Dee Finney's blog - November 12, 2013 page 594 NUMBER ZERO -WHEEL OF LIGHT

11-12-13 - NOON MEDITATION DREAM. I was in a city somewhere and my husband and I met a young blonde woman and she was acting frightened.

We wanted to help her but before we could ask her what her problem was, she was kidnapped by some men and they pulled her into the back seat of a beige car.

Somehow, we got in front of that car, but then it dropped back a bit and my husband asked me to read the license plate number.

So, my husband slowed down a bit and the beige car passed us up on the left side and got ahead of us.

The beige car then came up behind a trash truck and almost hit it and swerved to miss the truck and when it did, it started to tip over to the left.

We stopped our car and I ran ahead and someone said, "Get her out of there!" and I grabbed her by the arm and pulled her into our vehicle.

I thought we were going to get into a fight with the men in the other car for rescuing her, but we seeemd to be okay, and she said to me. "Thank you for saving me. My number is " 0 " and because of you, I am whole again. "

0 (zero; BrE: /ˈzɪərəʊ/ or AmE: /ˈziːroʊ/) is both a number^[1] and the numerical digit used to represent that number in numerals. It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems. In the English language, 0 may be called zero, nought or (US) naught /ˈnɔːt/, nil, or — in contexts where at least one adjacent digit distinguishes it from the letter "O" — oh or o /ˈoʊ/. Informal or slang terms for zero include zilch and zip.^[2] Ought or aught /ˈɔːt/ has also been used historically.^[3] (SeeNames for the number 0 in English.)

Main articles: Names for the number 0 and Names for the number 0 in English

The word zero came via French zéro from Venetian zero, which (together with cypher) came via Italian zefiro from Arabic صفر, ṣafira = "it was empty",ṣifr = "zero", "nothing". This was a translation of the Sanskrit word shoonya (śūnya), meaning "empty". The first known English use was in 1598.^[4]^[5]^[6]^[7]

In 976 AD the Persian encyclopedist Muhammad ibn Ahmad al-Khwarizmi, in his "Keys of the Sciences", remarked that if, in a calculation, no number appears in the place of tens, then a little circle should be used "to keep the rows". This circle was called صفر (ṣifr, "empty") in Arabic language. That was the earliest mention of the name ṣifr that eventually became zero.^[8]

Italian zefiro already meant "west wind" from Latin and Greek zephyrus; this may have influenced the spelling when transcribing Arabic ṣifr.^[9] The Italian mathematician Fibonacci (c.1170–1250), who grew up in North Africa and is credited with introducing the decimal system to Europe, used the term zephyrum. This became zefiro in Italian, which was contracted to zero in Venetian.

As the decimal zero and its new mathematics spread from the Arab world to Europe in the Middle Ages, words derived from ṣifr and zephyrus came to refer to calculation, as well as to privileged knowledge and secret codes. According to Ifrah, "in thirteenth-century Paris, a 'worthless fellow' was called a '... cifre en algorisme', i.e., an 'arithmetical nothing'."^[9] From ṣifr also came French chiffre = "digit", "figure", "number", chiffrer = "to calculate or compute", chiffré = "encrypted". Today, the word in Arabic is still ṣifr, and cognates of ṣifr are common in the languages of Europe and southwest Asia.

Modern usage

There are different words used for the number or concept of zero depending on the context. For the simple notion of lacking, the words nothing andnone are often used, while nought, naught and aught^[10] are archaic and poetic forms with the same meaning. Several sports have specific words for zero, such as nil in football, love in tennis and a duck in cricket. In British English, it is often called oh in the context of telephone numbers. Slang words for zero include zip, zilch, nada, scratch and even duck egg or goose egg.^[11^]

History

Egypt

nfr

heart with trachea
beautiful, pleasant, good

Ancient Egyptian numerals were base 10. They used hieroglyphs for the digits and were not positional. By 1740 BCE the Egyptians had a symbol for zero in accounting texts. The symbol nfr, meaning beautiful, was also used to indicate the base level in drawings of tombs and pyramids and distances were measured relative to the base line as being above or below this line.^[12]

Mesopotamia

By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system. The lack of a positional value (or zero) was indicated by a space between sexagesimal numerals. By 300 BC, a punctuation symbol (two slanted wedges) was co-opted as a placeholder in the same Babylonian system. In a tablet unearthed at Kish (dating from about 700 BC), the scribe Bêl-bân-aplu wrote his zeros with three hooks, rather than two slanted wedges.^[13]

The Babylonian placeholder was not a true zero because it was not used alone. Nor was it used at the end of a number. Thus numbers like 2 and 120 (2×60), 3 and 180 (3×60), 4 and 240 (4×60), looked the same because the larger numbers lacked a final sexagesimal placeholder. Only context could differentiate them.

India

The concept of zero as a number and not merely a symbol for separation is attributed to India, where, by the 9th century AD, practical calculations were carried out using zero, which was treated like any other number, even in case of division.^[14]^[15] The Indian scholar Pingala (circa 5th–2nd century BC) used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), making it similar to Morse code.^[16]^[17] He and his contemporary Indian scholars used the Sanskrit word śūnya to refer to zero or void.

