All good things

The sunset on the horizon
was a glimpse
into too many
an orphaned heaven
gazing on a pivot
colliding in desperation
to a world of
cruelty & anguish
such is reality
of misguided animosity
The fireflies attack
with ferocious intensity
only to burn their wings
in the struggle,
to plummet to the ground
waiting are the ants
to carry them away
they saw it all... coming along.
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War- The Meat hook of Life

The warrior the saviour flew their moral jets to free the lamb one by one desert flowers glitter & bloom destruction the blood of reality is starting to consume the children look deep into the barrel of the gun spark of the tempest the children of fright wide eyed, crying for love combing street alley's seeking shelter one day closer to death reduced them to whimpering beggars longing for mother having witnessed more suffering than an old man ever could
who destined their fate ? who gave them all a meat hook to hang so proudly upon ? be gentle be kind as the child silently dies.

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River Of Pain

How i wonder what it was all about with her breasts pressed firm by my side deep in dream emotions falling true and deep in the woman cherish her tenderness what joy in life the games we play her hair brushed by loving fingers the perfect angel of comfort
the cloud still gathers large and dark will she leave me hanging on a pivot as she did before, and before that ? is she coming to stay, or leave ? "will she give one last ultimatim for togetherness... forever ?" wondering where my mind went all those years her rivers of tears they feed the cloud so dark begging for mercy one last chance "you are the lord savior, the magician in the sky, the one and only, there can be no other" she cried !
time, memories, longing & pacing is all that love ever was, a river of pain a lot of fuckin' pain.
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Interesting review.
Book Extract: The Roots of Modern Mathematics By Anand Ramanujan
Let us accept for our purposes that mathematics is an essential foundation for science. We are forced to accept this idea because it is a long-cherished Western notion. If we are to say that non-European cultures had science long before the Europeans exported it to them, we must prove they had math. Even in America, sciences whose principles can-not be reduced to mathematical formulas have often been dismissed as "soft sciences." These include anthropology, medical science, certainly psychology, and, until this century, biology and chemistry. Chemistry first made the "hard" club in the 1920s, when the useful but mysterious order of the periodic chart of the elements was finally explained by quantum physics and the Pauli exclusion principle; biology became rigorous (or "hard") with the deciphering of the DNA molecule and the advent of molecular biology and its rigorous mathematical codes.
We might expect to find non-Western cultures to be mathematically weak throughout history. Yet nowhere is non-Western science stronger than in math. The mathematical foundation of Western science is an intellectual gift from the Indians, Egyptians, Chinese, Arabs, Babylonians and others. The Maya, too, developed powerful mathematics, their priests judged as much for their ability to calculate as to pray. In their civilization, numeracy was next to godliness.
George Gheverghese Joseph, who was born in India but teaches in the United Kingdom, cites this line from the Vedangajyotisa, the oldest (500 B.C.) extant Indian astronomical text: "Like the crest of a peacock, like the gem on the head of a snake, so is mathematics at the head of all knowledge " Few modern Western scientists would disagree with that sentiment.
The traditional Western story is that math was created by the ancient Greeks around 600 B.C. and elaborated by Greco-Roman culture until A D. 400, at which time the discipline fell dormant for a thousand years only to be revived in post-Renaissance Europe. There is ample evidence, however, that nonwhite, non-Western cultures made significant contributions to European mathematics—or, at the very least, developed mathematical techniques that predated Western discoveries.
For example:
The Indians developed the use of zero and negative numbers perhaps a thousand years before these concepts were accepted in Europe. The Maya invented their own zero—in fact, a whole slew of them—at about the same time as the Indians.
Clay tablets dated a thousand years before the Greek civilization reveal traces of a sophisticated algebra among the Sumerians. Papyri of the eighteenth century B.C. and earlier show that the Egyptians used simple equations to deal with problems in distribution of food and other supplies.
In the third millennium B.C. the Babylonians developed a place-value system. (In our base 10 system, 348, for example, stands for 8 ones 4 tens, and 3 hundreds.) The Babylonian sexagesimal (base 60) number system may at first appear cumbersome, but Copernicus used sexagesimal fractions to construct his model of the solar system, and we still use the system for keeping time and measuring angles (60 minutes per hour, each minute divided into 60 seconds).
The priestly scribes of Egypt knew the formula for calculating the volume of a cylinder—and thus recognized the existence of the mysterious factor Pi long before the Greeks—in fact, long before there were literate Greeks. The Egyptians also developed the concept of the lowest common denominator, as well as a fraction table that modern scholars estimate required twenty-eight thousand tedious calculations to compile.
In 2000 B.C., the priestly astronomers of Mesopotamia, in the area now known as Iraq, kept extensive tables of squares. We know this from the clay tablets of cuneiform script found in temple libraries. Remember that Europeans in the fourteenth century did not even keep times tables. Gottfried Leibniz, the co-inventor of the calculus, claimed to have discovered the secret of deciphering the diagrams of the ancient Chinese sage Fu Hsi. Leibniz maintained that Fu Hsi's diagrams corresponded to his own modern binary mode of arithmetic.
