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just0
Joined: 22 Jan 2006 Posts: 588

Posted: Tue Jul 17, 2007 7:50 pm Post subject: Toroidal Hypersphere 


Hi peeps,
noplacebo, I like that explanation, when it gets down to it, quantum physics is number physics. I'm no expert
but isn't it the quantum of action i.e. the photon, that determines the fundamental unit. And this photon is
a 'virtual' particle i.e. everywhere at once (timeless) and with zero mass and zero charge, very mystical if
you ask me.
Henry, thanks for the interesting papers, quantum fractals yes, but there's something about Ndimensional geometry
that never rang true for me.
I think Fuller was onto something when he described some of the problems which physics encountered back when
their theoretical models of how nature operated 'broke down'. This was probably when electricity was discovered to
be behaving in a way which the classical models could not explain. This is where physics adopted the use of 'pure'
mathematics which could not be intuitively understood, this is where we lost modeleability of what was going on
in nature. The reason why this change occurred relates to the question of dimensionality in '3'space, to keep a
long story short, it's another example of science refusing to go back on it's word. Of course, we now have
Ndimensional spaces etc., which IMO confuses the situation and doesn't even come close to solving any of the
real problems of dimensionality and the modeleability of nature.
It seems to me that the questions which mathematicians/geometers have been asking is where the real problem
may be. Our culturally inherited systems of logic is for the most part based on some fundamentals of mathematics.
Probably the primary question to our understanding of mathematics is 'How many', from there the question
is extended to include geometry (geometry  to measure the earth/land), here the question is 'How much'.
Ratioing one thing to another is how we measure, but this tells you nothing about the personal value or
quality of what your experience tells you.
Restricting ourselves to systems of logic which only account for the quantizeable i.e. physically countable
and measurable aspects of our experience, is somewhat limiting when it comes to understanding more than
the separate 'parts' of experience.
Although there are separate parts which can be 'counted', there is also this 'space between' which is non
quantizeable, continuous or infinite (Fundamental forces and the electromagnetic spectrum for example). In such
cases, we take the same tools which we used for counting pebbles and apply them to these continuous aspects,
this is a problem because synergy is operative and can be very subtle. Like color for example, we all know
that different hues can be mixed together to give us different colors and that by taking blue, red and yellow
we can mix them together to get white, but this isn't as trivial as it sounds because that in itself is a synergy.
We usually don't notice it because we already know so much about white light and that by dividing white light you
can get all other colors, the point is, we tend to overlook synergetic behaviors.
I think this is where we run into a lot of problems in developing a coherent cosmology, our math is limited
in scope and by it's very nature it overlooks the fact that synergy is always operative.
Think about it, we say 2+2=4  which is 'correct' for our culture and for the logical framework which we've
agreed upon. But if we we're to realize that this has nothing to do with the 'real world' and that in nature,
synergy is the name of the game, we might come to the conclusion that 2+2=5.. and why not ? Nature doesn't
work like a lego set, when nature 'builds' there are synergies, where the combination of one thing and another thing
can create something unexpected. This clearly violates logic in that you can never tell what will follow from logical
evaluation of what has proceeded. It's been said that anything that is logical has an antecedence i.e. a causal
relationship to what has gone before, but novelty must be the opposite of that which has an antecedence in that
it is something new and unexpected and cannot be predicted from what has gone before. That's how nature progresses
and 'grows', like perpetual motion, creating more and more novelty. This aspect is all over nature and is proven time
and time again, yet this is impossible in our view of number and mathematics, because logic is at it's foundation.
2+2=4 lol  sounds kinda like 1984
So back to the big questions of 'How many' and 'How much', I think that we've covered this well trodden path
for long enough, mathematicians are continually coming up with ever more sophisticated ways of counting up
larger and larger groups of things, maybe it's time we asked a new question and I think this is what we're
trying to do here. I'm not even sure what that question is, but it must relate to synergy and dynamic processes.
Luckily, this gets me off the hook when it comes to explaining this kind of stuff to mathematicians, because
the numbers being explored here aren't primarily referring to things because the questions of 'how many' and
'how much' doesn't tell you much about the quality of the larger whole. So I 'spose Geometry and Math are not
really the right words to use here.
Anyway, we're making some progress on the visual side of this, I've got a kind of compilation together where I'm
kicking around some ideas on synergetic shapes etc.
Near the end of this vid I got into relating the Torus to the Vector Equilibrium, this has been done before, but there's
a new twist to what's going on here i.e. the expansion and contraction of the torus reveals a lot more about the dynamics.
Anyway, I've put the clip up here for now, it's been acting up lately, hopefully it works; http://treeincarnation.com/articles/TEST.htm
The Torus has 2 Radii and you can make the Torus turn into a sphere (which would have TWO surfaces) by contracting one
radius to zero. This doubled up sphere is the same 'thing' as the doubled up Octahedron before it expands out into a VE.
And this is starting to gel really nicely with the Treeincarnation Hypersphere work and I'm seeing a lot of connections to
the synergetic number stuff too.
Looking at the profile of the torus resembles some of the illustrations in the shape and number article,
especially the singularity point at the center being the same as the point at the surface and again; 1, 0 and 8.
So the sphere with a doubledup surface is a torus with one of it's radii at zero, increase that radius and the sphere
'grows' into a torus. Maybe this is an overlooked aspect to the topological problem of turing a sphere inside out. If the
sphere had two surfaces to begin with it could simply turn itself into a torus.
I got the tipoff from the work of Arthur M. Young who strongly emphasised the Torus as a Universal model in his
'theory of process', particularly for it's ability to illustrate a universe where everything is separate and interconnected simultaneously.
Quote:  According to Young (1976a; 1980), the seven stages of process, which are found throughout ancient wisdom and esoteric literature, represent the seven topological distinctions possible with the torus, the most complex natural topological entity. The torus (Figure 2) is a selfreferential "timestructure" with numerous unique properties (Young, 1976) such as:
1) composition from two rotating "perpendicular circularities";
2) the shape of a vortex, an entity which is consubstantial with its matrixi.e., the only means by which selfsustained motion can exist in a given medium;
3) the same volume formula, 2pi²R³, as the EinsteinEddington universe, the socalled hypersphere.
4) a universal distribution, occurring with photons and particles through the cellular centriole to the universal hypersphere;
5) the ability to reconcile the continuum of relativity and the discreteness of quantum theory;
6) the means to explain the ancient puzzle of "free will in a universe run by God" or how there can be selfdetermined entities in the continuum; and
7) seven topological distinctions(i.e., a map drawn on the surface of a torus requires seven colors in order for all bordering countries to be distinguished by differences in color).
http://www.arthuryoung.com/barr.html 
_________________ ~"“True observation begins when devoid of set patterns, and freedom of expression occurs when one is beyond systems.”"~ 

