Greetings from cyberdelic space. This is Lorenzo and I'm your host here in the
psychedelic salon. Today's program is a continuation of the series of trial logs
held between Terrence McKenna, Ralph Abraham and Rupert Sheldrake at Esalen
in September of 1989 and again in 1990. So far the trial loggers, I guess that's
probably not a real word but it does have a nice ring don't you think? The
trial loggers. Anyway in the first podcast of this series the trial loggers
gave us a brief glimpse of their backgrounds and how they came together
and that was in our podcast number 58. We then heard tape one of the series which
was titled Creativity and Imagination. Now we move on to the first side of
tape two which is titled Creativity and Chaos and we begin with Ralph Abraham's
short introduction to chaos theory and then we'll get into a discussion between
Ralph and Rupert of why what is, is or something like that. Let's join Ralph and
Rupert now. Now it's a little presumptuous to call this chaos theory because as a
matter of fact there is no theory. We're in the exploration phase now and this is
experimental mathematics that we we are doing with supercomputers. But I think it
might help if you had just a little idea of chaotic dynamics and the idea of the
thing. So I want to give a two or three minute primer so that you could
understand what is a chaotic attractor and here now we've seen 16,000 of them.
What does one look like? And and that will conclude my introduction and then
I'll pass them on to Rupert. A good laboratory for the study of chaotic
dynamics is the dripping faucet and the dripping faucet was discovered as the
ideal demonstrator for chaos theory because the lectures are usually given
in a physics lecture hall and they always seem to have a sink with a faucet
in the front to do experiments or for the professor to wash the chalk off his
hands. Anyway you take the faucet you can do this immediately you get home. You
crack the tap a little bit and 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
and then you crack it a little more and then it begins to sound drip drip drip
like rain dripping off the roof. That's an example of a chaotic time series. If
you measure the time between drops and make a list of these numbers you have
the paradigmatic case of a chaotic time series. Now somebody decided to seriously
study this dripping faucet after seeing it in half a dozen physics lectures and
this person Rob Shaw, one of the leading people in chaos theory, did a very fine
study by placing a microphone in the sink where the drop would hit it getting
an electronic beat, just discretizing, getting it in the computer and analyzing
the results. And so all of this is taking place on that level one, the lowest
layer of the physical world. 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 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. So this is an
example showing the the value of modeling on these three levels for
gaining some understanding. There's sort of a hermeneutical circle. You look at
the data, try to build a model, you fail, but building the model tells you to
observe in a different way, you observe in this different way, that helps you to
build a better model and as this circle turns the level of our understanding
grows. So Rob Shaw came quickly to a good model for this. I think he was lucky
because it sounds simple, it's a very complicated system. It relates to
waterfalls for example when the spray comes off the waterfall and here's
another example of a chaotic system. Could you write some equations and obtain a
computer program that simulated the spray from a waterfall? I doubt it. The
new way of looking at the data that came to him from the theory was to take the
sequence of numbers, the time between drops, you just visualize a column of
numbers and you make a carbon copy of it and move it over to the side and then
you whack one number off the top and move it all up one number. Now you have a
series of pairs and then you plot these pairs on the plane as a set of points. So
he did this. There's a film or video available for Aerial Press that shows
the machine actually doing this and from this totally chaotic data viewed in this
particular way which is called chaoscopy, you get these points in the planes that
if the data was really random, the dots would be all over the plane. Instead they
lie on a curve, a smooth curve. So from the observation of the data in this way,
the smoothness of the curve suggests a kind of model that you can actually take
off the shelf in the building where the chaos theorists are working and apply it
to your data, you see. And the simplest model on the shelf of the chaos theorists
closet is called the logistic equation. It produces a series of numbers that are
apparently random but actually they comprise one of these simple geometric
