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  • Category: Geometry
  • Founded: Dec 10, 2001
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#1021 From: rybo6 <rybo6@...>
Date: Fri Oct 7, 2005 6:43 pm
Subject: Tree of Carnation( excellent! )
os_jbug
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   http://treeincarnation.com/


Cosmologists and GUTOEists,  this is must site for those of you willing to step out of convention and explore relationships between mind and matter.

Consciousness and pattern.

Awareness and hyper-space

2D and 3D.

Rybo




















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#1022 From: "toadboyjoe" <fustie@...>
Date: Tue Oct 11, 2005 6:56 pm
Subject: math question
toadboyjoe
Send Email Send Email
 
Anyone know how to figure out the force needed to move a 30 ton object,
600 feet in less than 10 seconds?
An instantaneous force, not constant :-)

#1023 From: Thomas Izaguirre <ratra@...>
Date: Tue Oct 11, 2005 9:16 pm
Subject: Re: math question
deep_nerd
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Kinda reminds me of that scene near the end of The Incredibles: how
much force would Mr. Incredible have to exert to throw a 1965 Jaguar
over 500 feet vertically into the air?

On Oct 11, 2005, at 2:56 PM, toadboyjoe wrote:

> Anyone know how to figure out the force needed to move a 30 ton object,
>  600 feet in less than 10 seconds?
>  An instantaneous force, not constant :-)
>
>
>
>
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#1024 From: rybo6 <rybo6@...>
Date: Sun Oct 9, 2005 11:14 pm
Subject: More Eversions( excellent! )
os_jbug
Send Email Send Email
 

Here is link to pictures I have been looking for.
Scroll to 2nd photo "Simplist Morin Surfaces and 3rd photo of the Cuboocatahedral Sphere Eversions.

This model was Bernards Morins( blind since age of 6 ) first eversion. There are pictures and more  text about the cubo-octahdral aspects of this eversion in "Islands of Truth: Mathematical Journey" by Ivars Peterson.

Here again we see the cubo-octahedron/VE( ergo the zero-volume tetrahedron ) as the basic, fundamental and a primary aspect of cosmic eversion that alludes to black holes, worm holes and any other inside-outing aspects that may be asscoiated with our physical universe, if not unvierse itself as a whole.

Rybo

On Oct 7, 2005, at 1:43 PM, rybo6 wrote:

Cosmologists and GUTOEists,  this is must site for those of you willing to step out of convention and explore relationships between mind and matter.

Consciousness and pattern.

Awareness and hyper-space

2D and 3D.

Rybo




















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#1025 From: rybo6 <rybo6@...>
Date: Tue Oct 11, 2005 5:21 pm
Subject: 26 Dimenisons( M-theory )
os_jbug
Send Email Send Email
 
I recently became interested in the 26 dimensions, plus one of time,  
27D of hyper-space that at one time had been associated with string  
theories.

At two links that follows I found 27 vertexes associtated with the  
four(  and only four ) lattice representations of the Isotropic Vector  
Equilibrium.

Scroll on page above to the red and green tetraherons, yellow  
octahedron and blue VE/cubo-octahedron that contain the primary 27  
vertexes of all four lattice groups.

Here above is the same 27 vertexes but you will need a VRML/wrl viewer 
( Cortona or Cosmo Player ) to see it.

It is said that the additional dimensions( beyond our normal 3 ) of  
string theory  are compactified( early universe ). 

I see these 4IVM  lattices as an uncompactification( ergo expansion ) of these 27  
dimensions into our normal 3D space.

Rybo









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#1026 From: rybo6 <rybo6@...>
Date: Wed Oct 12, 2005 3:14 am
Subject: Re: 26 Dimensions( M-theory? )
os_jbug
Send Email Send Email
 
Here corrected link for this one below.

Rybo
On Oct 11, 2005, at 12:22 PM, rybo6 wrote:
At two links that follows I found 27 vertexes associtated with the  
four(  and only four ) lattice representations of the Isotropic Vector  
Equilibrium.




#1027 From: "Alan Michelson" <amichelson2002@...>
Date: Wed Oct 12, 2005 3:13 am
Subject: Re: 26 Dimenisons( M-theory )
alanmich2005
Send Email Send Email
 
--- In Polytopia@yahoogroups.com, rybo6 <rybo6@u...> wrote:
>
> I recently became interested in the 26 dimensions, plus one of time,
> 27D of hyper-space that at one time had been associated with string
> theories.

Many physicists, including Michio Kaku, believe that there are either 8 or 24 [spatial and curled-up] dimensions. Of course, these physicists want to add 2 more dimensions, so that there are either 10 or 26 [spatial and curled-up] dimensions. If you believe that time is a dimension, then there are either 11 or 27 dimensions.