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DrewTerry Guest

Posted: Tue Jul 17, 2007 9:24 pm Post subject: 


The "8" is the two "0" with the "1" in the middle turned sideways.
'010' turned sideways looks like an 8. 

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just0
Joined: 22 Jan 2006 Posts: 588

Posted: Tue Jul 17, 2007 9:32 pm Post subject: 


DrewTerry wrote:  The "8" is the two "0" with the "1" in the middle turned sideways.
'010' turned sideways looks like an 8. 
Nice1 dude,
Sometimes it's so simple... it's complicated _________________ ~"“True observation begins when devoid of set patterns, and freedom of expression occurs when one is beyond systems.”"~ 

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just0
Joined: 22 Jan 2006 Posts: 588

Posted: Tue Jul 24, 2007 5:09 pm Post subject: 108 Hypersphere 


You can look at the sphere to torus another way...
0 = Infinity, InsideOut
= Infinity, OutsideIn
Or, is that the other way around ? _________________ ~"“True observation begins when devoid of set patterns, and freedom of expression occurs when one is beyond systems.”"~ 

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Peter
Joined: 26 Jun 2007 Posts: 2453 Location: The Canadian shield

Posted: Wed Jul 25, 2007 4:28 am Post subject: perspective depends a lot on your state of mind... 