The Indians invented a nascent form of calculus centuries before Leibniz invented calculus in Europe.
The Arabs coined the term algebra and invented decimal fractions: .25 for 1/4, etc.
Aristotle credited the Egyptians with developing math before his countrymen, in a somewhat backhanded manner: "The mathematical sciences originated in the neighborhood of Egypt because there the priestly class was allowed leisure.
Despite this, America's most prominent modern historian of mathematics, Morris Kline, wrote, "Compared with the achievements of their immediate successors, the Greeks, the mathematics of the Egyptians and Babylonians is the scrawling of children just learning how to write as opposed to great literature. In his classic work Mathematics: A Cultural Approach, Kline acknowledges that the Babylonians and Egyptians pioneered mathematics long before the Greeks, but he dismisses them as pragmatists. "The Egyptians and Babylonians did reach the stage of working with pure numbers dissociated from physical objects. But like young children of our civilization, they hardly recognized that they were dealing with abstract entities." The Greeks, he said were the first to recognize numbers as "ideas" and emphasized that this is now they must be regarded."
The rules keep changing. When we discuss ancient Indian physics, Western physicists will insist that it is meaningless because it was abstract, with no empirical backup. In the case of math, Kline seems to be saying the opposite, that the Babylonians and Egyptians were unsophisticated because they used their math. Because these civilizations saw math as "merely a tool in commerce, agriculture, engineering," says Kline, hardly any progress was made in the subject m a period of more than four thousand years." As for the math required to build the pyramids, Kline writes, "A cabinetmaker need not be a mathematician."
Another common charge is that non-Western mathematicians did not employ the ancient Greek custom of constructing proofs for their work. For example, Pythagoras gets credit for the Pythagorean theorem say Western scholars, even though the Babylonians had the concept centuries earlier. This is because he, or his followers, constructed the first proof for this overarching principle, while the Babylonians did not. Critics find the Greek-style proof so important that its nonexistence in non-European cultures, they contest, discredits thousands of years of mathematics. The controversy over proof is a thorny one. Some mathematicians claim that non-Western peoples did have proofs, while others doubt that one can really "prove" any concept for eternity and throughout the entire universe. For a brief debate on the topic, see below:
Robert Kaplan, in a letter to the author, August 12, 2000, writes: "Ted Williams and Hank Aaron had incredible eye-hand coordination. The ancient Greeks had incredible intuition-proof coordination. We owe to them alone the concept of a proof in mathematics. Others could see what they saw, could intuit beautifully, and many saw what they didn't—but no others felt any need, or devised any way, of tying their insights down by proofs: i.e., by a network of logical connections to a small set of ‘fundamental' insights. Without proof what you have is rumor, gossip, politics, I-said-he-said, mistaken and brilliant insights jumbled up together. It is this architecture that Morris Kline rightly admires, but too crudely exalts above the insights others had. It's crucial to see how important the issue of proof is in mathematics. There are too many cases in math—namely, an infinite number—ever to be able to verify any statement in it empirically. The claim, for example, that all numbers are less than 60,000 works for the first 59,999 positive integers, and the infinite number of negative integers, and the larger infinity of reals less than 60,000, but it turns out to be false after all. How could you ever test empirically whether or not pi was rational; or whether there was a last prime; or whether all Mersenne primes are in fact prime? How could you test empirically whether the three angle bisectors of any triangle all meet in one point? Careless drawing might make it look as if they did in one case and didn't in another, and the most careful drawing would, after all, be of only one particular triangle. What's always needed is a proof that covers all possible cases at once—and it was just this that the Greeks invented. It is the very fact that math's subject matter isn't just large but in fact always infinite that makes math without proof like baseball without its beloved umpires."
George Gheverghese Joseph, a mathematician at the University of Manchester (U.K.), responds: "The comment that follows confines itself to the proof tradition in Indian mathematics only. The situation is very complicated and Western math historians have not even started grappling with it. The sources of information on traditional proofs, rationales, derivations and demonstrations in Indian mathematics and astronomy are found in commentaries on the basic texts. Now, many commentaries restrict themselves to the explanation of the words of the texts and do not go further. But there are a certain number of commentaries which also explain rationales partly or fully. Then there are works which, mainly based on earlier siddhanta texts that introduce revisions, innovations, and methodologies, all aimed at arriving at better and more accurate results. Often these texts give the rationales as well. Finally, there are works wholly devoted to the elucidation of mathematical and astronomical rationale, and also short independent texts which take up for elucidation some topic or other. Sometimes marginalia and post-colophonic statements in manuscripts give valuable information. There are also large numbers of short tracts which demonstrate the rationale of minor points or specific topics. It has to be remembered here that in technical literature, as a rule, rationales, including innovations and inventions, generally form part of the intimate instruction from the teacher to the pupil, and are not always put on record in commentaries or in manuscripts.
