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Time Zero


Fractal Time
Documents concerned with time as a fractal and in particular Terence McKenna's Timewave Zero theory. http://serendipity.nofadz.com/ft

Note: Although the respectful Mr. Terrence McKenna is no longer with us, he is perhaps still observing from another realm. RIP


Terence McKenna relinquished his body at 2:15 a.m. Pacific time today,
April 3, 2000.

He died at peace and with people whom he loved and who loved him.

There will be memorial events in a few cities over the coming months, and
information about them will be available as plans are made.

Dan Levy

This web site is a repository of material concerning Timewave Zero (a.k.a. Novelty Theory), a way of thinking about time and history originated by the late Terence McKenna (though in typically McKenna-esque style he claimed it came from the Oversoul of the Species).

The Timewave — and Novelty Theory

Software for exploring this theory:

Fractal Time — the Software
Calculation of the Timewave Value
WEN_GRPH — Generation of the 384 Numbers

Gyrus: The End of the River — A critical view of Linear Apocalyptic Thought

Links to web pages concerned with:

The Timewave Fractals Time
Fractal Time History I Ching

This Fractal Time web site was created by Peter Meyer, who is solely responsible for its content. It first went online on December 28th, 1997.

<This message has been edited by Time02112 (edited 21 August 2000).>

Chaotic Experimentation
Terence McKenna's Time Wave Zero
Here is a quantified interpretation of history's vicissitudes, the
mutability of life or, if you prefer, a graphic representation of the
universe's rhythm here on our tiny planet.

McKenna purportedly bases this fractal wave graph approach to
documenting the rhythm of life on concepts gleaned from the
I Ching .

The following are a selection of graphs found on the web sites
listed below, apparently generated by McKenna's TWZ software
portraying this rhythm on chronologically decreasing scales. The
TWZ software is available for purchase by the public.

All lines appear to closely approach the horizontal axis sometime in
the first several decades of the 21st century. You'll notice there's a
distinct lack of apparent effort to extend the graph much beyond
that point. Apparently holistically inspired fractals don't reach negative
values. Or maybe you just buy the software to see what happens next.

Web references and lavish credits go to the following:
Sound PhotoSynthesis
Blue Water Publishing
Levity... whatever

And The Lovely and Talented
Terence McKenna

Temporal objects

Temporal provides a class for the general concept of temporal object, including all points, paths, volumes, undivided wholes, etc.

In particular, it currently contains:]:

Time points, which are non-decomposable, zero dimensional points in time; a single explicit subtype is defined here: zero-d-time. Zero dimensional points are usually referred to using prepositions such as ``at''.
Time as a general undecomposable substance. It is the combination of temporal and substance. This is used as an undifferentiated spatial concept that might support, for example, selection of the interrogative form ``when''.

<This message has been edited by Time02112 (edited 27 August 2000).>

New Maps of Hyperspace
by Terence McKenna
A talk given at the invitation of Ruth and Arthur Young of the Berkeley Institute for the Study of Consciousness, 1984. (Included as written word because this edited transcription appears in print as part of his book The Archaic Revival - dimitri)
Search this talk for
In James Joyce's Ulysses, Stephen Dedalus tells us, "History is the nightmare from which I am trying to awaken." I would turn this around and say that history is what we are trying to escape from into dream. The dream is eschatological. The dream is zero time and outside of history. We wish to escape into the dream. Escape is a key thing charged against those who would experiment with plant hallucinogens. The people who make this charge hardly dare face the degree to which hallucinogens are escapist. Escape. Escape from the planet, from death, from habit, and from the problem, if possible, of the Unspeakable.

The Spatial SVD Transform

Abstract: This document describes the spatial singular value decomposition transform (equivalent to PCA) that can be applied to any time domain file type (AVG, EEG, or CNT). This transform generates spatial component topographies, fraction of total variance explained by each component, and a linear derivation file for deriving component time series.

