Arthur Winfree – The Geometry of Biological Time


To understand the origins of fibrillation and potential treatments, Art initiated several different lines of enquiry. In careful numerical and experimental studies of two-dimensional excitable media, Art demonstrated that rotating spiral waves often meander in space—the exact geometry of the meander depending on the parameters of the differential equations or the experimental preparation (Winfree, 1990a).

Moreover, in some instances, spiral waves spontaneously break up, leading to many independently rotating spiral waves (Courtemanche and Winfree, 1991). In order to investigate the stability of the twisted and knotted scroll waves that he and Steve Strogatz predicted to exist and to determine initial conditions that might lead to these waves, Art and his students began an ambitious project of super-computer calculations of three-dimensional scroll wave dynamics (Nandapurkar and Winfree, 1987; Winfree, 1990b,1994; Henze and Winfree, 1991).

To determine the geometry of wave propagation in intact heart, Art collaborated with the late Frank Witkowski, a brilliant cardiologist who was building an optical mapping apparatus to study wave propagation in heart during fibrillatory rhythms by measuring the fluorescence of heart tissue stained with voltage-sensitive dyes. This work led to the observation of rotating spiral waves from the surface of a sheep heart during ventricular fibrillation (Witkowski, et al., 1998). Art’s ideas about cardiac arrhythmias and their relationship to rotating spiral and scroll waves are summarized in his book, When Time Breaks Down (Winfree, 1987).

This book helped to shape experimental and theoretical work by many investigators, including R. Ideker, J. Jalife, J. Keener and A. Karma. In 1987, Art moved from Purdue to the University of Arizona, where he continued his research on chemical reactions and cardiac muscle, somewhat incongruously, in the Department of Ecology and Evolutionary Biology.

Though good at it, Art was never truly comfortable with computer simulations. To him they were guides to his intuition, geometric vision, and experimental tinkering. How would it be possible to confirm experimentally the predicted existence of stable scroll rings and other more exotic, three-dimensional, rotating structures? Although it seemed likely that scroll rings could rotate deep in the heart, optical studies of wave propagation in heart tissue were only capable of imaging a thin surface layer, so it was impossible to observe scroll rings directly.

Hoping to find sound experimental evidence for the subtle and spectacular patterns playing out in his computer simulations, Art designed and built a system to measure with high resolution the concentration patterns of BZR intermediates in space and time. It was essentially a high-tech version of his stacked filter papers. By shining a light through the BZR and scanning the absorption of light at different angles, he used tomographic reconstruction techniques to determine the geometry of the three-dimensional rotating structure.

In Winfree et al. (1996), he described the many technical hurdles that had to be overcome and presented unequivocal evidence that the detailed anatomy of rotating scroll waves could in fact be observed in real systems. In what we believe is Art’s last paper on this problem, published post-humously, he addressed some of these matters computationally (Sutcliffe and Winfree, 2003). Unfortunately, following the demonstration of optical tomographic imaging of the BZR, the projected use of this method to study a host of other problems (such as the initial conditions needed to seed various three-dimensional structures, and the dynamics and stability of knotted and twisted scroll rings in real systems) was never completed. Those problems, many of which are sketched out in a recent review (Winfree, 2001), remain a part of Art’s legacy to future generations.

Golden Ratio in Life and Science

So called empty space is most likely structured. Buckminster Fuller already considered the possibility that the geometric structure of space was given by his Isotropic Vector Matrix (IVM): a network of interconnected tetrahedra and octahedra with a Vector Equilibrium in its center. This is what I have called the inner structure of Metatron’s Cube, a structure that scales inwards and outwards, and whose cartesian coordinates can be derived exclusively from integer and rational numbers, in fact from powers of 2 and 3 as in Aristoxenus musical scale. For Fuller, the IVM was a conceptual framework describing the symmetry of space, with which energy events could interact through its jitterbug property, producing a radiating wave of activity [3, p.192]. So the hypothesis is that, depending on the frequency of the sound source, a different geometric energy propagation pattern takes place in empty (structured) space. This geometric pattern may not captured by microphones, but it may interact with the subtle bodies of human beings, and it may be the source of the inherent qualities of sound that we are able to perceive but not yet to quantify.

The Heart is not a Pump


To any doctor trained in today’s medical schools, the idea that the heart may not be a pump would, at first sight, appear to be about as logi­cal as suggesting that the sun rises in the West or that water flows uphill. So strongly is the pump concept in­grained in the col­lective psyche that even trying to think otherwise is more than most people can man­age. Yet Rudolf Steiner, a man not given to unscien­tific or slipshod thinking, was quite clear on the matter and reiterated time and again that the heart is not a pump. “The blood drives the heart, not the heart the blood.”

