
Pigmentation in humans: Baltic blonde & blue eyes from Gulf stream & grain?
pigment

"There is only one spot on the planet where grains will grow despite sub-arctic sunlight.
It is where the warm waters of the Gulf Stream wash ashore. The Baltic is the only place on earth where ocean currents keep it warm enough to grow grain despite dim sunlight. When the inhabitants of this region switched to grain about 6 KYA, they suddenly got insufficient vitamin D to survive. They had stopped eating mostly meat and fish in a place where sunlight was too dim to produce vitamin D in normally pigmented skin. And so they adapted by retaining into adulthood the infantile trait of extreme paleness. Blonde hair and blue eyes were other infantile traits that were just swept along accidentally."

Why did they shift from hunting/gathering (grain processing sorghum in Mozambique 100ka) to complete absolute dependence on grain? What about their cattle/goats/dogs? Fishing seems to have increased rather than decreased amongst Baltic sea peoples with better boat/net technology. Camouflage is always important, whether for predator, prey or combat, but less for farmers. Clothing in cold? Baltic was warm in winter? Europeans also adapted by retaining the ability to digest lactose in adulthood, obtaining vitamin D from milk.
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Medieval rural Briton women had wider thicker bones than city women
http://www.guardian.co.uk/science/2009/dec/17/women-yorkshire-archeaology-find

Language evolution
http://schott.blogs.nytimes.com/2009/12/16/q-and-a-the-death-of-languages/

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Whale fossil 4.5ma in Spain: deposited on seafloor 50m deep, now 80m above ground 24km inland. So 4.5ma Medit was high, or tectonic uplifting or both.
http://www.sciencedaily.com/releases/2009/12/091215101716.htm

Dwarf suction-feeding Australian baleen whale
http://news.bbc.co.uk/2/hi/science/nature/8430402.stm

Relative volumes & concentric hierarchy

tetra tripod table, balloonage

Icosa alloys mimic elements:
Icosa
http://www.sciencedaily.com/releases/2005/02/050205125336.htm
http://www.sciencedaily.com/releases/2009/12/091228152348.htm


Sphere/tet/cube packing, entropy, tets in quasicrystal disks, density in box container
quasi-crystal tet packing
Researchers packed tetrahedra into a cubic box more densely than ever before: 85.03
(Cubes have a 100 percent packing fraction in a cubic box, while spheres pack at only 74 percent.) The tetrahedron was for decades conjectured to be the only solid that packs less densely than spheres, until just last year when U-M mathematics graduate student Elizabeth Chen found an arrangement of 77% that proved that speculation wrong.

the more significant finding is that the tetrahedrons can unexpectedly organize into intricate quasicrystals at a point in the computer simulation when they take up roughly half the space in the theoretical box.

In this computer experiment, many thousands of tetrahedrons organized into dodecagonal, or 12-fold, quasicrystals made of parallel stacks of rings around pentagonal dipyramids. A pentagonal dipyramid contains five tetrahedrons arranged into a disk. The researchers discovered that this motif plays a key role in the overall packing. In the simulation, the tetrahedrons organized into a quasicrystal and settled on a packing that, when compressed further, used up 83 percent of the space. Engel then reorganized the shapes into a "quasicrystalline approximate," which is a periodic crystal closely resembling the quasicrystal. He found an arrangement that filled more than 85 percent of the space.

This is the first result showing such a complicated self-arrangement of hard particles without help from attractive interactions such as chemical bonds, Glotzer said.

Thermos vacuum allows IR radiation outwards through glass, photonic crystals reduce IR heat loss better than pure vacuum
In a typical thermos, a vacuum is used to reduce heat transfer. Scientists have found that layers of photonic crystals in a vacuum can reduce the thermal conductance to about half that of a pure vacuum. Basically, heat can be transferred from one material to another in three main ways: convection, conduction, and radiation. Conduction and convection both require some kind of material medium for heat to pass through; therefore, the lack of material in a pure vacuum greatly minimizes the effectiveness of these two processes. However, heat can also be transferred through infrared radiation, a form of light that is invisible but can be felt as heat. In the example of the thermos, infrared radiation can travel through the vacuum to the thermos' outer wall; when absorbed by the outer wall, the radiation causes the molecules in the outer wall to vibrate and release heat. Significantly, photonic crystals can have band gaps that forbid propagation of certain frequency ranges of light. In this case, they could be used to block infrared radiation.