figures, this curve that the data plotted in this special way of the
chaos scale is a curve and that is called the chaotic attractor. So there are
models on level three which are good models for understanding certain behavior
on level one and level two is an intermediary which can either create the
model, the mathematical model from the real data or create experimental data
from the model to compare with laboratory data. Well to conclude, this
video was made out of these simplest possible dynamical systems called the
logistic equation and it just produces a series that is very similar to a dripping
faucet. So you could just as well imagine that we have 16,000 dripping faucets in
an array of 128 by 128 and the time between drops is represented as a color
on the screen. Now do you think that if you had 16,000 dripping faucets you could
get out of them a pattern like Calico Mountain? Now, well, it happens. I mean
there's a lot of theory behind this enough to suggest that it's not some
kind of artifact. No matter what kind of artifact it is, it's an interesting
artifact and I guess I'd like to call this a mathematical law. It has to do
with the emergence of form from a field of chaos. We don't know what else to call
it. It's not a mathematical law that was known to Pythagoras and I don't know if
it was always there since the beginning of time long before the Big Bang or if it
just emerged into the evolving field of the guy in mind through the fact that
computers make it visible. I mean, I don't know. But at this point I have, I hope,
arrived at an actual connection between the work I routinely do as a specialist
in the field of chaos and the discourse that we're trying to carry on here to
increase our understanding of our past, our future, and our possibility of even
having a future. The problem I have with chaos theory is that I'm never quite
sure what it's saying. There seem to me to be two things that are of interest
here. One is that the actual detailed models which chaos theoreticians make
and they love finding fairly simple equations that will generate complicated
and seemingly chaotic structures. And so there's this modeling aspect of chaos
which is at the forefront of modern mathematical chaos theory and modeling.
But the fact you can make mathematical models of chaos has given scientists
permission to recognize that in fact there's a vast deal of indeterminacy
throughout the physical world. In the 19th century it was generally believed
that there was no indeterminacy at all. Everything in the physical world was
totally conditioned by eternal laws of nature. Laplace thought that the whole
future and past of the universe could be calculated from its present state if
there were a mind powerful enough to do the calculations and to make the
observations. Now that view, the illusion of total predictability, held science
under its spell for generations. Scientists were dazzled by this
imagined power of totally predicting everything. And it was a kind of illusion.
They really did believe it. And of course they couldn't calculate everything. I mean
they couldn't even, they still can't even calculate the weather very accurately
more than a few days in advance. So in actual fact this idea of total
predictability was not realizable. But the idea was, well, we would, if we could
do enough calculations, be able to calculate it in principle. What seems to
me interesting is the fact that first with quantum mechanics there was a
recognition that indeterminacy, probability, intrinsic non-detailed
predictability were inherent in small-scale physical processes at the
quantum level. And here was a genuine indeterminism in nature which had to be
admitted in 1927. Until then practically everyone believed everything was fully
determinate. After that there's been a gradual recognition that indeterminacy
exists not just at the quantum level but at all levels of natural organization.
There's an inherent spontaneity, indeterminism, probability,
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. Even the old-time favorite model for total rational mathematical
order, namely the orbits of the solar system, the orbits of the planets in the
solar system, turn out to be unpredictable in terms of Newtonian
physics. They can be modeled in a chaotic manner. Anyway, this indeterminism has
been recognized at all levels of nature. So there's the idea that what we can
model with old-style physical models is an abstraction from a very small number
of idealized cases, that the natural world simply escapes the modeling, most
of the modeling processes which were the dominant features of traditional
physics. Now it seems to me this openness of nature, this indeterminism, this
spontaneity, this freedom, is something very interesting and it corresponds to
the intuition of chaos in its intuitive and mythological sense.
