Synthesis

Universally,
In perception or conception,
Manifestations
Synthesis of all
Possible quantum scenarios.

Reflection on the introduction, by Paul Davies, to “Six Easy Pieces” by Richard Feynman:

All physics is rooted in the notion of law – the existence of an ordered universe that can be understood by the application of rational reasoning. However, the laws of physics are not transparent to us in our direct observations of nature. They are frustratingly hidden, subtly encoded in the phenomena we study. The arcane procedures of the physicist- a mixture of carefully designed experimentation and mathematical theorizing are needed to unveil the underlying law-like reality…

The problem is that quantum ideas strike at the very heart of what we might call commonsense reality. In particular, the idea that physical objects such as electrons or atoms enjoy an independent existence, with a complete set of physical properties at all times, is called into question. For example, an electron cannot have a position in space and a well-defined speed at the same moment. If you look for where an electron is located, you will find it at a place, and if you measure its speed you will obtain a definite answer, but you cannot make both observations at once. Nor is it meaningful to attribute definite yet unknown values for the position and speed to an electron in the absence of a complete set of observations…

The Feynman method has the virtue that it provides us with a vivid picture of nature’s quantum trickery at work. The idea is that the path of a particle through space is not generally well defined in quantum mechanics. We can imagine a freely moving electron, say, not merely traveling in a straight line between A and B as common sense would suggest, but taking a variety of wiggly routes. Feynman invites us to imagine that somehow the electron explores all possible routes, and in the absence of an observation about which path is taken we must suppose that all these alternative paths somehow contribute to the reality. So when an electron arrives at a point in space-say a target screen—many different histories must be integrated together to create this one event. 

Heart Of The Matter

Mechanical energy is the sum of potential energy and kinetic energy.

Potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

The kinetic energy of an object is the form of energy that it possesses due to its motion

Motion is when an object changes its position with respect to a reference point in a given time

Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, and into the future.

Existence is the state of having being or reality in contrast to nonexistence and nonbeing.

Reality is the sum or aggregate of all that is real or existent within the universe, as opposed to that which is only imaginary, nonexistent or nonactual.

Energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of [thermodynamic] work and in the form of heat and light.

Thermodynamic work is one of the principal processes by which a thermodynamic system can interact with its surroundings and exchange energy.

A physical quantity, quantitative property (or simply quantity) is a property of a material or system that can be quantified by measurement.

A physical system is a collection of physical objects under study. A thermodynamic system is a body of matter and/or radiation separate from its surroundings that can be studied using the laws of thermodynamics.

Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation.

Radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium.

A physical object or physical body (or simply an object or body) is a collection of matter within a defined contiguous boundary in three-dimensional space.

Three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point.

A mathematical space is a set (sometimes known as a universe) endowed with a structure defining the relationships among the elements of the set.

A set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

A mathematical object is an abstract concept arising in mathematics, where an abstraction is a process where general rules and concepts are derived from the use and classifying of specific examples, literal (real or concrete) signifiers, first principles, or other methods.

That signified and its signifier refer to the two main components of a sign (anything that communicates a meaning that is not the sign itself to the interpreter of the sign), where signified is what the sign represents or refers to, known as the “plane of content”, and signifier which is the “plane of expression” or the observable aspects of the sign itself.

A concept is an abstract idea that serves as a foundation for more concrete principles, thoughts, and beliefs.

A universe is a collection that contains all the entities one wishes to consider in a given situation.

Matter is any substance that has mass and takes up space by having volume.

Volume is a measure of regions (a non-empty, connected, and open set) in a topological space, three-dimensional space.

Mass is an intrinsic property of a body. It  experimentally defined as a measure of the body’s inertia, meaning the resistance to acceleration (change of velocity) when a net force (the sum of all the forces acting on an object) is applied. The object’s mass also determines the strength of its gravitational attraction to other bodies.

An intrinsic property is a property of a specified subject that exists itself or within the subject.

