Microfilaments spanning cell
doublings and halvings in filament length
may suggest octave based
In base 10 math, each higher power multiplies the sum by 10, a convenience for dealing with large nmumbers.
But when cells reproduce, they double, they don't mutliply by 10.
When complex living systems bifurcate, they double, they don't multiply by 10
Christian De Duve, Nobel Prize winner, Physiology or Medicine, 1974
1. RHYTHMS IN HUMAN NATURE
So far our electron microscopes have only let us view cellular functions in frozen stillness on the smallest scale, where they are breathlessly beautiful. We can even see molecules. As soon as new techniques in scanning microscopy let us do real-time live cell imaging on the molecular scale, the music will become apparent, unavoidable really. It will strike us when we peer into the cell and see its microfilaments and microtubules moving, growing, waving, pruning back, vibrating like cell harps. Scientists will want to figure out the temporal relationships in those and many other cellular processes. From that moment, the balance between the material substrate and the oscillations it contains, between the instrument and the music it makes, will become more apparent. We will understand life then as an event in time, resonant on every level. Moreover, discerning the musical qualities inherent in change — for music is the art par excellence for representing change through time – we will develop tools to analyze biological processes in harmonic and octave relationships.
We can do this using a mathematics to the base two, rather than base ten, to quantify change, because it more faithfully represents the bifurcations, branching patterns, period doublings and halvings inherent in living nature. Using computerized musical analysis programs, we will develop methods that quantify nonlinear bio-oscillators clashing in complex ways. We will register out of tune notes, notes that are not quite noise, as beat frequencies. The influences of waveforms on each other, conceived biophysically, will link the non-living and the living world in a new way, joining physics with biology, biology with behavior, and behavior with culture.
The I Ching uses powers of two to express change. In the trigrams and hexagrams, there are only two symbols: the solid line and the dashed line. The solid line is about to bifurcate, the dashed line has already bifurcated and is in its resting condition, ready to come together. We can represent every curve on a waveform unfolding in time by trigrams built on powers of two. The notation makes perfect sense.
Integral nature, with us in it, is built on a thru-line of rhythm. Bio-oscillating systems interact in an ecology of rhythms. Organisms engage with each other by transferring their frequency and waveform characteristics. And this happens through bifurcations, period doublings and halvings that can be represented in base 2 math, or, more simply put (at least more meaningfully for me) in musical notation. These oscillators behave according to
simple rules. In the simplest couplings, two rhythms fall into phase with each other and draw other close frequencies in.
Winfree explained that
“despite the variety of mechanisms that underlies rhythmic timing and its control in living organisms, several modest generalizations stand out. For example, any spontaneously rhythmic mechanism (‘oscillator’) can be expected to lock on to the nearby period of a strong enough rhythmic influence… This ability of most nonlinear oscillators to entrain or synchronize rests on their time-dependent sensitivity: exposed to some standard disturbance beginning at different times in the cycle, there will be different phase shifts inflicted.” 9
Rhythmic entrainment, resonance, dissonance, frequency pulling, constructive and destructive interference, and other kinds of modulation, make the movements of life coherent.
Frequency matching must have entered into evolutionary selection from the beginning. Species living in resonant relationships with each other, it follows, move, ship materials, transmit energy and share information in common frequency ranges.10
Interactions that work between pairs of oscillators within individuals must also work in larger arrays, stimulating biochemical reactions between as well as inside organisms, including those of different species.
Browsing animals follow the ripening grasses, plankton float and sink to the changing temperature gradients of the sun-warmed waters. Predators follow prey animals whose feeding patterns follow the vegetation. These rhythmic patterns repeat year after year. If the grass is late, the browsing herds are late. If the climate changes, the rhythms reset. At the mouth of the Navarro River near where I live, for instance, the sea birds gather to feed on the salmon fry as they swim down river at the end of the summer. But the fish can’t get out to sea until the sand bar that blocks the river mouth breaks down with the high tides in the first winter storms.
Species are entrained to each other through weather and seasons.
Christian De Duve described the basic information and energy transfers that go on in these interactions. One or the other has to apply:
1) One oscillator may provide or remove ingredients required by another, creating positive or negative feedback loops.
2) They may intrude on one another’s space of operation, take up room, and block activity, as in receptor site blocking.
3) They can add or subtract energy. Temperature increases generally speed reactions.
4) One oscillator may agitate the medium in which another oscillator functions. Wind on water influences the patterns of surface planktonic life.
5) They may have their own clock cycles that open or close gates, adding or blocking materials or energy needed by another oscillator.
The same five energy, information and material transfer processes that shape all life undergird love and wisdom too. They are emergent properties of the primordial rhythms. They evolved into love and wisdom during paleolithic times.
In the rest of the chapter I will develop an approach to the life sciences that builds on the concepts of evolutionary chronobiology. (Warning. The science gets tough. If you only want to hear about love and wisdom skip ahead to chapter two. But stick with me now to get the grounding you need to understand where emergent love and wisdom are likely to go in the future.
Base 2 Math:
Each higher power doubles the sum just as the note A above middle C= 440cps while the note A an octave higher= 880cps
Base 10 Math: