Program Notes
Guest speakers: Terence McKenna, Ralph Abraham, and Rupert Sheldrake
(Minutes : Seconds into program)
01:23 Ralph Abraham: A short primer on chaos theory… . The emergence of form from a field of chaos.
08:57 Rupert Sheldrake:
“The problem I have with chaos theory … ” The issue of indeterminacy in the real world… . The illusion of total predictability… . Indeterminacy may exist not just at the quantum level but at all levels of natural organization… . How form arises from chaos… . In some sense, energy may be seen as an agent of change.
21:24 Rupert:
The question of how do new fields, new forms, come into being in the first place? Where do they come from? … The nature of the mathematical realm, the formative realm. Is there a kind of mathematical realm before the universe, somehow beyond space and time. [lozo: he goes on a kind of Olaf Stapelton riff] …
26:04 Rupert:
“The view that I want to consider is that the world soul, or the world imagination, makes up these forms as it goes along, that there isn’t, out there, a kind of mathematical mind already fixed or already full.”
28:40 Ralph:
“I think that with mathematics we can make a model for anything.” … “Mathematics could be regarded simply an extension of language… . Words, I think, are frequently inadequate.”
34:18 Ralph:
“But the truth is this theory can be used to model everything. So it never settles any questions as to the origin of things or the true nature of ordinary reality.”
37:40 Rupert:
“Are the fields of reality more real than the models we use to model them with. Or is there a kind of mathematics yet more fundamental the fields?”
38:57 Ralph:
What mathematics means to me … a description of the mathematical landscape… . “Mathematics is the supreme tool for the extension of our language for dealing with complex systems.”
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061 - Creativity and Imagination (Part 2)
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Transcript
00:00:00 ►
Greetings from Cyberdelic Space.
00:00:19 ►
This is Lorenzo, and I’m your host here in the Psychedelic Salon.
00:00:23 ►
Today’s program is a continuation of the
00:00:26 ►
series of trilogues held between Terrence McKenna, Ralph Abraham, and Rupert Sheldrake at Esalen in
00:00:32 ►
September of 1989 and again in 1990. So far the trilogues, I guess that’s probably not a real
00:00:40 ►
word, but it does have a nice ring don don’t you think? The Trialogers.
00:00:48 ►
Anyway, in the first podcast of this series,
00:00:53 ►
the Trialogers gave us a brief glimpse of their backgrounds and how they came together.
00:00:55 ►
And that was in our podcast number 58.
00:01:01 ►
We then heard tape one of the series, which was titled Creativity and Imagination.
00:01:07 ►
Now we move on to the first side of tape two, which is titled Creativity and Chaos.
00:01:11 ►
And we begin with Ralph Abraham’s short introduction to chaos theory.
00:01:17 ►
And then we’ll get into a discussion between Ralph and Rupert of why what is, is.
00:01:19 ►
Or something like that.
00:01:22 ►
Let’s join Ralph and Rupert now.
00:01:27 ►
Now it’s a little presumptuous to call this chaos theory,
00:01:29 ►
because as a matter of fact, there is no theory.
00:01:31 ►
We’re in the exploration phase now,
00:01:36 ►
and this is experimental mathematics that we are doing with supercomputers.
00:01:46 ►
But I think it might help if you had just a little idea of chaotic dynamics and the idea of the thing.
00:01:53 ►
So I want to give a two or three minute primer so that you could understand what is a chaotic attractor.
00:01:56 ►
And now we’ve seen 16,000 of them.
00:01:58 ►
What does one look like?
00:02:06 ►
And that will conclude my introduction and then I’ll pass them on to Rupert.
00:02:14 ►
A good laboratory for the study of chaotic dynamics is the dripping faucet.
00:02:20 ►
And the dripping faucet was discovered as the ideal demonstrator for chaos theory because the lectures are usually given in a physics lecture hall,
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and they always seem to have a sink with a faucet in the front
00:02:29 ►
to do experiments or for the professor to wash the chalk off his hands.
00:02:34 ►
Anyway, you take the faucet.
00:02:36 ►
You can do this immediately you get home.
00:02:38 ►
You crack the tap a little bit, and the water drips out,
00:02:42 ►
drip, drip, drip, and it’s regular.
00:02:45 ►
If you crack a little more, then the water drips out, drip, drip, drip, and it’s regular. If you crack a little more, then the drips speed up, but they’re regular.
00:02:51 ►
And then you crack it a little more, and then it begins to sound,
00:02:55 ►
drip, drip, drip, like rain dripping off the roof.
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That’s an example of a chaotic time series.
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If you measure the time between drops and make a list of these numbers,
00:03:08 ►
you have the paradigmatic case of a chaotic time series.
00:03:14 ►
Now, somebody decided to seriously study this dripping faucet
00:03:18 ►
after seeing it in half a dozen physics lectures.
00:03:22 ►
This person, Rob Shaw, one of the leading people in chaos
00:03:25 ►
theory, did a very fine study by placing a microphone in the sink where the drop
00:03:31 ►
would hit it, getting an electronic beat, just discretizing, getting it in the
00:03:36 ►
computer, and analyzing the results. And so all of this is taking place on that level one, the lowest layer of the physical world.
00:03:49 ►
Then he made a mathematical model on level three. He went up there, he made a mathematical model for the water drop gets bigger and bigger,
00:03:57 ►
so it’s characterized by a certain mass. When the mass reaches a critical value, the drop falls off. And from this mathematical model, he then wrote a program, a computer program, on level two and ran it and produced data that was exactly like the experimental data from level one.
00:04:13 ►
So this is an example showing the value of modeling on these three levels for gaining some understanding.
00:04:21 ►
There’s sort of a hermeneutical circle. You look at the data, try to build a model, you fail.
00:04:28 ►
But building the model tells you to observe in a different way.
00:04:31 ►
You observe in this different way.
00:04:33 ►
That helps you to build a better model.
00:04:35 ►
And as this circle turns, the level of our understanding grows.
00:04:41 ►
So Rob Shaw came quickly to a good model for this
00:04:45 ►
I think he was lucky because it sounds simple
00:04:47 ►
it’s a very complicated system
00:04:49 ►
it relates to waterfalls for example
00:04:53 ►
when the spray comes off the waterfall
00:04:54 ►
here’s another example of a chaotic system
00:04:57 ►
could you write some equations and obtain a computer program
00:05:01 ►
that simulated the spray from a waterfall
00:05:04 ►
I doubt it.