> At two links that follows I found 27 vertexes associtated with the
> four( and only four ) lattice representations of the Isotropic Vector
> Equilibrium.

Here's that number 27 again!

> http://www.verbchu.com/crystals/patterns4.htm
>
> Scroll on page above to the [actually yellow] and green tetraherons, [actually red]
> octahedron and blue VE/cubo-octahedron that contain the primary 27
> vertexes of all four lattice groups.
>
> http://www.users.bigpond.com/dharmraj/gallery/4IVMCore2.wrl
> Here above is the same 27 vertexes but you will need a VRML/wrl viewer
> ( Cortona or Cosmo Player ) to see it.
>
> It is said that the additional dimensions( beyond our normal 3 ) of
> string theory are compactified( early universe ).
>
> I see these 4IVM lattices as an uncompactification( ergo expansion )
> of these 27 dimensions into our normal 3D space.
>
> Rybo
>
>
>
>
>
>
>
>
>
>
> Support Our Troops, Bring Them Home Now!
>

#1028 From: "Alan Michelson" <amichelson2002@...>
Date: Wed Oct 12, 2005 5:18 am
Subject: Re: physics question
alanmich2005
Send Email Send Email
 
--- In Polytopia@yahoogroups.com, "toadboyjoe" <fustie@h...> wrote:
>
> Anyone know how to figure out the force needed to move a 30 ton object,
> 600 feet in less than 10 seconds?
> An instantaneous force, not constant 

Depends on what you call "instantaneous", e.g. "less than 10 seconds". According to Newton's Second Law, f*t=m*v; in another words, impulse equals momentum. If you want "instantaneous", then tremendous force has to be exerted. Energy is force times distance, or E=m*v^2.

#1029 From: "toadboyjoe" <fustie@...>
Date: Wed Oct 12, 2005 7:15 am
Subject: Re: physics question
toadboyjoe
Send Email Send Email
 
I call "instantaneous" a fraction of a second. 0.3 seconds perhaps?
:-)
I suspect my mass would have to move at a speed of at least 60
feet/second



--- In Polytopia@yahoogroups.com, "Alan Michelson"
<amichelson2002@y...> wrote:
>
> --- In Polytopia@yahoogroups.com, "toadboyjoe" <fustie@h...> wrote:
> >
> > Anyone know how to figure out the force needed to move a 30 ton
object,
> > 600 feet in less than 10 seconds?
> > An instantaneous force, not constant :)
>
> Depends on what you call "instantaneous", e.g. "less than 10
seconds". According to Newton's Second Law, f*t=m*v; in another
words, impulse equals momentum. If you want "instantaneous", then
tremendous force has to be exerted. Energy is force times distance,
or E=m*v^2.
>

#1030 From: "Rybo" <rybo6@...>
Date: Wed Oct 12, 2005 10:57 pm
Subject: Re: 26 Dimenisons( M-theory )
os_jbug
Send Email Send Email
 
--- In Polytopia@yahoogroups.com, "Alan Michelson" <amichelson2002@y...> wrote:
> Many physicists, including Michio Kaku, believe that there are either 8 or 24
[spatial and
curled-up] dimensions. Of course, these physicists want to add 2 more
dimensions, so that
there are either 10 or 26 [spatial and curled-up] dimensions. If you believe
that time is a
dimension, then there are either 11 or 27 dimensions.

Alan, to be clear her, i suggested 27 dimesnions of string theory and
hypeer-space but Im
not sure Wittens M-theory ergo 11 dimesnions translates to 27D.

Previosuly it was only 26D and Ive not found any info anyewhere saying Wittens
new M-
Theory is is also works as 27D.

Doesnt matter too much because it means we drop the nulcear vertex of the 27 and
stil have
26 with one of thos being time. 27 works better I think but its all good and
intersting to me,
these 4IVM's as a uncompacticationof the the 25 or 26 plus one of time.

Rybo

#1031 From: John Berglund <anisohedral@...>
Date: Thu Oct 13, 2005 11:51 am
Subject: Re: Re: physics question
anisohedral
Send Email Send Email
 
Yes, you have to give some length of time over which the force is exerted. One second? 0.5 seconds? 0.0001 seconds? The shorter the length of time, the more force is needed.

Alan Michelson <amichelson2002@...> wrote:
--- In Polytopia@yahoogroups.com, "toadboyjoe" <fustie@h...> wrote:
>
> Anyone know how to figure out the force needed to move a 30 ton object,
> 600 feet in less than 10 seconds?
> An instantaneous force, not constant 

Depends on what you call "instantaneous", e.g. "less than 10 seconds". According to Newton's Second Law, f*t=m*v; in another words, impulse equals momentum. If you want "instantaneous", then tremendous force has to be exerted. Energy is force times distance, or E=m*v^2.