"Consider just one example, the commentaries on the works of Aryabhata (c. A.D. 500). You may well have chosen the commentaries on the works of Brahmagupta or Bhaskara 2 (Bhaskaracharya) instead. The works of Bhaskara 1, the great Aryabhata commentator are absolutely essential in understanding the methods and rationale of Aryabhatiya. And similarly are some of the works in Kerala. From about 7th century onwards, if not earlier, Kerala became the centre of the Aryabhatan School of astronomy and mathematics. Let me mention a few texts that go into a detailed rationale and proofs on a whole host of topics, of which the work on infinite series relating to circular and trigonometric functions is the most notable, being one of the two strands that went into the creation of what we would describe as modern mathematics. Any list of such texts would include Nilakanthais Aryabhatiyabhasya (c. A.D. 1500), Kriyakrmakari of Narayanan and Sankara Variyar, Yuktibhasa of Jysthadeva. If you study any of these texts you will come across uppapitis (or demonstrations) of a whole series of results. To ignore these works and state that there were no proofs in the Indian tradition would be going against all the facts.”
Skepticism is appropriate to all research, but the researcher in non-Western mathematics must often face a high hurdle. Ayele Bekene, of Cornell University, who has studied ancient Ethiopian number systems, describes how Western scholars once refused to accept that this African civilization had developed its own numerals. Ethiopian numbers resemble, not surprisingly, the more ancient Egyptian numbers and, to a lesser extent, ancient Greek numbers-again not surprisingly, because of Ethiopia s geographical proximity to Egypt and because Egypt influenced Greek mathematics. The controversy involves letters written by Ethiopians to Greeks. These letters contain both Ethiopian and Greek numbers. One explanation is that the letters were written in both languages so the Greeks could understand. Western skeptics maintained that Africans were not capable of such sophistication, that these letters had actually been written by Greeks, who thus introduced the Ethiopians to a crude alphabet and number system that they now claim as their own. Of course, this makes little sense, since the letters were found in Greece. If the Greeks had written to the Ethiopians, the letters should have been found in Ethiopia. The dispute, according to Bekerie, was finally solved by chemists. The ink on the pre-Christian era parchment in question was of an unusual hue. Chemical analysis showed that the ink had been made from berries indigenous to Ethiopia.
Our Western mathematical heritage and pride are critically dependent on the triumphs of ancient Greece. These accomplishments have been so greatly exaggerated that it often becomes difficult to sort out how much of modern math is derived from the Greeks and how much is from the Babylonians, Egyptians, Indians, Chinese, Arabs, and so on. The math of the Greeks was wonderfully imaginative, and a great debt is owed to them. But if our math today were based entirely on Pythagoras, Euclid, Democritus, Archimedes, et al., it would be a highly deficient discipline.
Before we get into the mathematical history of ancient non-Western peoples, let us first briefly discuss how the math we study arrived in Western classrooms of the twentieth century. The different paths de-scribed by scholars are often in violent disagreement. We shall pass no judgment here on the correct solution.
The "traditional" Western view-and I put "traditional" in quotes here because this tradition is hardly a century old-is best summed up by two respected mathematical historians. Rouse Ball and Morris Kline. In 1908 Ball wrote, "The history of mathematics cannot with certainty be traced back to any school or period before that of the Ionian Greeks." In 1952, Kline wrote, "[Mathematics] finally secured a new grip on life in the highly congenial soil of Greece and waxed strongly for a short period. . . . With the decline of Greek civilization the plant remained dormant for a thousand years . . . [until] the plant was transported to Europe proper and once more embedded in fertile soil." Fleshed out, this is often interpreted to mean that there have been three stages in the history of mathematics:
1) Circa 600 B.C. the ancient Greeks invent math, which thrives for a thousand years until approximately 400 A.D., at which time it disappears from the face of the earth. 2) A dark age of mathematics ensues, lasting over a thousand years. Some scholars concede that the Arabs kept Greek math alive during the Middle Ages. 3) Greek math is rediscovered in sixteenth-century Europe, and mathematics flowers again from then until the present.
This view is controversial. Our modern numerals—0 through 9— were developed in India during stage 2, the so-called dark age of mathematics. Mathematics existed long before the Greeks constructed their first right angle. We can perhaps excuse Rouse Ball, writing in 1908, for being unaware of the Greeks' mathematical predecessors. On the other hand, George Gheverghese Joseph points out that Ball should have been aware of the early Indian mathematics contained in the Sulbasutras (The Rules of the Cord). Written somewhere between 800 and 500 B.C., the Sulbasutras demonstrate, among other things, that the Indians of this period had their own version of the Pythagorean theorem as well as a procedure for obtaining the square root of 2 correct to five decimal places. The Sulbasutras reveal a rich geometric knowledge that preceded the Greeks.
Kline’s statement, says Joseph, is more problematic, ignoring a rich body of non-European mathematics that had been unearthed by the mid-twentieth century, including math from Mesopotamia, Egypt, China, India, the Arab world, and pre-Columbian America. There is the problem, too, that the Greeks themselves—Democritus, Aristotle, Herodotus—lavished praise upon the Egyptians, crediting them as their mathematical gurus (though not in those words). The fact is that many people were counting before the Greeks.
Note: The above article is an excerpt from "Lost Discoveries: The Ancient Roots of Modern Science - from the Babylonians to the Maya" by Dick Teresi. Simon & Shuster, 2002.
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