Transcript
from March 25, 2004 9:0010:00 PM Eastern
Copyright © by
International Society for Complexity, Information, and Design
ISCID Moderator (Mar 25, 2004 9:06:12 PM)
Our guest speaker today is Carlos Puente. Puente received his PhD in
Hydrology from Massachusetts Institute of Technology in 1984. Since
then, he has published over 40 journal papers. Some of his most recent
works include Chaos and Stochasticity in Deterministically Generated
Multifractal Measures for the journal Fractals; DNA, Pi and the Bell
for the journal Complexity; and the book The Hypotenuse, an illustrated
scientific parable for turbulent times, submitted to BerrettKoehler.
He has also made over 85 presentations at numerous conferences relating
to topics in Nonlinear Dynamics and Hydrology.
ISCID Moderator (Mar 25, 2004 9:06:34 PM)
Puente's research interests include uncertainties and variability of
hydrologic processes; rainfall modeling in space and time; fluvial
geomorphology; groundwater contamination; rainfallrunoff modeling;
complexity; chaos; fractals; turbulence.
ISCID Moderator (Mar 25, 2004 9:06:50 PM)
In his latest book, Treasures Inside the Bell, Puente discusses what
he views as a new paradigm for the emergence of order of a host of
natural patterns including snow crystals and biochemical rosettes
(such as DNA).
ISCID Moderator (Mar 25, 2004 9:07:10 PM)
I'm not going to hand the chat over to Dr. Puente... feel free to start
sending in your questions.
ISCID Moderator (Mar 25, 2004 9:07:16 PM)
I'm "now"
ISCID Moderator (Mar 25, 2004 9:07:29 PM)
Sorry;)
carlos puente (Mar 25, 2004 9:08:45 PM)
Thanks to ISCID for the opportunity to share a bit about my research
carlos puente (Mar 25, 2004 9:10:13 PM)
As perhaps you already know, my research pertains some very lovely
geometric discoveries that turn out to have implications beyond hydrology.
carlos puente (Mar 25, 2004 9:12:12 PM)
It all got started some years ago trying to develop models of complex
looking sets, like many we get in hydrology such as rainfall and
runoff. The idea just ocurred of describing such patterns as shadows
made by a simple fractal object, in a manner that resembles the old
ideas of Plato.
carlos puente (Mar 25, 2004 9:15:20 PM)
It happens that one can describe very complexlooking sets as shadows
when the fractal object in question has a low enough dimension and
when it is illuminated by a socalled multifractal object. But we
were in for a surprise for rather distinct shapes are generated as
the fractal object fillsup space. In such a case one finds a Gaussian
distribution all the time, and this was the beginning of an exploration
that have exceeded our expectations.
carlos puente (Mar 25, 2004 9:17:14 PM)
As time went by, the ideas were extended to higher dimensions, and
with those we could get rather complex natural sets as shadows of
a fractal "wire" that lives in three dimensions. And there
in the limit there was again a Gaussian distribution, but now over
two dimensions, like the ones seen on churches.
carlos puente (Mar 25, 2004 9:18:42 PM)
As we struggled with finding a proof for this last result, it so happened
that we tried to see how circles were being formed, and as a result
we discovered the "treasures" inside the bell, which are
lovely geometric designs made explicit by iterating two very simple
mappings.
benito (Mar 25, 2004 9:18:59 PM)
i read your book Treasures and i am amazed at the complexity and order
inherent in the patterns. Unlike the monsters of the Mandelbrot set,
the natural patterns of those of order and suggest an underlying
design. What do you think underpins the order and complexity of such
design: is there a Design in the designs we see?
carlos puente (Mar 25, 2004 9:22:46 PM)
Thanks benito, the object one gets via these ideas certainly evoke
those in the Mandelbrot set, but these ones turn out not be fractal,
for if one looks inside at increased resolutions one would not find
additional structure. The objects are indeed mathematical designs,
for once a trail of iterations is set one always finds them. The
order one sees is rather lovely and at the same time mysterious for
it depends in a non trivial manner on the actual iterations.
ptz (Mar 25, 2004 9:23:15 PM)
Carlos Puente, what do you think are the most signficant implications
of your research?
carlos puente (Mar 25, 2004 9:25:47 PM)
Thanks ptz, i think what is most relevant is the realization that many
objects and designs that appear to be generated by a mechanism of
chance, may, according to the ideas, not be so, but rather determinsitic
projections. I believe the ideas provide a new framework for thinking
about complexity in a Platonic way, one that may shed light to the
genesis of order of crystals, physical and biochemical.
Algorithm (Mar 25, 2004 9:26:27 PM)
What role do you suppose selfordering phenomena might have played
in the generation of linear digital bioinformation?
carlos puente (Mar 25, 2004 9:31:02 PM)
Thanks Algorithm. I could say that, according to the ideas, "selfordering" only
happens when the fractal object, which I often call a wire, fillsup
space. It is only in the limit when crystal patterns emerge, and hence
the information appears related to the infinity of the wire. This suggests
that the biological nature prefers such a limit in a way that needs
to be further understood.
