Physics is the heart of the Universe. Everything is explained, or should be explained, by the Laws of Physics.

Mathematics is the heart of Physics. Mathematics include Arithmetics, Algebra, Geometry, and Trigonometry, plus plenty of other disciplines, especially Calculus, which is the mathematics of change.

Mechanics, both Newtonian and Quantum, is a branch of Physics. Still, I posit that the Mathematics of Mechanics is the heart of Mathematics.

Waves are at the heart of Mechanics.

Vibrations are the heart of Waves. Vibrations are the HEART OF THE MATTER, Heart of Hearts of the Universe.

D-SP posits: Vibrations are essences of matter and energy, and thus, are at the heart of everything that is in the Universe.

In fact, the quality of the vibrations defines what is Matter and what is Energy. And their kind, too.

Heat-induced vibrations are the ones that charaterize the usual ones present in the surface of the atoms of the matter we are used to. The vibrations are variable in frequency and amplitude, according to the temperature and also mechanical influences. Since the atomic surface is virtual, created by the speeding clouds of the outmost electrons creating the fictional surface, it is the these electrons which suffer such influences. The vibrations are of a simple --mechanical-- nature.

Significant augmentation of those mechanical vibrations cause waves, a manifestation of vibratory energy. In a conducting --elastic-- medium, these waves may become audible.

Electromagnetic (E-M) waves are the product of vibrations of the internal electrons, while the most energetic ones, or gamma-rays, arise from vibration of the nucleons. Those waves carry their propagating medium along, as electric and magnetic fields.

It is essential to understand the difference between these two types of waves, and also the fact that at the end, both act through vibratory effects. But the essential difference is that E-M radiations (photons) transport a modicum of energy, as vibratory information or code, to the target atoms and molecules. The energy will now result from the activity of the target's different atoms and molecules. There is energy in earth's matter, which in fact is a derivative of an exploding supernova. Life started in the absence of photons, using energy stored in earth's interior. Friction can start a fire inside a dark room.
In contrast, mechanical vibrations contain the energy in themselves, which is mostly conveyed in the resulting waves, or else is completely converted into heat. In a vacuum, the heat (vibrations of the external electrons) will be "dissipated" as infrared waves.

To follow the mini-essay structure of D-SP writings, I shall limit this one to an example that might offer a gist of the subject under treatment. The infrared E-M radiations emitted by the electrons of hot atoms are energetically lesser than those of visible light (red to violet). Yet, light does not cause damage nor heating. In fact, infrared photons are not "hot." But their waves, resulting from heated electrons' specific vibrations, are penetrating, and excite the surface of the target atoms. Those surfaces vibrate attuned to the photonic specific wave-information, and the resulting interatomic surface friction causes the vibrations that are manifested as heat at the target.

Thus, friction is a factor to be contended with, for the understanding of many physical phenomena. In fact, friction is basic to comprehending static electricity, the atmospheric effects of El Nin~o, tempests, hurricanes and typhoons. The latter manifestations are better understood by learnig basics on COMPLEXITY AND CHAOS.

Ultraviolet photons damage the DNA of the skin cells, with the possible causation of skin cancers. X-rays and gamma-rays cause this damage deep in the body of living organisms. However, the immediate effect is activation of the apoptotic mechanisms, resulting in immediate cell death of the more susceptible tissues, at depths depending on the wavelenght. Here is an example of strongly energetic photons not even heating target molecules.

It is also relevant to know that photons, as existing naturally, are actually the pairing of two constituents having opposite charges. The two can be separated artificially, behaving then as physico-telepathically connected halfs. The two halfs do not destroy mutually for reasons of their peculiar electromagnetic nature, thus being the only neutral particles known.

The classic example of the pebble causing waves in the water is explained as follows. The kinetic energy of the pebble is transformed into vibratory energy in the water molecules hit by it, the waves being the final manifestation of the vibratory energy.
But mechanical --simple-- vibrations have their own Limits of the Second Kind, that is, critical points, as I intend to delve upon, with the intention of explaining hitherto unthought, or not sufficiently explained, realities.

Memory, seemingly a "non-physical" entity, for instance, I posit that is kept in "memory banks" made of neurons in which cognition and affection are deposited as "SUPER-PROTEINS" that I call COPROTS and FEPROTS. These molecules act through the vibrations of their complex electrical charges in an array-like disposition.
Memory makes for awareness. Self-consciousness --a higher-level of awareness, i.e., at its most developed-- exists only in Homo sapiens.

Consciousness is the final result of memory-proteins vibratory waves interfering with the respective cognitive and affective vibratory waves from incoming actual experiences, once these are processed through the immediate memory processors in specialized neurons. The result is the production of inchoate memory super-proteins, which might become saved or soon destroyed, depending on their structural stability.

The interaction of the memory and immediate-experience vibratory waves results in what is called interference. A perfectly creative, positive interference, by the exact superposition of the waves, results in the sensation of 'deja-vue' and, if complex in nature, of the 'peak experience.'

There are two kinds of mechanical vibrations. Those of the passive, "first" kind, are classically represented by an elastic string responding to a stimulus with a limit in its capacity of producing the maximum vibratory response.
It is of magnificent interest to recall that Pithagoras sudied the resultant sounds, thus discovering harmonics and starting to believe that "all is number." I would paraphrase him by saying that "all is vibrations."

The study of vibrations added grandly to the knowledge of mathematics and mechanics. Roger Bacon wrote about the importance of mathematics and of experiment to further knowledge. Then Francis Bacon was attracted by mechanics, and again insisted in the need for experimentation. By asking to leave aside preconceptions, he anticipated Descartes and created empiricism. Galileo took to practice experimenting in testing hypotheses. He based his support for Copernicus heliocentric theory on observations of Jupiter's moons, and used analogical thinking, perhaps without realizing that ANALOGY is the bedrock of hypotheses. He was also drawn to the study of waves, as were other well-known mathematicians, like Bernoulli, Fournier and Laplace.

