Centroids

Conclusion:The state of mind of the observer plays a crucial role in the perception of time.Einstein

It is often I consider the Center of Gravity(Mass) as an illustration of the perspective that exists "around and within us" as a product of the natural world. We are limited by our own knowledge, yet when given, and lead to observation of what is natural in our world, we see where we had not seen before.

\bar z = \frac{\int z dm}{m}The center of gravity (or mass), abbreviated as COM, of any object is that point within the object upon which gravity (or any body force) acts, regardless of the orientation of the object. The COM of an object may be calculated by using the principle of equilibrium.

First off you must know that I work according to a set of principles that were discovered after a time through "subjective reflection" on the nature of mind and how it works. Of course I am no expert here, but the principles themself are realizable as an active function in the recognition of how one might interpret the world.

\bar y = \frac{\int y \rho dV}{\int \rho dV}In the event that the density ρ of an object is not uniform throughout, the calculation of COM may be done by a similar set of equations involving the addition of density to the analysis.

It is by taking one to recognisance of the title of this blog entry that I wanted to discuss the "subjective part" and the understanding of the "mathematical construct" that one, in my opinion exists. Just as we progress to understand the natural world around us, I believe these are synonymous with each other.

\bar Y = \frac{\sum m \bar y}{\sum m}If a body is made up of multiple sections, each of which has a unique mass, the method for evaluating the centroid of that body is to evaluate the composite body by finite element analysis of each of the sections through the use of moment balancing, as above.

Liminocentric structures



You can find much on this site in regards to this issue, and I now relate centroid for consideration in the case of this topic. I presented it at the Backreaction site today to show an advancement in the thinking as we move to incorporate the knowledge. As we come to understand the natural world around us.

Giving earth a new understanding in terms of its densities and it's relation to the gravitational contribution, it has in our new views of the globe, helped me learn and understand the feature of gravity as it extends to the cosmos.

I have taken it a step further as many of you know to include the emotive states as valued physiological relations to what manifests in the immediate environs of the body home. While this is a far cry from the understanding of gravitational research it was inevitable for me to see an extension of how one can topological relate to the world, in this inductive/deductive mode to reason.

While living on this earth, we always come home for reflection, and if any have not taken stock of what has accumulated during the day, then it is inevitable that is will come to reside very close to home as one sleeps through the nocturnality night. This research of subjectivity and mind had to entail "all of our activities." It had to include an understanding of the "mathematical constructs" that we observe, in order to relate to nature.

List of Centroids

Shape	Figure			Area
Triangular area
Quarter-circular area
Semicircular area
Quarter-elliptical area
Semielliptical area	The area inside the ellipse and above the axis
Semiparabolic area	The area between the curve and the axis, from to
Parabolic area	The area between the curve and the line
Parabolic spandrel	The area between the curve and the axis, from to
General spandrel	The area between the curve and the axis, from to
Circular sector	The area between the curve (in polar coordinates) and the pole, from to
Quarter-circular arc	The points on the circle and in the first quadrant
Semicircular arc	The points on the circle and above the axis
Arc of circle	The points on the curve (in polar coordinates) , from to

Why are Planets Round?

It is always interesting to see water in space.

Image: NASA/JPL-

Planets are round because their gravitational field acts as though it originates from the center of the body and pulls everything toward it. With its large body and internal heating from radioactive elements, a planet behaves like a fluid, and over long periods of time succumbs to the gravitational pull from its center of gravity. The only way to get all the mass as close to planet's center of gravity as possible is to form a sphere. The technical name for this process is "isostatic adjustment."

With much smaller bodies, such as the 20-kilometer asteroids we have seen in recent spacecraft images, the gravitational pull is too weak to overcome the asteroid's mechanical strength. As a result, these bodies do not form spheres. Rather they maintain irregular, fragmentary shapes.

See:Isostatic Adjustment is Why Planets are Round?

Second Life

Creating secure places for meetings and creating the individuals for this interaction while retaining anonymity is part of the idea behind discussing strategy while not revealing who these individuals are in this exercise.