Look at the infinity sign as if it were in 3D...it's a freakin' Ruffles potato chip!!! _________________ The grand design, reflected in the face of Chaos. 

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just0
Joined: 22 Jan 2006 Posts: 588

Posted: Wed Jul 25, 2007 7:27 am Post subject: 


Quote:  perspective depends a lot on your state of mind... 
Nice1, how about, Perspective IS a state of Mind.
And ultimeately, all life shares a common perspective.
which always strives for more perspective.
Quote:  Look at the infinity sign as if it were in 3D...it's a freakin' Ruffles potato chip!!! 
Hehe, yeah, Infinity = Ruffles potato chips  (from a totally stoned perspective.) _________________ ~"“True observation begins when devoid of set patterns, and freedom of expression occurs when one is beyond systems.”"~ 

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just0
Joined: 22 Jan 2006 Posts: 588

Posted: Wed Jul 25, 2007 9:22 am Post subject: Microscopic Patterns 


It's often quite easy to overlook some of the basic rules of pattern which nature
employs repeatedly  because the 'rules' are often hidden in fractal progressions.
Like with Radiolaria for example;
Haeckel's radiolaria;
Illustrations from 'Kunstformen der Natur' by Ernst Haeckel (1904)
Quote:  Geometry and Pattern in Nature 1: Exploring the shapes of diatom frustules with Johan Gielis' Superformula
I have always been intrigued by geometry and patterns. Examining diatom frustules for the first time under the microscope, I was captivated by the perfection of their symmetry. It was through my motivation to find out more about the precise regularity in the simple, but perfect, frustule forms that I came across Johan Gielis' Superformula, a fascinating concept that interlinks a number of shapes found in living organisms through variations on a single mathematical equation.
Some sources have stated that previous mathematical concepts relating to the properties of shapes and patterns have tended to “exist in isolation”, sharing few unifying characteristics with other concepts. Johan Gielis' Superformula, by contrast, can generate a spectacular array of symmetrical organic forms, including those of diatoms, starfish and flowers. The Belgian scientist's Superformula draws on an equation originated by Piet Hein more than 200 years ago. Advancements in the past few years have only really been made through the development of computer technology, which has facilitated the discovery of the apparently endless shapegenerating ability of the equation!
The Superformula is a combination of the equation for a circle (r², where r=radius) with that for a superellipse. A superellipse is a specific type of mathematical curve that produces a number of different shapes, for example, astroids, circles and diamonds, depending on the power the sine and cosine terms are raised to. For a more detailed explanation and mathematical equations, please see: http://astronomy.swin.edu.au/~pbourke/surfaces/superellipse and http://astronomy.swin.edu.au/~pbourke/curves/supershape.
The resulting Superformula equation has the potential to create a wide variety of shapes due to the presence of a number of variables, or parameters, within it. Adjusting these variables, of which there are 6 in all, produces not only circles but triangles, squares, star shapes and other manysided figures, figures with bilateral (reflective) symmetry rather than rotational symmetry, and asymmetric figures; these "ideal" figures generated in this way are termed “Supershapes”. The equations for the Superformula may also be combined with those of the logarithmic spiral to produce spiral shapes, or with those of other Supershapes to produce threedimensional forms; more variables could in theory be added to describe more complex structures. It has been argued that the formula is open to accommodating too many parameters. A humorous quote by a mathematician suggests that the formula for an elephant could be arrived at using sufficient parameters; the point of view being made here is that more parameters, in mathematical terms, are not necessarily better, and that a simpler but more effective equation would be less complicated to use.
Nature may or may not function along similar lines of logic when creating its own Supershapes! However, the similarity between shapes created by the Superformula and those in nature is striking, and Gielis' method proves an interesting one for describing and investigating geometry in living organisms.