The spatial SVD (singular value decomposition) transform is equivalent to spatial PCA (principal component analysis) without rotation of components. A series of spatial components – i.e. unit magnitude channel vectors or topographies -- are derived such that the first component accounts for a maximum of the temporal variability in the data; the second spatial component is orthogonal to the first and accounts for a maximum of the residual temporal variability; etc. Spatial SVD is a linear decomposition which produces "statistical sources" for the data. The rationale for making a linear decomposition is based on the rationale for performing a full-fledged biophysical source analysis, i.e., the quasi-static approximation for volume conduction in biological media (Plonsey, 1969) implies that transmission from brain sources to measured scalp potentials is instantaneous and linear. All of the statistical sources considered together span a "signal space" that corresponds to the biophysical projection of the brain source signals to the scalp. However, there is not in general a 1-1 correspondence between individual spatial SVD components and brain sources. In particular, note that the spatial SVD components are mathematically required to be mutually orthogonal, whereas the biophysical projections of actual brain sources to the scalp are not orthogonally constrained.

Creating Fractals
by Caitlin, Randall School
Hi! My name is Caitlin. As you know, I'm working on a project with fractals. I think Mr. Wagler gave me the idea of working on fractals, but the idea grew by looking through old It Figure! journals and finding a lot of articles on fractals. In those articles, I noticed that they were just drawing the fractals and seeing how they looked. I wanted to do something more. Finally I thought of a problem: how do you mathematically create a fractal?

Two Steps to Fibonacci Numbers
I started looking through a book called Fractals in the Classroom. I was looking at two-step problems and I came across a really neat example: there is one pair of rabbits which are born at time 0. After one month that pair is mature, a month later gives birth to a new pair of rabbits, and continues to do so as every month a new pair is born to the original pair. Moreover, each new pair of rabbits matures after one month and begins producing pairs of offspring every month after that ad infinitum. One assumes that the rabbits live forever. What is the number of pairs after n months?I started that problem. Here it is:

Accel-1D Time Dilation Plots

When I began to think about teaching special relativity for my first modern physics course, I could usually guess which observer in a given problem would see a clock running slow relative to his own. But I wondered, couldn't we then call the phenomenon "time compression" from the vantage point of the frame in which it runs fast? For the answer, continue reading...
In my desire to visualize this more concretely, I decided to illustrate the process with an x-ct diagram. Even though the sound byte "time dilation" was familiar to me, and even though my intuition usually told me how to solve time dilation problems, I didn't really understand the concept until this was done. As Jonathon Swift's Gulliver might have said, "When I could hold the fruit in my hand and taste it, the inadequacy of my prior wisdom became apparent." This was one of my first object lessons in the sloppiness of our own language for dealing with relativistic spacetime effects.

In special relativity terms, "time dilation" problems involve two events - which we might refer to as start and stop events which take place on one particular clock. As I looked at the diagrams I realized that in time dilation problems, one and only one inertial frame, namely the "undilated one", was accorded and deserved special status. This special frame, inherent to the statement of the problem, is the frame in which the clock is traveling. All other inertial frames see the clocks in this priviledged frame as traveling slower. Thus when you look at any moving clock, or equivalently when any clock moves, it's time is "dilated" and thus slowed down. Moving a clock never causes its time to "compress" or move faster!

To pose a specific problem, imagine an inertial clock which times an interval of one year, and an inertial frame which observes the start and stop of this timing adventure from frame traveling at constant inertial velocity of one third of a lightyear per inertial year (i.e. w = c/3) to the right.

To draw the x-ct plot below, the four steps are:

The rest frame of the clock is chosen as the one with orthogonal axes.
Imagine that the tick marks on the green grid denote times (vertical) of one year, and distances (horizontal) of one light-year. (This would work as well with seconds & light-seconds, respectively, if we wanted to have the experiment over more quickly.)
The red line denotes the world line (path through time) of the clock. The red boxes denote the start and stop events under consideration, spaced one year apart in the frame of our clock.
The blue grid shows lines of constant inertial time b (about 18 degrees up from the horizontal right) and constant position (about 18 degrees rightward from the vertical) for an inertial observer moving to the right at one third of a lightyear per inertial year (i.e. w=c/3). The start event occurs at "time zero" for each observer. The red dash illustrates the rightward moving observer's measurement of the time of the stop event. Since a year on the rightward frame's clock is marked by the dotted blue axis crossing, the stop event happens a bit more than a year after the start event in that frame. Since gamma for the rightward frame is 1/Sqrt<1-(w/c)^2> = 1/Sqrt<1-1/9> = Sqrt<9/8> = 1.06, the time interval measured in the blue frame between events is 1.06 years.