  • A subject is a being that exercises agency, undergoes conscious experiences, and is situated in relation to other things that exist outside itself; thus, a subject is any individual, person, or observer.
  • An object is any of the things observed or experienced by a subject, which may even include other beings (thus, from their own points of view: other subjects).

H.H. the Dalai Lama’s commentary “Defending the Two Truths, Practicing Wisdom” 

By meditating on the sphere wherein all dualistic elaborations have been pacified, we accumulate wisdom. And we accumulate merit by deepening our conviction in the validity of the casual principles within the context of conventional truth.

Categories such as “subject and object,” “perception and object,” “one and many,” “self and others,” and of course, the “existence of all phenomena” are dependent upon worldly conventions. They are thus relative.

Bodhicharyavatara: 

[108] Analysis and what is to be analyzed
Are linked together, mutually dependent.
It is on the basis of conventional consensus
That all examination is expressed.

[110] If phenomena are truly analyzed,
No basis for analysis remains.
Deprived of further object, it subsides.
That indeed is said to be nirvana.

When the object of an inquiry is subjected to critical analysis, the subject too is revealed to be devoid of any intrinsic reality or intrinsic origination. This absence is described as nirvana, the state beyond sorrow (defined in terms of the cessation of karma and afflictions). So while a meditator is directly experiencing the emptiness of intrinsic existence of all phenomena, there is no basis for grasping onto the intrinsic existence of anything else.

For the meditator in this state, there is no awareness of subject and object. A subject-object distinction could be made, but since the meditator’s mind is totally fused with the absence of inherent existence, there is no need to analyze the emptiness of the analyzing mind itself.

A History of Cobb County Georgia

From: “The First Hundred Years” (1935. Sarah Blackwell Gober Temple)
 
CHAPTER I: EVENTS LEADING TO THE ORGANIZATION OF COBB COUNTY
 

§ TREATY RELATIONS WITH THE CHEROKEE INDIANS

1
 
    On the morning of May 29, 1820, a tall weatherbeaten man stood at the Shallow Ford on the Chattahoochee River, in Georgia. He surveyed the pleasant scene before him. The river sparkled in the spring sunlight. The wooded slopes were covered with fresh green foliage, the distant reaches veiled in a blue haze.
    He was not actually thinking of the scene itself, but of the struggle for the possession of the land upon which he stood. It was his consideration of the animosities attendant upon the ultimate outcome of this struggle between the Indians and the white people which gave him pause.
    Whatever that outcome, he was here now to uphold the law. He bent his head to write. He was often not good at spelling, but he always made himself understood.
    “Intruders on the Cherokee lands, beware,” he began with his customary directness. “I am required to remove all white men found trespassing on the Cherokee lands not having a written permit from the agent, Colo. R. J. Meigs, this duty I am about to perform. The Regulars and Indian Light horse will be employed in performing this service, and any opposition will be promptly punished. All white men with there live stock found trespassing on the Indian land will be arrested and handed over to the civil authorities of the United States to be dealt with as the law directs, there families removed to U. S. land, there crops, houses and fences destroyed …”
    He signed his name. Andrew Jackson. Then he posted his notice, mounted his horse, and turned toward Alabama.
    “On the excursion through the Cherokee Nation,” he wrote to Mr. Calhoun, the Secretary of War, on June 15, “I found a great many intruders and those on the north of the Chatahoochey not only numerous but insolent and threatening resistance.”
    Those fertile acres along the Chattahoochee River, which forms the southern boundary of the present Cobb County, were coveted by the white man and held by the Cherokees. Again and again intruders settled upon them, only to be driven off by Indian agents appointed by the United States Government, or by the Indians themselves. Eighteen years were to elapse before the destiny of the Cherokees east of the Mississippi was determined. Twelve years went by before Cobb County came into being. General Jackson, as he stood near the edge of the county that spring morning in 1820, foresaw only a part of the complications which would attend the organization of the county, and the coming of the day when white men would finally become the legal owners of land which for years beyond the memory of man had been in the possession of the Indians.
    Cobb and the other counties formed from the Cherokee Nation came into being with reverberations which shook the country and Georgia from end to end; arrayed friend against friend; threatened the state with disciplinary measures by the general government; caused Georgia to defy the nation; and unloosed upon the people of the state such criticism and odium as has not been experienced except at the time of the War Between the States and during the subsequent reconstruction period.
    We must turn back some years if we are to understand properly this dramatic chapter in the history of the nation and its relation to the history of the county. We shall see how cessions of Cherokee land to the government lessened the Indian holdings and provided opportunity for settlement by white men in a time when most men were seeking new land. The slow, merciless march of time wrought inevitably the changes in the fortunes of white men and Indians which resulted in the organization of Cobb County. Historians have written vindictively of this group or that, this white man or that Indian, whose machinations caused the tide of affairs to boil more furiously at one point, to recede at another. This is futile. Bitterness and recrimination have no place in the long reach of history, and are to be considered, in arriving at truth, only as details of the great pageant.