The expression of variations on the Superformula as computergenerated “virtual” shapes shares interesting parallels with the mechanism of gene expression. The phenotype of an organism is a direct expression of its genotype (barring environmental influences), with the role of the numbered variables in the Superformula being taken by DNA molecules made up of nucleotides that in combination govern the dimensions and proportions of an organism. In the same way that the science of genetics assumes the evolution of organisms, and genes, from a common “ancestor” or ancestral gene, so too do Supershapes originate from the Superformula, where the simplest shape, in terms of mathematical description and form, is that of the circle. It is worthy of note that the simplest and most primitive organisms are circular, although their form is probably due to the environmental forces surrounding and acting upon them, and also their relatively small size.
Obviously, Gielis' equation does not and cannot encompass all natural forms; Gielis himself makes no claims that the formula is a “theory of everything”, as has been cited in some spheres. Whilst it can be used to describe a number of organic forms, it most certainly cannot be used to describe inorganic forms, such as crystal structures, easily; nor does it take account of fractal forms, which are found throughout the organic and inorganic worlds.
The drawings of diatoms shown below are from slides by Brian Darnton, prepared from material collected at the Westerschelde, The Netherlands. Diatoms are a group of organisms worthy of study in conjunction with the Superformula, since their many different frustule shapes coincidentally show the type of variation expressed through alteration of certain variables within the equation, and also very clearly defined rotational and/or reflective symmetry.
It is not easy to explain how the parameters of the Gielis equation combine to create the shapes that they do, but, broadly, radial symmetry is controlled by the parameter m, inside the sine and cosine functions. By changing the value of m, the number of sides of a figure can be adjusted. This may lead, in combination with the other parameters in the equation, to shapes mimicking those of the pennate diatoms with two sides, Triceratium favum with three sides, and the four and fivesided diatoms.
For example:
The circular shape of the centric diatom Actinoptychus senarius occurs where m=0 (r=1).
Actinoptychus senarius Ehrenberg.
The ovoid shape of this Surirella species, as well as the shapes of most other pennate diatoms, could be best described by increasing the value of m to 2.
Surirella fastuosa (Ehrenberg) Kutzing.
Triangular shapes such as that of Triceratium favum are produced when m=3....
Triceratium favum Ehrenberg. This species is abundant in samples taken from the Westerschelde.
...whereas the foursided shapes shown here, including the rhomboid shape of the pennate diatom Pleurosigma angulatum, are achieved when m=4.
Biddulphia antediluviana (Ehrenberg) van Heurk forma antediluviana.
Pleurosigma angulatum (Quekett) Wm. Smith. N.B. The twisted appearance of P.angulatum would not be possible without the addition of more parameters. This particular species was a favourite test diatom with the Victorians.
The relative sizes of the powers (n1, n2, n3) determine whether the figure takes on a “pinched” or “bloated” appearance, and the degree to which it does so. The extent of curvature of the sides of the figure is controlled by the absolute values of the npowers.
Lastly, the 3D shape shown here could be arrived at through a combination of Supershapes! To view the effects of combining Supershapes, please see: http://astronomy.swin.edu.au/~pbourke/surfaces/supershape3d/#2d
Biddulphia aurita (Lyngbye) de Brebisson.
My especial thanks go to Paul Bourke, for clarifying the Superformula equations, and to Brian Darnton, for providing the diatom slides and species identification.
Identification source: An Introductory Account of the Smaller Algae of British Coastal Waters, Part V  Bacillariophyceae (Diatoms). N.Ingram Hendey, HMSO, 1964.
Paul Bourke's homepage: http://astronomy.swin.edu.au/~pbourke
Brian Darnton's homepage: www.darnton.freeserve.co.uk
Additionally, the following sites may prove of interest:
Johan Gielis' website: http://www.geniaal.be/#
The following page from “Mathworld”: http://mathworld.wolfram.com/Superellipse.html
Please contact the author, Christina Brodie if there are requests about image use or if interested
in her other artwork.
All images © Christina Brodie 2003.
Microscopy UK Front Page
Micscape Magazine
Article Library
http://www.microscopyuk.org.uk/mag/indexmag.html?http://www.microscopyuk.org.uk/mag/artapr04/cbdiatom2.html 
_________________ ~"“True observation begins when devoid of set patterns, and freedom of expression occurs when one is beyond systems.”"~ 