Cosmology is one of the grand sciences, a domain of research
whose results have enormous intellectual consequences, at least
for people who care about what they are and where they are.
Martin Rees (Cambridge University, UK) presents an essay on the
near-future research expectations of cosmologists, the author
making the following points:
1) Astronomers still do not know what the Universe is made
of. Observable radiation-emitting objects -- such as stars,
*quasars, and galaxies -- apparently constitute only a small
fraction of the matter in the Universe. The vast bulk of matter
is dark and unaccounted for, and most cosmologists believe this
dark matter is composed of weakly interacting particles left over
from the *Big Bang. But dark matter could be something more
exotic. "Whatever the case, it is clear that galaxies, stars and
planets are a mere afterthought in a Cosmos dominated by quite
different stuff." The author suggests that intensive searches for
dark matter, mainly via sensitive underground experiments
designed to detect elusive subatomic particles, will continue in
the coming decade, and that within the next decade both the
amount and nature of dark matter will be clarified.
2) The author suggests that research in the near-future is
also likely to focus on the evolution of the large-scale
structure of the Universe. The current view is that ever since
the Big Bang, gravity has been amplifying inhomogeneities,
building up structures and enhancing temperature contrasts -- "a
prerequisite for the emergence of the complexity that lies around
us now and of which we're a part." The author suggests that
astronomers are now learning more about the 10 billion year
process of Cosmic evolution by creating virtual universes on
computers, and that in the coming years researchers will be able
to simulate the history of the Universe with ever improving
realism and then compare the results with astronomical
3) The author suggests that the great mystery for
cosmologists is the series of events that occurred less than 1
millisecond after the Big Bang, when the Universe was
extraordinarily small, hot, and dense. "The laws of physics with
which we are familiar offer little firm guidance for explaining
what happened during this critical period." To solve this
problem, it will necessary to improve and refine current
observations in order to understand the characteristics of the
Universe when it was only one second old: its expansion rate, the
size of its density fluctuations, and its proportions of ordinary
atoms, dark matter, and radiation.
4) The author suggests the following Cosmic timeline for the
evolution of the Universe from the Big Bang to the present:
... ... a) 10^(-43) seconds after the Big Bang: the *Quantum
Gravity Era.
... ... b) 10^(-36) seconds after the Big Bang: Probable *Era of
... ... c) 10^(-5) seconds after the Big Bang: Formation of
protons and neutrons from *quarks.
... ... d) 3 minutes after the Big Bang: Synthesis of atomic
... ... e) 300,000 years after the Big Bang: First atoms form.
... ... f) 1 billion years after the Big Bang: Appearance of
first stars, galaxies, and quasars.
... ... g) 10 to 15 billion years after the Big Bang: Appearance
of modern galaxies.
5) The author concludes: "How did a hot amorphous fireball
evolve, over 10 to 15 billion years, into our complex Cosmos of
galaxies, stars, and planets? How did atoms assemble -- here on
Earth and perhaps on other worlds -- into living beings intricate
enough to ponder their own origins? These questions are a
challenge for the new millennium. Answering them may well be an
unending quest."
Martin Rees: Exploring our Universe and others.
(Scientific American December 1999)
QY: Martin Rees, Cambridge University, UK.
Text Notes:
... ... *quasars: (quasi-stellar objects). Extremely luminous
sources radiating energy over the entire spectrum from x-rays to
radio waves, and which are apparently the oldest and most distant
objects in the universe. They are believed to involve massive
black holes.
... ... *Big Bang: The Big Bang theory is the general
cosmological model that proposes that all matter and radiation in
the universe originated in an explosion at a finite time in the
... ... *Quantum Gravity Era: Quantum field theory is the
mathematical fusion of quantum mechanics with special relativity
theory, and the term "quantum gravity" refers to the fusion of
quantum mechanics with general relativity theory. The essential
basis for these fusions is the so-called "equivalence principle",
which identifies the mass involved in the gravitational force
equation with the inertial mass in the equation that relates any
force to the product of inertial mass and acceleration. The
"quantum gravity era" is the time-frame during which both quantum
effects and gravity determined the behavior of particles.
... ... *Era of Inflation: The inflationary model, first
proposed by Alan Guth in 1980, proposes that quantum
fluctuations in the time period 10^(-35) to 10^(-32) seconds
after time zero were quickly amplified into large density
variations during the "inflationary" 10^(50) expansion of the
universe in that time frame.
... ... *quarks: A quark is a hypothetical fundamental particle,
having charges whose magnitudes are one-third or two-thirds of
the electron charge, and from which the elementary particles may
in theory be constructed.
Summary & Notes by SCIENCE-WEEK <http://scienceweek.com> 28Jan00
<For more information: [A HREF="http://scienceweek.com/swfr.htm>" TARGET=_blank]http://scienceweek.com/swfr.htm]</A>

