Sunday, December 7, 2014

Of Zero and Golwalkar's Stupid Children

Sushma Swaraj pushes for declaring Gita as national scripture

Last Updated: Sunday, December 7, 2014 - 21:06
New Delhi: Pressing for the Centre to declare Bhagwad Gita as a 'Rashtriya Granth' (national scripture), External Affairs Minister Sushma Swaraj said on Sunday only a formality remained to be done in this regard, triggering a controversy with Trinamool Congress saying Constitution is the "Holy Book" in a democracy.
Swaraj was speaking at 'Gita Prerna Mahotsav', organised "to celebrate 5,151 years of religious book Gita" at the Red Fort Maidan here where VHP President Ashok Singhal said Prime Minister Narendra Modi should immediately declare the sacred text of Hindus as a national scripture.
The Minister said she was able to face the challenges as External Affairs Minister only because of the teachings of Bhagwad Gita.
She also said that the respect of a "national scripture" was accorded to Gita when Prime Minister Modi gifted it to US President Barack Obama during his visit to the country in September this year.
"Bhagwad Gita has answers to everybody's problems and that's why I said it while standing in the Parliament that, 'Shrimad Bhagwad Gita' should be declared as the national holy book.
"The formal announcement for it hasn't been made for it since the government came in power but Swamiji Maharaj, I am happy to say that the Prime Minister has already given it the honour of a national 'Rashtriya Granth' when he handed over the 'Shrimad Bhagwad Gita' to America's President Barack Obama
"Everyone should read two shlokas of Gita everyday...It is a scripture of 700 shlokas and it can be finished in a year. Read it again and continue this till the end. After reading it three to four times, you will discover a path to lead a life, the way I discovered," she said, addressing the crowd.
"When I read Gita for the first time, I did not agree with the concept of whatever happens, happens for the best and whatever happens in future, will be for good.
"But when I read it for the third and fourth time, I understood its meaning. This has helped me all through my life. Even now, when I am handling the External Affairs and the challenges related to it," she said.
Referring to cases where people consume chocolates and pop pills to fight depression, she said, "Eating chocolates or popping pills won't reduce depression. Instead, one must read Gita. This will help relieve the stress and depression in life. It will help in dealing with challenges of life."
Reacting to Swaraj's remarks, Trinamool Congress said, "Our Constitution says India is a secular country. The Constitution is the Holy Book in a democracy"
"We respect all Holy Books. Quran, Puran, Ved, Vedanta, Bible, Tripitak, Zend Avesta, Guru Granth Sahib, Gita - All are our pride," the TMC said in a tweet.
Congress leader Manish Tewari said the essence of the Gita lies in its substance and not in its symbolism.
"So, if anybody has seriously read and internalise the teachings of the Gita they would not make such a frivolous statement," he said.
Singhal said, "There are two ways here. First is to pass a bill and declare it as a national scripture. But if the Prime Minister immediately declares it as a national scripture...Sushma Swaraj is present here today. As a member of the Union Cabinet, I request Swaraj to make Prime Minister Modi declare Gita as the national scripture."
Senior RSS leader Indresh Kumar said the UN should also declare Gita Divas as it is announcing June 21 as Yoga Day.

First Published: Sunday, December 7, 2014 - 21:06

Join the discussion…


My only comment on comments below is that, if SiDeVillam wants to either support, counter or have a different say about the subject, he should write an article in HT instead of filling up the space meant for comments. I would have loved to hear his views, but the way it is presented at present makes it impossible to read.

  • Comments? Moksha is a commentator? You are a commentator? You are bunch of deluded dunces, Golwalkars' lost cildren with zero knowledge. HT censored my comments that I made before on the same article, three times. Idiot!
    Let us get at the bottom of it. India under Modi, wants to make Indian history (school textbooks) positive. I think it is not wise. Children in Gujarat, already getting false version of Indian history. Say a child not yet mature get to America for his further education and rants and raves about a zero (0) numeral with his professor. Professor would not only dismiss him from the class but recommend the university to rusticate him. Without university's good behavior and good scholarship, he may have to return to Modi's Gujarat and start a factory-of-sorts.
    Genuine stupid University. Admission only with a donation of $10,000 per student/year.
    A win-win situation for Modi Sarkar. All graduates would find a permanent job in Modi's cabinet.
    I invented GSU, I invented GSU, I invented GSU. Eureka!, Oops, Modika! Bunch of idiots!
    ...and I am Sid Harth

Dear friends, the tyranny of the british imperialists was worse than the tyranny of the muslim invaders. The later only invaded our territory the former (the british) brutalised our mind along with our land. The seculars, liberals and intellectuals are all regents and agents of the british. Thru them the british hegemony and imperialism still continues. Let's free our mind. Remember India was once a land so coveted by the entire world, that it was in the process of seeking it that today's america got discovered. Let these intellectuals tell us about a single other land that was so coveted by the world as was this marvelous land of ours. It was not for nothing that it was called a golden bird and a wonder of the world. these epithets are not myths.

  • Where is the myth in saying that the Zero was discovered in India? And that the decimal system and the modern numerical system (0-9) originated in India? It is a fact. Self hating seculars cannot bear to feel pride in their country and in themselves. Their joy is in eternal self flagellation. Disgraceful fellows.

    Moksha, one thing for sure, you have zero intelligence. Shut up. Idiot!
    ...and I am Sid Harth

    • Avatar

      Russell, Bertrand (1942). Principles of mathematics (2 ed.). Forgotten Books. p. 125. ISBN 1-4400-5416-9., Chapter 14, page 125
      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.
      aught at
      Douglas Harper (2011), Zero,
      Etymology Dictionary, Quote="figure which stands for naught in the
      Arabic notation," also "the absence of all quantity considered as
      quantity," c.1600, from French zéro or directly from Italian zero, from
      Medieval Latin zephirum, from Arabic sifr "cipher," translation of
      Sanskrit sunya-m "empty place, desert, naught";
      Menninger, Karl (1992). Number words and number symbols: a cultural history of numbers. Courier Dover Publications. pp. 399–404. ISBN 0-486-27096-3.;
      ""zero, n.". OED Online. December 2011. Oxford University Press. (accessed 4 March 2012).". Archived from the original on 6 March 2012. Retrieved 2012-03-04. French zéro (1515 in Hatzfeld & Darmesteter) or its source Italian zero , for *zefiro , < Arabic çifr
      Smithsonian Institution, Oriental Elements of Culture in the Occident, p. 518, at Google Books,
      Annual Report of the Board of Regents of the Smithsonian Institution;
      Harvard University Archives, Quote="Sifr occurs in the meaning of
      “empty” even in the pre-Islamic time. (...) Arabic sifr in the meaning
      of zero is a translation of the corresponding India sunya.”;
      Jan Gullberg (1997), Mathematics: From the Birth of Numbers, W.W. Norton & Co., ISBN 978-0393040029,
      page 26, Quote = ‘‘Zero derives from Hindu sunya - meaning void,
      emptiness - via Arabic sifr, Latin cephirum, Italian zevero.’’;
      Robert Logan (2010), The Poetry of Physics and the Physics of Poetry, World Scientific, ISBN 978-9814295925,
      page 38, Quote = “The idea of sunya and place numbers was transmitted
      to the Arabs who translated sunya or “leave a space” into their language
      as sifr.”
      Zero, Merriam Webster online Dictionary
      Ifrah, Georges (2000). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Wiley. ISBN 0-471-39340-1.
      'Aught' definition, – Retrieved April 2013.
      'Aught' synonyms, – Retrieved April 2013.
      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.
      Kaplan, Robert. (2000). The Nothing That Is: A Natural History of Zero. Oxford: Oxford University Press.
      Bourbaki, Nicolas (1998). Elements of the History of Mathematics. Berlin, Heidelberg, and New York: Springer-Verlag. 46. ISBN 3-540-64767-8.
      Britannica Concise Encyclopedia (2007), entry algebra
      Math for Poets and Drummers (pdf, 145KB)
      Kim Plofker (2009), Mathematics in India, Princeton University Press, ISBN 978-0691120676,
      page 55-56. Quote - “In the Chandah-sutra of Pingala, dating perhaps
      the third or second century BCE, there are five questions concerning the
      possible meters for any value “n”. (...) The answer is (2)7 =
      128, as expected, but instead of seven doublings, the process
      (explained by the sutra) required only three doublings and two squarings
      - a handy time saver where “n” is large. Pingala’s use of a zero symbol
      as a marker seems to be the first known explicit reference to zero.”
      Ifrah, Georges (2000), p. 416.
      Bill Casselman (University of British Columbia), American Mathematical Society, "All for Nought"
      Ifrah, Georges (2000), p. 400.
      Aryabhatiya of Aryabhata, translated by Walter Eugene Clark.
      Agarwal, M.K. (23 May 2012). From Bharata to India: Chrysee the Golden. iUniverse. p. 206. ISBN 9781475907650.
      O'Connor, Robertson, J.J., E. F. "Aryabhata the Elder". School of Mathematics and Statistics University of St Andrews, Scotland. Retrieved 26 May 2013.
      William L. Hosch, ed. (15 August 2010). The Britannica Guide to Numbers and Measurement (Math Explained). The Rosen Publishing Group. pp. 97–98. ISBN 9781615301089.
      Algebra with Arithmetic of Brahmagupta and Bhaskara, translated to English by Henry Thomas Colebrooke, London1817
      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.
      Crossley, Lun. 1999, p.12 "the ancient Chinese system is a place notation system"
      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
      Mathematics in the Near and Far East, p. 262
      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."
      Pannekoek, A. (1961). A History of Astronomy. George Allen & Unwin. p. 165.
      Will Durant (1950), The Story of Civilization, Volume 4, The Age of Faith: Constantine to Dante - A.D. 325-1300, Simon & Schuster, ISBN 978-0965000758, p. 241, Quote
      = "The Arabic inheritance of science was overwhelmingly Greek, but
      Hindu influences ranked next. In 773, at Mansur's behest, translations
      were made of the Siddhantas - Indian astronomical treatises
      dating as far back as 425 BC; these versions may have the vehicle
      through which the "Arabic" numerals and the zero were brought from India into Islam. In 813, al-Khwarizmi used the Hindu numerals in his astronomical tables."
      Brezina, Corona (2006). Al-Khwarizmi: The Inventor Of Algebra. The Rosen Publishing Group. ISBN 978-1-4042-0513-0.
      Will Durant (1950), The Story of Civilization, Volume 4, The Age of Faith, Simon & Schuster, ISBN 978-0965000758, p. 241, Quote = "In 976, Muhammad ibn Ahmad, in his Keys of the Sciences,
      remarked that if, in a calculation, no number appears in the place of
      tens, a little circle should be used "to keep the rows". This circle the
      Mosloems called ṣifr, "empty" whence our cipher."
      Sigler, L., Fibonacci's Liber Abaci. English translation, Springer, 2003.
      Grimm, R.E., "The Autobiography of Leonardo Pisano", Fibonacci Quarterly 11/1 (February 1973), pp. 99–104.
      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.
      Diehl, p. 186
      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.
      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
      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.
      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.
      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