In 498 AD, Indian mathematician and astronomer Aryabhata stated that "sthānāt sthānaṁ daśaguņaṁ syāt"^[18] i.e. "from place to place each is ten times the preceding,"^[18]^[19] which is the origin of the modern decimal-based place value notation.^[20]^[21]

The oldest known text to use a decimal place-value system, including a zero, is the Jain text from India entitled the Lokavibhâga, dated 458 AD, whereshunya ("void" or "empty") was employed for this purpose.^[22] The first known use of special glyphs for the decimal digits that includes the indubitable appearance of a symbol for the digit zero, a small circle, appears on a stone inscription found at the Chaturbhuja Temple at Gwalior in India, dated 876 AD.^[23]^[24] There are many documents on copper plates, with the same small o in them, dated back as far as the sixth century AD, but their authenticity may be doubted.^[13]

Rules of Brahmagupta

The rules governing the use of zero appeared for the first time in Brahmagupta's book Brahmasputha Siddhanta (The Opening of the Universe),^[25]written in 628 AD. Here Brahmagupta considers not only zero, but negative numbers, and the algebraic rules for the elementary operations of arithmetic with such numbers. In some instances, his rules differ from the modern standard. Here are the rules of Brahmagupta:^[25]

The sum of zero and a negative number is negative.

The sum of zero and a positive number is positive.

The sum of zero and zero is zero.

The sum of a positive and a negative is their difference; or, if their absolute values are equal, zero.

A positive or negative number when divided by zero is a fraction with the zero as denominator.

Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator.

Zero divided by zero is zero.

In saying zero divided by zero is zero, Brahmagupta differs from the modern position. Mathematicians normally do not assign a value to this, whereas computers and calculators sometimes assign NaN, which means "not a number." Moreover, non-zero positive or negative numbers when divided by zero are either assigned no value, or a value of unsigned infinity, positive infinity, or negative infinity.

China

This is a depiction of zero expressed in Chinese counting rods, based on the example provided by A History of Mathematics. An empty space is used to represent zero.^[26^]

The Sunzi Suanjing, of unknown date but estimated to be dated from the 1st to 5th centuries, and Japanese records dated from the eighteenth century, describe how counting rods were used for calculations. According to A History of Mathematics, the rods "gave the decimal representation of a number, with an empty space denoting zero."^[26] The counting rod system is considered a positional notation system.^[27]

Zero was not treated as a number at that time, but as a "vacant position", unlike the Indian mathematicians who developed the numerical zero.^[28] Ch’in Chu-shao's 1247 Mathematical Treatise in Nine Sections is the oldest surviving Chinese mathematical text using a round symbol for zero.^[29] Chinese authors had been familiar with the idea of negative numbers by the Han Dynasty (2nd century CE), as seen in the The Nine Chapters on the Mathematical Art,^[30] much earlier than the fifteenth century when they became well established in Europe.^[29^]

Islamic world

The Arabic-language inheritance of science was largely Greek, initially from Nestorian Christians in Persia, but the first influences in astronomy wereHindu.^[31] In 773, at Al-Mansur's behest, translations were made of the Siddhantas, Indian earliest astronomical treatises dating as far back as 425 B.C.; these versions may have been the vehicle through which the "Arabic" numerals and the zero were brought from India into the Muslim world.^[32]

The Hindu-Arabic numerals and the positional number system were introduced around 500 AD, and about 825 AD, it was introduced by a Persianscientist, al-Khwārizmī,^[8] in his book on arithmetic, which was translated into Latin in the 12th century under the title Algoritmi de numero Indorum. This title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name.^[33] This book synthesized Greek and Hindu knowledge and also contained his own fundamental contribution to mathematics and science including an explanation of the use of zero. It was only centuries later, in the 12th century, that the Arabic numeral system was introduced to the Western world through Latintranslations of his treatise Arithmetic.

Greeks and Romans

Records show that the ancient Greeks seemed unsure about the status of zero as a number. They asked themselves, "How can nothing besomething?", leading to philosophical and, by the Medieval period, religious arguments about the nature and existence of zero and the vacuum. Theparadoxes of Zeno of Elea depend in large part on the uncertain interpretation of zero.

Example of the early Greek symbol for zero (lower right corner) from a 2nd-century papyrus

By 130 AD, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero (a small circle with a long overbar) within a sexagesimal numeral system otherwise using alphabetic Greek numerals. Because it was used alone, not just as a placeholder, thisHellenistic zero was perhaps the first documented use of a number zero in the Old World. However, the positions were usually limited to the fractional part of a number (called minutes, seconds, thirds, fourths, etc.)—they were not used for the integral part of a number. In laterByzantine manuscripts of Ptolemy's Syntaxis Mathematica (also known as the Almagest), the Hellenistic zero had morphed into the Greek letter omicron (otherwise meaning 70).

Another zero was used in tables alongside Roman numerals by 525 (first known use byDionysius Exiguus), but as a word, nulla meaning "nothing", not as a symbol. When division produced zero as a remainder, nihil, also meaning "nothing", was used. These medieval zeros were used by all future medieval computists (calculators of Easter). The initial "N" was used as a zero symbol in a table of Roman numerals by Bede or his colleague around 725.

Medieval Europe – zero as a decimal digit

Positional notation without the use of zero (using an empty space in tabular arrangements, or the word kha "emptiness") is known to have been in use in India from the 6th century. The earliest certain use of zero as a decimal positional digit dates to the 5th century mention in the text Lokavibhaga. The glyph for the zero digit was written in the shape of a dot, and consequently called bindu ("dot"). The dot had been used in Greece during earlier ciphered numeral periods.

