The Resonant Interval: The Word Vibrating in the Spaces of Time

Say: It is in Our power, should We wish it, to cause all created things to expire in an instant, and, with the next, to endue them again with life. The knowledge thereof, however, is with God alone, the All-Knowing, the All-Informed.

(Baha'u'llah, The Summons of the Lord of Hosts: 39)

From last post we understood that there are two main ways to understand resonance as the balance, equilibrium, symmetry, and harmony of things: either  through acoustic or auditory metaphors, or through visual images, such as the Lewis structure in chemistry.  We can call these balances, equilibriums, and harmonies vibrating resonant structures.

We learned, too, that resonance, as what goes on in the excited state of anti-symmetry, i.e. disequilibrium, is connected with freedom and creativity.  A physical system can have as many resonant frequencies as it has degrees of freedom, each degree of freedom can vibrate as a harmonic oscillator.  But too much reinforcing positive feedback on a frequency can break down the system—as when a glass breaks at a certain frequency that is held too long—because the system stores vibrational energy until it reaches its limit.  Too much negative feedback brings about a rigid, sclerotic equilibrium that is death.

All this implies, in my mind, several principles.  First, not only the periodic breakdown of a resonant structure, but also the building of new ones upon different frequencies and new vibrations can occur.  This, in turn, suggests profound implications for the power of the human will to bring forth new reality—implications which I cannot go into in detail in this post.  Briefly, I mean that an intentional, volitional attitude (which is a thought at certain frequency or vibration) when held long enough and intensely enough may have the power to shape or reshape reality.  Certainly the Manifestations of God had this power to a supreme degree.  Does not Baha’u’llah unequivocally state of the effect of His Revelation upon a moribund human society that: “The world's equilibrium hath been upset through the vibrating influence of this most great, this new World Order.” (Gleanings from the Writings of Baha'u'llah: 136)

But further than human society, yet intertwined with its changes and transformations, is the effect of Revelation upon even the physical foundations of the entire universe.  Consider this statement: “I testify that no sooner had the First Word proceeded, through the potency of Thy will and purpose, out of His mouth, and the First Call gone forth from His lips than the whole creation was revolutionized, and all that are in the heavens and all that are on earth were stirred to the depths. Through that Word the realities of all created things were shaken, were divided, separated, scattered, combined and reunited, disclosing, in both the contingent world and the heavenly kingdom, entities of a new creation, and revealing, in the unseen realms, the signs and tokens of Thy unity and oneness.

"No sooner had that Revelation been unveiled to men's eyes than the signs of universal discord appeared among the peoples of the world, and commotion seized the dwellers of earth and heaven, and the foundations of all things were shaken. The forces of dissension were released, the meaning of the Word was unfolded, and every several atom in all created things acquired its own distinct and separate character.” (Prayers and Meditations by Baha'u'llah: 295-296)

So where does this change and upheaval take place?  I say it takes place in what I am calling the resonant interval.  By resonant interval I mean the spaces between all living and created things, spaces that define the boundaries of resonant structures.  It is a kind of boiling cauldron of potentials that flow into existence when intention is focused upon it, something like lava erupting onto the surface of the earth that cools into rich soil.  Let us recall here Baha’u’llah’s statement that: “The world of existence came into being through the heat generated from the interaction between the active force and that which is its recipient.” (Tablets of Baha'u'llah: 140)

I also call it a resonant interval to denote, on the auditory side, the vastly intricate activity of creating new harmonies and balances that is the result of the Word of God calling into being a new creation.  For there are no absolutely empty spaces.  The universe is a plenum not a vacuum, but a plenum of various and discrete orders and kingdoms.  The gaps or spaces or intervals are laboratories of creation, the place to glimpse the substratum of life, the dark matter behind visible matter, the realm of becoming or coming into being.

In the resonant interval is turbulence and disequilibrium, death and birth, where chaos rules, complexity is built, and new harmonies are established because a new master vibration, a new Name or Title of God, has upset equilibrium, where either positive feedback or negative feedback, or both, has pushed the system to its break boundary. 

The resonating interval is the interface of vibrational orders whose myriad recombinations in creative interplay renews creation in new form.  It is where final states return to their opposite, where energy can reverse and flow backwards, where end states become new beginnings and new beginnings incorporate what ended. It brings the extremes into conjunction.  These reversals are not only in structure but also in polarity and the flow of energy.  Enantiodromia means “to flow backward” the name of the counterpart of movement.