Continue reading “A History of Cobb County Georgia”

V838 Monocerotis Light Echo

V838 Monocerotis a spectroscopic binary star system (a binary star evident from the Doppler effect) in the constellation Monoceros about 19,000 light years from the Sun. Identified as a luminous red novae, thought to have been [caused by the] merger of two stars within a triple system.

V838 Monocerotis and its light echo as imaged by the Hubble Space Telescope on December 17, 2002
CreditNASA/ESA
Images showing the expansion of the light echo. Credit: NASA/ESA.

light echo is a physical phenomenon caused by light reflected off surfaces distant from the source, and arriving at the observer with a delay relative to this distance. The phenomenon is analogous to an echo of sound

Reflected light following path B arrives shortly after the direct flash following path A but before light following path C. B and C have the same apparent distancefrom the star as seen from Earth.
Direct light from a stellar outburst (white spot) reaches the observer (path 0) followed by light reflected off particles on progressively wider paraboloids (1–5): the observed disc apparently initially expands faster than light but the illusion is due to light reflecting off different unrelated particles
Animation of 11 images of light echo of V838 Mon

In the case of V838 Monocerotis, the light echo produced was unprecedented and is well documented in images taken by the Hubble Space Telescope. While the photos appear to depict an expanding spherical shell of debris, they are actually formed by the illumination of an ever-expanding ellipsoid with the progenitor star at one focus and the observer at the other. Hence, despite appearances, the structures in these photos are actually concave toward the viewer.

Source Wikipedia: V838 Monocerotis, Light echo

Foundations (of Equivalent Exchange)

Transmutation Circle from Fullmetal Alchemist

Newtonian mechanics is built on the foundation of Newton’s three laws of motion (cause and effect) 

Which state: 

1. An object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. Because inertia is the property of a body to resist any change in its state of rest or uniform motion, this law is also known as the law of inertia. In this sense, the mass of a body is a measure of its inertia and is called the inertial mass of the body.

2.  If a net force acts on an object, it will cause an acceleration of that object. The relationship between an object’s mass m, its acceleration a and the applied force F is given by the vector equation

F = ma

3. When one object exerts a force on another object, the second object exerts an equal force in the opposite direction on the first object. Said another way, that for every action there is an equal and opposite reaction, hence the alternative name for this law as the action-reaction law.

Commensurately:

Buddhist philosophy is built on the foundation of cause and effect (Tibetan: rgyu ‘bras; Sanskrit: hetuphala) the primary features of this law being:

1. Nothing evolves uncaused

2. Any entity which itself lacks a process of change cannot cause any other event

3. Only causes which possess natures that accord with specific effects can lead to those effects

 

“It is mind itself that sets in place the myriad array of beings in the world, and the world that contains them…living beings all arise from karma, and so without mind, there could be no karma.”