The Hubble discovery
In the 1920s the astronomer Edwin Hubble using the new telescope at Mount Wilson Observatory was able to identify a cloud of celestial objects that clearly did not belong to our own galaxy. He then proceeded to analyze the Doppler shift of these stars and made the extraordinary discovery that they were receding from our own position in the Universe. He was also able to relate the distance between the galaxy with their relative speed measured from our own frame of reference and proved that the more distant galaxies are moving away from us more rapidly than the ones that are closer.

The Big Bang Theory

Hubble's observations clearly implied that the Universe is expanding. Galaxies are moving away from each other. The implications are immediate: whatever originated the Universe resulted in an expansion. Thinking backwards, if the Universe is expanding it must be doing so from some primordial state where and when it was not expanding. It would be difficult to conceive that the expansion started from a position in which the galaxies were initially separated by a certain distance. It is far more logical to conceive an initial instant in which all matter was infinitely close and an explosion that originated the expansion : the Big Bang.

However, things are not so simple. The above explanation is an intuitive approach to trying to guess the sequence of events that originated the Universe and it can indeed be helpful to understanding the general principle and the way scientists approached the problem, but unfortunately our conventional Newtonian logic cannot be used beyond a certain point.

As we go further back in time and we rewind an imaginary tape that shows the history of the Universe, we find that at a hypothetical time zero the Universe is infinitely contracted, there is no distance between particles, the volume is zero and the Universe is literally infinitely dense. The problem starts there. Classical physics cannot explain what goes on at that point. We enter the realm of Einstein's general theory of relativity, that envelops the special theory of relativity to include gravitational effects. In this theory we part with most of our traditional conceptions. Space and time are no longer independent magnitudes, and, according to Einstein, they are just variables or modes and not natural conditions inherent to life. The most surprising implication of the general theory of relativity when applied mathematically to the Big Bang is that time and space did not exist before the primordial instant. What we call the Big Bang is in fact the starting point for the dimensions we know that also include time. It makes no sense to talk of time or space before the singularity that we call the Big Bang.

Which was not a Big Bang at all. According to the theory, during the first second of existence the Universe was very dense and hot, and full of extremely energetic elementary stable and unstable particles. During the next instants, the unstable particles decayed away and nuclear reactions took place. After some minutes temperature had dropped enough so that no further nuclear reactions could happen.

All throughout this initial process, matter emitted and absorbed electromagnetic radiation that gradually subsided in intensity as the Universe rapidly cooled off. Thus, according to the Big Bang theory, in our present era the Universe should only emit a background cosmic radiation corresponding to very low temperatures. In 1965, Robert Wilson and Arno Penzias from Bell Laboratories managed to discover background cosmic radiation corresponding to only a temperature of only a few degrees above absolute zero, providing thus further evidence for the Big bang theory.