Some say, why not do this with legit names, and to some, see this as a cowardice for not standing up to what is being said. Well that's not the issue here and creating the purpose for advancement of "free thinking" is to allow one to speak freely and assign a character to the individual for the expression of that medium.

It is allowing a freedom to speak regardless of the restraints a public name can bring to one's public life. See, how I don't care how important your name is, and I see you as an individual first, who has an opinion, so I would want you to share that regardless of the public stature with which you operate in public life.

We want you to share even if it under the anonymity of this character you choose. So how do we go about creating the venue of this events to take place whether you might call it a Quebec summit or a summit in Banff it will be under the auspice of this technology that we meet.

Second Life (abbreviated as SL) is an Internet-based 3D virtual world launched June 23, 2003 and developed by Linden Research, Inc, which came to international attention via mainstream news media in late 2006 and early 2007. A free downloadable client program called the Second Life Viewer enables its users, called "Residents", to interact with each other through motional avatars, providing an advanced level of a social network service combined with general aspects of a metaverse. Residents can explore, meet other residents, socialize, participate in individual and group activities, and create and trade items (virtual property) and services with one another

Three-body problem and WMAP

"We all are of the citizens of the Sky" Camille Flammarion

In 1858, by the set of its relations, it will allow Camille Flammarion, the 16 years age, to enter as raises astronomer at the Observatory of Paris under the orders of Urbain the Glassmaker, at the office of calculations.

See:The Gravity Landscape and Lagrange Points



Now there is a reason that I am showing "this connection" so that the jokes that go around at the PI institute in regards to Tegmark( not that I am speaking for him and have absolutely no affiliation of any kind) and the "mathematical constructs are recognized" beyond just the jeering section, that while not being a party too, will and can be shown some light.

Three-body problem

For n ≥ 3 very little is known about the n-body problem. The case n = 3 was most studied, for many results can be generalised to larger n. The first attempts to understand the 3-body problem were quantitative, aiming at finding explicit solutions.

* In 1767 Euler found the collinear periodic orbits, in which three bodies of any masses move such that they oscillate along a rotation line.
* In 1772 Lagrange discovered some periodic solutions which lie at the vertices of a rotating equilateral triangle that shrinks and expands periodically. Those solutions led to the study of central configurations , for which \ddot q=kq for some constant k>0 .

The three-body problem is much more complicated; its solution can be chaotic. A major study of the Earth-Moon-Sun system was undertaken by Charles-Eugène Delaunay, who published two volumes on the topic, each of 900 pages in length, in 1860 and 1867. Among many other accomplishments, the work already hints at chaos, and clearly demonstrates the problem of so-called "small denominators" in perturbation theory.
The chaotic movement of 3 interacting particles
The chaotic movement of 3 interacting particles

The restricted three-body problem assumes that the mass of one of the bodies is negligible; the circular restricted three-body problem is the special case in which two of the bodies are in circular orbits (approximated by the Sun-Earth-Moon system and many others). For a discussion of the case where the negligible body is a satellite of the body of lesser mass, see Hill sphere; for binary systems, see Roche lobe; for another stable system, see Lagrangian point.

The restricted problem (both circular and elliptical) was worked on extensively by many famous mathematicians and physicists, notably Lagrange in the 18th century and Poincaré at the end of the 19th century. Poincaré's work on the restricted three-body problem was the foundation of deterministic chaos theory. In the circular problem, there exist five equilibrium points. Three are collinear with the masses (in the rotating frame) and are unstable. The remaining two are located on the third vertex of both equilateral triangles of which the two bodies are the first and second vertices. This may be easier to visualize if one considers the more massive body (e.g., Sun) to be "stationary" in space, and the less massive body (e.g., Jupiter) to orbit around it, with the equilibrium points maintaining the 60 degree-spacing ahead of and behind the less massive body in its orbit (although in reality neither of the bodies is truly stationary; they both orbit the center of mass of the whole system). For sufficiently small mass ratio of the primaries, these triangular equilibrium points are stable, such that (nearly) massless particles will orbit about these points as they orbit around the larger primary (Sun). The five equilibrium points of the circular problem are known as the Lagrange points.