The scientists found that a 100-micron-thick structure made of a stack of 10 photonic crystal layers, each 1 μm thick and separated by 90-μm gaps of vacuum, could reduce the thermal conductance to about half that of a pure vacuum. In a more recent study, Fan and his colleagues calculated the fraction of all frequencies that the photonic crystal allows through. They were somewhat surprised to find that the thermal conductance doesn't depend on the thickness of the layers but only on how fast light travels through the material, or its index of refraction.


Circles & spheres, flakes and crystals, water & ice
NYTimes
link
super cold
water-tet
Take a regular tetrahedron and set the distance from vertex to tet center as unit 1. Then an
edge of the tet is 1.632993.. . So this number is directly related to the ubiquitous Maraldi angle, 109.47.. degrees (the caltrop angle -- the vertex-center-vertex angle in a regular tet).
CircumsphereRadius/Edge = (1/4)*SQRT(6)
Edge/CircumsphereRadius = 4/SQRT(6)
Vertex-Vertex central Maraldi Angle = arc cos -1/3 ( or ) 2*ACOS(SQRT(1/3))
Giacomo_F._Maraldi: "In math known for obtaining experimentally the angle in the
rhombic dodecahedron shape in 1712, which is still called Maraldi angle."

"Water is a network-forming matter. You can imagine the structure of the network as a kitchen sponge, Matsumoto continues. The sponge structure is originally a kind of foam but membranes are lost, and only the beams - bonds - remain. In both network of water and kitchen sponge, four bonds meet at a point, or node, to form a three dimensionally connected random network. As Plateau pointed out in 19th century, four beams of a foam crosses at a node with regular tetrahedral angle - Maraldi's angle - similar to the waters hydrogen bond network. Matsumoto used computer simulation to look at three ways to change the volume of the foam cells: extension of the bonds, a change in the containing angle between the bonds, and a change in network topology. By discriminating the three contributions, the mechanism became very clear. One contributes to thermal expansion, another one contributes to thermal contraction, and the last one does not. Density maximum is a result of these competing contributions, he explains. "

Caltrops: reg tet 'land mines' The simple design paradigm says that the most elegant, efficient, iconic inventions are necessarily the simplest; like the elastic band, the brick, and the pizza. A caltrop is a simple piece of shaped metal (concrete tank killers); a spiky tetrahedron which, when liberally scattered on the ground, causes a great deal of annoyance to any passing dudes or ponies. And the brilliant thing is that however you drop them, they always land spiky point up.

Biological size, volume, area, fluid flow
size & form


Interaction on Bucky Fuller's tetrahedra as unit volume in synergetic sequence, with input from Allan, Kirby, myself:

Shape: Volume (notes)
MITE: 1/8 (AAB mods)
Tetra: 1 (24 A mods)
Coupler: 1 (8 MITE's)
Stella Octangula: 1.5 (Little octahedron of .5 volume + little tets totalling volume of 1. Notice that the Stella Octangula occupies half the volume of its enclosing cube.)
Cubocta: 2.5 (1/2 ƒ)
Octa: 4 (dual of cube)
Cube: 3 (dual of octa)
Cube-Octahedron Compound: 4.5 (first stellation of cub-octahedron)*
Rh-Dodeca: 6 (12 half-couplers, other ways)
Escher's Solid: 12 tetras (or 12 couplers [see above], other ways. Notice that the Escher's Solid occupies half the volume of its enclosing cube.)
Cubocta: 20 (volume = 8*2.5)
Cube: 24 (2ƒ)
Stella Octangula: 12 (Octa volume of 4 + 8 tets. Notice that the Stella Octangula occupies half the volume of its enclosing cube.)
Octahedron: 32 (2ƒ)
Cube-Octahedron Compound: 36 (larger version)

*The (small) cube-octahedron compound has a volume of 4.5, since the cube corners are
half the heights of the regular tetrahedrons.




Relative Volume Sequence: (mine, preliminary, w/ response from Allan)

tet 1 (reg or irreg)
reg tet volume, of course!
coupler 1 (irreg octa)

tet duo 2 (vertex/edge/face bonded)
two tetrahedrons

duotet cube 3
The volume of the cube is 3 tetrahedrons.

octa 4
The volume of the octahedron is 4 tetrahedrons.