The Hindu-Arabic numeral system (base 10) reached Europe in the 11th century, via the Iberian Peninsula through Spanish Muslims, the Moors, together with knowledge of astronomy and instruments like the astrolabe, first imported by Gerbert of Aurillac. For this reason, the numerals came to be known in Europe as "Arabic numerals". The Italian mathematician Fibonacci or Leonardo of Pisa was instrumental in bringing the system into European mathematics in 1202, stating:

After my father's appointment by his homeland as state official in the customs house of Bugia for the Pisan merchants who thronged to it, he took charge; and in view of its future usefulness and convenience, had me in my boyhood come to him and there wanted me to devote myself to and be instructed in the study of calculation for some days. There, following my introduction, as a consequence of marvelous instruction in the art, to the nine digits of the Hindus, the knowledge of the art very much appealed to me before all others, and for it I realized that all its aspects were studied in Egypt, Syria, Greece, Sicily, and Provence, with their varying methods; and at these places thereafter, while on business. I pursued my study in depth and learned the give-and-take of disputation. But all this even, and the algorism, as well as the art of Pythagoras, I considered as almost a mistake in respect to the method of the Hindus (Modus Indorum). Therefore, embracing more stringently that method of the Hindus, and taking stricter pains in its study, while adding certain things from my own understanding and inserting also certain things from the niceties of Euclid's geometric art. I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters. Almost everything which I have introduced I have displayed with exact proof, in order that those further seeking this knowledge, with its pre-eminent method, might be instructed, and further, in order that the Latin people might not be discovered to be without it, as they have been up to now. If I have perchance omitted anything more or less proper or necessary, I beg indulgence, since there is no one who is blameless and utterly provident in all things. The nine Indian figures are: 9 8 7 6 5 4 3 2 1. With these nine figures, and with the sign 0 ... any number may be written.^[34]^[35]

Here Leonardo of Pisa uses the phrase "sign 0", indicating it is like a sign to do operations like addition or multiplication. From the 13th century, manuals on calculation (adding, multiplying, extracting roots, etc.) became common in Europe where they were called algorismus after the Persian mathematician al-Khwārizmī. The most popular was written by Johannes de Sacrobosco, about 1235 and was one of the earliest scientific books to beprinted in 1488. Until the late 15th century, Hindu-Arabic numerals seem to have predominated among mathematicians, while merchants preferred to use the Roman numerals. In the 16th century, they became commonly used in Europe.

The Americas

The back of Olmec stela C from Tres Zapotes, the second oldest Long Count date discovered. The numerals 7.16.6.16.18 translate to September, 32 BC (Julian). The glyphs surrounding the date are thought to be one of the few surviving examples ofEpi-Olmec script.

The Mesoamerican Long Count calendar developed in south-central Mexico and Central America required the use of zero as a place-holder within its vigesimal (base-20) positional numeral system. Many different glyphs, including this partial quatrefoil——were used as a zero symbol for these Long Count dates, the earliest of which (on Stela 2 at Chiapa de Corzo, Chiapas) has a date of 36 BC.^[36] Since the eight earliest Long Count dates appear outside the Maya homeland,^[37] it is assumed that the use of zero in the Americas predated the Maya and was possibly the invention of the Olmecs. Many of the earliest Long Count dates were found within the Olmec heartland, although the Olmec civilization ended by the 4th century BC, several centuries before the earliest known Long Count dates.

Although zero became an integral part of Maya numerals, with a different, empty tortoise-like "shell shape"used for many depictions of the "zero" numeral, it did not influence Old World numeral systems. Quipu, a knotted cord device, used in the Inca Empire and its predecessor societies in the Andean region to record accounting and other digital data, is encoded in a base ten positional system. Zero is represented by the absence of a knot in the appropriate position.

In mathematics

Elementary algebra

The number 0 is the smallest non-negative integer. The natural number following 0 is 1 and no natural number precedes 0. The number 0 may or may not be considered a natural number, but it is a whole number and hence a rational number and a real number (as well as an algebraic number and acomplex number).

The number 0 is neither positive nor negative and appears in the middle of a number line. It is neither a prime number nor a composite number. It cannot be prime because it has an infinite number of factors and cannot be composite because it cannot be expressed by multiplying prime numbers (0 must always be one of the factors).^[40] Zero is, however, even (see parity of zero).

The following are some basic (elementary) rules for dealing with the number 0. These rules apply for any real or complex number x, unless otherwise stated.

Addition: x + 0 = 0 + x = x. That is, 0 is an identity element (or neutral element) with respect to addition.

Subtraction: x − 0 = x and 0 − x = −x.

Multiplication: x · 0 = 0 · x = 0.

Division: ⁰⁄_x = 0, for nonzero x. But ^x⁄₀ is undefined, because 0 has no multiplicative inverse (no real number multiplied by 0 produces 1), a consequence of the previous rule; see division by zero.

Exponentiation: x⁰ = ^x/_x = 1, except that the case x = 0 may be left undefined in some contexts; see Zero to the zero power. For all positive real x, 0^x = 0.

The expression ⁰⁄₀, which may be obtained in an attempt to determine the limit of an expression of the form ^f(x)⁄_g(x) as a result of applying the limoperator independently to both operands of the fraction, is a so-called "indeterminate form". That does not simply mean that the limit sought is necessarily undefined; rather, it means that the limit of ^f(x)⁄_g(x), if it exists, must be found by another method, such as l'Hôpital's rule.