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#1032 From: Michael Angelicus <astralogos999@...>
Date: Thu Oct 13, 2005 8:08 pm
Subject: Re: Re: 26 Dimenisons( M-theory )
astralogos999
Send Email Send Email
 
Rybo,
 
I'm curious...why do you personally choose to opt for the 27 dimensions instead of 11 ? 
 
Doesn't the Mathematics now suggest 11  [10 of space + 1 of time] as the more generally accepted of the two ?
 
Do you know how they arrive at 11 dimensions ?
 
[By the way I prefer the number 27 as well, but I'd to know why you find it more to your liking.]
 
Curious,
 
Mike

Rybo <rybo6@...> wrote:
--- In Polytopia@yahoogroups.com, "Alan Michelson" <amichelson2002@y...> wrote:
> Many physicists, including Michio Kaku, believe that there are either 8 or 24 [spatial and
curled-up] dimensions. Of course, these physicists want to add 2 more dimensions, so that
there are either 10 or 26 [spatial and curled-up] dimensions. If you believe that time is a
dimension, then there are either 11 or 27 dimensions.

Alan, to be clear her, i suggested 27 dimesnions of string theory and hypeer-space but Im
not sure Wittens M-theory ergo 11 dimesnions translates to 27D.

Previosuly it was only 26D and Ive not found any info anyewhere saying Wittens new M-
Theory is is also works as 27D.

Doesnt matter too much because it means we drop the nulcear vertex of the 27 and stil have
26 with one of thos being time. 27 works better I think but its all good and intersting to me,
these 4IVM's as a uncompacticationof the the 25 or 26 plus one of time.

Rybo






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#1033 From: "belenos1@..." <belenos1@...>
Date: Fri Oct 14, 2005 2:59 am
Subject: Re: Re: 26 Dimenisons( M-theory )
belenos_anu
Send Email Send Email
 
I tend to support the possibility of numerous "other" dimensions, or should I
say, "sub-dimensions" which are curled-up within the primary 11 theoretical
dimensions. Consider that each of the 5th through the 11th dimesions each
consists of 3 inner dimensions as a single root, tied together within our
"normal" 3 dimensional reality. This would explain why the perception of time
(the 4th Dimension) is outside of our normal frame of reference. Each of these
tied 3-dimensional frames, although peculiar to each of the 5th-11th dimensions
(7 primary dimensions)would function in a similar manner to both each other and
to the particular dimension simultaneously. In "reality" (parden the pun) there
would be 7x3 dimensions + the 4 of our own, for 25 dimensions. The mathematics
referenced to a 26 or even 27 dimensional Universe are, at best, fragmented and
highly subjective, while the mathematics supporting a 24 or 25 dimensional
Universe are much more formulative and objective with very few subjective
matracies. Joe

#1034 From: "belenos1@..." <belenos1@...>
Date: Fri Oct 14, 2005 3:02 am
Subject: Re: Re: 26 Dimenisons( M-theory )
belenos_anu
Send Email Send Email
 
I tend to support the possibility of numerous "other" dimensions, or should I
say, "sub-dimensions" which are curled-up within the primary 11 theoretical
dimensions. Consider that each of the 5th through the 11th dimesions each
consists of 3 inner dimensions as a single root, tied together within our
"normal" 3 dimensional reality. This would explain why the perception of time
(the 4th Dimension) is outside of our normal frame of reference. Each of these
tied 3-dimensional frames, although peculiar to each of the 5th-11th dimensions
(7 primary dimensions)would function in a similar manner to both each other and
to the particular dimension simultaneously. In "reality" (parden the pun) there
would be 7x3 dimensions + the 4 of our own, for 25 dimensions. The mathematics
referenced to a 26 or even 27 dimensional Universe are, at best, fragmented and
highly subjective, while the mathematics supporting a 24 or 25 dimensional
Universe are much more formulative and objective with very few subjective
matracies. Joe

#1035 From: "astralogos999" <astralogos999@...>
Date: Fri Oct 14, 2005 3:31 am
Subject: Re: 26 Dimenisons( M-theory )
astralogos999
Send Email Send Email
 
Joe, are you saying that given there are 3 spatial dimensions in
our ordinary work-a-day world, we should be using 3 as a multiplier
for dimensions 5 through 11 ?  In other words I'm trying to understand
where you are deriving your multipler.

If 3 is the key...then three 3's or 3 x 3 x 3 = 27 seems esthetically
pleasing though as you say it may be subjective to have 27 dimensions.

Getting back to my initial point, what criteria are you  or others
using for making 3 the multiple of these sub-dimensions.