Mathematicians have used this word chaos in a variety of technical senses and
it's not entirely clear to me how these technical models of chaotic systems
correspond to the kind of intuitive notion of chaos. But what I want to do is
to consider how form arises from chaos, starting from a simple, intuitively
obvious way in which more form appears from less, through familiar physical
processes. And I'm thinking of the process of cooling. If you start with
something at a very, very high temperature, atoms can't exist. The
electrons fly off the nuclei and you get something called a plasma, which is a
sort of soup of atomic nuclei and electrons in a kind of gas. There's no
longer individual atoms. The whole thing, they disintegrate into a mÃ©lange, a
mixture of their component parts, the plasma, which has its own kinds of
properties. If you cool these plasmas down, when you reach a certain
temperature, it's low enough for atoms to form and atoms begin to come into
existence. Electrons start circulating around nuclei. You get atoms forming, you
get a gas of atoms. But the temperature is still too high for any molecules to
form. And say it's a hydrogen plasma and you cool it down, you'll get hydrogen
atoms, but you won't yet get any hydrogen molecules. Cool it down further, now you
get hydrogen molecules. You cool the system down further and you get a stage
where more complex molecules can come into being, but they're still gaseous.
Cool it down further and they turn into a liquid, which has more form, can form
drops and flow around and has quite complex ordered arrays of molecules
within it. Cool it further still and you get a crystal, which is an extremely high
highly regularly ordered formal arrangement of the atoms and the
molecules. So you get a progressive increase in complexity of form as you
lower the temperature. 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 form as the cooling process takes place.
Now we all know from the cooling of steam into water, the cooling of water
into ice, that we know about this process from everyday experience. We've
seen this aspect of it and we've seen how if you cool water vapor down, you get
ice crystals emerging. And these ice crystals have a considerably high degree
of order. So there's this formative process, which we see through cooling,
occurs as the thermal chaos in the ordinary sort of everyday sense of chaos
is reduced, because as cooling happens more form emerges. The opposite happens
if you warm things up. If you warm up snowflakes, they first turn into water,
then they turn into steam, then the steam, the water vapor disintegrates into the
molecules break up into atoms, then those break up into a plasma as you raise the
temperature. So there seems to be an inverse relationship between temperature,
which is this highly agitated motion of things, essentially chaotic in the
traditional theory of gases and plasmas, and an increase of form when things cool
down. Now in a sense that's what has happened according in the entire
universe. We're led to believe that the universe started off exceedingly hot,
billions of billions of degrees centigrade, so hot that stable forms were
not able to emerge. By expanding, it cooled down. The cooling process of the
universe is associated with expansion. The cosmic expansion both creates more
space in which new forms can appear, and by making bigger gaps between things
somehow cools the universe down, so the temperature drops. And as the
temperature drops in the developing universe, according to standard models,
more and more form comes into being. First you get atoms, then stars and
galaxies condense, then you get solar systems, and through the cooling of
matter you can get planets. The planets are the cooled remnants of exploding
stars. The elements in us and in our planets are stardust formed from super
navy. So there's a cooling down of these things that came from
immensely hot sources. Then you can get rocks forming crystals. And in a
sufficiently cool planet, and yet a sufficiently warm one, within a fairly
narrow range of temperature, you can have the evolution of life as we have had on
Earth. 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. There's a
formative process going on, and we can call this one way of looking at the
emergence of form from chaos or disorder. Well, how do these forms come into being?
This is the big problem of evolutionary creativity. How do the first molecules,
how did the first zinc atoms come into being, how did the first methane
molecules, how did the first salt crystals, how did the first living cells,
how did the first vertebrates, how did the first of anything come into being in
this evolving universe as it expanded and cooled? Well, one way of looking at
this is to see the expansion and cooling process, and indeed the flow of events, as
being, thinking of it in terms of the flux of energy. And one of the great
unifying concepts of 19th century physics is a unified conception of energy.