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The new way of looking at the data
00:05:09 ►
that came to him from the theory
00:05:12 ►
was to take the sequence of numbers,
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the time between drops,
00:05:17 ►
you just visualize a column of numbers,
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and you make a carbon copy of it
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and move it over to the side.
00:05:29 ►
And then you whack one number off the top and move it all up one number.
00:05:31 ►
Now you have a series of pairs,
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and then you plot these pairs on the plane as a set of points.
00:05:37 ►
So he did this.
00:05:42 ►
There’s a film or video available for aerial press that shows the machine actually doing this.
00:05:44 ►
And from this totally chaotic data, viewed in this particular way, which is called chaoscopy,
00:05:50 ►
you get these points in the planes that if the data was really random,
00:05:56 ►
the dots would be all over the plane.
00:05:58 ►
Instead, they lie on a curve, a smooth curve.
00:06:02 ►
So from the observation of the data in this way, the smoothness
00:06:06 ►
of the curve suggests a kind of model that you can actually take off the shelf
00:06:10 ►
in the building where the chaos theorists are working and apply it to your data, you
00:06:16 ►
see. And the simplest model on the shelf of the chaos theorists closet is called
00:06:22 ►
the logistic equation. It produces a series of numbers
00:06:26 ►
that are apparently random,
00:06:27 ►
but actually they comprise
00:06:29 ►
one of these simple geometric figures,
00:06:33 ►
this curve that the data plotted
00:06:35 ►
in this special way of the chaos guilt
00:06:37 ►
is a curve,
00:06:38 ►
and that is called the chaotic attractor.
00:06:41 ►
So there are models on level three
00:06:44 ►
which are good models for understanding certain behavior on level 1.
00:06:50 ►
And level 2 is an intermediary which can either create the mathematical model from the real data
00:06:59 ►
or create experimental data from the model to compare with laboratory data.
00:07:07 ►
Well, to conclude, this video was made out of these simplest possible dynamical systems called the logistic equation.
00:07:15 ►
And it just produces a series is we have 16000 dripping faucets in an array of 128 by 128.
00:07:30 ►
And the time between drops is represented as a color on the screen.
00:07:36 ►
Now, do you think that if you had 16000 dripping faucets, you could get out of them a pattern like calico mountain now well it happens I mean it’s there’s a lot of
00:07:51 ►
theory behind this enough to suggest that it’s not some kind of artifact no
00:07:55 ►
matter what kind of artifact it is it’s an interesting artifact and I guess I’d
00:08:03 ►
like to call this a mathematical law.
00:08:06 ►
It has to do with the emergence of form from a field of chaos.
00:08:10 ►
We don’t know what else to call it.
00:08:11 ►
It’s not a mathematical law that was known to Pythagoras.
00:08:15 ►
And I don’t know if it was always there since the beginning of time, long before the Big Bang,
00:08:20 ►
or if it just emerged into the evolving field of the guy in mind
00:08:26 ►
through the fact that computers make it visible.
00:08:28 ►
I mean, I don’t know.
00:08:29 ►
But at this point, I hope arrived at an actual connection
00:08:38 ►
between the work I routinely do as a specialist in the field of chaos
00:08:43 ►
and the discourse that we’re trying to carry on here
00:08:48 ►
to increase our understanding of our past, our future,
00:08:52 ►
and our possibility of even having a future.
00:08:56 ►
The problem I have with chaos theory is that I’m never quite sure what it’s saying.
00:09:02 ►
There seem to me to be two things that are of interest
00:09:05 ►
here. One is that the actual detailed models which chaos theoreticians make, and they love
00:09:14 ►
finding fairly simple equations that will generate complicated and seemingly chaotic
00:09:19 ►
structures. And so there’s this modelling aspect of chaos
00:09:26 ►
which is at the forefront of modern mathematical chaos theory and modelling
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but the fact you can make mathematical models of chaos
00:09:36 ►
has given scientists permission to recognise that in fact
00:09:40 ►
there’s a vast deal of indeterminacy throughout the physical world.
00:09:45 ►
In the 19th century, it was generally believed that there was no indeterminacy at all.
00:09:50 ►
Everything in the physical world was totally conditioned by eternal laws of nature.
00:09:54 ►
Laplace thought that the whole future and past of the universe could be calculated from its present state
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if there were a mind powerful enough to do the calculations and to make the observations.
00:10:04 ►
if there were a mind powerful enough to do the calculations and to make the observations.
00:10:15 ►
Now, that view, the illusion of total predictability, held science under its spell for generations.
00:10:20 ►
Scientists were dazzled by this imagined power of totally predicting everything.
00:10:24 ►
And it was a kind of illusion. They really did believe it. And, of course, they couldn’t calculate everything. And it was a kind of illusion. They really did believe it. And
00:10:25 ►
of course they couldn’t calculate everything. I mean, they still can’t even calculate the
00:10:30 ►
weather very accurately more than a few days in advance. So in actual fact, this idea of
00:10:38 ►
total predictability was not realisable. But the idea was, well, we would, if we could do enough calculations,
00:10:46 ►
be able to calculate it in principle.
00:10:51 ►
What seems to me interesting is the fact that first with quantum mechanics,
00:10:54 ►
there was a recognition that indeterminacy, probability,
00:11:00 ►
intrinsic non-detailed predictability
00:11:03 ►
were inherent in small-scale physical processes at the quantum level.
00:11:08 ►
And here was a genuine indeterminism in nature which had to be admitted in 1927.
00:11:15 ►
Until then, practically everyone believed everything was fully determinate.
00:11:20 ►
After that, there’s been a gradual recognition that indeterminacy exists not just at the quantum level, but at all levels of natural organization.
00:11:29 ►
There’s an inherent spontaneity, indeterminism, probabilism in the weather, in the breaking of waves, in turbulent flow, in nervous systems, in living organisms, in biochemical cycles, in a whole range of phenomena.