Mike

--- In Polytopia@yahoogroups.com, "belenos1@n..." <belenos1@n...> wrote:
>
> I tend to support the possibility of numerous "other" dimensions, or
should I say, "sub-dimensions" which are curled-up within the primary
11 theoretical dimensions. Consider that each of the 5th through the
11th dimesions each consists of 3 inner dimensions as a single root,
tied together within our "normal" 3 dimensional reality. This would
explain why the perception of time (the 4th Dimension) is outside of
our normal frame of reference. Each of these tied 3-dimensional frames,
although peculiar to each of the 5th-11th dimensions (7 primary
dimensions)would function in a similar manner to both each other and to
the particular dimension simultaneously. In "reality" (parden the pun)
there would be 7x3 dimensions + the 4 of our own, for 25 dimensions.
The mathematics referenced to a 26 or even 27 dimensional Universe are,
at best, fragmented and highly subjective, while the mathematics
supporting a 24 or 25 dimensional Universe are much more formulative
and objective with very few subjective matracies. Joe
>

#1036 From: "belenos1@..." <belenos1@...>
Date: Fri Oct 14, 2005 3:43 am
Subject: Re: Re: 26 Dimenisons( M-theory )
belenos_anu
Send Email Send Email
 
Mike,
    The 3 dimensions of our ordinary experience + the 4th Dimension, tend to
become extremely complicated, but from 5 to 10 tend to simplify. The 8th
dimension, which seems to be the simplest and most "beautiful" of the
dimensions, is actually itself the cubed factor of a two dimensional world
(3D-1) such that as the 8th (simplest) dimension is 3cubed-1. Hence the use of
the 3rd dimension is not randomn but objectively derived at by simplex (i.e.,
the cube). Sincerely, Joe

#1037 From: "Alan Michelson" <amichelson2002@...>
Date: Fri Oct 14, 2005 12:44 am
Subject: Re: ? Dimenisons (M-theory)
alanmich2005
Send Email Send Email
 
http://en.wikipedia.org/wiki/Why_10_dimensions?
http://en.wikipedia.org/wiki/Dimension
http://www.geocities.com/xulfrepus/docs/dimen.html
http://www.absoluteastronomy.com/encyclopedia/w/wh/why_10_dimensions.htm
http://www.astronomy.com/ASY/CS/forums/2/289478/ShowPost.aspx

--- In Polytopia@yahoogroups.com, Michael Angelicus <astralogos999@y...> wrote:
Rybo,
I'm curious...why do you personally choose to opt for the 27 dimensions instead of 11 ?
Doesn't the Mathematics now suggest 11 [10 of space + 1 of time] as the more generally accepted of the two ?
Do you know how they arrive at 11 dimensions ?
[By the way I prefer the number 27 as well, but I'd to know why you find it more to your liking.]
Curious,
Mike

Rybo rybo6@u... wrote:
Alan, to be clear here, i suggested 27 dimesnions of string theory and hypeer-space but I'm not sure Wittens M-theory ergo 11 dimesnions translates to 27D.
Previosuly it was only 26D and I've not found any info anyewhere saying Wittens new M-Theory is is also works as 27D.
Doesn't matter too much because it means we drop the nulcear vertex of the 27 and stil have 26 with one of those being time. 27 works better I think but its all good and intersting to me, these 4IVM's as a uncompactication of the 25 or 26 plus one of time.
Rybo

--- In Polytopia@yahoogroups.com, "Alan Michelson" amichelson2002@y... wrote:
Many physicists, including Michio Kaku, believe that there are either 8 or 24 [spatial and curled-up] dimensions. Of course, these physicists want to add 2 more dimensions, so that there are either 10 or 26 [spatial and curled-up] dimensions. If you believe that time is a dimension, then there are either 11 or 27 dimensions.



#1038 From: rybo6 <rybo6@...>
Date: Fri Oct 14, 2005 1:06 pm
Subject: Re: Re: 26 Dimenisons( M-theory )
os_jbug
Send Email Send Email
 
On Oct 14, 2005, at 3:43 AM, belenos1@... wrote:
>  The 8th dimension, which seems to be the simplest and most
> "beautiful" of the dimensions, is actually itself the cubed factor
> of a two dimensional world (3D-1) such that as the 8th (simplest)
> dimension is 3cubed-1. Hence the use of the 3rd dimension is not
> randomn but objectively derived at by simplex (i.e., the cube).
> Sincerely, Joe

Joe, Im not good at math. What is the easiest way to explain this
simplest and beautiful 8thD to a layperson beginner.

1) but first of all I'm confused as to whether or not time( t ) is
included in your 8thD i.e. is any of the 1-8 time?

2) If not then great, so we have 3D ergo XYZ( cartesian perpendiculars
{90 degree ergo cubic} ).