Now, it's not entirely clear what energy is. Energy, in some senses, the principle
of change. The more there is, the more change that can be brought about. It's in
a sense a causative principle, and it's a causative principle which exists in a
process. In this process, the energetic flux of the universe underlies time,
change, becoming, and the flux process itself seems to have an inherent
indeterminism to it. This flux process, the universal flux, is organized into
forms by fields. Matter is now thought of as energy bound within fields, the
quantum matter fields and the fields of molecules and so on. And I think there
are many of these organizing fields, the morphic fields. And the fields are
somehow organizing the ongoing flux of energy, which is always associated with
this spontaneity and chaotic qualities. So even organized systems of a high
level of complexity still have this probabilistic quality. The fields that
organize this energy to give rise to material and physical forms are
themselves probabilistic. Chaos is never eliminated. 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 principle, which
I think has the chaos inherent in it. It's a kind of change, which left as pure
change would be chaos. One way of thinking of these is in terms of the
Indian notion of Shakti as the energy indeterminate principle, and Shiva as the
formative principle, working together in a kind of tantric union to give the world
that we know. Now, if there's this formative principle that comes through
the fields of nature, then one of the questions is, how do fields operate? How
are these fields governed? How do they have the forms, shapes, and properties
they do? Well, I think that the organizing fields of living organisms, of crystals,
of molecules, and so on, are organized by, I think that they are what I call morphic
fields, and these fields contain an inherent memory, so that these fields are
essentially habitual, and nature is the theater of these habitual fields
organizing the indeterminate flux of energy. Fields themselves, by having this
energy within them, have this indeterminate quality too. But this then
brings us to the question of creativity. How do new fields, new forms, come into
being in the first place? Where do they come from? Well, this morning with Terence,
I was discussing how they may arise out of the interaction between chaos and
some kind of formative, unifying, some kind of unifying aspect of the cosmic
mind, which Ralph has hijacked for the Pythagorean sect by calling the realm of
mathematics. That there's an interaction here between these two levels, giving the
world of becoming that he's shown by the wiggly line in the middle. Well, this is
one way of looking at it, and this brings us back to the question of the nature of
what he calls the mathematical realm, this sort of formative realm. Is it, is
there a kind of mathematical realm before the universe, somehow beyond space
and time altogether, which conditions all forms of creativity, all patterns and
possible systems of organization that come into, can come into being with the
world? Or are these all made up as the evolutionary process goes along? These
are questions we've already touched on this morning. I myself think that if
we take the view of things coming into being as evolution goes along, if we
think of the cosmic, the soul of the world as having a kind of imagination, we
can think of these as coming into being as nature goes along, and we can see this
imagination as having many levels. There'd be a kind of cosmic imagination,
which would be the soul of the world, the anima mundi, the soul of the universe, a
cosmic mind, soul, and imagination. Within that, there'd be clusters of galaxies,
each of which would have their own mind, soul, or imagination. Then there'd be galactic
ones, then ones for solar systems, then one for planets, then ones for ecosystems,
then ones for societies of organisms, and individual 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. Then there'd be the possibility of a whole range of imaginations, that we
don't have to leap straight from what's happening in a social insect colony, or
in an animal or a plant, or in a social system, a human social system, straight to
the divine imagination, or the mathematical mind of God, or the
transcendent realm of mathematics. There's a whole level of imaginations in
between, a whole level, and within the earth, we're embedded within the solar
system with its own particular kind of soul and imagination, and that within the
galaxy. So there'd be a whole set of levels at which creativity could come
forth from souls with imaginations. Now, I think the difference that we might have
to consider between all this and the traditional doctrine of the world soul,
is that in the traditional doctrine of the world soul, of Plotinus and of
Plato, they had a threefold system, where there was the intellect, with the
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 within it, and was concerned
with the realm of becoming, namely the cosmos, not with the realm of being, which
was the realm of these pure forms. And as the prototype of the cosmos, the world
soul had this cosmic attractor as its intelligy, its goal, and this was a
striving towards the eternal perfection of the divine. And then, within the world
soul, there were hosts, hierarchical levels within levels, of souls of all the
different systems within the universe, each of which had its own autonomous
existence, a holistic or holarchic vision of souls within souls. The view that they
had was that the qualities of the world soul were all fixed in by the eternal
forms, the eternal mathematical mind. 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, already