Madhyamakāvatarā, VI: 89
Bibliography:
A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity by Peter Collier

The Handbook of Tibetan Culture, 1993. 
Compiled by Graham Coleman

SOME MATHEMATICAL THEOREMS ON PERSPECTIVE DRAWING

From: Chapter 10, Mathematics for the Nonmathematician, Morris Kline

Let us accept, then, the principle that the canvas must contain the same section that a glass screen placed between the eye of the painter and the actual scene would contain. Since the artist cannot look through his canvas at the actual scene and may even be painting an imaginary scene, he must have theorems which tell him how to place his objects on the canvas so that the painting will, in effect, contain the section made by a glass screen.

Suppose then that the eye at E (Fig. 10–8) looks at the horizontal line GH and that GH is parallel to a vertical glass screen. The lines from E to the points of GH lie in one plane, namely the plane determined by the point E and the line GH, for a point and a line determine a plane. This plane will cut the screen in a line, G′H′, because two planes which meet at all meet in a line. It is apparent that the line G′H′ must also be horizontal, but we can prove this fact and so be certain. We can imagine a vertical plane through GH. Since GH is parallel to the screen and the latter is also vertical, the two planes must be parallel. The plane determined by E and GH cuts these parallel planes, and a plane which intersects two parallel planes intersects them in parallel lines. Hence G′H′ is parallel to GH, and since GH is horizontal, so is G′H′. But GH was any horizontal line parallel to the screen. Hence the image on the screen of any horizontal line parallel to the screen or picture plane must be horizontal. Thus in a painting which is to contain what this glass screen contains, the line G′H′ must be drawn horizontally.

We can present practically the same argument to show that the image of any vertical line, which is automatically parallel to the vertical screen, must appear on the screen as a vertical line. Thus all vertical lines must be drawn vertically. Continue reading “SOME MATHEMATICAL THEOREMS ON PERSPECTIVE DRAWING”

Indo-European Language-Tree

French Dieu
Spanish Dios from
Latin Deus from 
Ancient Greek Zeus from
Proto-Hellenic *dzéus from
Proto-Indo-European *deiwos meaning "celestial" or "shining"

Iuppiter or Jūpiter from
Roman Diespiter (deus + Latin: pater = English: father) from 
Proto-Italic *djous patēr from
Proto-Indo-European root *Dyḗws*Pahtḗr 
	literally meaning "Sky Father"
Whence is also derived the name of the Hindu sky god Dyáuṣ Pitṛ́ (Vedic Sanskrit: Dyáuṣpitṛ́)
and Proto-Germanic *Tīwaz or Tius hence Old Norse Týr 

English mother from 
Middle English moder from 
Old English mōdor from 
Proto-Germanic *mōdēr from 
Proto-Indo-European *méh₂tēr 
Other cognates include 
  Spanish madre
  Latin māter
  Greek mā́tēr/mā́tar 
  Slavic *mati 
  Persian madar
  Sanskrit mātṛ 

English Sin from
Old English synn "moral wrongdoing" from 
Proto-Germanic *sundiō probably "it is true" from 
Proto-Indo-European *snt-ya-, a collective form from 
*es-ont- "becoming" 
  present participle of root *es- "to be"

Sanskrit Bodhisattva "one whose essence is perfect knowledge," from 
bodhi "perfect knowledge" + sattva "reality, being" from 
sat-, sant- "existing, true, virtuous" from 
Proto-Indo-European root *es- "to be"

Laniakea (Hawaiian: Immense Heaven)

Superclusters, the biggest structures in the Universe, are regions of space that are densely packed with galaxies. This image maps Laniakea according to the flow of galaxies across space.
Map of superclusters of galaxies and voids in a distance of one billion light years from the milky way. The supercluster Laniakea is marked in yellow.
The Local Group’s location within the Virgo Supercluster as part of the larger Laniakea Supercluster.
Local Group and nearest galaxies (not to scale).
The Milky Way