3) then we have the 4thD ergo the diametric diagonals( 45 degrees )
of the cube that give us 4D hyper cube
http://www.geocities.com/CapeCanaveral/7997/hypercube.html

4) now if you can again explain this most simple 8thD in relation to
the above( or not ) maybe I can get it.

Thanks

Rybo















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#1039 From: rybo6 <rybo6@...>
Date: Fri Oct 14, 2005 12:48 pm
Subject: Re: Re: 26 Dimenisons( M-theory )
os_jbug
Send Email Send Email
 
On Oct 13, 2005, at 10:31 PM, astralogos999 wrote:
If 3 is the key...then three 3's or 3 x 3 x 3 = 27 seems esthetically
pleasing though as you say it may be subjective to have 27 dimensions.

Here is link that give visual explanaiton of this math.

Rybo














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#1040 From: rybo6 <rybo6@...>
Date: Thu Oct 13, 2005 11:27 pm
Subject: Re: Re: 26 Dimenisons( M-theory )
os_jbug
Send Email Send Email
 
On Oct 13, 2005, at 3:08 PM, Michael Angelicus wrote:
> I'm curious...why do you personally choose to opt for the 27
> dimensions instead of 11 ?

Because of this link
http://www.verbchu.com/crystals/patterns.htm

where if you go to mid page you can find the three polyhedra( duo-
tetraehedron, octahedron and cubo-ocatahedron/VE ) with the primary
27 vertexes of the four, and only four,  Euclidean( straight edge )
types  of Isotropic Vector Matrices each of which fills all space.

These IVM's are given high reverance by some of us familar with
Buckys Fullers Synergetics 1 & 2 ergo the tet., the oct. and the
cuboo-octahedron/VE.

>  Doesn't the Mathematics now suggest 11  [10 of space + 1 of time]
> as the more generally accepted of the two ?

Yes, I agree and made some attempts to point any discrepancy that
might arise between the two in translating from Wittens new 11
dimensional( 10 + 1{t} ).

>  Do you know how they arrive at 11 dimensions?

Witten made this leap using somethig called "duality".  There is
description of it by Micko Kaku this ecellent link
http://www.fortunecity.com/emachines/e11/86/dimens.html

Here be is some  of the critical info for that "duality" process,
found on that link above.

...."Duality in Maxwell's theory is rather trivial. But in M-theory,
we find another duality: g«1/g. This relationship, though simpler,
turns out to be incredibly powerful. When I first saw it, I could
hardly believe my eyes. It meant that a string theory defined for
large g, which is usually impossible to describe using present-day
mathematics, can be shown to be equivalent to another type of string
theory for small g, which is easily described using perturbation theory.

Thus, two different string theories can be dual to each other. In the
non- perturbative region of string theory was another string theory.
This is how, in fact, we prove the equivalence of all five string
theories. Altogether, three different types of duality called S, T
and U have been discovered , which yield an intricate web of
dualities linking string theories of various dimensions and types. At
an incredible pace , physicists have now mapped almost all the
solutions and dualities that exist in 10, 8 and 6 dimensions"....


>  [By the way I prefer the number 27 as well, but I'd to know why
> you find it more to your liking.]

As stated previously it has to do with my fondness for the the IVM,
the 4IVM lattices at link at top of page and teh curved IVEM which
you may not be familiar with but IMHO has graphisc of a graviton,
Higgs boson and the Higgs Field as well as being the only known 3D
version the the ancient 2D "Flower of Life" pattern.

I think of the primary 27 vertexes( the 4IVM lattices ) as a true
uncompactification( expansion ) of the alleged compactfied 25D, 26D
or 27D( or 9, 10 and 11 ) of hyper-space and string theory, into our
ordianry( visible ) 3D space.

Here is another fantactic VRML interactive graphic of the 27 primary
vertexes. You will need Cortona or Comso player to view it.  Alan M
led me to Cortona and I highly recommend to all for viewing the
beauty of VRML and .wrl interactive graphics.


Rybo












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#1041 From: rybo6 <rybo6@...>
Date: Thu Oct 13, 2005 11:29 pm
Subject: Re: Re: 26 Dimenisons( M-theory )
os_jbug
Send Email Send Email
 
Mike here is 27 vertexes VRML graphic I forgot to post.
http://www.users.bigpond.com/dharmraj/gallery/4IVMCore2.wrl

Cortona or Cosmo Player is needed.

Rybo

#1042 From: rybo6 <rybo6@...>
Date: Fri Oct 14, 2005 5:52 pm
Subject: Re: Re: ? Dimenisons (M-theory)
os_jbug
Send Email Send Email
 
Alan what I find there that is most key( at least to Synergetics ) is
the following about Ramanujan mathematician and the number 24.
...Ramanujan modular functions

..."1968 "Veneziano model" Euler beta function describes the strong
nuclear force.