So the thing is, that while one may not of found an anomalousness version of what is written into the pattern of WMAP( some Alien signal perhaps in a dimension of space that results in star manipulation), and what comes out, or how string theory plays this idea that some formulation exists in it's over calculated version of mathematical decor.

String Theory

In either case, gravity acting in the hidden dimensions affects other non-gravitational forces such as electromagnetism. In fact, Kaluza and Klein's early work demonstrated that general relativity with five large dimensions and one small dimension actually predicts the existence of electromagnetism. However, because of the nature of Calabi-Yau manifolds, no new forces appear from the small dimensions, but their shape has a profound effect on how the forces between the strings appear in our four dimensional universe. In principle, therefore, it is possible to deduce the nature of those extra dimensions by requiring consistency with the standard model, but this is not yet a practical possibility. It is also possible to extract information regarding the hidden dimensions by precision tests of gravity, but so far these have only put upper limitations on the size of such hidden dimensions.

Bold was added by me for emphasis. See also:Angels and Demons on a Pinhead

This is/was to be part of the hopes of people in research for a long time. I have seen it before, in terms of orbitals(the analogical version of the event in the cosmos) and how such events could gave been portrayed in those same locations in space. Contribute, to the larger and global distinction of what the universe is actually doing. If it's speeding up, what exactly does this mean, and what should we be looking for from what is being contributed to the "global perspective" of WMAP from these locations??

But lets move on here okay.

If you understand the "three body problem" and being on my own, and seeing things other then what people reveal in the reports that they write, how it is possible for a lone researcher like me to come up with the same ideas about the universe having some kind of geometrical inclination?

You would have to know that "such accidents while in privy to data before us all", and what is written into the calculations by hand would reveal? Well, I never did have that information. What I did know is what Sean Carroll presented of the Lopsided Universe for consideration. This coincided nicely with my work to comprehend Poincaré in a historical sense. The relationship with Klein.

As mentioned before, at the time, I was doing my own reading on Poincaré and of course I had followed the work of Tegmark and John Baez's expose' on what the shape of the universe shall look like. This is recorded throughout my bloggery here for the checking.

What I want to say.

Given the mathematics with which one sees the universe and however this mathematical constructs reveals of nature, nature always existed. What was shown is that the discovery of the mathematics made it possible to understand something beautiful about nature. So in a sense the mathematics was always there, we just did not recognize it.:)

Using the Architecture of Disaster Capitalism

I have read that 80% of the world do not have access to the Web. ) The Web has been largely designed by the developed world for the developed world. But it must be much more inclusive in order to be of greater value to us all.

Tim Berners-Lee Speech before Knight Foundation-14 September 2008

There is always this patience factor that we could build in any system. What we may see in the introduction to transforming society must be a slow growth and careful process. But, if we were to institute large changes, then how could we do it without stirring the "public pot" and introducing large scale reformations for what we thought most apropos for these societies and the principals with which we shall imbue this change. "Elect new governments" who bring this to bear as a platform to our cities and small towns across the globe.

The crisis on Wall Street? Not much time now before the changes are made under the principals of the "banking system" under the bailout initiative.

It was important to me to understand how "paradigmatic changes" were sitting at the heart of these initiatives." How capitalism can rear it's head to employ such tactics, for those same changes "filtered down to a public."

Politically enshrined capitalism, had become distant too, from the heart of the society with which it seeks to govern. The negotiation features of the elite were signs of a time intrade when "such distance was created." This auspice of change is the idea of the WTO which is again "transforming itself" into the framework of the FTAA(Free Trade Area of the Americas). EU by example sought to create a strength, and brings purpose under this initiative?

The Free Trade Area of the Americas (FTAA) (Spanish: Área de Libre Comercio de las Américas (ALCA), French: Zone de libre-échange des Amériques (ZLÉA), Portuguese: Área de Livre Comércio das Américas (ALCA), Dutch: Vrijhandelszone van de Amerika's) was a proposed agreement to eliminate or reduce the trade barriers among all countries in the Americas. In the latest round of negotiations, trade ministers from 34 nations met in Miami, Florida, United States, in November 2003 to discuss the proposal.[1] The proposed agreement was an extension of the North American Free Trade Agreement (NAFTA) between Canada, Mexico and the United States. Against the market are positioned Cuba, Venezuela and later Bolivia, Ecuador, Dominica, Nicaragua and Honduras, which entered the Bolivarian Alternative for the Americas in response, and not strongly opposing but not supporting Argentina, Chile and Brazil.

