ARTICLES
RESOURCES
GEOMETRY
HYPERMEDIA
METAPAGES
MISCELLANOUS
another outtake from Dr. Michiu Kaku - Professor of Theoretical Physics
Department of Mathematical Sciences at Loughborough University
1. The Hypercube
How to build the 4 dimensional analogue of the cube. Includes movies of a spinning hypercube.
2. An ``Inflated Hypercube''
The hypercube may be though of as a crude approximation to the hypersphere. By inserting new vertices into the edges of a hypercube, it may be ``inflated'' to give a better
approximation, with more points lying on the surface of the corresponding hypersphere.
3. Hyper-torus
Adding together three vectors rotating in 4-space with different frequencies and amplitudes produces a trajectory along the surface of a hyper-torus.
4. How the models were produced
Details of the maths needed to model the structures, and how to turn the numbers into an animation.
Useful references on higher dimensional topics
by Michael Clive Price
Since 1985 there has been much theoretical progress on traversable wormholes. At first they were thought to enable time travel, so not
taken seriously. More recent work rules out time travel and associated paradoxes, but still permits faster-than-light travel. This article
explores some of the implications traversable wormholes have on the expansion of civilisations through the universe.
Internet Science Education Project
SARFATTI Group
Einstein-Podolsky-Rosen Animation
Quantum Teleportation
Primordial Traversable Wormholes?
PSI WARS
Rants and Raves
Quantum Mind & Microtubules
Star Force Academy
UFOs Fact or Fancy?
Star Maker
Sarfatti Live on Digital Video
Nanotechnology
Through the Web Hole
On-Line Physics Handbook
Animated and Simply
Explained!
a point event in spacetime, Geometry of the light cone
Jack Sarfatti, 1995
Flatland - A Romance of Many Dimensions
by Edwin A. Abbott (1884)
A true classic of hyperdimensionality. Inspiration for Rudy Rucker
This Work is Dedicated
By a Humble Native of Flatland
In the Hope that
Even as he was Initiated into the Mysteries
Of THREE DIMENSIONS
Having been previously conversant
With ONLY TWO
So the Citizens of that Celestial Region
May aspire yet higher and higher
To the Secrets of FOUR FIVE or EVEN SIX Dimensions
Thereby contributing
To the Enlargment of THE IMAGINATION
And the possible Development
Of that most and excellent Gift of MODESTY
Among the Superior Races
Of SOLID HUMANITY
The Theory of Evolutionary Process of Arthur M. Young
by Frank Barr
According to Young (1976a; 1980), the seven stages of process represent the seven topological distinctions possible with the torus, the most complex natural topological entity. The torus is a self-referential "time-structure" with numerous unique properties such as:
1) composition from two rotating "perpendicular circularities";
2) the shape of a vortex, an entity which is consubstantial with its matrix--i.e., the only means by which self-sustained motion can
exist in a given medium;
3) the same volume formula, 2pi²R³, as the Einstein-Eddington universe, the so-called 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 self-determined 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).
Relativity and Faster Than Light Travel
1995 by John H Kim
Faster-than-light travel between star systems is a staple of much
science fiction. SF authors thus come up with various pseudo-scientific
explanations for it. Consequently, there is a lot of confusion about the
Theory of Relativity. This is only natural - it is a very complicated
theory which even physicists often have trouble with.
A Structured World of Liquid And Foamy Ether
An article on Theoretical Physics by Peter Hahn
The Warp Drive: Hyper-Fast Travel Within General Relativity
Miguel Alcubierre
It is shown how, within the framework of general relativity and without the introduction of wormholes, it is possible to modify a spacetime in a way that allows a spaceship to travel with an arbitrarily large speed. By a purely local expansion of spacetime behind the spaceship and an opposite contraction in front of it, motion faster than the speed of light as seen by observers outside the disturbed region is possible. The resulting distortion is reminiscent of the ``warp drive'' of science fiction. However, just as it happens with wormholes, exotic matter will be needed in order to generate a distortion of spacetime like the one discussed here.
Visualising Hypersolids
Synthetic Dimensionality,
Scale-Space for N-dimensional discrete signals,
How to Fill n-Dimensional Space with Hoops,
The n-dim project at EDRC,
Halayudha, Hexagons, Hypercubes, Hermes & Plato:
N-dimensional cubes (basic program included) by Jonathan Bowen.
A popular work which describes nineteenth century views on the subject of the fourth dimension is to be found in a work of fiction called "Flatland" by E.A. Abbot (1884). This is a story about a being who has spent his entire life in a country that exists in two dimensions. He has no idea about dimensions higher than the one on which he lives, himself being a two dimensional shape. The main character is simply a square with eyes and a mouth on one of his vertices.
Society for the Advancement of Autodynamics
Autodynamics is a superset of Special Relativity. Among its implications are: the
ability to describe important experimental data that Special Relativity cannot (e.g., muon decay, nucleus-nucleus collision,
proton-proton annihilation), the theoretical lifting of the light speed barrier (including an outline of an experiment for creating
faster-than-light-speed photons).
Here are a few essays regarding manifolds. We address questions relating to their differentiable structure (and analytic structure) as
well as to their geometry.
Thinking about the definition of a manifold
What is the gradient (in differential topology)?