When a string moves in space-time by splitting and recombining (see
worldsheet diagram at right), a large number of mathematical
identities must be satisfied. These are the identities of Ramanujan's
modular function.

The KSV loop diagrams of interacting strings can be described using
modular functions.

The "Ramanujan function" (an elliptic modular function? satisfies the
need for "conformal symmetry") has 24 "modes" that correspond to the
physical vibrations of a bosonic string.

When the Ramanujan function is generalized, 24 is replaced by 8 (8 +
2 = 10) for fermion strings"....



Rybo


On Oct 13, 2005, at 7:44 PM, Alan Michelson wrote:

> http://en.wikipedia.org/wiki/Why_10_dimensions?
> http://en.wikipedia.org/wiki/Dimension
> http://www.geocities.com/xulfrepus/docs/dimen.html
> http://www.absoluteastronomy.com/encyclopedia/w/wh/
> why_10_dimensions.htm
> http://www.astronomy.com/ASY/CS/forums/2/289478/ShowPost.aspx
>
> --- In Polytopia@yahoogroups.com, Michael Angelicus
> <astralogos999@y...> wrote:
> Rybo,
> I'm curious...why do you personally choose to opt for the 27
> dimensions instead of 11 ?
> Doesn't the Mathematics now suggest 11 [10 of space + 1 of time] as
> the more generally accepted of the two ?
> Do you know how they arrive at 11 dimensions ?
> [By the way I prefer the number 27 as well, but I'd to know why you
> find it more to your liking.]
> Curious,
> Mike
>
> Rybo rybo6@u... wrote:
> Alan, to be clear here, i suggested 27 dimesnions of string theory
> and hypeer-space but I'm not sure Wittens M-theory ergo 11
> dimesnions translates to 27D.
> Previosuly it was only 26D and I've not found any info anyewhere
> saying Wittens new M-Theory is is also works as 27D.
> Doesn't matter too much because it means we drop the nulcear vertex
> of the 27 and stil have 26 with one of those being time. 27 works
> better I think but its all good and intersting to me, these 4IVM's
> as a uncompactication of the 25 or 26 plus one of time.
> Rybo
>
> --- In Polytopia@yahoogroups.com, "Alan Michelson"
> amichelson2002@y... wrote:
> Many physicists, including Michio Kaku, believe that there are
> either 8 or 24 [spatial and curled-up] dimensions. Of course, these
> physicists want to add 2 more dimensions, so that there are either
> 10 or 26 [spatial and curled-up] dimensions. If you believe that
> time is a dimension, then there are either 11 or 27 dimensions.
>
>
>
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#1043 From: rybo6 <rybo6@...>
Date: Sat Oct 15, 2005 12:30 pm
Subject: 24 & Leech Lattice
os_jbug
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Hypersphere Packing

   **Dimension 24** is special due to the existence of the Leech  
lattice, which has the best kissing number and for a long time was  
suspected to be the densest lattice packing. In 2004, Cohn and Kumar  
1 published a preprint proving this conjecture, and in addition  
showing that an irregular packing may improve over the Leech lattice  
packing, if at all, by no more than 

Rybo
















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#1044 From: rybo6 <rybo6@...>
Date: Sun Oct 16, 2005 6:36 pm
Subject: 24 & Leech Lattice
os_jbug
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Hypersphere Packing

   **Dimension 24** is special due to the existence of the Leech  
lattice, which has the best kissing number and for a long time was  
suspected to be the densest lattice packing. In 2004, Cohn and Kumar  
1 published a preprint proving this conjecture, and in addition  
showing that an irregular packing may improve over the Leech lattice  
packing, if at all, by no more than"....


The cubo-octahedron/Vector Equilibrium, has 24 cirmcuferential edges.

Rybo










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#1045 From: "Alan Michelson" <amichelson2002@...>
Date: Tue Oct 18, 2005 5:30 am
Subject: Re: 24-cell Lattice
alanmich2005
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--- In Polytopia@yahoogroups.com, rybo6 <rybo6@u...> wrote:
>
> Hypersphere Packing
> http://encyclopedia.thefreedictionary.com/Leech+lattice
>
> **Dimension 24** is special due to the existence of the Leech
> lattice, which has the best kissing number and for a long time was
> suspected to be the densest lattice packing. In 2004, Cohn and Kumar
> 1 published a preprint proving this conjecture, and in addition
> showing that an irregular packing may improve over the Leech lattice
> packing, if at all, by no more than"....
>
>
> The cubo-octahedron/Vector Equilibrium, has 24 cirmcuferential edges.

I believe that the 3D sphere packing has the 12 direction vectors:
{ (0,±1,±1), (±1,0,±1), (±1,±1,0) }
This is in accordance to the vertices of the Vector Equilibrium.