None of them, though, realized that the most interesting mechanical vibrations-waves are those of an active, "second" kind.
Notice that an elastic body will reach a boundary limiting the vibratory energy it can generate as a result of a mechanical action upon it. But, analogically with the principles enunciated in LIMITS, the energy that can be added (from without) to the selfsame body has a very wide spectrum, with the corresponding critical points. By learning these points, it becomes possible to understand how energy-matter are affected by the application of vibratory energy.

The D-SP essay on LIMITS deals with the changes suffered by the H2O molecule when the temperature is decreased or increased. It is rational to choose less or more heat as the change effector, because heat is the primary energy to which the others tend to converge. Heat is the heart of ENTROPY, of wastage, and of most CHAOS. (A situation when sudden changes occur due to a number of simultaneous influences, until a new or similar order is established as equilibrium is reached.)
That is the main reason for D-SP's contention that the Big Bang was a dark and cold brutal expansion, and that heat and the resulting light called star were then created when helium formed from the brutal compression of hydrogen.
It would be most revealing activating a charge of dynamite on the moon or in space.

The Greek root for heat is 'thermos,' while the Latin one is 'calor.' Speaking of heat causes mental confusion, due to its sensory connotation. The Laws of Thermodynamics refer to thermos as the Basic Energy, and it is only fitting that vibration and heat be intimately related entities, even though describable as separate concepts, where friction plays a leading role.
But it must be always kept in mind that this is true only with mechanically created vibrations-waves.

The number of oscillations per second (frequency) of a given E-M vibration-wave specify its nature --from radio to gamma-ray-- while the amplitude defines its intensity.
In contrast, both the frequency and the amplitude of mechanical vibrations in the surface of an atom or molecule are augmented by simply applying external heat. Contrariwise, the Bose-Einstein condensate is the end result of the opposite action: decreasing both the number and the amplitude of the target's vibrations to the lowest possible, which cannot be zero. Subtracting energy cannot destroy atoms.

A heated iron rod becomes red and incandescent because of the vibratory effects of the heat on the atoms' surfaces. When the vibrations increase to a critical point, the structure of the rod is destroyed, and next the component iron molecules melt.
Similarly, should a metallic string be subjected to a critical frequency of vibrations by a 'supervibrator,' it would reach the melting point. This is a situation of active, "second" kind mechanical vibrations. Yet these phenomena are relatively innocuous, because the atoms remain intact. But take those atoms, and make their surface vibrate at increased oscillations even further. The outermost electrons are expelled, then the others, while emiting light, ultraviolet and X-ray photons, and finally, the nucleons emit gamma-rays, until reaching the breaking point.
Now the nuclear particles are released --as the seeds leave a broken pommegranate, although at the speed of light. The potential energy stored in the gluons created by the brutal pressure of the hydrogen cloud will be released as "plasma gluons."

But to reach that critical limit, the only way is through heating the atom at an intensity equivalent to a million or more times the present at the sun's surface. How can that be acomplished? By smashing atoms with similar atoms heavy with nucleons, and traveling at near-light speed.
The friction resulting from that stupendous encounter of atoms increases the temperature to the point of nucleon-destroying vibrations.

When one thinks of smashing something, the image is of a broken bone or of a crushed vehicle. That is smashing of the first kind. We are dealing now with the titanic second kind, which if not powerful enough, will just heat and deform the atom's nucleus for an instant. But when reaching the critical point of both vibration frequency and intensity, the resulting heat causes an insufferable deformation and rupture of the nucleons' boundaries, whatever their nature is.
Friction is the royal road to mechanical vibrations, manifested as increased temperature. Prometheus taught this basic fact to Homo sapiens, according to Greek legend. Friction also causes static electricity, which is the basic electricity, the one we use being artificial.

It is of D-SP interest to notice that the Second Law of Thermodynamics refers to the natural tendency to disorder, or chaos. Now, such chaos is of the First Kind, not to be confused with the CHAOS of the Second Kind, considered in COMPLEXITY AND CHAOS.
This law is called The Supreme Law, and it might be offered as a physical parallel to the D-SP's evolutionary BAD. Which is not correct, because the parallel physical GOOD is the application of energy to prevent or revert the simple chaos of disorder. But mainly, because the evolutionary BAD is what allows for the individual's advancement.

Unraveling the phenomenon of interference is one of the fruits growing out from the study of waves. This essay dealt with it at the beginning, when attempting to explain memory, awareness, and H. sapiens' consciousness. These manifestations are expressions of interference, when the elecromagnetic vibratory waves of the memory super-proteins react with the waves of the sensory impressions at the present moment. To understand the time-lapse required for such highly complex process, it should be well-taken the advice of reading the essay NOW.
Applications to the phenomenon of constructive and destructive interference, as revealed by interferometry, are legion, but of no further interest to D-SP.

Note: I became aware of my ignorance on the subject of vibrations and waves while explaining the Second Law of Thermodynamics to my not-yet 13 yr. old granddaughter visiting from Jerusalem. I had always been mystified by the choosing of the word thermos when refering actually to Laws of Energy Dynamics. Thinking of this, I realized that indeed, heat is the basic energy. Then I associated with vibrations, and further on I read about these subjects... The present essay was sketched two days later, and then developed two days later and further on, during many hours. I phoned my grand daughter to thank her for the part she took in this pleasurable intellectual exercise, when willing to learn physical basic facts as one of D-SP's underpinnings.