Is the smooth image of a manifold still a manifold? (no)
Review of the "long line" (the imposter manifold), along with some questions.
Deriving the equations of a torus.
Can you determine analytic functions on a manifold from the values on a set with an accumulation point? (no -- read to see djr mix up
results from complex analysis with real manifolds.)
Are most manifolds hyperbolic?
Finding a manifold with boundary RP^n
Classification of 4-dimensional manifolds (up to homeo- or diffeo-morphism), and applications to mathematical physics.
inventor of the Bell Helicopter, cosmologist and author of The Reflexive Universe and The Geometry of
Meaning,
addresses issues in physics, mathematics, consciousness and evolution. Learn about ongoing work to extend the theory into new areas from medicine, cognitive science, brain research and cellular biology to developmental psychology, problem solving and organizational planning.
What you will find on the pages linked to this one are a series of computer generated
projections of analogs of 3 of the 5 platonic solids in 4-space. The remaining 2 are in the
works. In addition there is a projection of a regular polytope that exists only in 4-space.
If you are wondering what I mean by hyperspace, I am referring to a Euclidian space of
more than 3 dimensions. Can I stand in my office and point in the direction of the 4th
dimension, No. Neither can I deny it's existance.
The Flat Torus in the Three-Sphere
One of the most interesting surfaces in four-dimensional space is the Flat Torus in the Three-Sphere.
To see the changing three-dimensional shadows created as this object completes a rotation in four-dimensional space, select any
point in the image below to download an animation. Thomas Banchoff's Project List
4Dice Project A Glimpse into the Fourth Dimension
Center for Innovative Computer Applications
An animation of four-dimensional dice
Many-dimensional Geometry
A reference page
The Geometry Forum is an electronic community focused on geometry and math education based at Swarthmore college.
Multimedia Documents
It is a visual dictionary of surfaces and other
mathematical objects, consisting primarily of movies, still images and interactive pictures.
Special Exhibits:
Higher Dimensional Objects,
Knots and Links,
Fractals,
Hyperbolic Geometry,
George P. Landow
Navigation in Hyperspace and Cognitive Representation
This page is being developed during the Cognitive Ergonomics course CO440 of Cognitive Science at the Nijmegen University, The Netherlands. The subject is on how people build
up mental representations of information collected in a hypermedia tour.
Californian Ideology never trust a hippie Basic Banalities elementary truths TechnoWhores visit the whorehouse Media Freedom democracy and representation Dissimulations the illusion of interactivity Babbage's Intelligence the labour of computing The Pinnochio Theory review of "Out of Control" Electronic Democracy politics in cyberspace
described by Vannevar Bush in his seminal article "As We May Think," the Memex is the protoypical hypermedia machine. Although never actually built, the Memex had all the features now associated with the multimedia computer workstation including: hyperlinked text and images (microfiche filing system), networking capabilities (via broadcast television), display terminal (television screen), keyboard for inputing text, and data storage (electromagnetic memory cards).
Vannevar Bush, the US Defense Department's most revered engineer during World War II, was the key computer scientist to make the leap to the larger issues of information technology. In his seminal article, "As We May Think", written in 1945 for the Atlantic Review, he forecast the future of hypermedia with his visionary Memex, the prototypical multimedia workstation that influenced generations of knowledge pioneers.
Mark Amerika (1995) What happens when HTC is teleported through cyberspace? How can we reconfigure our conceptions of authorship so that they allow for a new breed of writers called cyborg-narrators and what will these cyborg-narrators do once they enter virtual reality?
Hypertext and Hypermedia -- A Subject Catalogue
and general index
realtime visualisation of the structure of a set of web pages
The hyperspace system allows a user to create a realtime visualisation of the structure of a set of web pages whilst browsing through them. hyperspace builds upon two strands of research within the Advanced Interaction Group at Birmingham: firstly, visualisation of complex
interacting systems (Hyper/Narcissus), and secondly, communications architectures to support multi-agent systems (cameo).
hyperspace is highly dynamic and can be extensively tailored and extended through its user and programming interfaces. The system is not
restricted to visualising hypertext structures either; it can be used for other data too.
Useful WWW sites regarding hypertext, hypermedia, and world wide web.
Introductions to Hypertext Bibliographic Resources History of Hypertext Authoring Hypertext Hypertext and Literary Theory Hypertext Publishers Some Interesting Examples World Wide Web Other Sites of Note
This is a glossary of terms used within the WWW project. In most cases, their use corresponds to conventional use in hypertext circles.
a hyperspace fan-page
The Deoxyribonucleic Hyperdimension
"listen, there's a hell of a universe next door: let's go!" e.e.cummings
PHYSIC and PSYCHIC EXPERIENCES OF A HYPERSPATIAL NATURE
High Energy Astrophysics Science Archive Research Center,
inline animations of supernovas and black holes
Toward a Science of Consciousness 1996 ("Tucson II")
What is consciousness? The nature of our conscious experience has returned to the forefront of scientific interest. Representatives from philosophy, neuroscience, psychology, cognitive science, medicine, physiology, biochemistry, physics, mathematics, ethnology, contemplative studies and other fields are invited to a second major interdisciplinary conference on consciousness.