Ralph Marinelli* and his co-workers published a paper refuting the generally-accepted pressure-propulsion premise. For a start, they draw atten­tion to the sheer volume of work which the heart would have to do if it were solely responsible for pumping inert blood through the vessels of the circula­tory system. Blood is five times as vis­cous as water. According to the propul­sion premise the heart would have to pump 8000 liters of blood a day in a body at rest and considerably more during ac­tivity, through millions of capillaries the diameters of which are sometimes smaller than the red blood cells them­selves – a huge task for a relatively small, muscular organ weighing only 300 grams.

Once the questions start being asked, the anomalies in currently accepted dogma become apparent. For instance, if blood were pumped under pressure out of the left ventricle into the aorta dur­ing systole, the pressure pulse would cause the aortic arch to try and straighten out, as happens in any Bourdon tube pressure gauge. In practice the exact oppo­site happens; the curve increases, indi­cating that the aorta is undergoing a nega­tive, rather than a positive, pressure.

Another paradoxical finding con­cerns the mechanics of fluid flow under pulsatile pressure. When a pressure pulse is applied to a viscous fluid in a closed vessel, the liquid initially resists move­ment through its own inertia. The pres­sure, therefore, peaks before the fluid velocity peaks. In the aorta, exactly the opposite happens where a peak flow markedly precedes peak pressure, a fact which was observed in 1860 by Chaveau and Lortet. So just what is going on in­side the circulation?

Misleading sketch of the heart by Leonardo do Vinci (1). The left ventricle wall is shown uniform in thickness as it would he in a pressure chamber. Actually the left ventricle wall thickness varies by about 1800% as Marinelli and his group measured in bovine hearts (2). The apex wall is so soft and weak that it can be pierced with the index finger. The peculiar variability in the ventricular wall thickness is not in keeping with the heart as pressure generator. However, Leonardo’s Notebooks has been used in most biology, physiology, and medical texts during the last few hundred  years as well as in most modern anatomy texts in the last decades (3). Thus, false sketches have served to bear witness to a false premise.

As Marinelli et al point out, the pres­sure-propulsion model of blood circula­tion rests on four major premises: (1) blood is naturally inert and must, there­fore, be forced to circulate; (2) there is a random mix of formed particles in the blood; (3) blood cells are under pressure at all times; (4) blood is amorphous and is forced to fill its vessels and take on their form.

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Thunderbolts – Turning Sound Into Light

by Jimmy Mikecz

What if sound didn’t only flow through matter but could produce unexpected phenomena like light? Research in sound has revealed the capacity of sound to influence matter in a way that produces light. The phenomenon of sonoluminescence (SL) is one example of this relationship.

The Equipment.

“If you want to find the secrets of the universe, think in terms of energy, frequency, and vibration.”
― Nikola Tesla

Sonoluminescence occurs when high-frequency sound vibrates tiny gas bubbles to reach star-like temperatures and emit flashes of light. The mechanism of sonoluminescence is not fully understood but its occurrence is well documented. As SL researchers probe deeper into the phenomenon, they have found that current fluid dynamic equations cannot explain why it happens. SL is a natural phenomenon as well, and marine biologists observe some species of shrimp using it as an attack against other creatures. It is the bridge between sound and light and can offer a deeper understanding of nature’s laws.


In a study at UCLA called Sonoluminescence: How Bubbles Turn Sound into Lightscientists S.J. Putterman and K.R. Weninger explore the mathematics and phenomenology of sonoluminescence. It is known that this phenomenon is caused by the rapid expansion and contraction of a bubble. This is known because the broad-band UV light emitted appears at a frequency, though not continuously. Think of a strobe light as an analogy where flashes of light last only pico-seconds (trillionths of a second.) According to Prof. Putterman, the phenomenon of sonoluminescence can heat bubbles up to tens of thousands of degrees. The surface of these bubbles burns at about 20,000 K (~35,000 °F) and look like “little stars.”

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The IllustrisTNG Project – Large Scale Cosmological Simulation


Somehow these guys are still thinking “Big Bang” and “Dark Matter”.

From their website:

The IllustrisTNG project is a suite of state-of-the-art cosmological galaxy formation simulations. Each simulation in IllustrisTNG evolves a large swath of a mock Universe from soon after the Big-Bang until the present day while taking into account a wide range of physical processes that drive galaxy formation. The simulations can be used to study a broad range of topics surrounding how the Universe — and the galaxies within it — evolved over time.