00:11:47 ►
Even the old-time favorite model for total rational mathematical order, namely the orbits of the solar system,
00:11:54 ►
the orbits of the planets in the solar system, turn out to be unpredictable in terms of Newtonian physics.
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They can be modeled in a chaotic manner.
00:12:06 ►
Anyway, this indeterminism is being recognized at all levels of nature.
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So there’s the idea that what we can model with old-style physical models
00:12:14 ►
is an abstraction from a very small number of idealized cases,
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that the natural world simply escapes most of the modeling processes
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which were the dominant features of traditional physics.
00:12:28 ►
Now it seems to me this openness of nature, this indeterminism, this spontaneity, this freedom,
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is something very interesting, and it corresponds to the intuition of chaos in its intuitive and mythological sense.
00:12:43 ►
Mathematicians have used this word chaos
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in a variety of technical senses and it’s not entirely clear to me how these
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technical models of chaotic systems correspond to the kind of intuitive
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notion of chaos. But what I want to do is to consider how form arises from chaos, starting from a simple, intuitively obvious way
00:13:09 ►
in which more form appears from less,
00:13:13 ►
through familiar physical processes.
00:13:16 ►
And I’m thinking of the process of cooling.
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If you start with something at a very, very high temperature,
00:13:22 ►
atoms can’t exist.
00:13:24 ►
The electrons fly off the nuclei, and you get something called a plasma, which is a sort of soup of
00:13:29 ►
atomic nuclei and electrons in a kind of gas. There’s no longer individual atoms. The whole
00:13:36 ►
thing, they disintegrate into a mélange, a mixture of their component parts, the plasma,
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a mixture of their component parts, the plasma, which has its own kinds of properties.
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If you cool these plasmas down, when you reach a certain temperature,
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it’s low enough for atoms to form, and atoms begin to come into existence.
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Electrons start circulating around nuclei.
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You get atoms forming. You get a gas of atoms.
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But the temperature is still too high for any molecules to form.
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And say it’s a hydrogen plasma and you cool it down, you’ll get hydrogen atoms.
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But you won’t yet get any hydrogen molecules.
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Cool it down further. Now you get hydrogen molecules.
00:14:18 ►
You cool the system down further and you get a stage where more complex molecules can come into being.
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But they’re still gaseous.
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Cool it down further and they turn into a liquid
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which has more form, can form drops and flare around
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and has quite complex ordered arrays of molecules within it.
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Cool it further still and you get a crystal
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which is an extremely highly regularly ordered formal arrangement
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of the atoms and the molecules.
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So you get a progressive increase in complexity of form as you lower the temperature.
00:14:52 ►
And in traditional kinetic theory, lowering temperature means less random kinetic motion of the particles. So you’re getting a cooling down and an increase in complexity of
00:15:07 ►
form as the cooling process takes place. Now, we all know from the cooling of steam into water,
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the cooling of water into ice, that we know about this process from everyday experience. We’ve seen
00:15:22 ►
this aspect of it, and we’ve seen how if you cool water
00:15:25 ►
vapor down you get ice crystals emerging and these ice crystals have a considerably high degree of
00:15:31 ►
order. So there’s this formative process which we see through cooling occurs as the thermal chaos
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in the ordinary sort of everyday sense of chaos is reduced because as cooling happens,
00:15:46 ►
more form emerges. The opposite happens if you warm things up. If you warm up snowflakes,
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they first turn into water, then they turn into steam, then the steam, the water vapor disintegrates
00:15:57 ►
into the molecules break up into atoms, then those break up into a plasma as you raise the
00:16:03 ►
temperature. So there seems to be an inverse relationship between temperature,
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which is this highly agitated motion of things,
00:16:10 ►
essentially chaotic in the traditional theory of gases and plasmas,
00:16:15 ►
and an increase of form when things cool down.
00:16:19 ►
Now, in a sense, that’s what has happened, according, in the entire universe.
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We’re led to believe that the universe started off exceedingly hot,
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billions of billions of degrees centigrade,
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so hot that stable forms were not able to emerge.
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By expanding, it cooled down.
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The cooling process of the universe is associated with expansion.
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The cosmic expansion both creates more space in which new forms can appear,
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and by making bigger gaps between things, somehow cools the universe down,
00:16:53 ►
so the temperature drops.
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And as the temperature drops in the developing universe, according to standard models,
00:16:58 ►
more and more form comes into being.
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First you get atoms, then stars and galaxies condense,
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then you get solar systems
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and through the cooling of matter you can get
00:17:08 ►
planets. The planets are the
00:17:10 ►
cooled remnants of exploding stars.
00:17:12 ►
The elements in us and in our planets
00:17:14 ►
are stardust formed from
00:17:16 ►
supernovae. So
00:17:17 ►
there’s a cooling down of these things
00:17:20 ►
that came from immensely hot sources.
00:17:22 ►
Then you can get rocks forming
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crystals.
00:17:30 ►
And in a sufficiently cool planet, and yet a sufficiently warm one,
00:17:32 ►
within a fairly narrow range of temperature,
00:17:35 ►
you can have the evolution of life as we have had on Earth.
00:17:42 ►
So this appearance of forms comes out of an initial state where these forms are not present and they appear through a kind of cooling.
00:17:46 ►
There’s a formative process going on.
00:17:49 ►
And we can call this one way of looking at the emergence of form from chaos or disorder.
00:17:56 ►
Well, how do these forms come into being?
00:18:00 ►
This is the big problem of evolutionary creativity.
00:18:03 ►
How do the first molecules, how did
00:18:05 ►
the first zinc atoms come into being? How did the first methane molecules, how did the first salt
00:18:09 ►
crystals, how did the first living cells, how did the first vertebrates, how did the first of
00:18:15 ►
anything come into being in this evolving universe as it expanded and cooled? Well,
00:18:20 ►
expanded and cooled.
00:18:26 ►
Well, one way of looking at this is to see the expansion and cooling process
00:18:29 ►
and indeed the flow of events
00:18:32 ►
as being, thinking of it in terms of the flux of energy.
00:18:37 ►
And one of the great unifying concepts
00:18:39 ►
of 19th century physics
00:18:40 ►
is a unified conception of energy.
