Melting ice caps
Melting Ice Caps

arthur winfree




Perturbed Rhythms

     With their many contrasting frequencies, the oscillators in love and wisdom can clash in complex ways. We do not tick with the precision of quartz watches. External influences can draw our bio-oscillators away from their resident frequencies. Their phase relationships to other oscillators in the body can shift. Frequencies can pull on each other. In the interpenetrating fields of multiple vibrations that constitute inner and outer life, all kinds of dissonant interactions can disrupt body functions.
        The complex phase relationships between the 24-hour day and the 25-hour drift of the circadian clock or the 27 and 29 day solar and lunar months, themselves may produce beat frequencies between body systems. The persistence of these out-of-phase harmonic relationships over huge spans of evolutionary time suggests that organisms have made use of them to adjust or reset their biological clocks.
          However, there are limits to our resilience. Beyond a certain range of frequencies, beats and dissonances may derange the body, disrupt communications and degrade the instructions they bring from one body system to another. Derhythmization can lead to illness, ecological disasters or extinctions.


    Glass and Mackay illustrate simple perturbations in an experiment that analyzes

“The effects of a brief electrical shock delivered to an aggregate of spontaneously beating cells derived from the ventricles of an embryonic chick heart. In response to a brief electrical stimulus, there is a resetting of the phase of subsequent action potentials, but the original cycle time is reestablished within several beats… Poincare called such oscillations stable limit cycles… If, on the other hand, a small perturbation induces a change in the dynamics so that the original dynamics are not reestablished, then the steady state or limit cycle is unstable…. Any value of a parameter at which the number and/or stability of steady states and cycles change is called a bifurcation point and the system is said to undergo a bifurcation… Since small changes in parameters lead to qualitatively different dynamics at bifurcation points, systems are not structurally stable at bifurcation points.” 3

     Arthur Winfree, a pioneering biophysicist and chronobiologist, makes the case that small perturbations to rhythms, when precisely timed, can have big effects. In his studies on cardiac arrhythmias, especially ventricular fibrillation, he observed, “a small local depolarization can trigger transition to fibrillation…If the stimulus is too big or too small or wrongly timed, it won’t work. There is an atrial vulnerable phase and, later, a ventricular vulnerable phase."4


        Biophysicists call the rhythm-resetting moments, when they come, bifurcation points. They have been studied across an enormous range of physical, chemical, biological, social and even economic systems. Paul Davies describes them clearly: “At the bifurcation point,” he writes, “the inescapable fluctuations, which in ordinary equilibrium thermodynamics are automatically suppressed, instead become amplified to macroscopic proportions, and drive the system into its new phase which then becomes stabilized.”5

                                                           bifurcation in Hopi life plan

                                                          Hopi Life Plan Showing Bifurcated Pathway
     We will encounter these fluctuations on all levels, from cells to civilizations. They work their way through human life in every venue. Possibly every biological rhythm by the time we get to see it is already perturbed, reset, become a compound rhythm, a carrier of near and distant echoes, timbres and modulations. You rarely encounter a timbreless tone in nature or a pure sine wave in music.


     I tentatively conclude from this that our vulnerability to perturbation, because it is itself subject to natural selection, has evolved to give us tools for restoring or replacing rhythms under varying assaults from inside and outside. Since rhythmic organization is the foundation for many life processes (and for the human meaning bestowing experiences we have already touched on) a selective process to restore rhythm to disturbed body processes, probably through epigenetic signals to clock genes, would have increased our fitness. This could explain why rhythm and phase resetting capabilities are found everywhere in nature.
     We are creatures built of multiplexed, nonlinear bio-oscillating systems partly coupled to the surrounding medium, partly resistant to it and partly rhythmically dominating it. This is to say that when we are perturbed we are adapted to respond to it. We try to resist disruption. We make efforts to restore rhythmic functioning. We will fight off or get away from the perturbing forces. Our physiology is designed to return to homeostasis. A robust response to perturbation allows for adjustment, repair and renewal. The plasticity in the nervous system, the duplications of pathways, the alternate routes in the brain, the cascading interactions of biochemical processes on regulatory genes all cope with perturbation.


     The most crucial messages sent and received in the rhythmic fields of life, from its most primordial expressions on, have to do with love and wisdom, the principal focus of the book.

                                         sea horses                                chimp family

     In primitive organisms these take the form of rudimentary approach/separation and withdrawal/return oscillations, in higher organiams to group or family life. The biochemical signals transmitted by these same dynamics tell us whether we are alone or not, coherent or not, safe or not. The perturbations to those rhythms, when they hit, raise alarms. All species have evolved means for restoring rhythmic functioning. The physiology in them regulates the temporal aspects of homeostasis in living organisms. That is why to understand love and wisdom,  even inwardly, as experienced, we have to see how we fit in primal nature generally.

Planetary Nature

planetary spirals Look at it ecologically. That’s where it starts. We live in a vibrating world whose waves and rhythms surround and course through us. The length of the day, the seasonal cycles of light and dark, variations in solar radiance, geomagnetic, electrostatic, hydrodynamic and many other frequencies are in our makeup. The month is in the menstrual cycle, the day is in the sleep/waking cycle. Even the simplest cyanobacteria have circadian clock genes.6    All organisms without exception live by rhythm. 7
     Arthur Winfree described the coupling of environmental rhythms to the rhythms of life this way:

“We began with daily time organization in a piece of rotating machin-ery none of whose parts (mountains, oceans) has an intrinsic daily rhythm; but coupled together and pulling one another along in se-quence, they constitute a clock. We passed through wide-ranging studies of chemical life-forms evolved on the surface of that clock, finding many chemical oscillators.”8
water cycle

     Many of them move in frequencies associated with the hydrological cycle: ocean currents, tidal movements, temperature change, barometric pressure, evaporation, weather and
ocean currents climate.                  
  Rhythmic influences are as fundamental to life as are the atoms of carbon, oxygen, nitrogen and hydrogen that give it mass. However, they are not, strictly considered, material entities. They are processes, patterns of movement that ride on matter.
     Our gait is rhythmical, our heart and breath interact rhythmically. Respiration inside the cells is rhythmical. Catabolism and anabolism, sodium/potassium transport through the cell membrane, nerve conduction, and the acid/base oscillations in blood chemistry all have oscillatory characteristics, reflecting prebiotic solar and hydrological rhythms (See # 24-26.)
     When we reach out to say or do something our words and gestures are pulsatile and move in specific frequency ranges. Every spoken word that comes out of us we deliver on an exhalation; the heart registers every arousal, and all musical tempos pulse at heart rates from largos of 40 BPM to prestos of 240 BPM. Melodic phrases follow breath lengths. All the rhythmic patterns of music conform to locomotion, gestures and dexterity. Every larger pattern of behavior that builds from these components in every animal species, from mating to feeding, fighting and healing, plays out rhythmically, with wave fronts interfering and entraining each other, amplifying, reflecting, diffracting, all in pulsatile movements that we can quantify by frequency and amplitude and locate in phase relationships to other oscillators in nature.
     It is not the case that waves are secondary to the sea, or the heartbeat to the heart, or the spoken word to the vocal cords or music to the instruments that play it.
     If you make this wrong assumption, you commit what Alfred North Whitehead called the fallacy of misplaced concreteness.