full, that what we do is make mathematical models of various aspects
of nature. And I think that the one way, one thing that happens then, is these
models can be projected as if they're a real thing out there, as if the world
soul is engulfed within a kind of eternal mathematical mind. That may just
be a projection of ours. The world soul may have an autonomy. It may be no more
mathematical than our own souls are when we're dreaming. I mean, there are certain
numbers and numerical forms come into dreams, but there's no sense when we're
dreaming these dreams are being generated by equations, or that they're
essentially mathematical in structure. So, what I'm suggesting is that the
world soul may have an autonomy to it. It may have a kind of mathematical realm as
part of it, but that if we think of it as having its relation to mathematics and
its relation to the creation of form, the ordering of chaos into patterns and
forms and structures, then this mathematical aspect of it may evolve
along with nature, just as our own understanding of mathematics evolves in
time. Well, I think that we are talking about complicated things, complex, obtuse,
and difficult ideas, and we're talking about them in a language which seems
more or less appropriate. So, as you speak, I get an idea, I get a picture. I mean,
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. 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, soul, and so on. If we draw that as a
picture instead of a word picture, then that's officially mathematics. That's
geometry. That's a geometric model for 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. And if you think that there are three sexes on the moon and
then we can make a model for that, you see. So mathematics could be regarded as
simply an extension of language. 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. And the more complex, the
more structured, the more difficult to engulf in our minds, the more appropriate
mathematics might be, or maybe music might be. But words, I think, are frequently
inadequate. That 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, and which is inadequate to understand the whole world, or the
world soul, or the ecosystem, the biosphere of planet Earth or something. So
mathematics has only a little more magic than language. And we could say, well,
the conservation of energy, that's a verbal description of something that you
could also say mathematically. So I think that your maligning mathematics in this
way is unjustified. And I guess I have been quoted in the Chaos book as saying
that Chaos theory is the biggest thing since the wheel. Well, I believe that. I
also think the wheel was a really big thing. But on the other hand, I've been
quoted as saying that Chaos theory is no big deal. So whatever you say, I agree
with you. But, I mean, about determinism, if I could reply to that, it's a long
time ago. But that, well, you said you had a complaint about Chaos theory, about
determinism and prediction. And there are two or three reasons why Chaos theory is
good for you. One thing is, if you accepted Chaos theory as a way of modeling
anything that we're interested in, which personally I don't, not by itself, it's
too simple, then it's still good for you. Because according to Chaos theory,
prediction and determinism are impossible. Even though it uses the
language that the deterministic thinkers used, when you look into the technical
details of it, prediction is impossible. You only get a sort of a probabilistic
something or other. Secondly, the models for anything that you want to talk about,
such as cooling, is a good one. They don't come from Chaos theory, they come from
bifurcation theory. And that is really good for you, because bifurcation theory
exemplifies the best in mathematics. The most it can possibly do for you is rule
out a lot of possibilities that you might imagine might happen, and then the
mathematics says, "Well, no, according to the assumptions that you said
you believe, then all this won't happen. Only this." And then you get a list of
three or four of these so-called bifurcations. They are the only things
you're going to expect to see in any system which is well modeled by the
theory where these models come from. So when you have cooling, then you have, let
us say, a control knob where you're turning down the heat under the pan, and
the boiling is gradually subsiding to simmering, which is subsiding to a little
bit of waving, which is subsiding to nothing. Then we have at each stage,
coming from the mathematics, a model which has attractors, which has maybe
chaotic attractors. But every time you change the knob, you get a different
model. And therefore, if you can't predict how the knob is going to change, the
models don't give any prediction at all, and they're irrelevant. And the only
interesting thing is that the theory can tell you certain transformations you'll
expect and others not. For example, Terence had pointed to the punctual
aspect of evolution, that many transformations are saltatory, they are
catastrophic, they are abrupt. And here the theory comes in and say, "In models of
this type, in this theory, most of the transformations are abrupt." And they have
kind of a theory why, which is a geometrical model, which is only of use
to those people who are thinking of the structure of the theory as
opposed to what is happening in the ordinary world. So this bifurcation
theory is good for you, and it gets rid of all... if chaos theory wasn't enough,
that says determinism is impossible, using mathematical models, forget it. Then we
don't even think those models are appropriate anyway. Instead, you have
these models that are changed by a parameter, which experience bifurcations.