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Peter
Joined: 26 Jun 2007 Posts: 2453 Location: The Canadian shield

Posted: Thu Jul 26, 2007 3:45 pm Post subject: Perspective is all about prospecting.... 


just0 wrote: 
Nice1, how about, Perspective IS a state of Mind.
And ultimeately, all life shares a common perspective.
which always strives for more perspective.
Quote:  Look at the infinity sign as if it were in 3D...it's a freakin' Ruffles potato chip!!! 
Hehe, yeah, Infinity = Ruffles potato chips  (from a totally stoned perspective.) 
Quite right, ad infinitem. Indeed, perspective is one of the principle quality/defects of the mind. The egoself uses the intellect to weigh the options and compare the aspects to determine which action to choose from the reactive memory.
The whole point of creativity is to discard perspective and engender new relationships that depend on the component parts and not their relative positions. (Synergy)
The duality of our experiential existance leads us to the conclusion that true and false are value comparisons. They are actually sympathetic versions of the same extant reality.
Intelligence is the movement of the source as manifested in the material plane.
You cannot be intelligent alone. _________________ The grand design, reflected in the face of Chaos. 

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just0
Joined: 22 Jan 2006 Posts: 588

Posted: Thu Jul 26, 2007 6:39 pm Post subject: 


Hi peter and (a belated) Welcome to the Forum !!
A lot of truth to what you've got there, let me try to add some thoughts...
(BTW, I get confused when I hear about these material planes and higher planes etc.
It must relate to my difficulty with anything to do with 'plane geometry'. )
Quote:  The whole point of creativity is to discard perspective and engender new relationships that depend on the component parts and not their relative positions. (Synergy) 
There are many forms of creativity, if you think about it in terms of creative
spaces, like with painting, music, dance or any science for that matter, the
creative space is your medium or the stage where you play your play etc. The
space also has certain techniques and methods worked out in advance (rules) so
as to help you to create whatever you want without having to reinvent the wheel
every time you want to create. It's easy to over genaralise with creativity, but
in general, heres how I've come to see it.
sometimes it's a matter of staying within the boundaries of a creative space and
combining elements in a newunique fashion or using the elements of that space to
'paint' a new idea.
Sometimes the creative space itself is explored (extended/combined with other 'spaces')
to generate opportunities and new techniques that will create more unique combinations etc.
Or sometimes an entirely new creative space is explored, in which case the 'rules'
are not clearly defined, the territory is not well known and may even look strange.
These are the frontiers, where previously unknown creative spaces are developed.
This is the kind of creativity that BFN'ers are contributing to on many levels.
We see a lot of people not wanting to play the same boring old games anymore,
which calls for new creative spaces to be explored, whether that's political or artistic.
Quote:  You cannot be intelligent alone. 
Comparisons and relationships (ratios etc.) seem to be functions of the intellect.
But Value is experiential, having experienced something brings a different kind
of knowing, like the sense of being here and now. Or 'Knowing' that fire burns...
I've felt it !! (and nothing compares )
Value is felt and theres no need for comparisons between one thing and another
for a value to be 'known'.
And so, to the intellect, Value (a different kind of 'knowledge') is completely unknowable.
It's the difference between a map (concept) and a place (an experience). _________________ ~"“True observation begins when devoid of set patterns, and freedom of expression occurs when one is beyond systems.”"~ 

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Peter
Joined: 26 Jun 2007 Posts: 2453 Location: The Canadian shield

Posted: Thu Jul 26, 2007 7:48 pm Post subject: nothing is just everything all added up... 