J. Nelse (Mar 25, 2004 9:31:39 PM)
Dr. Puente, how does your research relate to Intelligent Design, if
at all?
carlos puente (Mar 25, 2004 9:35:38 PM)
Thanks J. Nelse, well, this research is not classical intelligent design
research as practiced by others at ISCID, but certainly the objects
that one encounters inside the bell are indeed designs, and the relevance
to nature of some of them, i.e., ice crystals and biochemical rosettes,
clearly show an intelligent way to think about them. That there is
aconnection between the binary expansion of pi and the rosette structure
of DNA inside the bell, certainly makes one wonder how is it that
such is there.
ISCID Moderator (Mar 25, 2004 9:35:39 PM)
We are currently low on questions. Feel free to send some more our
way.
Algorithm (Mar 25, 2004 9:35:53 PM)
Crystals are highly ordered rather than complex. Fractals are monotonous
iterations of the same pattern. The most “complicated” iteration
of any fractal can be fully described by a lowinformational compression
algorithm. A fractal may be “complicated” compared to
the same fractal with many fewer iterations, but it would not really
be “complex” in a Kolmogorov sense (noncompressible).
Can you shed any light on how chaos theory and fractals could have
produced such highly informational genes?
carlos puente (Mar 25, 2004 9:42:38 PM)
Thanks Algorithm, you are right that fractals are monotonous and crystals
highly order, but the beauty of the notions is that via projections
one may actually get a rather broad set of patterns (nonfractal
but "complex" in the Kolmogorov sense) whcih when understood
as shadows have a rather minimal description. For instance, one can
use the ideas of shadows to generate onedimensional data sets that
when classified according to methods on nonlinear dynamics would
result in seemingly "random" sets (i.e., highdimensional)
and also, just by varying the parameters, one could get even a "chaotic" set.
Chaos and fractals are useful notions in science and certainly in
geophysics, but our results indicate that one has a better handle
of the sets available by thinking about them as deterministic shadows.
Dreamer (Mar 25, 2004 9:43:08 PM)
The indications that apparently "random designs" might be
merely manifestations on our plane of existence of intelligent design
processes on another reminds me of the work of Dr. Robert A. Herrmann,
developed from nonstandard topology and logic. Are you familiar with
this?
carlos puente (Mar 25, 2004 9:48:07 PM)
Hi Dreamer, I am also another one. Well, I am not aware of Dr. Hermann's
work. Perhaps I should just repeat that Plato may perhaps have been
right all along when he argued that what we see are shadows of objects
outside a cave. Ore findings suggest that many natural sets may be
accurately modeled as the shadow of a wire. The ideas turn out to
be "intelligent" for some the sets we encounter in applications...
Dreamer (Mar 25, 2004 9:49:31 PM)
The "wires" imagery also reminds me of "string theory".
Has anyone looked into a possible connection there?
carlos puente (Mar 25, 2004 9:51:05 PM)
Yes dreamer, I sense that the connection should exist. But these wires
do not really vibrate as they are just fixed, and although one can
constructed in as many dimensions as used in string theory, staying
within four dimensions appears to be sufficient to study a host of
geophysicla phenomena.
ISCID Moderator (Mar 25, 2004 9:51:37 PM)
Any last questions?
Algorithm (Mar 25, 2004 9:51:55 PM)
Don’t we have to be careful of semantics when using the word “design”?
A design might be what we see in a kaleidoscope, which we know is highly
ordered and very low informational. But the kind of design these folks
like to investigate is algorithmically generated. An algorithm is a
sequence of decisionnode switch settings. The fractals seem to deterministic,
don't they?
Algorithm (Mar 25, 2004 9:55:19 PM)
too deterministic. Sorry about that!
carlos puente (Mar 25, 2004 9:57:16 PM)
Well, there are fractals that are deterministic and others which may
be done in a random way, just by introducing chance in the generating
mechanism. In regards to being careful with semantics, I certainly
agree. In the geophysical sciences it is a common practice just to
assume that whatever data set at hand must a the realization of a
random process. Our findings suggest that calling them "random" may
not be proper. There is fractality in such sets, but not at any scale,
as in classical fractals. Here is were the Platonic ideas provide
a nice geometric model, one that produces (in the limit) lovely patterns
(crystallike but not at all trivial).
ISCID Moderator (Mar 25, 2004 9:57:33 PM)
Here's the last quesiton...
Dreamer (Mar 25, 2004 9:57:49 PM)
The intricate order patterns generated from one "wire" by
multifractional sources would seem to indicate, at any rate, that beyond
the simplicity there is more complexity... right?
carlos puente (Mar 25, 2004 10:01:22 PM)
Well my fellow dreamer, inside the infinite spacefilling wires there
are infinitely many patterns (alefs as Jorge Luis Borges would surely
called them). Using distinct iteration pathways to sample such an
object leads distinct patterns in a manner that boggles the mind.
Yes, the procedure is rather simple and the patterns usually are
symmetric kaleidoscopes that appear to be simple, but trying to dream
them all is indeed rather complex, although they make a remarkable
jigsaw puzzle giving rise to a circular Gaussian.
ISCID Moderator (Mar 25, 2004 10:01:56 PM)
ISCID would like to thank Carlos Puente for being with us for this
online chat. Thank you!
carlos puente (Mar 25, 2004 10:02:05 PM)
Thank you all
ISCID Moderator (Mar 25, 2004 10:02:19 PM)
A transcript of the chat will be posted online in the near future.
Dreamer (Mar 25, 2004 10:03:12 PM)
Fascinating. Thank you.
Algorithm (Mar 25, 2004 10:03:17 PM)
Thank you very much.
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