We have a very good encyclopedia of bifurcations, and those are good models
for sudden changes, as for example in the emergence of form, as for example in the
Neolithic Revolution, as for example in the crystallization of the planets, of
the stardust. So that's the good news, but the truth is that this theory can be
used to model everything, so it never settles any question as to the origin of
things or the true nature of the ordinary reality, and therefore it's
worthless. What's good about it, like language, is it's good for communication,
it's good for a certain feeling of understanding and gaining comfort in a
new environment, because modeling is part of our basic process of grokking, and
always the models are no good. They're no good as models, but they're good for the
growth of understanding, the evolution of understanding. Well, I mean, you put the
whole case impressively and modestly, in the sense that you're claiming that
mathematicians are making models, here's a new range of models. I mean, it's
like before there were any mechanical instruments, and now we've got electronic
instruments. A whole new category of models have come onto the market, and we
can look forward to more models in the future, and there'll be the latest, the
1990 model will soon be out. We've got this ongoing evolutionary system of
mathematical models which enable us to model various aspects of reality. It
seems to me an eminently modest claim, but I suspect there's more in the
background, because, at least there is for some people, because the
traditional assumption is that these models correspond to something. The
reason why they work is because there's some aspect of nature to which
they mysteriously relate, and that aspect of nature is, in essence,
mathematical, which is why mathematical modeling is possible. Now, this seems to
me the interesting question, why mathematical models work in certain
areas. There are large areas where they don't work, and they aren't used, and it
may be they could be used, and they could work, but, I mean, I'm often meeting
mathematicians or physicists who say quantum physics is the most brilliant
predictive system that mankind has ever known. It predicts things to the 25
places of decimals, and it's obviously correct. Well, as an agricultural
scientist, when I was working in India, you know, we're predicting the outcomes
of my crop experiments. There was nobody who could predict those, and those
experiments were, I mean, vast distance beyond the capabilities of any
quantum physical modeling process, or anything based on the so-called
fundamental principles of physics. You can produce sort of string and ceiling
wax models for crop production, and we had people doing that, and we had a
computer, and there were these simple models. But it wasn't that, they didn't seem to
me to be pointing towards a convincing demonstration that the whole thing
depended on a hidden mathematical order. There were phenomena going on.
Some of them mathematicians have modeled fairly well. Others, there's huge areas of
reality that are hardly modeled at all yet. But the question is, is there a, is it
that mathematical models somehow fix on features of the fields of reality? 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 than the fields? Is the
electromagnetic field, the magnetic field for example, the north and south poles of
the magnet, is that field polar? In a sense it has a north pole and a south
pole, it has, clearly has a polarity. And is the electromagnetic field polar? In
electric charge as well, there's a positive and there's a negative charges. These
polarities we find inherent, for example, in the electric and magnetic fields. Are
those because there's some kind of Pythagorean two system, or duality, in
some archetypal realm, beyond nature that's reflected in everything that
happens in nature? Or is that just the way fields are, and that when we look at
lots of fields we make an abstraction and we make conscious in a mathematical
model something which is inherent in the nature of the organizing fields of
reality, but which doesn't exist in some transcendent mathematical realm? Well you
could ask different mathematicians and get different answers. I'll give you mine.