00:18:43 ►
Now, it’s not entirely clear what energy is. Energy,
00:18:47 ►
in some sense, is the principle of change. The more there is, the more change that can be brought
00:18:51 ►
about. It’s, in a sense, a causative principle. And it’s a causative principle which exists in a
00:18:58 ►
process. In this process, the energetic flux of the universe underlies time, change, becoming,
00:19:08 ►
and the flux process itself seems to have an inherent indeterminism to it.
00:19:15 ►
This flux process, the universal flux, is organized into forms by fields.
00:19:23 ►
Matter is now thought of as energy bound within fields,
00:19:27 ►
the quantum matter fields and the fields of molecules and so on. And I think there are
00:19:32 ►
many of these organizing fields, the morphic fields. And the fields are somehow organizing
00:19:37 ►
the ongoing flux of energy, which is always associated with this spontaneity and chaotic qualities.
00:19:46 ►
So even organized systems of a high level of complexity
00:19:49 ►
still have this probabilistic quality.
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The fields that organize this energy to give rise to material and physical forms
00:19:57 ►
are themselves probabilistic.
00:19:59 ►
Chaos is never eliminated.
00:20:01 ►
There’s always this indeterminism or spontaneity at all levels of organization. So there’s a formative principle, which is the fields, and there’s an energetic
00:20:09 ►
principle, which I think has the chaos inherent in it. It’s a kind of change which left as pure
00:20:16 ►
change would be chaos. One way of thinking of these is in terms of the Indian notion of shakti
00:20:23 ►
as the energy indeterminate principle, and shi as the energy and determinant principle,
00:20:25 ►
and Shiva as the formative principle,
00:20:27 ►
working together in a kind of tantric union to give the world that we know.
00:20:33 ►
Now, if there’s this formative principle that comes through the fields of nature,
00:20:39 ►
then one of the questions is, how do fields operate?
00:20:43 ►
How are these fields governed?
00:20:45 ►
How do they have the forms, shapes, and properties they do?
00:20:49 ►
Well, I think that the organizing fields of living organisms,
00:20:54 ►
of crystals, of molecules, and so on,
00:20:57 ►
are organized by, I think that they are what I call morphic fields,
00:21:01 ►
and that these fields contain an inherent memory,
00:21:04 ►
so that these fields contain an inherent memory, so that
00:21:05 ►
these fields are essentially habitual, and nature is the theatre of these habitual fields
00:21:11 ►
organising the indeterminate flux of energy. Fields themselves, by having this energy within
00:21:17 ►
them, have this indeterminate quality too. But this then brings us to the question of
00:21:22 ►
creativity. How do new fields, new forms, come into being in the first place? Where do they come from?
00:21:44 ►
and some kind of formative unifying,
00:21:49 ►
some kind of unifying aspect of the cosmic mind,
00:21:55 ►
which Ralph has hijacked for the Pythagorean sect by calling the realm of mathematics.
00:22:00 ►
There’s an interaction here between these two levels,
00:22:04 ►
giving the world of becoming that he’s shown by the wiggly line in the middle.
00:22:11 ►
Well, this is one way of looking at it.
00:22:15 ►
And this brings us back to the question of the nature
00:22:18 ►
of what he calls the mathematical realm, this sort of formative realm.
00:22:22 ►
the mathematical realm, this sort of formative realm.
00:22:28 ►
Is there a kind of mathematical realm before the universe, somehow beyond space and time altogether
00:22:31 ►
which conditions all forms of creativity,
00:22:34 ►
all patterns and possible systems of organization
00:22:38 ►
that can come into being with the world?
00:22:42 ►
Or are these all made up as the evolutionary process goes along?
00:22:46 ►
These are questions we’ve already touched on this morning.
00:22:51 ►
I myself think that
00:22:53 ►
if we take the view of things coming into being as evolution goes along,
00:23:01 ►
if we think of the cosmic, the soul of the world,
00:23:04 ►
as having a kind of
00:23:05 ►
imagination, we can think of these as coming into being as nature goes along,
00:23:10 ►
and we can see this imagination as having many levels. There’d be a kind of
00:23:14 ►
cosmic imagination, which would be the soul of the world, the anima mundi, the
00:23:20 ►
soul of the universe, a cosmic mind, soul, and imagination. Within that, there’d be
00:23:26 ►
clusters of galaxies, each of which would have their own mind, soul, or imagination. Then there’d
00:23:31 ►
be galactic ones, then ones for solar systems, then one for planets, then ones for ecosystems,
00:23:36 ►
then ones for societies of organisms and individual organisms, organs, tissues, and so on.
00:23:48 ►
organisms, organs, tissues, and so on. There’d be many levels of organizing soul. I think these morphic fields could be regarded as an aspect of the souls of systems at different levels of being.
00:23:55 ►
Then there’d be the possibility of a whole range of imaginations, that we don’t have to leap
00:24:01 ►
straight from what’s happening in a social insect colony
00:24:05 ►
or in an animal or a plant or in a social system,
00:24:09 ►
a human social system, straight to the divine imagination
00:24:14 ►
or the mathematical mind of God or the transcendent realm of mathematics.
00:24:18 ►
There’s a whole level of imaginations in between,
00:24:20 ►
a whole level, and within the earth we’re embedded within the solar system
00:24:25 ►
with its own particular kind of soul and imagination, and that within the galaxy.
00:24:30 ►
So there’d be a whole set of levels at which creativity could come forth from souls with
00:24:38 ►
imaginations.
00:24:40 ►
Now, I think the difference that we might have to consider between all this and the traditional doctrine of the world soul
00:24:48 ►
is that in the traditional doctrine of the world soul, of Plotinus and of Plato,
00:24:55 ►
they had a threefold system where there was the intellect, with the intelligence,
00:25:01 ►
which was really the realm of forms or ideas or the logos.
00:25:06 ►
intelligence, which was really the realm of forms or ideas or the logos. And embedded within that was the world soul, which had as its characteristic an attractor. The world soul had space and time
00:25:13 ►
within it and was concerned with the realm of becoming, namely the cosmos, not with the realm
00:25:19 ►
of being, which was the realm of these pure forms. And as the prototype of the cosmos, the world soul
00:25:25 ►
had this cosmic attractor as its intellikey, its goal. And this was a striving towards
00:25:31 ►
the eternal perfection of the divine. And then within the world soul, there were hosts,
00:25:37 ►
hierarchical levels within levels of souls of all the different systems within the universe,
00:25:43 ►
of souls of all the different systems within the universe,
00:25:47 ►
each of which had its own autonomous existence.