The sum of 0 numbers is 0, and the product of 0 numbers is 1. The factorial 0! evaluates to 1.

Other branches of mathematics

In set theory, 0 is the cardinality of the empty set: if one does not have any apples, then one has 0 apples. In fact, in certain axiomatic developments of mathematics from set theory, 0 is defined to be the empty set. When this is done, the empty set is the Von Neumann cardinal assignment for a set with no elements, which is the empty set. The cardinality function, applied to the empty set, returns the empty set as a value, thereby assigning it 0 elements.
Also in set theory, 0 is the lowest ordinal number, corresponding to the empty set viewed as a well-ordered set.
In propositional logic, 0 may be used to denote the truth value false.
In abstract algebra, 0 is commonly used to denote a zero element, which is a neutral element for addition (if defined on the structure under consideration) and an absorbing element for multiplication (if defined).
In lattice theory, 0 may denote the bottom element of a bounded lattice.
In category theory, 0 is sometimes used to denote an initial object of a category.
In recursion theory, 0 can be used to denote the Turing degree of the partial computable functions.

Related mathematical terms

A zero of a function f is a point x in the domain of the function such that f(x) = 0. When there are finitely many zeros these are called the roots of the function. See also zero (complex analysis) for zeros of a holomorphic function.
The zero function (or zero map) on a domain D is the constant function with 0 as its only possible output value, i.e., the function f defined byf(x) = 0 for all x in D. A particular zero function is a zero morphism in category theory; e.g., a zero map is the identity in the additive group of functions. The determinant on non-invertible square matrices is a zero map.
Several branches of mathematics have zero elements, which generalise either the property 0 + x = x, or the property 0 × x = 0, or both.

In science

Physics

The value zero plays a special role for many physical quantities. For some quantities, the zero level is naturally distinguished from all other levels, whereas for others it is more or less arbitrarily chosen. For example, for an absolute temperature (as measured in Kelvin) zero is the lowest possible value (negative temperatures are defined but negative temperature systems are not actually colder). This is in contrast to for example temperatures on the Celsius scale, where zero is arbitrarily defined to be at the freezing point of water. Measuring sound intensity in decibels or phons, the zero level is arbitrarily set at a reference value—for example, at a value for the threshold of hearing. In physics, the zero-point energy is the lowest possible energy that a quantum mechanical physical system may possess and is the energy of the ground state of the system.

Chemistry

Zero has been proposed as the atomic number of the theoretical element tetraneutron. It has been shown that a cluster of four neutrons may be stable enough to be considered an atom in its own right. This would create an element with no protons and no charge on its nucleus.

As early as 1926, Professor Andreas von Antropoff coined the term neutronium for a conjectured form of matter made up of neutrons with no protons, which he placed as the chemical element of atomic number zero at the head of his new version of the periodic table. It was subsequently placed as a noble gas in the middle of several spiral representations of the periodic system for classifying the chemical elements.

In computer science

The most common practice throughout human history has been to start counting at one, and this is the practice in early classic computer scienceprogramming languages such as Fortran and COBOL. However, in the late 1950s LISP introduced zero-based numbering for arrays while Algol 58introduced completely flexible basing for array subscripts (allowing any positive, negative, or zero integer as base for array subscripts), and most subsequent programming languages adopted one or other of these positions. For example, the elements of an array are numbered starting from 0 in C, so that for an array of n items the sequence of array indices runs from 0 to n−1. This permits an array element's location to be calculated by adding the index directly to address of the array, whereas 1 based languages precalculate the array's base address to be the position one element before the first.

There can be confusion between 0 and 1 based indexing, for example Java's JDBC indexes parameters from 1 although Java itself uses 0-based indexing.

In databases, it is possible for a field not to have a value. It is then said to have a null value. For numeric fields it is not the value zero. For text fields this is not blank nor the empty string. The presence of null values leads to three-valued logic. No longer is a condition either true or false, but it can beundetermined. Any computation including a null value delivers a null result. Asking for all records with value 0 or value not equal 0 will not yield all records, since the records with value null are excluded.

A null pointer is a pointer in a computer program that does not point to any object or function. In C, the integer constant 0 is converted into the null pointer at compile time when it appears in a pointer context, and so 0 is a standard way to refer to the null pointer in code. However, the internal representation of the null pointer may be any bit pattern (possibly different values for different data types).

In mathematics −0 = +0 = 0, both −0 and +0 represent exactly the same number, i.e., there is no "negative zero" distinct from zero. In some signed number representations (but not the two's complement representation used to represent integers in most computers today) and most floating pointnumber representations, zero has two distinct representations, one grouping it with the positive numbers and one with the negatives; this latter representation is known as negative zero.

In other fields

In telephony, pressing 0 is often used for dialling out of a company network or to a different city or region, and 00 is used for dialling abroad. In some countries, dialling 0 places a call for operator assistance.
DVDs that can be played in any region are sometimes referred to as being "region 0"
Roulette wheels usually feature a "0" space (and sometimes also a "00" space), whose presence is ignored when calculating payoffs (thereby allowing the house to win in the long run).
In Formula One, if the reigning World Champion no longer competes in Formula One in the year following their victory in the title race, 0 is given to one of the drivers of the team that the reigning champion won the title with. This happened in 1993 and 1994, with Damon Hill driving car 0, due to the reigning World Champion (Nigel Mansell and Alain Prost respectively) not competing in the championship.