I believe that the 4D hypersphere packing has the 24 direction vectors:
{ (0,0,±1,±1), (0,±1,0,±1), (0,±1,±1,0), (±1,0,0,±1), (±1,0,±1,0), (±1,±1,0,0) }
This is in accordance to the 24-cell.

Now what is the general formula for the set of direction vectors of the Leech Lattice?
{(±a,±b,±c,±d,±e,±f,±g,±h,±j,±k,±l,±m,±n,±p,±q,±r,±s,±t,±u,±v,±w,±x,±y,±z)}


#1046 From: rybo6 <rybo6@...>
Date: Wed Oct 19, 2005 11:41 pm
Subject: 7thD Max-Surface Area
os_jbug
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http://www.blazelabs.com/f-u-hds.asp
..."One would easily think that as we go higher in dimensions, the
surface area of the n-sphere would increase at each stage, and yet,
something very strange occurs, as a maxima in its surface area is
reached at the 7th dimension. Could this indicate the real ultimate
dimension of the universe?.


Dimension...Volume.....Area
1..........2.0000......2.0000
2..........3.1416......6.2832
3..........4.1888......12.5664
4..........4.9348......19.7392
5..........5.2638......26.3189
6..........5.1677......31.0063
7.........*4.7248*....*33.0734*
8..........4.0587......32.4697
9..........3.2985......29.6866
10.........2.5502......25.5016

Rybo















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#1047 From: rybo6 <rybo6@...>
Date: Tue Oct 18, 2005 11:57 pm
Subject: Re: Re: 24-cell Lattice
os_jbug
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On Oct 18, 2005, at 12:30 AM, Alan Michelson wrote:
> The cubo-octahedron/Vector Equilibrium, has 24 cirmcuferential edges.
AM] I believe that the 3D sphere packing has the 12 direction vectors:
{ (0,±1,±1), (±1,0,±1), (±1,±1,0) }
This is in accordance to the vertices of the Vector Equilibrium.

Probably true

I believe that the 4D hypersphere packing has the 24 direction vectors:
{ (0,0,±1,±1), (0,±1,0,±1), (0,±1,±1,0), (±1,0,0,±1), (±1,0,±1,0), (±1,±1,0,0) }
This is in accordance to the 24-cell.

Alsn, this hyper-link did not work. Would liek to compare teh 24 cell with that Penn scuplture.

Now what is the general formula for the set of direction vectors of the Leech Lattice?
{(±a,±b,±c,±d,±e,±f,±g,±h,±j,±k,±l,±m,±n,±p,±q,±r,±s,±t,±u,±v,±w,±x,±y,±z)}

Darn of  I know. I just posted link cause it was related to 24 and sphere packing :--))
Rybo



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#1048 From: rybo6 <rybo6@...>
Date: Thu Oct 20, 2005 1:42 am
Subject: 8thD a.k.a E8 Lattice
os_jbug
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http://www.quadibloc.com/math/pakint.htm
.."If we continue until we reach *eight* dimensions, there will be
room to add new eight-dimensional spheres at points that are one
square away from the central sphere in every one of the eight
dimensions involved. This packing is known as the E8 lattice.

In that packing, *240* spheres touch the central sphere"....

Aha!, I think there is relationship between the 8th dimesnion and the
24th.  I dunno.

1D = 2

2D = 2^2 = 4

3D = 2^3 = 8( 8 tetrahedra of the cubo-octahedron/VE? )

4D = 2^4 = 16

5D = 2^5 = 32

6D = 2^6 = 64

7D = 2^8 = 128

8D = 2^9 = 256 and not 240, hmmm, so I guess im not a mathematician
{8^))

Wait, I read more  of the link and see there are 256 but only 240
touch the central sphere. Cool!

Rybo






















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#1049 From: "Alan Michelson" <amichelson2002@...>
Date: Thu Oct 20, 2005 2:27 am
Subject: Re: 24-cell Lattice Solution
alanmich2005
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See http://groups.yahoo.com/group/synergeo/

--- In Polytopia@yahoogroups.com, "Alan Michelson" <amichelson2002@y...> wrote:
>
> --- In Polytopia@yahoogroups.com, rybo6 rybo6@u... wrote:
> >
> > Hypersphere Packing
> > http://encyclopedia.thefreedictionary.com/Leech+lattice
> >
> > **Dimension 24** is special due to the existence of the Leech
> > lattice, which has the best kissing number and for a long time was
> > suspected to be the densest lattice packing. In 2004, Cohn and Kumar
> > 1 published a preprint proving this conjecture, and in addition
> > showing that an irregular packing may improve over the Leech lattice
> > packing, if at all, by no more than"....
> >
> >
> > The cubo-octahedron/Vector Equilibrium, has 24 cirmcuferential edges.
>
> I believe that the 3D sphere packing has the 12 direction vectors arranged FCC:
> { (0,±1,±1), (±1,0,±1), (±1,±1,0) }
> This is in accordance to the vertices of the Vector Equilibrium.
>
> I believe that the 4D hypersphere packing has the 24 direction vectors arranged FCC:
> { (0,0,±1,±1), (0,±1,0,±1), (0,±1,±1,0), (±1,0,0,±1), (±1,0,±1,0), (±1,±1,0,0) }
> This is in accordance to the 24-cell.