00:25:53 ►
A holistic or holarchic vision of souls within souls.
00:25:59 ►
The view that they had was that the qualities of the world soul were all fixed by the eternal forms,
00:26:02 ►
the eternal mathematical mind.
00:26:04 ►
The view that I want to consider is that the world soul or the world imagination
00:26:09 ►
makes up these forms as it goes along,
00:26:11 ►
that there isn’t out there a kind of mathematical mind already fixed, already full,
00:26:18 ►
that what we do is make mathematical models of various aspects of nature.
00:26:23 ►
And I think that one thing that happens then
00:26:28 ►
is these models can be projected
00:26:30 ►
as if they’re a real thing out there,
00:26:33 ►
as if the world soul is engulfed
00:26:35 ►
within a kind of eternal mathematical mind.
00:26:37 ►
That may just be a projection of ours.
00:26:39 ►
The world soul may have an autonomy.
00:26:42 ►
It may be no more mathematical
00:26:43 ►
than our own souls are when we’re dreaming.
00:26:46 ►
I mean, there are certain numbers and numerical forms come into dreams,
00:26:50 ►
but there’s no sense when we’re dreaming
00:26:52 ►
that these dreams are being generated by equations
00:26:54 ►
or that they’re essentially mathematical in structure.
00:26:59 ►
So what I’m suggesting is that the world soul may have an autonomy to it.
00:27:05 ►
It may have a kind of mathematical realm as part of it.
00:27:08 ►
But if we think of it as having its relation to mathematics
00:27:12 ►
and its relation to the creation of form,
00:27:14 ►
the ordering of chaos into patterns and forms and structures,
00:27:18 ►
then this mathematical aspect of it may evolve along with nature,
00:27:23 ►
just as our own understanding of mathematics evolves in time.
00:27:32 ►
Well, I think that
00:27:35 ►
we are talking about
00:27:39 ►
complicated things, complex, obtuse and difficult ideas, and we’re talking about them in a language which
00:27:50 ►
seems more or less appropriate. So as you speak, I get an idea, I get a picture. I mean,
00:27:55 ►
for me, it’s frequently a picture. And I don’t see that mathematics is substantially different from verbal description as a strategy for making models.
00:28:08 ►
I mean, certainly, if you talk about Plotinus, for example, we have really, you described a geometric, a visualizable model for the all and everything including within it the world
00:28:28 ►
soul and so on if we draw that as a picture instead of a word picture then
00:28:34 ►
that’s officially mathematics that’s geometry that’s a geometric model for
00:28:38 ►
the thing I think that with mathematics we can make a model for anything. And if you think there’s a Big Bang, we can make a model for that.
00:28:48 ►
And if you think that there are three sexes on the moon,
00:28:53 ►
then we can make a model for that.
00:28:55 ►
So mathematics could be regarded as simply an extension of language.
00:29:01 ►
It’s not that mathematical laws describe the universe. I mean, it’s true that that’s the old paradigm. But I’m thinking that mathematics is a particularly good language for describing, discussing, imagining things that are really complicated.
00:29:23 ►
discussing, imagining things that are really complicated.
00:29:26 ►
And the more complex, the more structured,
00:29:29 ►
the more difficult to engulf in our minds,
00:29:32 ►
the more appropriate mathematics might be,
00:29:34 ►
or maybe music might be.
00:29:37 ►
But words, I think, are frequently inadequate.
00:29:42 ►
They have evolved, our language has evolved, through the necessity of sharing our experience on a level of complexity which is more or less traditional,
00:29:51 ►
and which is inadequate to understand the whole world or the world soul or the ecosystem, the biosphere of planet Earth or something.
00:29:59 ►
So mathematics has only a little more magic than language.
00:30:06 ►
And we could say, well, the conservation of energy,
00:30:08 ►
that’s a verbal description of something that you could also say mathematically.
00:30:14 ►
So I think that your maligning mathematics in this way is unjustified.
00:30:21 ►
And I guess I’ve been quoted in the chaos book
00:30:24 ►
as saying that chaos theory is the biggest thing since the wheel
00:30:27 ►
well I believe that
00:30:29 ►
I also think the wheel was a really big thing
00:30:32 ►
but on the other hand I’ve been quoted as saying
00:30:35 ►
that chaos theory is no big deal
00:30:38 ►
so whatever you say I agree with you
00:30:41 ►
but
00:30:44 ►
I mean about determinism,
00:30:48 ►
if I could reply to that,
00:30:50 ►
it’s a long time ago,
00:30:51 ►
but you said you had a complaint
00:30:52 ►
about chaos theory,
00:30:53 ►
about determinism and prediction.
00:30:56 ►
And there are two or three reasons
00:31:01 ►
why chaos theory is good for you.
00:31:04 ►
One thing is, if you accepted chaos theory
00:31:07 ►
as a way of modeling anything that we’re interested in,
00:31:10 ►
which personally I don’t,
00:31:12 ►
not by itself, it’s too simple,
00:31:14 ►
then it’s still good for you
00:31:17 ►
because according to chaos theory,
00:31:20 ►
prediction and determinism are impossible.
00:31:23 ►
Even though it uses the language
00:31:24 ►
that the
00:31:25 ►
deterministic thinkers used, when you look into the technical details of it, prediction
00:31:30 ►
is impossible. You only get a sort of a probabilistic something or other. Secondly, the models for
00:31:37 ►
anything that you want to talk about, such as cooling, is a good one. They don’t come
00:31:42 ►
from chaos theory. They come from bifurcation theory.
00:31:45 ►
And that is really good for you, because bifurcation theory exemplifies the best in mathematics.
00:31:52 ►
The most it can possibly do for you is rule out a lot of possibilities that you might
00:31:57 ►
imagine might happen, and then the mathematics says, well, no, according to the assumptions
00:32:02 ►
that you said you believed, then all this won’t happen, only this.
00:32:05 ►
And then you get a list of three or four of these so-called bifurcations.