So we are all the wiser now, of institutional changes that can be brought into the society. Have you seen "this feature before?" Look to our governments and the rules of governance? Sure countries have been overthrown , but this is not what we seek here. We seek to bring equality to every facet of the world's populations that we might all share in the prosperity of knowledge that can help us bring change to our current situations in a "peaceful and intentional way."

A few years ago I chatted with a woman involved in relief work in war-ravaged areas. I wondered aloud whether Internet access should be low on the priority list after clean water, and other critical resources. She responded by telling me the story of a young man who had taught himself English, and with a connection to the Internet, how he set up his own translation business. This business provided income for the village as well as opening up new communications opportunities. I learned that I should not prioritize for others. Instead, I should listen to their concerns and opportunities and then do what I can to help.Tim Berners-Lee Speech before Knight Foundation

20% of the Population only Aware?

Well the transformation process then begins. It is to recognize that the potential exists for an advancement for business to bring information to the greater population, then, to what has already existed.

It is here that the idea of an humanitarian effort seeks to include the rest of our societies in education freely gathered. Open access to education. That we would seek our governments to ensure that "access to information" would be part of the initiatives to bring small town prosperity, in terms of knowledge, to all who seek to advance and be transformed by their personal ideology and freedoms. To seek from, and develop, the platforms that are implemented in a "open and free society" which seeks to invent, and be creative. One that does not discriminate between the rich and the poor. Gender, or the colour of ones skin. To participate in the advancing of views of alls it people "globally" regardless of which country you come from.


Where the Architecture comes in.

A shift in paradigm can lead, via the theory-dependence of observation, to a difference in one's experiences of things and thus to a change in one's phenomenal world.

ON Thomas Kuhn

How many of us are quite liberal to understand that "crisis" brings about change? In the case of "ole institutions" falling away like Wall Street, to see it become something much more in terms of the access to investment and the way we trade? That contractor development(mercennaries) in the face of war has brought new business to bear instead of countries who are out to provide peace keepers. Instead of an offensive fighting force that governments can distant themself under reconstruction.

But lets move on here to consider the ramification of "Revolution for change." The understanding of how the implication of capitalism could change under the auspice of "this seeking" to bring the humanitarian effort to freedom and access to information that the rest of that 80% of the global society may be included?

Who are in control of your access to the internet?

I am advocating an access and freedom to information which may alter the course of these businesses/governments, intranet creation , which can allow access to the internet. I am also "guessing" that the telecommunications would be changed in that assess to conversation has now been preceded by a communication that can happen in real time through such a high speed internet access. Many of us played with this feature before is would a new business on the internet.

Such historical developments, in terms of the Internet as to profiteering has sought to compartmentalize, to gain access to money creation and wealth. Who controls the Internet?

Earlier, I posted on the idea of "the Library" as a universal implement(hot zone) whereby all people can gain access to information. That like the laptop-book, becomes a source of information to develop further, what we are doing in the real world. This would be moving slowly, while we know this exists now and is a security infraction to those who do not guard their own access to the internet.

Product development currently in existence would bring about potentials greater then currently are being expressed by the 20% of the population. If given to the ability of advertising, would see it's product manufacture base, if it were already sitting at the precipice of this change, access to a greater market?

But again I have gone to far here.

It was only to demonstrate what might be recognized, if for instance, we saw a health care system, and the businesses that provide the insurance under employer/employee negotiated settlements, recognize, that as a cost to providing this benefit to it employees, it is much cheaper in a country like Canada for providing that benefit. It serves to help business recognize what profiteering seeks to do by implementing a "for profit health care system."

It demonstrates that as "two tier system" those that have money, and those that don't, have preferential treatment to moving ahead of those who have the same needs at the same time.