Symbols and representations of zero

Main article: Symbols for zero

The modern numerical digit 0 is usually written as a circle or ellipse. Traditionally, many print typefaces made the capital letter O more rounded than the narrower, elliptical digit 0.^[41] Typewriters originally made no distinction in shape between O and 0; some models did not even have a separate key for the digit 0. The distinction came into prominence on modern character displays.^[41]

A slashed zero can be used to distinguish the number from the letter. The digit 0 with a dot in the center seems to have originated as an option on IBM 3270 displays and has continued with some modern computer typefaces such as Andalé Mono, and in some airline reservation systems. One variation uses a short vertical bar instead of the dot. Some fonts designed for use with computers made one of the capital-O–digit-0 pair more rounded and the other more angular (closer to a rectangle). A further distinction is made in falsification-hindering typeface as used on German car number plates by slitting open the digit 0 on the upper right side. Sometimes the digit 0 is used either exclusively, or not at all, to avoid confusion altogether.

Zero as a year label

Main article: 0 (year)

In the BC calendar era, the year 1 BC is the first year before AD 1; no room is reserved for a year zero. By contrast, in astronomical year numbering, the year 1 BC is numbered 0, the year 2 BC is numbered −1, and so on.^[42^]

Notes

Jump up^ Russel, Bertrand (1942). Principles of mathematics (2 ed.). Forgotten Books. p. 125. ISBN 1-4400-5416-9., Chapter 14, page 125
Jump up^ Soanes, Catherine; Waite, Maurice; Hawker, Sara, eds. (2001). The Oxford Dictionary, Thesaurus and Wordpower Guide (Hardback) (2nd ed.). New York: Oxford University Press. ISBN 978-0-19-860373-3.
Jump up^ aught at etymonline.com
Jump up^ Menninger, Karl (1992). Number words and number symbols: a cultural history of numbers. Courier Dover Publications. p. 401.ISBN 0-486-27096-3.
Jump up^ ""zero, n.". OED Online. December 2011. Oxford University Press. (accessed March 04, 2012).". Archived from the original on 6 March 2012. Retrieved 2012-03-04.
Jump up^ "cipher | cypher, n.". OED Online. December 2011. Oxford University Press. (accessed 4 March 2012).
Jump up^ Merriam Webster online Dictionary

^ Jump up to:^a ^b Will Durant, 'The Story of Civilization', Volume 4, The Age of Faith, pp. 241.

^ Jump up to:^a ^b Ifrah, Georges (2000). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Wiley. ISBN 0-471-39340-1.
Jump up^ 'Aught' definition, Dictionary.com – Reterieved April 2013.
Jump up^ 'Aught' synonyms, Thesaurus.com – Reterieved April 2013.
Jump up^ George Gheverghese Joseph (2011). The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition). Princeton. p. 86.ISBN 978-0-691-13526-7.

^ Jump up to:^a ^b Kaplan, Robert. (2000). The Nothing That Is: A Natural History of Zero. Oxford: Oxford University Press.
Jump up^ Bourbaki, Nicolas (1998). Elements of the History of Mathematics. Berlin, Heidelberg, and New York: Springer-Verlag. 46. ISBN 3-540-64767-8.
Jump up^ Britannica Concise Encyclopedia (2007), entry algebra
Jump up^ Binary Numbers in Ancient India
Jump up^ Math for Poets and Drummers (pdf, 145KB)

^ Jump up to:^a ^b Aryabhatiya of Aryabhata, translated by Walter Eugene Clark.
Jump up^ Agarwal, M.K. (23 May 2012). From Bharata to India: Chrysee the Golden. iUniverse. p. 206. ISBN 9781475907650.
Jump up^ O'Connor, Robertson, J.J., E. F. "Aryabhata the Elder". School of Mathematics and Statistics University of St Andrews, Scotland. Retrieved 26 May 2013.
Jump up^ The Britannica Guide to Numbers and Measurement (Math Explained). The Rosen Publishing Group. 15 August 2010. pp. 97–98. ISBN 9781615301089.
Jump up^ Ifrah, Georges (2000), p. 416.
Jump up^ Bill Casselman (University of British Columbia), American Mathematical Society, "All for Nought"
Jump up^ Ifrah, Georges (2000), p. 400.

^ Jump up to:^a ^b Algebra with Arithmetic of Brahmagupta and Bhaskara, translated to English by Henry Thomas Colebrooke, London1817

^ Jump up to:^a ^b Luke Hodgkin (2 June 2005). A History of Mathematics : From Mesopotamia to Modernity: From Mesopotamia to Modernity. Oxford University Press. p. 85. ISBN 978-0-19-152383-0.
Jump up^ Crossley, Lun. 1999, p.12 "the ancient Chinese system is a place notation system"
Jump up^ Kang-Shen Shen; John N. Crossley; Anthony W. C. Lun; Hui Liu (1999). The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford University Press. p. 35. ISBN 978-0-19-853936-0. "zero was regarded as a number in India... whereas the Chinese employed a vacant position"