00:32:09 ►
They’re the only things you’re going to expect to see in any system which is well modeled
00:32:14 ►
by the theory where these models come from.
00:32:20 ►
So when you have cooling, then you have, let us say, a control knob where you’re turning down the heat under the pan,
00:32:26 ►
and the boiling is gradually subsiding to simmering, which is subsiding to a little bit of waving, which is subsiding to nothing.
00:32:34 ►
Then we have at each stage, coming from the mathematics, a model which has attractors, which has maybe chaotic attractors.
00:32:43 ►
But every time you change the knob, you get a
00:32:46 ►
different model. And therefore, if you can’t predict how the knob is going to change,
00:32:52 ►
the models don’t give any prediction at all, and they’re irrelevant. And the only interesting thing
00:32:57 ►
is that the theory can tell you certain transformations you’ll expect and others not. For example, Terence had pointed to the punctual
00:33:07 ►
aspect of evolution, that many transformations are saltatory, they are catastrophic, they are abrupt.
00:33:14 ►
And here the theory comes in and says, in models of this type, in this theory, most of the
00:33:19 ►
transformations are abrupt. And they have kind of a theory Y, which is a geometrical model,
00:33:25 ►
which is only of use to those people who are thinking of the structure of the theory
00:33:30 ►
as opposed to what is happening in the ordinary world.
00:33:34 ►
So this bifurcation theory is good for you, and it gets rid of all, if chaos theory wasn’t enough,
00:33:40 ►
that says determinism is impossible, using mathematical models, forget it.
00:33:45 ►
Then we don’t even think those models are appropriate anyway.
00:33:49 ►
Instead, you have these models that are changed by a parameter,
00:33:52 ►
which experience bifurcations.
00:33:56 ►
We have a very good encyclopedia of bifurcations,
00:33:59 ►
and those are good models for sudden changes.
00:34:02 ►
As, for example, in the emergence of form. As, for example, in the emergence of form,
00:34:05 ►
as, for example, in the Neolithic revolution,
00:34:08 ►
as, for example, in the crystallization of the planets,
00:34:11 ►
of the stardust.
00:34:13 ►
So that’s the good news.
00:34:17 ►
But the truth is that this theory can be used to model everything,
00:34:21 ►
so it never settles any question
00:34:24 ►
as to the origin of things or
00:34:26 ►
the true nature of the ordinary reality. And therefore it’s worthless. What’s good about
00:34:32 ►
it, like language, is it’s good for communication, it’s good for a certain feeling of understanding
00:34:39 ►
and gaining comfort in a new environment, because modeling is part of our basic process of grokking.
00:34:50 ►
And always the models are no good.
00:34:53 ►
They’re no good as models,
00:34:55 ►
but they’re good for the growth of understanding,
00:34:59 ►
the evolution of understanding.
00:35:04 ►
Well, I mean, you put the whole case impressively and modestly, in the sense that
00:35:11 ►
you’re claiming that mathematicians are making models. Here’s a new range of models. I mean,
00:35:18 ►
it’s like before there were only mechanical instruments, and now we’ve got electronic
00:35:23 ►
instruments. A whole new category of models have come onto the market.
00:35:27 ►
And we can look forward to more models in the future.
00:35:31 ►
And there’ll be the latest, the 1990 model will soon be out.
00:35:36 ►
We’ve got this ongoing evolutionary system of mathematical models
00:35:40 ►
which enable us to model various aspects of reality.
00:35:42 ►
This seems to me an eminently modest claim.
00:35:46 ►
But I suspect there’s more in the background.
00:35:49 ►
Because, at least there is for some people,
00:35:52 ►
because the traditional assumption is that these models correspond to something.
00:35:56 ►
The reason why they work is because there’s some aspect of nature
00:35:59 ►
to which they mysteriously relate.
00:36:02 ►
And that aspect of nature is, in essence, mathematical,
00:36:05 ►
which is why mathematical modelling is possible.
00:36:08 ►
Now, this seems to me the interesting question.
00:36:11 ►
Why mathematical models work in certain areas?
00:36:14 ►
There are large areas where they don’t work and they aren’t used.
00:36:17 ►
And maybe they could be used and they could work.
00:36:20 ►
But I’m often meeting mathematicians or physicists who say
00:36:24 ►
quantum physics is the most brilliant predictive system that mankind has ever known.
00:36:28 ►
It predicts things to the 25 places of decimals, and it’s obviously correct.
00:36:34 ►
Well, as an agricultural scientist when I was working in India, you know, predicting the outcomes of my crop experiments,
00:36:41 ►
there was nobody who could predict those. And those experiments were
00:36:46 ►
I mean
00:36:47 ►
vast distance beyond the
00:36:49 ►
capabilities of any
00:36:51 ►
physical, quantum
00:36:54 ►
physical modelling process or anything
00:36:56 ►
based on the so-called fundamental principles
00:36:58 ►
of physics.
00:36:59 ►
You can produce sort of
00:37:02 ►
string and sealing wax models
00:37:04 ►
for crop production,
00:37:05 ►
and we had people doing that, and we had a computer,
00:37:08 ►
and there were these simple models.
00:37:12 ►
But it wasn’t that they didn’t seem to me to be pointing towards
00:37:16 ►
a convincing demonstration that the whole thing depended on a hidden mathematical order.
00:37:21 ►
There were phenomena going on.
00:37:23 ►
Some of them mathematicians have
00:37:25 ►
modelled fairly well, others there’s huge areas of reality that are hardly modelled
00:37:29 ►
at all yet. But the question is, is it that mathematical models
00:37:36 ►
somehow fix on features of the fields of reality? Are the fields of reality more
00:37:42 ►
real than the models we use to model them with?
00:37:45 ►
Or is there a kind of mathematics yet
00:37:47 ►
more fundamental than the fields?
00:37:50 ►
Is the electromagnetic
00:37:51 ►
field, the magnetic field for example,
00:37:54 ►
the north and south poles of the magnet,
00:37:56 ►
is that field polar
00:37:57 ►
in the sense it has a north pole and a south
00:38:00 ►
pole? It clearly has a polarity.