The volume of the cube-octahedron compound or first stellation of cub-octahedron is 4.5 tetrahedra. If the octants are elevated even more to regular tetrahedra, then you will get the cuboctahedral star with a volume of 5. (see below)

star tet 5 [tetra-star]
The star tetrahedron is the unfolded net of the pentachoron, which is bounded by 5 tetrahedra.
rhombic triacontahedron 5
reg tet stell cubocta 5 [cubocta star w/ reg tet ecto]

rh dodeca 6
Rhombic dodecahedron has twice the volume of the cube. The volume of the stellated rhombic dodecahedron is 12, which is half the volume of the enclosing 2ƒ cube of volume 24. (below)

star octa 12 [octa star]
Stellated octahedron has half the volume of the enclosing 2ƒ cube of volume 24.
stellated rh dodeca 12

icosa int 18.51 endo
If you think that the icosahedron has volume 20, then you're obviously from another (fourth) dimension! The icosahedron, as we know in our flat Euclidean three-dimensional realm, has a endo- volume of about 18.51 tetrahedra.

cubocta 20 endo
This is the jitterbug, fully extended.

star icosa ext 20 [icosa star reg tet ecto]
But that's assuming that each face has a REGULAR tetrahedron on it.

star cubocta 40 [cubocta star reg tet endo ecto]
The 2ƒ version of the cube-octahedron compound or stellated cuboctahedron has a volume of 36 tetrahedra. For the star cuboctahedron to have a volume of 40, each face would have to be stellated with equilateral triangles (i.e. half-octahedra and regular tetrahedra). (see above)
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> Icosa (Fuller explanation, Amy Edmondson, paraphrased)
> Its endo-volume of approximately 18.51 does not fit rationally into
> the cosmic hierarchy with whole numbers nor click-stop when
> jitterbugging.

> I found this interesting, a clue perhaps re. 18.51 1/electron

> "The icosahedron contracts to a radius less than the radii of the
> vector equilibrium from which it derived. There is a sphere that is
> tangent to the other 12 spheres at the center of an icosahedron, but
> that sphere is inherently smaller. Its radius is less than the
> spheres in tangency which generate the 12 vertexes of the vector
> equilibrium or icosahedron. Since it is no longer the same-size
> sphere, it is not in the same frequency or in the same energetic
> dimensioning. The two structures are so intimate, but they do not
> have the same amount of energy. For instance, in relation to the
> tetrahedron as unity, the [endo]volume of the icosahedron is 18.51 in
> respect to the vector equilibrium's [endo]volume of 20 [and also the
> star icosa's ectovolume of 20]. The ratio is tantalizing because the
> mass of the electron in respect to the mass of the neutron is one
> over 18.51. That there should be such an important kind of seemingly
> irrational number provides a strong contrast to all the other
> rational data of the tetrahedron as unity, the octahedron as four,
> the vector equilibrium as 20, and the rhombic dodecahedron as six:
> beautiful whole rational numbers". Syn 400.00 system

> "When the volume of a tetrahedron is specified as one unit, other
> ordered polyhedra are found to have precise whole-number volume
> ratios, as opposed to the cumbersome and often irrational quantities
> generated by employing the cube as the unit of volume. Furthermore,
> the tetrahedron has the most surface area per unit of volume".
> (sphere has least) A Fuller Explanation

> http://www.grunch.net/synergetics/ivm.html
> shows IVM in a tet
> from previous:

> Relative volumes: (endo = interior, ecto = exterior shell)

> Tet: (@IVM), vol 1
> Oct: (@IVM), vol 4
> Star Tet: center tet endovol 1 + ectovol 4 (ext tets), vol 5
> Star Oct: center oct endovol 4 + ectovol 8 (@IVM), vol 12
> Star Icosa: center icosa endovol 18.51 + ectovol 20, vol 38.51
> Star Cubocta: endovol 20 + ectovol 20, vol 40

> DD
> On Nov 23, 2009, at 8:00 AM, rybo6 wrote:

> > "Topologically, lines are composed of points."

> > I don't know how it is defined elsewhere, but to me, a line is a
> > point with depth (not = zero), and a point is a line with depth = 0.
> > [Where 'depth' is any direction.] This does not conflict with the
> > definition of a point being a line crossing (which is the same as 2
> > or more vectors meeting at a vertex).
> > The irreg tets that make an icosa, do their struts meet at the
> > center, or do each reach to the opposite face? I thought each face
> > triangle had a tet apex at the icosa center (not modelable with
> > toothpicks), but maybe it goes to the opposite side at a point. Or
> > are there no irreg tets in an icosa?