The face-centered-cubic contacts for E8 are {(±2,±2,0,0,0,0,0,0), (±2,0,±2,0,0,0,0,0), (±2,0,0,±2,0,0,0,0), (±2,0,0,0,±2,0,0,0), (±2,0,0,0,0,±2,0,0), (±2,0,0,0,0,0,±2,0), (±2,0,0,0,0,0,0,±2), (0,±2,±2,0,0,0,0,0), (0,±2,0,±2,0,0,0,0), (0,±2,0,0,±2,0,0,0), (0,±2,0,0,0,±2,0,0), (0,±2,0,0,0,0,±2,0), (0,±2,0,0,0,0,0,±2), (0,0,±2,±2,0,0,0,0), (0,0,±2,0,±2,0,0,0), (0,0,±2,0,0,±2,0,0), (0,0,±2,0,0,0,±2,0), (0,0,±2,0,0,0,0,±2), (0,0,0,±2,±2,0,0,0), (0,0,0,±2,0,±2,0,0), (0,0,0,±2,0,0,±2,0), (0,0,0,±2,0,0,0,±2), (0,0,0,0,±2,±2,0,0), (0,0,0,0,±2,0,±2,0), (0,0,0,0,±2,0,0,±2), (0,0,0,0,0,±2,±2,0), (0,0,0,0,0,±2,0,±2), (0,0,0,0,0,0,±2,±2)}.
Plus there must be either an even or odd number of minuses for all of (±1,±1,±1,±1,±1,±1,±1,±1) for the other contacts of E8. This is according to http://www.quadibloc.com/math/pakint.htm, which also has the solution for the Leech Lattice:

> Now what is the general formula for the set of direction vectors of the Leech Lattice?
> {(±a,±b,±c,±d,±e,±f,±g,±h,±j,±k,±l,±m,±n,±p,±q,±r,±s,±t,±u,±v,±w,±x,±y,±z)}



#1050 From: rybo6 <rybo6@...>
Date: Tue Oct 18, 2005 11:35 pm
Subject: Spherical 4
os_jbug
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http://mathworld.wolfram.com/SphericalCode.html

The 4, in the first equation in the link above, may be intimately
relevant to;

1) the 4 equatorial, 60 degree oreinted, hexagonal planes, of the
cubo-octahedron/VE, ergo,

2) the 4 60 degree oriented, face-planes of the tetrahedron, ergo,

3) the 4 vertexial-points of the tet, ergo,

4) the 4 perpendicular axi of the tet, ergo,

5) the 4 axi of the duo-tet, ergo,

6) the 4 diametric axi of cube, ergo,

7) the 4 diagonals of 4th( or more ) dimensions( see hyper cube ), ergo,

8) inside outing through tets triangular openings ergo,

9) any alledged parrallel( convex-concave ) universes, and,

10) the 2D openings assoiated with Holographic cosmology scenarios,
ergo,

11) black holes phenomena, which,

12) if extrapolated out, from proven experiments of complex
( polypetides ) arising from high pressure events( metorite
impacts ), we arrive at the radical conclusion that,

13) a complex patterning of human RNA-DNA coding being  produced and
emitted from the internal( entropy ) via the event( surface )
horizon, of black holes, which may in-turn also be interpreted as,

14)  Fullers "Cosmic Egg" as stated in "Critical Path".

Also,  what is not mentioned here above is,

1) the relationship that may exist betwwen the VE/cubo-octahedron, as
a static model of black hole, and,

2) this VE/jbug as seen in one, of its 6 or 7 exotic, folded phases/
forms configurations, that alludes to, bilateral symmetry of,  a
complex *quadra-pedic*( 4 ) animal ergo,

3) the VE/cubo-octahedron folds into the topology, of not only the EM
sine-wave( a simple photon ) but with a slight variation of its
orientation, into this compeling possibility, of the most simple
form, of the most complex animals( humans ) having this bilateral
symmetry and 4 quad-like appendages.

For graphic view of this go to following link and scroll to bottom of
pages. Sorry for any wait of page loading.
http://home.usit.net/~rybo6/rybo/id7.html


----Take a walk on the wild side, of the geometry of thinking----

Rybo






















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