In the resonant interval the primary focus is not on things, not upon objects created or creations transformed, but on emerging relations of creation and transformation from the active force of Will,  Defining these new relations, bringing them out from their invisibility, clothing them in language or numbers so they may be perceived, is to peer inside the exploding nova of creative activity.  Changing the focus of the mind from things to their hidden relations does tend to blur the outline of the things themselves, much as physicists cannot know simultaneously the position and momentum of a photon.  That is, relations are hidden when the mind is focused on the things. Things become hidden if the focus is on relations and interaction and interplay as things.  But if the things are concretions of relations then “these two are the same, yet they are different”.  This is the glorious structure of the interactions of the active force and that which is its recipient.  Cosmologically and archetypically that is Divine Will acting upon primal matter through the universal Intellect.

Between divine unity (things created spiritually perfect and complete from the first) and earthly union (the last and perfectly manifest form of the thing, its essence) is the vast realm of indeterminacy.  At every stage of this journey from unity to union there is the resonant gap where all possibility exists until a determinate choice is made.  This is where Destiny takes shape.

Resonant intervals appear at the boundary/union of both extreme and end states of an organic system or living thing.  From one view, end states are the exhaustion of creative possibility, the state of total equilibrium which is approaching death.  They are, nonetheless, states ready for transformation and sacrifice.  The system is in crisis.  Extreme states are the transformative energies at work. These have a different dynamic from those incremental growth stages occurring within an order. End states are the prerequisite conditions for extreme states to be manifest.  Extreme states generate energy for humanity to make leaps, the final leap being to transcend the entire order.  But from the view of unity, these two states are actually stages of one process leading to union.

In previous posts I have named these two stages as The End of Time and the Eclipse of Distance.  The end of time is an end state, but the eclipse of distance is an extreme state. It is the state where, as Baha’u’llah says, “Paradise hath been brought nigh, and Hell made to blaze!” (Gems of Divine Mysteries: 16), where the B and the E are joined and knit together.

Last post we read that resonance only occurs when the first object is vibrating at the natural frequency of the second object.  Creation must periodically be recreated so that it resonates with the new spiritual message.  In fact, it is the new Revelation that causes the excited state that breaks balanced resonance, revelation being the new master vibration.  What happens in that universal interval is the recreation of the universe.  Thus for acoustic resonance that is the “calling into being” of all things.  For the visual image it is the reconfiguration of creation.

More in next post.

Resonance: Joining and Knitting Together

All that is known owes its renown to the splendour of Thy Name, the Most Manifest, and every object is deeply stirred by the vibrating influence emanating from Thine invincible Will.

(The Bab, Selections from the Writings of the Bab: 195)

In this post and the next, through the phenomenon of resonance, I will propose a way to look at how the bonding, the joining and knitting together, of the spiritual worlds and material worlds may take place.

Briefly, because the spiritual and the material are exact counterparts, resonance operates or can operate between the spiritual and material realms.  When they are joined and knit together these realms are coherent at every level, like fractal spun yarn or large scale symmetry between levels of matter.  Resonance, the harmony of frequencies effected by the “vibrating influence” of the divine Will calling into being a new creation, is the mechanism of joining and knitting.  When coherence is achieved between the spiritual and material they become a resonant structure.  The finding of equivalent material vibration to manifest a vibrating spiritual reality is the creation of harmony between these two realms (the treble and bass, so to speak) and is, I believe, the basis of the phenomenon of manifestation.  First, what is resonance?

The word resonance comes from Latin and means to "resound"—to sound out together with a loud sound: an apt metaphor when linked with metaphors of creation by uttering the Word.  Resonance phenomena occur with all types of vibrations or waves.  Resonance needs a medium for waves and vibrations to travel through.  Resonance is the reinforcement or prolongation of sound by reflection from a surface or by the synchronous vibration of a neighboring object. 

There is resonance as the harmonics of interplay between interacting things, the vibratory frequencies that combine harmoniously to create, enhance and reinforce the equilibrium of living things.  The concept of resonance captures the interplay of the qualities of the field and all its interacting parts.  It is a fundamental quality of creation.

Resonance works in auditory harmonics as vibratory resonance.  In music, the natural frequencies of a musical instrument are sometimes referred to as the harmonics of the instrument. An instrument can be forced into vibrating at one of its harmonics if another interconnected object pushes it with one of those frequencies. When one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion that is resonance.  Resonance only occurs when the first object is vibrating at the natural frequency of the second object. 

In physics, resonance is a phenomenon in which a vibrating system or external force drives another system to oscillate with greater amplitude at a specific preferential frequency.  Frequencies at which the response amplitude is a relative maximum are known as the system's resonant frequencies. At these frequencies, even small periodic driving forces can produce large amplitude oscillations, because the system stores vibrational energy.

That means that acoustic resonance can result in catastrophic breakdown of the object at resonance with too much positive feedback. The classic example of this is breaking a wine glass with sound at the precise resonant frequency of the glass.  Soldiers tramping across abridge in lockstep can set up such a vibration that it can shake the bridge down, whereas if they break stride and go over with separate steps all is well, for individual vibrations cancel out.

In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of the bodies. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists—similar to the breakdowns in acoustic resonance. Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance.

Resonance also occurs not only between structures or things but also within structures when a system is able to store and easily transfer energy between two or more different storage modes (such as kinetic energy and potential energy in the case of a pendulum). However, there are some losses from cycle to cycle, called damping. When damping is small, the resonant frequency is approximately equal to the natural frequency of the system, which is a frequency of unforced vibrations. Some systems have multiple, distinct, resonant frequencies. The exact response of a resonance, especially for frequencies far from the resonant frequency, depends on the details of the physical system, and is usually not exactly symmetric about the resonant frequency.  This is like Dissipative structures.

In chemistry, resonance is a way of describing delocalized electrons within certain molecules where the bonding cannot be expressed by one single Lewis Structure. (A Lewis Structure is a kind of diagram or formula that shows the bonding between atoms of a molecule and the lone pairs of electrons that may exist in the molecule.)  A molecule or ion with such delocalized electrons is represented by several contributing structures, also called resonance structures or canonical structures.  The greater the number of contributing structures, the more stable the molecule.

In Lewis formulas, electrons are paired between atoms to form covalent bonds.  In molecules or ions that have a combination of one or more single and multiple bonds, often the exact position of the respective bonds cannot be indicated by a single Lewis structure. (Indeterminancy is a basic quantum principle.) That is, the bonded electrons appear to occupy an intermediate position between molecules. To solve this problem, the concept of resonance is used, and the molecule is represented by several contributing structures, each showing a possible distribution of single and multiple bonds. The actual structure has a lowered overall energy and an intermediate bond order.  The molecule is said to be "stabilized by resonance" or "resonance-stabilized".  The Lewis Structure is a visual image to try and capture what is really this shared, resonance energy. 

Every structure is associated with a certain quantity of energy, which determines the stability of the molecule or ion--the lower the potential energy, the greater stability because more of the potential energy has become manifest in form. The actual structure of a molecule in the normal quantum state (the molecule with its contributing structures) has the lowest possible value of total energy. This shared structure of the molecule and all its contributing structures is called the "resonance hybrid" of that molecule.

The resonance hybrid has a structure that is we can say is “intermediate” between the contributing structures; the total quantity of potential energy, however, is lower than the intermediate and hybrids are therefore always more stable than any of the contributing structures would be, because they are all together in balance or equilibrium.   The difference between the potential energy of the actual structure (the resonance hybrid) and that of the contributing structure with the lowest potential energy is called the "resonance energy.”

It is important to remember that resonance structures—the totality of connected molecules mapped by Lewis structures—are not transient states between stable contributing states, a form oscillating between stable states or existing as a temporary equilibrium between them.  Resonance-stability is a hybrid state existing in only one form, the form of a balance of forces.  Since no actual form of the resonance-hybrid can be observed to be resonating it can be said to be nonlocalized, or delocalized. Resonance energy would, too, be delocalized energy existing not in a field but as a field of which any particular molecule would be a concretion and configuration of that energy.

Quantum mechanics requires that the wavefunction of a molecule obeys its observed symmetry. If a single contributing structure does not achieve this, resonance is invoked.  Thus resonance is associated with symmetry.  If contributing structures have equal energy, they are equal contributors to the overall structure.  But this need not be the case. The symmetric combination gives the ground state while the antisymmetric combination gives the first excited state.

Hence, as we read with the breakdown that can occur with acoustic resonance and in celestial mechanics, chemical and molecular resonance is not just about achieving stability, symmetry, and balanced structure, but is also connected with freedom and creativity.  A physical system can have as many resonant frequencies as it has degrees of freedom, each degree of freedom can vibrate as a harmonic oscillator.  But there is the potential for instability, disequilibrium and new harmonics built into the system.  Here we transition to resonant intervals.  That is the topic of the next post.