^ Jump up to:^a ^b Mathematics in the Near and Far East, p. 262
Jump up^ Struik, Dirk J. (1987). A Concise History of Mathematics. New York: Dover Publications. pp. 32–33. "In these matrices we find negative numbers, which appear here for the first time in history."
Jump up^ Pannekoek, A. (1961). A History of Astronomy. George Allen & Unwin. p. 165.
Jump up^ Sarton, G. Introd. to the History of Science. p. 530.
Jump up^ Brezina, Corona (2006). Al-Khwarizmi: The Inventor Of Algebra. The Rosen Publishing Group. ISBN 978-1-4042-0513-0.
Jump up^ Sigler, L., Fibonacci's Liber Abaci. English translation, Springer, 2003.
Jump up^ Grimm, R.E., "The Autobiography of Leonardo Pisano", Fibonacci Quarterly 11/1 (February 1973), pp. 99–104.
Jump up^ No long count date actually using the number 0 has been found before the 3rd century AD, but since the long count system would make no sense without some placeholder, and since Mesoamerican glyphs do not typically leave empty spaces, these earlier dates are taken as indirect evidence that the concept of 0 already existed at the time.
Jump up^ Diehl, p. 186
Jump up^ Lemma B.2.2, The integer 0 is even and is not odd, in Penner, Robert C. (1999). Discrete Mathematics: Proof Techniques and Mathematical Structures. World Scientific. p. 34. ISBN 981-02-4088-0.
Jump up^ Bunt, Lucas Nicolaas Hendrik; Jones, Phillip S.; Bedient, Jack D. (1976). The historical roots of elementary mathematics. Courier Dover Publications. pp. 254–255. ISBN 0-486-13968-9., Extract of pages 254–255
Jump up^ Reid, Constance (1992). From zero to infinity: what makes numbers interesting (4th ed.). Mathematical Association of America. p. 23.ISBN 978-0-88385-505-8.

^ Jump up to:^a ^b Bemer, R. W. (1967). "Towards standards for handwritten zero and oh: much ado about nothing (and a letter), or a partial dossier on distinguishing between handwritten zero and oh". Communications of the ACM 10 (8): 513–518. doi:10.1145/363534.363563.
Jump up^ Steel, Duncan (2000). Marking time: the epic quest to invent the perfect calendar. John Wiley & Sons. p. 113. ISBN 0-471-29827-1. "In the B.C./A.D. scheme there is no year zero. After 31 December 1 BC came AD 1 January 1. ... If you object to that no-year-zero scheme, then don't use it: use the astronomer's counting scheme, with negative year numbers."

References

This article is based on material taken from the Free On-line Dictionary of Computing prior to 1 November 2008 and incorporated under the "relicensing" terms of the GFDL, version 1.3 or later.

Barrow, John D. (2001) The Book of Nothing, Vintage. ISBN 0-09-928845-1.
Diehl, Richard A. (2004) The Olmecs: America's First Civilization, Thames & Hudson, London.
Ifrah, Georges (2000) The Universal History of Numbers: From Prehistory to the Invention of the Computer, Wiley. ISBN 0-471-39340-1.
Kaplan, Robert (2000) The Nothing That Is: A Natural History of Zero, Oxford: Oxford University Press.
Seife, Charles (2000) Zero: The Biography of a Dangerous Idea, Penguin USA (Paper). ISBN 0-14-029647-6.
Bourbaki, Nicolas (1998). Elements of the History of Mathematics. Berlin, Heidelberg, and New York: Springer-Verlag. ISBN 3-540-64767-8.
Isaac Asimov (1978). Article "Nothing Counts" in Asimov on Numbers. Pocket Books.

External links

Wikimedia Commons has media related to 0 (number).

Look up zero in Wiktionary, the free dictionary.

Wikiquote has a collection of quotations related to: Zero

A History of Zero
Zero Saga
The History of Algebra
Edsger W. Dijkstra: Why numbering should start at zero, EWD831 (PDF of a handwritten manuscript)
"My Hero Zero" Educational children's song in Schoolhouse Rock!

Zero on In Our Time at the BBC. (listen now)

Texts on Wikisource:
- Chisholm, Hugh, ed. (1911). "Zero". Encyclopædia Britannica (11th ed.). Cambridge University Press
- "Zero". Encyclopedia Americana. 1920.

[hide]

Integers

[hide] 0s

0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99

[show] 100s

[show] 200s

[show] 300s

[show] 400s

[show] 500s

[show] 600s

[show] 700s

[show] 800s

[show] 900s

The Wheel of Light

Monthly Newsletter - November 2013

The most significant planetary event this month is the new Moon solar eclipse on November 3. Eclipses are relatively rare events, taking place about five times each year. Eclipses can be either at the time of a full Moon (when the earth blocks the light of the Sun from being reflected by the Moon) or at the new Moon (when the Moon passes in front of the Sun and blocks some portion of its light from reaching the Earth). If the new Moon takes place when the Moon is close to the Earth’s equator, the Moon may entirely block out the solar light. Such is the case this month when the eclipse will appear as total in the Atlantic Ocean and into Africa.

Ancient teachings proclaimed eclipses to bring negative events. Just because something is rare, however, doesn’t mean that it portends something bad. What it may simply indicate is that something unusual or unexpected will tend to occur on earth when something rare occurs in the sky. Furthermore, these events are more likely to take place where the eclipse is strongest or total. Since most of us don’t live in the Atlantic Ocean or in Africa, we may conclude that unexpected activities are less likely to happen to us.