Another consequence of the application of the general theory of relativity that is hard to grasp is our misconception about the relative movement of the galaxies. We have already stated that the red shift observed proves that the Universe is expanding, but contrary to our most primary notion of movement, the galaxies themselves are not physically moving but instead the space between them is expanding while they remain still, thus increasing the physical distance between them. An analogy that is often used is that of points on the surface of a balloon that is being inflated. As the balloon is inflated the points do not actually move on their own. The balloon stretches out and separates them.

Discovering Zero
© Copyright 2000, Jim Loy

A friend of mine imagines (or pretends to imagine) that in ancient times zero was some kind of well-guarded secret. Some countries had this secret, and reaped the obvious benefits, and others did not.

"When you travel, don't tell any one about zero."

"He found out about zero; we will have to kill him."

"Sir, there are rumors of a number less than I."

"Preposterous. You enlisted men will believe anything."

Eventually, word got out, as with most secrets, and zero was no longer a secret. And we now use zero. This is a humorous, but slightly skewed, story.


The number systems of ancient cultures (See Egyptian Numbers and Roman Numerals Defined) normally did not have a symbol for zero. They got along fine. Their cultures had a concept like zero (none, empty, no money, etc.). But this concept was not even considered a number, just as 1/2 is not a whole number, or infinity is not a number today. But, without a zero digit, they had two problems. Their arithmetic was cumbersome, and they had difficulties representing very large numbers.

Positional notation was invented in Babylonia. It was re-invented in India. I will use modern numbers in this article. In this notation, we count this ************************ as 24 asterisks. The two (in 24) does not represent 2 at all, but 20 because of its position in the number. The four does indeed represent a four, because of its position. The three in 324 represents 300, and so on. In describing this, I have used zeros. Zero is a place holder. The zero in 4017 means zero 100's. So 4017 means 4x1000+0x100+1x10+7x1. Arithmetic becomes somewhat easier, and very large numbers are easy to represent. This notation is often called Arabic numbers (or numerals), because it was introduced to Europe by the Moslems. But it is more correctly called Hindu-Arabic numbers (or numerals).

And it wasn't a secret. It was just unknown to Europeans. And, had they known about it, they may not have seen the advantages, just as many Americans do not see the advantages of the metric system. I wonder how many centuries it took for Europe to convert to Hindu-Arabic numbers.

Reversal of Magnetization

We have theoretically traced the dynamics of the reversal of magnetization in a ferromagnetic system by solution of the nonlinear partial differential equations of motion (Landau-Lifschitz equation) for the magnetization density M(x,t).

The figure shows three snapshots taken during the reversal process in an ellipsoid with aspect ratio 4.6:1 (chosen because experimental data is available) of gamma Fe2O3. The minor radius is equal to the exchange length. The unit of time is 1/gammaMs, which is approximately 1/6 ns. No crystalline anisotropy was included in this calculation, although its inclusion is straightforward.

As the figure shows, the magnetization is initially uniformly downward. At time zero,...

In the time it takes to read this sentence…
…our universe will increase in size by 100 trillion cubic light-years — still being propelled by the unimaginable force of its explosive birth approximately 15 billion years ago.
Over half century of meticulous observation of the recession of distant galaxies has proven beyond doubt that this expansion is occuring. Bolstered by discoveries in both astronomy and quantum physics, research is now beginning to probe the moment of creation — dubbed the Big Bang — which has hurled cosmic matter outward with such force that it is still flying away to this day.

For many years it was assumed that whatever produced the Big Bang would remain a "singularity" — something forever inscrutable. Theoreticians and scientists think they have found one plausible explanation for the creation of all that we know exists.

ZERO... (The missing Time Element in the Gregorian Calander) 07/1997

The debate over when the new millennium begins is by now a familiar one, and involves, as everyone knows, a missing year. But why was the year missing in the first place? The answer has to do with the belated invention of an essential number

by Dick Teresi
When does the new millennium begin -- in 2000 or 2001? The public has voted with its checkbooks for the former. The Fairmont Hotel in San Francisco has fielded numerous calls to reserve rooms for the evening of December 31, 1999 -- and precious few for December 31, 2000. The story is the same at the Palmer House in Chicago, and at the Plaza in New York City.

<This message has been edited by Time02112 (edited 21 August 2000).>
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