ISCID - Live Chat with Carlos Puente

ISCID Chat With Carlos Puente

Transcript from March 25, 2004 9:00-10:00 PM Eastern

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 Berrett-Koehler. 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; rainfall-runoff 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 complex-looking sets as shadows when the fractal object in question has a low enough dimension and when it is illuminated by a so-called multifractal object. But we were in for a surprise for rather distinct shapes are generated as the fractal object fills-up 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 self-ordering 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, "self-ordering" only happens when the fractal object, which I often call a wire, fills-up 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 low-informational 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 (non-fractal 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 one-dimensional data sets that when classified according to methods on nonlinear dynamics would result in seemingly "random" sets (i.e., high-dimensional) 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 decision-node 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 (crystal-like 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 space-filling 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.