The influence of an eclipse may be experienced by people who have a planet or angle of their natal horoscope activated by the eclipse. This eclipse will be at eleven degrees of Scorpio. This doesn’t mean that something bad will happen to these people. It simply suggests they are most likely to experience something unusual. A clue as to where they might experience something strange could be reflected by what part of their natal horoscope the eclipse will activate. For example, if it’s the tenth house it could pertain to career. The seventh would suggest relationship. The fourth house would activate the home and family.

When an eclipse takes place, the Sun, Moon and Earth are in alignment both in longitude as well as latitude. Astrologers reference these points as “nodes”. There is a south node and a north node. This eclipse coincides with the north node. This is traditionally seen as a time when positive, beneficial events and opportunities present themselves. Sometimes this can be in the form of supportive relationships. So those whose horoscopes connect to the eclipse could also look forward to something positive, if unexpected, taking place. This could also pertain to leaders of nations. There may an outpouring of public support or some type of beneficial situation that unexpectedly presents itself. Again, this would be most likely to effect leaders of African nations or those whose charts in some significant way correspond to the eclipse.

Another consideration is how long these unexpected events are likely to take place. The ancient rule is that the effects of a solar eclipse will last in years the same duration as the eclipse itself lasts in hours. This one will last about 5 ½ hours. I don’t know anyone who has actually tracked this so I can’t vouch for it. I can suggest, however, that when Mars or Sun aspect eleven degrees of Scorpio, an unexpected event might occur well beyond the duration of the eclipse itself. Interestingly enough, both Mars and the Sun aspect the eclipse point in August 2014. Stay tuned.

Aries (March 21-April 20)
Aries: At times you can be brusque and impulsive. This is a good time to work on refining your technical skills and becoming more tactful. Growth can come from noticing ways to improve yourself and then doing the work to do so. Discipline can be strong in early month and family support can arrive in mid-month.

Taurus (April 21-May 21)
Taurus: The eclipse could bring emotional clarity about your primary relationship. Use this as a time to be receptive to and supportive of your partner. Emotions could be intense and passions run high, so keep your focus on the developing a deeper connection. Relationship transformation could ensue.

Gemini (May 22-June 21)
Gemini: There could be tendencies to be self-critical this month. Use this as a time to work on yourself but don’t get bogged down in extraneous details or excessive self-undermining behavior. Spending time in quiet contemplation could prove productive.

Cancer (June 22-July 22)
Cancer: The eclipse could bring awareness of deep feelings or emotional connections you have with important people in your life. Let the awareness percolate for a while. The full Moon on the 17th would be a good time to share in a more personal, intimate way with others.

Leo (July 23-August 23)
Leo: The eclipse could impact your relationship to your family. You could feel a deep sense of personal responsibility or feel limited and restricted in some way. Growth comes from not responding to either experience with attempts at controlling others. React in measured ways and cautious tones.

Virgo (August 24-Sept 22)
Virgo: Being authentic and self-affirming can enable you to generate both social support and professional opportunities. This is a good time to take risks that you might usually avoid.

Libra (Sept 23-Oct 23)
Libra: Focus on personal and domestic issues this month. Notice areas where changing your relationship to yourself or members of your family are required. The energy is present to make those changes and the timing is perfect. Failure to make voluntary changes now could lead to extreme or abrupt ones later on.

Scorpio (Oct 24-Nov 22)
Scorpio: A lot of energy in your sign this month. Growth comes from being measured in using it. Strive to avoid the extremes of being too explosive or too secretive. The former can be intimidating to others while the latter merely causes others to not realize how sensitive you may be.

Sagittarius (Nov 23-Dec 21)
Sagittarius: In a time of intense feeling and unexpected events, you might find this period to be fairly calm and supportive. You could use the energy this month to do some serious introspection for the purpose of spiritual growth or emotional clarity. Spending quality time alone would be beneficial.

Capricorn (Dec 22-Jan 20)
Capricorn: The eclipse could be useful in the process of working to define who you are. By extension, notice how your energy affects others. Growth can come from integrating a sense of well-being and personal fulfillment on your path to achieving long-range goals.

Aquarius (Jan 21 to Feb 19)
Aquarius: Relationship or financial challenges could arise in mid-month. Growth can come from being neither reactive nor controlling. Striving to see things from another’s point of view can be beneficial.

Pisces (Feb 20-March 20)
Pisces: Your intuition keeps expanding with the potential to bring greater clarity and wisdom all the time. Being more open about what you perceive is a good way to be of service to others.

Rio Olesky has been a professional astrologer since 1976. He is the author of A Manual for the Modern Mystic and Astrology and Consciousness. He offers both private readings as well as classes for both beginning and intermediate students. To make an appointment for a reading or to find out more information about classes and lectures, call Rio at 707-887-1820. Check out his website:www.starwatcher.com.

The American Tragedy: A Symbolic Event, Manifest Revelation

Sep 11, 2001 ... When all in each generation have done so, the wheel of light will be complete." [ end of excerpt]. Other dreams and coincidences indicated that ...

NOTE: I received a Christmas gift of a pair of silver earrings each with 3 silver feathers dangling from them. That same night I had the following dream:

I was living in a city. I found a huge green emerald beaded necklace. Intertwined in the necklace was another necklace on two silver chains. On the chains was a silver pendant of a particular shape with 3 silver feathers hanging from it.

I took the silver necklace off the beaded necklace - separated them- and kept the silver necklace with the three feathers. It twinkled and sparkled as it twisted around on the chains.