00:38:02 ►
And is the electromagnetic field
00:38:04 ►
polar in
00:38:05 ►
electric charge as well as positive
00:38:07 ►
and there’s negative charges
00:38:09 ►
these polarities we find inherent for example
00:38:12 ►
in the electrical and magnetic fields
00:38:13 ►
are those because there’s some kind of
00:38:15 ►
Pythagorean 2 system or duality
00:38:18 ►
in some archetypal
00:38:20 ►
realm beyond nature that’s
00:38:21 ►
reflected in everything that happens in nature
00:38:23 ►
or is that just the way fields are and that when we look at lots of fields we make
00:38:28 ►
an abstraction and we make conscious in a mathematical model something which is
00:38:32 ►
inherent in the nature of the organizing fields of reality but which doesn’t
00:38:36 ►
exist in some transcendent mathematical realm well you could ask different
00:38:41 ►
mathematicians and get different answers. I’ll give you mine.
00:38:49 ►
And other mathematicians would say it doesn’t count because I’m not a mathematician.
00:38:53 ►
And this answer, in fact, is the proof of that.
00:39:10 ►
But I think that for me, mathematics is a beautiful landscape, an alternate reality, and there’s infinite possibilities not yet loomed into view,
00:39:17 ►
not seen, but I suppose they exist. It’s just a fantasy. And there may be other parts which don’t exist, but they’ll be created by the efforts of people such as myself who just go there all the time and hang out there and
00:39:26 ►
study there and give it energy, which is the nutrition and so on. So there is some older
00:39:32 ►
part and some younger part in the mathematical landscape. And this entire system is in co-evolution,
00:39:41 ►
I suppose, with the evolution in ordinary reality.
00:39:50 ►
In this mathematical landscape, there is only small parts which have been used and probably ever will be used
00:39:53 ►
for modeling anything in ordinary reality.
00:39:56 ►
From the viewpoint of any non-mathematician, which is almost everyone,
00:40:02 ►
then those pieces of mathematics that have been used by somebody
00:40:06 ►
for modeling something familiar, like the simmering in the bottom of the boiling water,
00:40:13 ►
those parts are the only parts of mathematics that are visible.
00:40:16 ►
So then they proclaim how amazing the perfect fit between the mathematical concept evolved solely in the context of the human mind
00:40:26 ►
and this boiling pot of water. How amazing. Something real, something only in the mind,
00:40:33 ►
the resonance, you see, but it’s just like some small parts of mathematics that have ever become
00:40:37 ►
visible in that way. Furthermore, they became visible primarily in the context of mathematical physics.
00:40:50 ►
And mathematical physics, I guess, is unfortunately an evolutionary dead end.
00:40:55 ►
So you have to carefully watch out to take any inspiration from it,
00:40:57 ►
especially something like quantum electrodynamics.
00:41:03 ►
You have a really good one, you know, mathematical physicists, such as Stephen Hawking’s, going on record in several of his books,
00:41:07 ►
saying that theoretical physics is done.
00:41:11 ►
Everything we can figure out is figured out now.
00:41:14 ►
And other theoretical physicists would like to say,
00:41:17 ►
I’m sure that, you know, we’ll progress a little further.
00:41:19 ►
But basically, although Hawking is probably wrong,
00:41:22 ►
in essence, he’s kind of right, because this whole subject
00:41:28 ►
is devoted to the study of the simplest possible systems. Now when you talk about your experience
00:41:34 ►
as an agricultural scientist and so on, there you are talking of experience in a realm which
00:41:39 ►
is infinitely more complicated than the most complex system that a physicist ever looked
00:41:44 ►
at. So the parts of mathematics that a physicist ever looked at.
00:41:50 ►
So the parts of mathematics that have been used by these physicists are the parts that are the least interesting to us. And I want to tell you this good news that, at least in my opinion,
00:41:56 ►
mathematics offers much more to the more complex sciences than it offers to physics.
00:42:03 ►
And the whole potential of mathematics to aid us in our own evolution comes from the
00:42:08 ►
fact that it can extend our understanding of systems that are too complex to understand
00:42:14 ►
without it.
00:42:15 ►
It might be good for that, you see.
00:42:17 ►
So that when you just change the weather a little bit and these peas grow at the expense
00:42:21 ►
of those and so on, the understanding of that complexity could be aided.
00:42:26 ►
I mean, in any ecosystem, you have so many different things.
00:42:30 ►
You talk about the butterfly effect,
00:42:32 ►
and we don’t know that one oil spill off the coast here
00:42:39 ►
could produce desertification
00:42:41 ►
and bring on the equivalent of nuclear winter.
00:42:44 ►
This is possible, but we don’t understand it, and we never will,
00:42:47 ►
but our understanding can be advanced by mathematics,
00:42:50 ►
because mathematics is the supreme tool for the extension of our language
00:42:54 ►
for dealing with complex systems.
00:42:57 ►
That’s its main appeal for application, for ordinary use, for garden variety life.
00:43:04 ►
We can have models of emotional relationships,
00:43:07 ►
of love affairs, of arms race between nations,
00:43:10 ►
of the nuclear club of the United Nations,
00:43:13 ►
of the society of people of nations,
00:43:16 ►
of the society of species, and so on.
00:43:20 ►
We can model these things with models that are no good,
00:43:23 ►
but they’re better than no models.
00:43:26 ►
And the construction of these models is part of our evolution,
00:43:29 ►
and is part of the evolution of the mathematical landscape as well.
00:43:37 ►
Yes. Well, that’s all very moderate and reasonable.
00:43:41 ►
No extravagant platonic claims.
00:43:43 ►
moderate and reasonable, no extravagant platonic claims.
00:43:50 ►
What interests me, I must admit that my interest in mathematical models has enormously increased since I came across attractors.
00:43:54 ►
And my ability to understand attractors, or at least even a little bit about them,
00:43:59 ►
was greatly increased by your visual dynamics books,
00:44:02 ►
which for the first time made these things visible.
00:44:06 ►
I should say, for those who haven’t followed Ralph’s work,
00:44:09 ►
that he’s done more than any mathematician I know
00:44:12 ►
to make the essential features of this mathematics visible.
00:44:15 ►
He’s produced four volumes of books on dynamics, visual dynamics.