And other mathematicians would say it doesn't count because I'm not a
mathematician, and this answer in fact is the proof of that. But I think
that for me mathematics is a beautiful landscape, an alternate reality, and
there's infinite possibilities not yet loomed into view, 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 study there and give it energy, which is
the nutrition and so on. So there is some older part and some younger part in the
mathematical landscape, and this entire system is in co-evolution, I suppose, with
the evolution in ordinary reality. In this mathematical landscape there is
only small parts which have been used and probably ever will be used for
modeling anything in ordinary reality. From the viewpoint of any non-mathematician,
which is almost everyone, then those pieces of mathematics that have been
used by somebody for modeling something familiar, like the simmering in the
bottom of the... in the boiling water, those parts are the only parts of
mathematics that are visible. So then they proclaim how amazing the perfect
fit between the mathematical concept evolved solely in the context of the
human mind and this boiling pot of water, how amazing. Something real,
something only in the mind, the resonance, you see, but it's just like some small
parts of mathematics that have ever become visible in that way. Furthermore,
they became visible primarily in the context of mathematical physics, and
mathematical physics, I guess, is unfortunately an evolutionary dead end, so
you have to carefully watch out to take any inspiration from it, especially
something like quantum electrodynamics. You have a really good one, you know,
mathematical physicists such as Stephen Hawking's going on record in several of
his books saying that theoretical physics is done, everything we can figure
out is figured out now. And other theoretical physicists would like to say,
"I'm sure that, you know, we'll progress a little further," but basically, although
Hawking is probably wrong, in essence he's kind of right, because this whole
subject is devoted to the study of the simplest possible systems. Now, when you
talk about your experience as agricultural scientist and so on, there
you are talking of experience in a realm which is infinitely more complicated
than the most complex system that a physicist ever looked at. 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, mathematics offers much more to the more complex sciences than it
offers to physics. And the whole potential of mathematics to aid us in
our own evolution comes from the fact that it can extend our understanding of
systems that are too complex to understand without it. It might be good
for that, you see, so that when you just change the weather a little bit and
these peas grow at the expense of those and so on, the understanding of that
complexity could be aided. I mean, in any ecosystem you have so many different
things. You talk about the butterfly effect, and we don't know that one oil
spill off the coast here could produce desertification and bring on the
equivalent of nuclear winter. This is possible, but we don't understand it, and
we never will, but our understanding can be advanced by mathematics, because
mathematics is the supreme tool for the extension of our language for dealing
with complex systems. That's its main appeal for application, for ordinary use,
for garden variety life. We can have models of emotional relationships, of
love affairs, of arms race between nation, of the nuclear club of the United
Nations, of the society of people of nations, of the society of species, and
and so on. We can model these things with models that are no good, but they're
better than no models, and the construction of these models is part of
our evolution, and it's part of the evolution of the mathematical landscape
as well. Yes, well, that's all very moderate and reasonable. No extravagant
platonic claims. What interests me, I must admit that my interest in
mathematical models has enormously increased since I came across
attractors, and my ability to understand attractors, or at least even a little bit
about them, was greatly increased by your visual dynamics books, which for the
first time made these things visible. I should say for those who haven't
followed Ralph's work that he's done more than any mathematician I know to
make the essential features of this mathematics visible. He's produced a
four-volume, four volumes of books on dynamics, visual dynamics. There's not a
single equation in the four volumes, and through diagrams he tries to give you
the essence of what dynamic systems are, and what the science, the mathematical
branch of dynamics is, how it models them, and how it understands them. It's very
illuminating, and normally mathematics is hidden between, behind an opaque cloud
of symbols, which most of us can't penetrate beyond. It's as if all we knew
of music was looking at scores of symphonies, but never actually hearing
the symphony. These symbols refer to things which for real mathematicians are
intuitions, visual intuitions, and so Ralph helps make that clear. But what
interests me is in these attractors, no one else in any other branch of
science has been able to think in terms of teleological principles which pull
from in front, and mathematicians have sort of snuck in round the back, and
because it's an abstruse branch of an abstruse subject, which the
anti-teleological inquisitions of modern science don't really understand very
much, it's somehow grown up in the back without anyone noticing. And now we've
got this whole system of dynamical attractors, including chaotic attractors,
that have been developing for years without those who police the frontiers
of science noticing what was going on, sort of illicit crops of models have
grown up in clearings and backyards as it were. And it seems to me that they've
really quite changed our way of thinking about nature, because they have made it
conceivable to think of what Aristotle called the 'intelliki' or what this
dynamical, this pulling process. Now what I'd like to know is how you think
attractors work. I mean I know you'll say that all we're doing is modeling what
actually happens, we're not saying anything about the underlying reality or
fields or structures that make it happen, we're just describing or modeling what
actually happens in the physical world. The interesting thing is the models of
attractors imply that a future state draws the system towards it, and I
suppose you can say well the model isn't in the future or the state isn't really
in the future, it's only a description of what you've observed in the past.