Thank you, your nothingness. Being just0 is in fact everything
Your creativity is absolutely limited by yourself. The actualization depends on how you choose to deal with the energy as it becomes available.
Nonetheless, the sum of any duality is indeed zero. This property affords you the freedom to access the entirety of all of the forms in the proportions required by the situation at hand.
The presence of another source is not referential but rather it is consequential. As you exchange on any plane of existance, (fortunately planar geometry only applies to study and not to our reality as far as we are concerned....who wants to be a flathead anyway?...lol) you are able to discern the elements of your own person that deleteriously affect your ability to choose. This external presence is required to permit you access to a clear vision of your own self, free of all internal influence.
The intellect is a zerosum game. It was not created to generate knowledge but it was rather the result of the ego requiring a function that could differentiate the current state of incident forms for the purpose of alignment and positioning. Kind of like a speedometer.....it is fine when you are moving....but serves no real purpose when the needle is at 0 When the ego is finally incorporated into the psychic mechanism, the intellect will be but a minor aspect of this secondary supramental aspect of human consciousness. _________________ The grand design, reflected in the face of Chaos. 

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just0
Joined: 22 Jan 2006 Posts: 588

Posted: Thu Jul 26, 2007 8:49 pm Post subject: 


You are one wise Dolphin, but I thought Dolphins
where just 'sposed to be intelligent. Maybe we
need to do more testing on them. (on philosophy maybe)
Quote:  Your creativity is absolutely limited by yourself. The actualization depends on how you choose to deal with the energy as it becomes available. 
That's a nice, short 'n' sweet way of saying it. Thanks !!
Quote:  The intellect is a zerosum game. It was not created to generate knowledge but it was rather the result of the ego requiring a function that could differentiate the current state of incident forms for the purpose of alignment and positioning. Kind of like a speedometer.....it is fine when you are moving....but serves no real purpose when the needle is at 0 When the ego is finally incorporated into the psychic mechanism, the intellect will be but a minor aspect of this secondary supramental aspect of human consciousness. 
Right on Peter, the Intellect is a tool.
But just like any other tool, it serves it's
purpose well only when it is used 'properly'.
But what do we need it for?
Whats it's Ultimate porpoise (or purpose )?
The way the ancient mythologies put it,
the Mind(intellect) is the slayer of the
real  and only the mind can slay the slayer.
It's the story of medusa with her head of many
snakes and who turns all to stone with her gaze.
The perfect representation of the Intellect.
And how is she defeated? With a Mirrored shield.
Reflecting back on itself, only the intellect can
defeat the intellect.
So, not only is the intellect secondary as you say,
but ultimately it has the important purpose of being
the cause of it's own undoing.
But as with everything, the process is where it's at,
the journey is the destination.
Keep on truckin' _________________ ~"“True observation begins when devoid of set patterns, and freedom of expression occurs when one is beyond systems.”"~ 

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Peter
Joined: 26 Jun 2007 Posts: 2453 Location: The Canadian shield

Posted: Fri Jul 27, 2007 6:58 am Post subject: The future is just what you have yet to create.... 


Thanks just0.
That the intellect is a tool is for sure. That it can be used badly and even against our own best interests is something that few manage to discern let alone describe. The materialistnihilist retarding action of all of our "encumbrances" are finally coming to light. As our consciousness level raises us above the fray, the new perspective gives us an overall point of view. This new point of view must be expressed as that is how it will become "real" for us. You have made an important and necessary step in this evolutionary phase of our existance.
Hats off to you dude! _________________ The grand design, reflected in the face of Chaos. 

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