00:44:21 ►
There’s not a single equation in the four volumes,
00:44:23 ►
and through diagrams he tries to give you the essence of what dynamic systems are and
00:44:28 ►
what the science of the mathematical branch of dynamics is how it models them
00:44:33 ►
and how it understands them it’s very illuminating and normally mathematics is
00:44:38 ►
hidden between behind an opaque cloud of symbols which most of us can’t penetrate
00:44:43 ►
beyond it’s as if all we knew of music was looking at scores of symphonies
00:44:48 ►
but never actually hearing the symphony.
00:44:50 ►
These symbols refer to things which, for real mathematicians,
00:44:53 ►
are intuitions, visual intuitions.
00:44:57 ►
And so Ralph helps make that clear.
00:45:01 ►
But what interests me is, in these attractors,
00:45:07 ►
no one else in any other branch of science has been able to think in terms of teleological
00:45:11 ►
principles which pull from in front. And mathematicians have sort of snuck in
00:45:17 ►
round the back and because it’s an abstruse branch of an abstruse subject
00:45:21 ►
which the anti-teleological inquisitions of modern science don’t really
00:45:26 ►
understand very much. It’s somehow grown up in the back without anyone noticing. And now we’ve got
00:45:33 ►
this whole system of dynamical attractors, including chaotic attractors, that have been
00:45:39 ►
developing for years without those who police the frontiers of science noticing what was going on.
00:45:45 ►
Sort of illicit crops of models have grown up in clearings and backyards as it were.
00:45:51 ►
And it seems to me that they’ve really quite changed our way of thinking about nature
00:45:58 ►
because they have made it conceivable to think of what Aristotle called the intellikey or this dynamical, this pulling process.
00:46:07 ►
Now, what I’d like to know is how you think attractors work.
00:46:15 ►
I mean, I know you’ll say that all we’re doing is modelling what actually happens.
00:46:18 ►
We’re not saying anything about the underlying reality or fields or structures that make it happen.
00:46:23 ►
We’re just describing or modelling what actually happens in the physical world. The interesting thing is the models of attractors
00:46:32 ►
imply that a future state draws the system towards it. And I suppose you can say, well,
00:46:38 ►
the model isn’t in the future or the state isn’t really in the future. It’s only a description of
00:46:42 ►
what you’ve observed in the past.
00:46:50 ►
Can you believe that I’m going to leave this discussion hanging in midair like this?
00:46:57 ►
Well, I wish we had time to go on today, but I’ve got to get back to my never-ending project of working on a new and improved version of the psychedelic salon’s website. And if I don’t spend
00:47:03 ►
a few hours every day working on it, I’m never going to get it done.
00:47:06 ►
But what I’ll do to try to make up for it a little bit
00:47:09 ►
is to post the second half of this tape early next week
00:47:12 ►
before I post another non-trialogue program.
00:47:16 ►
That way we’ll at least get both sides of each tape
00:47:19 ►
in back-to-back podcasts.
00:47:21 ►
A few programs ago, I mentioned a fellow podcaster, KMO, who podcasts on the
00:47:27 ►
Sea Realm channel. That stands for Consciousness Realm, I’m told. Well, he called me the other
00:47:33 ►
day to ask me to pass along his thanks to all of you who have checked out his podcast.
00:47:38 ►
Apparently, some of us salonners are finding his programs interesting as well. I guess
00:47:44 ►
I should give full disclosure here
00:47:46 ►
because part of his 10th podcast includes an interview with me. My first podcast interview,
00:47:52 ►
by the way. One of the things I noticed about KMO’s website, which can be found at podomatic.com that’s c-r-e-a-l-m p-o-d-c-a-s-t
00:48:06 ►
dot podomatic dot com
00:48:08 ►
and the link’s on the
00:48:10 ►
Psychedelic Salon’s podcast page
00:48:11 ►
if you didn’t catch all of that
00:48:13 ►
anyway KMO has done a really
00:48:16 ►
great job of providing extended
00:48:18 ►
program notes where you can
00:48:19 ►
find links to some of the things that we talked about
00:48:22 ►
and you might want to check it out
00:48:24 ►
if you have the time.
00:48:26 ►
And now that I’ve heard a live podcast slash phone interview, I’ve decided to try one myself.
00:48:33 ►
And so the podcast after the next one will include a phone conversation between me and my friend, the great Sheldoni,
00:48:41 ►
otherwise known as Sheldon Norberg, author of the groundbreaking book, Confessions of a Dope Dealer.
00:48:48 ►
So if you’ve ever wondered about the dope dealing business,
00:48:51 ►
you might find that upcoming program of interest.
00:48:54 ►
And I guess I should put in a special note here to my friends.
00:48:57 ►
I’m assuming you’re my friends in the DEA and other fascist enterprises
00:49:03 ►
who are monitoring these podcasts in a pretense of doing some investigative work,
00:49:08 ►
Sheldon has been out of the dope-dealing business for a long time now.
00:49:12 ►
Long enough for all the statute of limitations to run, for sure.
00:49:16 ►
And you won’t hear any tips on how to get started in the business, either.
00:49:19 ►
But you will hear a fascinating story of how the war on drugs helped to spawn an entire new class of entrepreneurs.
00:49:27 ►
In junior high school, no less.
00:49:30 ►
And if you don’t want to wait until next week to hear Sheldon’s story,
00:49:34 ►
you can always go to our Amazon store at matrixmasters.com,
00:49:38 ►
and you’ll find his book at the top of the page.
00:49:41 ►
Before I go, I should mention that this and all of the podcasts from the Psychedelic Salon Thank you. matrixmasters.com slash podcast. And if you still have questions, you can send them an email to
00:50:05 ►
lorenzo at matrixmasters.com.
00:50:09 ►
I’d like to thank Chateau Hayuk
00:50:12 ►
for the use of their music here in the Psychedelic Salon.
00:50:15 ►
And thanks again to Ralph Abraham,
00:50:17 ►
both for participating in the trial logs
00:50:19 ►
and for letting Bruce Dahmer and me
00:50:21 ►
digitize your tapes of these sessions
00:50:23 ►
and put them online for our friends here in the psychedelic salon to enjoy.
00:50:28 ►
And for now, this is Lorenzo signing off from cyberdelic space.
00:50:33 ►
Be well, my friends. L-A-L-I-A I’m L-A-L-I-A