I took the green emerald beaded necklace to a woman who collected emeralds like this. She had a whole room full of polished stones and beads as well as rough cut stellae shaped stones by the million. In the center of the room was an uncut emerald as least 5 feet tall by 4 feet wide with millions of other emeralds all around it.

She knew immediately that the silver feathered necklace belonged with the beaded emerald necklace I brought to her. She knew it was supposed to be an entwined pair. She told me that the silver feathered part was far more valuable than the jewels because it belonged to a people of antiquity.

She immediately sent two of her henchmen out to find the silver parts, not knowing that I had it in my pocket with my hand on it. I became worried that I might be in some kind of trouble for having it because of it's value, but I didn't admit that I had it.

NOTE: After I had this dream, I was compelled to find out why the three silver feathers had more value than her whole room full of emeralds.

This is what I found: In the book "Dream Feather by Viento Stan-Padilla, a little Indian boy hears a song drifting down from the sun. He knew that from the ancient stone etchings on the cave walls, that the feather was foretold and would be his guide if he but followed it and return to the source.The feather took him on an inner journey where he met a shining presence, where a flash of light and a flame beheld gave him the seed that reunited and fused forever the center of his heart to the circle of creation. He says we should all watch for a Dream Feather and join the circle because when each generation has done so, the wheel of light will be complete.

In Joseph Campbell's book, "The Inner Reaches of Outer Space - Metaphor as Myth and Religion, he shows an Egyptian scene of the weighing of the heart of the deceased against a feather symbolic of Ma'at, goddess of the moral order of the universe. Ma'at is the goddess of truth and represents truth and justice of the Supreme God. The weight of the heart of the deceased is found to be just only if guilt has not made the heart heavier than Ma'at's feather. The heart must be ma'ati (in accordance with Ma'at) if the deceased is to 'become Osiris' (i.e. take on immortality) If the heart does not pass the test, the soul must be reborn.

Four feathers adorned the headdress of the god Anhur, (Onouris), a warrior-like figure from the Upper Egyptian city of Thiis. The dispeller of demons Beset was also portrayed with a crown of feathers.

The polyvalent god and hero Quetzallccoatl was portrayed as a snake covered with iridescent-green feathers of the quetzal bird. These feathers also made up the insignias of Mexican kings. Each feather in the headdresses of the native inhabitants signified an act of bravery of the wearer.

I and an oriental man went to a house to buy Avon pefume. It was raining hard. I wrote a check and placed it on the porch. A very big man let us into the house. My oriental companion had to take off his head and hold it under his arm. The big man led us into a split-level bedroom, with the bed on the higher level.

Another very big man was there, who looked mean. This big man started chasing us. They ran for the front door, but the other big man was guarding the door, holding a knife. We all ran around in a circle in the living room. After a while, the big man at the door said he would let us out.

Instantly, the knife turned into a feather and we were set free. The strange thing was - that I realized all along that the knife was really a feather, but for some reason I perceived it as a knife.

Shortly after hearing the dream, I "just happened" to read in "The Sacred Symbols of Mu," that the feather represented "Truth" to the ancient Egyptians. They choose the feather to symbolize Truth, because it can be so easily blown away.

The dream speaks in a big way. The truth will set you free . . . we dwell in the land of Maya/illusion. The oriental man (foreigner from another land) is The Divine Ka, the Divine Double, The Self. The perfume is related to the "flower" symbolism, symbolic of the Oversoul. The check is karma - in the "learning" sense. We have nothing to fear but our own fears. We are eternal beings - nothing can really harm us. etc.

I was on the big tractor and in the field when I noticed something strange laying between two rows of grain. I'm not sure what this crop was however. Anyway I drove the tractor up near it and it vanished, I couldn't see this thing anymore. I wasn't sure what it was I thought it might be a dead animal but it was like nothing I had ever seen before. I backed up again and there it was and I would draw close to it and it would vanish. I came near it this second time and accidentally ran over some of the crop. I looked down and saw a HUGE white feather laying on the ground between two rows. I recall thinking there's no birds that large on this Earth, it must have fallen from a huge angel.

Again I backed up and this time I looked down and saw what certainly appeared to be a large women laying on the ground at the edge of one of the rows. I stopped and looked at her face wondering if she were dead. I saw no movement or indications of life and the more I looked the more it looked like an illusion. Her face almost looked like it was made up out of cobwebs as it was just that color and texture. I backed the tractor up and the right front wheel came across this form and it appeared to just roll up and vanish.

So here's a strange dream for everyone to try to figure out. We know the crop is the harvest but this crop I didn't recognize even what it was. It was about the height of a bean crop. That first thing I saw was some kind of dead animal all right but the only thing I can think of to describe it was that kind of bird that has a really huge head and beak. The bird isn't all that big but the head is way larger than you would think it would be. I can't think of the name of it. All I can say is this first dead animal I saw reminded me of something like that.

The huge white feather is on the ground. I can say the white feather is an Indian sign of peace and wisdom when wore hanging down over the ear. I really don't know if this is a sign of the end of peace or not in this dream but I get the impression it is a symbol of war to see the large white feather on the ground like this in the middle of a harvest of what ever it was. The harvest itself is a war and death symbol.

The large image on the ground appeared to be a large dead women or dead angel perhaps but it was hollow like a shell made from something else but it looked so very real like you could reach out and touch it.