Can you believe that I'm going to leave this discussion hanging in midair like
this? 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
salons website, and if I don't spend a few hours every day working on it I'm
never going to get it done. But what I'll do to try to make up for it a little bit
is to post the second half of this tape early next week before I post another
non-trial log program. That way we'll at least get both sides of each tape and
back-to-back podcasts. A few programs ago I mentioned a fellow podcaster KMO who
podcasts on the C Realm channel. That stands for consciousness realm I'm told.
Well he called me the other day to ask me to pass along his thanks to all of
you who have checked out his podcast. Apparently some of us salonners are
finding his programs interesting as well. I guess I should give full disclosure
here because part of his 10th podcast includes an interview with me. My first
podcast interview by the way. One of the things I noticed about KMO's website
which can be found at C Realm podcast dot podomatic dot com. That's C-R-E-A-L-M-P-O-D-C-A-S-T
dot podomatic dot com. And the links on the psychedelic salons podcast page if
you didn't catch all of that. Anyway KMO has done a really great job of
providing extended program notes where you can find links to some of the things
that we talked about. You might want to check it out if you have the time. And
now that I've heard a live podcast slash phone interview I've decided to try one
myself. And so the podcast after the next one will include a phone conversation
between me and my friend the great Sheldonie, otherwise known as Sheldon
Norberg, author of the groundbreaking book Confessions of a Dope Dealer. So if
you've ever wondered about the dope dealing business you might find that
upcoming program of interest. And I guess I should put in a special note here to
my friends, I'm assuming you're my friends in the DEA and other fascist
enterprises who are monitoring these podcasts in a pretense of doing some
investigative work. Sheldon has been out of the dope dealing business for a long
time now. Long enough for all the statute of limitations to run for sure. And you
won't hear any tips on how to get started in the business either. But you
will hear a fascinating story of how the war on drugs helped to spawn an entire
new class of entrepreneurs in junior high school no less. And if you don't
want to wait until next week to hear Sheldon's story you can always go to our
Amazon store at www.matrixmasters.com and you'll find his book at the top of the
page. Before I go I should mention that this and all of the podcasts from the
Psychedelic Salon are protected under the Creative Commons Attribution
Non-Commercial Share Alike 2.5 license. And if you have any questions about that
you can click on the link at the bottom of the Psychedelic Salon web page which
you can find at www.matrixmasters.com/podcasts. If you still have questions you can
send them an email to Lorenzo@matrixmasters.com. I'd like to thank
Chetul Hayuk for the use of their music here in the Psychedelic Salon and
thanks again to Ralph Abraham both for participating in the trialogues and for
letting Bruce Dahmer and me digitize your tapes of these sessions and put
them online for our friends here in the Psychedelic Salon to enjoy. And for now
this is Lorenzo signing off from Psyberdelic Space. Be well my friends.
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