> > Here (@ link bottom) see the regular icosa and star icosa:
> > http://en.wikipedia.org/wiki/Small_triambic_icosahedron

> > Here see that 2 halves of duotet = cubocta & 2 halves of cubocta =
> > duotet. Do the relative volumes equate?
> > http://groups.yahoo.com/group/synergeo/attachments/folder/1932305706/item/652172707/view

> > http://www.rwgrayprojects.com/synergetics/s09/figs/f5031.html
> > http://www.rwgrayprojects.com/synergetics/s10/figs/f0632.html
> > Relative volumes: (endo = interior, ecto = exterior)

> > Tet: vol 1 (@IVM)
> > Oct: vol 4 (@IVM)
> > Star Tet: center tet endovol 1 + ectovol 4 (ext tets)
> > Star Oct: center oct endovol 4 + ectovol 8 (@IVM)
> > Star Icosa: center icosa endovol 18.51 + ectovol 20
> > Star Cubocta: endovol 20 + ectovol 20

> > Icosa (Fuller explanation, Amy Edmondson, paraphrased)
> > Its endo-volume of approximately 18.51 does not fit rationally into
> > the cosmic hierarchy with whole numbers nor click-stop when
> > jitterbugging. The icosahedron is a phase in between octahedron and
> > vector equilibrium, rather than a definitive stopping point in the
> > flow. The icosahedron is thus restricted to single-layer
> > construction, able to contract/collapse to rigidity, its radius too
> > small to permit having same-size nuclear sphere. (461.05)
> > You could not have two adjacent layers of vector equilibria and then
> > have them collapse to become the icosahedron, it has to be an outside
> > layer, remote from other layers... . It may have as high a frequency
> > as nature may require. The center is vacant. (456.20-1).

> > If the center of an icosa is vacant, should its structural volume be
> > zero? Consider the volume of a donut/torus, is the donut hole volume
> > included in the donut's volume? The donut hole does not contribute to
> > the structure of the donut, it is vacant, but it is part of the donut
> > definition. That is sort of what I think the inner volume of an icosa
> > is, a sort of donut hole, a vestige, therefore not a whole number,
> > perhaps like the interstitial spaces in ball packing.

> > DD

Cubocta = cube & octahedron dual intercept, VE when complete
Octet = octahedron & tetrahedron 3D lattice (CCP), cubocta or star oct IVM
Cuboctet = IVM with cubocta voids (vector flexor) expand-contract jitterbug
shrinks from 20 tetvol hollow cubocta with single bonds to 4 tetvol octet with double bonds

Relativity on earth
Bucky's design science goal was "To make the world work for 100% of humanity in the shortest possible time through spontaneous cooperation without ecological offense or the disadvantage of anyone." Tim Tyler: How can you tell if the world is 'working' for someone? What % of humanity is the world 'working' for today? It seems rather unrealistic to expect nobody to be disadvantaged. Advantages in nature are relative - "evolution is driven by relative fitnesses, not absolute fitnesses. Santayana's aphorism, ``It is not enough to succeed; others must fail.''
At any time, an organism's chances of surviving depend not on how fit it is, but on how fit it is relative to its competition."

http://www.swintons.net/deodands/archives/cat_neutron_teaspoon.html
Neutron stars do really exist. Long after the protons and electrons have long given up the struggle to maintain their identity against the force of gravity, all that is left is neutrons, pressed together into one big atomic nucleus a few kilometres across.

Stars are big balls of gases. Their size is determined by the balance between two opposing forces: gravity pulling the gas inwards, and pressure pushing it outwards. Just like the pressure of air in a balloon, pressure reflects the fact that it's hard to push things together. The pressure depends on how many things you're trying to push together (density), but it also depends on how hard they are to push together. At higher temperatures, the air molecules have more energy, so it takes more effort to keep them from bouncing off each other. There's a relation, then, between the amount of matter and the pressure it exerts in a given setting, which is called the equation of state. We have a fairly good idea of this relationship for the interior of stars like our own sun. Eventually, as our sun radiates energy away, the internal pressure will fall and the gravitational force will increase the density until the point at which electrons are forced together (or, more precisely into degenerate states) forming a white dwarf, and for these conditions we also have a fairly good idea of the equation of state. But for more massive stars, the collapse keeps going past this point and is only halted when the remaining neutrons are forced too 'close' together. And at this point we reach some uncertainty (at least according to 1980 era graduate texts) in what the equation of state is. So there is some real scientific uncertainty in the mass of the neutron teaspoon.