Scientific Goals

The goals of constructing such a large and ambitious simulation suite are to shed light on the physical processes that drive galaxy formation, to understand when, why, and how galaxies are evolving into the structures that are observed in the night sky, and to make predictions for current and future observational programs to broaden and deepen our understanding of galaxy formation. These goals are achieved not in a single step, but rather through a series of extended analyses of the simulations, each targeting specific science questions. Some of the first questions that have been specifically addressed using the TNG suite are characterizing the stellar masses, colors, and sizes of galaxies, understanding the physical origin of the heavy element (metallcity) distribution in galaxies and galaxy clusters, drawing connections between the presence of dynamically important magnetic fields and the observed radio emission from galaxies, and the clustering signal of galaxies and matter on large scales. Subsequent studies are expected to canvass an even broader range of topics.

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In Silico – A Short History of “Liesegang Rings”

In Silico

Periodic precipitation or the “Liesegang phenomenon” is a special type of chemical pattern formations. It was discovered by a German chemist and photographer, Raphael Eduard Liesegang in 1896 but did not have any general explanation more than a century ago.

Patterns in Nature

In the last decades of the 20th century different kinds of chemical, physical and biological pattern formations have excited an ever increasing interest in the scientific community. In chemical patterning one of the most intensively investigated area was the so-called Belousov-Zhabotinsky reaction, but there were many publications about viscous fingering, diffusion limited aggregation, morphogenesis of fungal colonies and some other simple living bodies, and last but not least patterning during electrochemical deposition too.

Although at first sight the above mentioned systems are quite different there are many similarities in the way they form the corresponding patterns, and the methods by that they can be handled. All of them contain at least one or several diffusion-limited steps, while the formation of the spatial or spatiotemporal order is always a result of a complicated interplay of these and the underlying chemical, physical or biological processes.

Mathematics and the modeling of reaction-diffusion processes

Mathematical description of such systems consists of so-called reaction-diffusion differential equations. Unfortunately these are usually systems of coupled nonlinear partial differential equations, that cannot be treated by standard analytical methods. The only viable way is the application of different numerical methods. Numerical solution of such systems of equations is computationally very demanding, moreover it is sometimes computationally prohibitive even nowadays.

The story of the so-called Liesegang phenomenon is good example for this problem.

Liesegang Patterns

Liesegang patterning is a special type of chemical pattern formation in which the spatial order is formed by density fluctuations of a weakly soluble salt. From analytical chemistry we know many different reactants that form a precipitate (sparingly soluble salt) when they react with each other. A good example for this behavior is the reaction of silver-nitrate (AgNO3) and potassium-dichromate (K2Cr2O7).

If one of these components is evenly distributed in a swollen gel (e.g. in gelatine), and the solution of the other diffuses into it, the spatial distribution of the slowly forming precipitate will not be continuous. A series of precipitate zones (bands or rings depending on the geometry of the experimental setup) will form according to some simple scaling laws.

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Favourable and Unfavourable EMF Frequency Patterns in Cancer: Perspectives for Improved Therapy and Prevention

Carcinogenesis fits in a frequency pattern of electromagnetic field (EMF) waves, in which a gradual loss of cellular organization occurs. Such generation of cancer features can be inhibited by adequate exposure to coherent electromagnetic frequencies. However, cancer can also be initiated and promoted at other distinct frequencies of electromagnetic waves. Both observations were revealed by analyzing 100 different EMF frequency data reported in a meta-analyses of 123 different, earlier published, biomedical studies.

The studied EM frequencies showed a fractal pattern of 12 beneficial (anti-cancer) frequencies, and 12 detrimental (cancer promoting) frequencies, that form the central pattern of a much wider self-similar EMF spectrum of cancer inhibiting or promoting activities. Inhibiting of the cancer process, and even curing of the disease, can thus be considered through exposure to the coherent type of EM fields.

Stabilization of the disease can be understood by constructive resonance of macromolecules in the cancer cell with the externally appied coherent EMF field frequencies, called solitons/polarons.

The latter, for instance, have been shown earlier to induce repair in DNA/RNA conformation and/or epigenetic changes. The field of EMF treatment of cancer disorders is rapidly expanding and our studies may invite further experimental and clinical studies in which systematically various potential EMF treatment protocols could be applied, with combined and modulated frequencies, to obtain even more efficient EMF anti-cancer therapies.

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