      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"
      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.

      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 science programming languages such as Fortran and COBOL. However, in the late 1950s LISP introduced zero-based numbering for arrays while Algol 58
      introduced 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 be undetermined.
      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 point
      number 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.

      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. This is related to 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 by f(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.
      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.

      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.

      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 a complex 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).[39] Zero is, however, even.
      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.
      Exponentiation: x0 = x/x = 1, except that the case x = 0 may be left undefined in some contexts. For all positive real x, 0x = 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 lim operator 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.

      See also: parity of zero
      0 is the integer immediately preceding 1. Zero is an even number,[37] because it is divisible by 2. 0 is neither positive nor negative. By most definitions[38] 0 is a natural number, and then the only natural number not to be positive. Zero is a number which quantifies a count or an amount of null size. In most cultures, 0 was identified before the idea of negative things (quantities) that go lower than zero was accepted.
      The value, or number, zero is not the same as the digit zero, used in numeral systems using positional notation.
      Successive positions of digits have higher weights, so inside a numeral
      the digit zero is used to skip a position and give appropriate weights
      to the preceding and following digits. A zero digit is not always
      necessary in a positional number system, for example, in the number 02.
      In some instances, a leading zero may be used to distinguish a number.
      Elementary algebra

      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.[35]
      Since the eight earliest Long Count dates appear outside the Maya homeland,[36] 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.

      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 be printed
      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.

      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.[33][34]


      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 be
      something?", leading to philosophical and, by the Medieval period,
      religious arguments about the nature and existence of zero and the vacuum. The paradoxes 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, this Hellenistic 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
      later Byzantine 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 by Dionysius 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

      Islamic world
      The Arabic-language inheritance of science was largely Greek,[29] followed by Hindu influences.[30] In 773, at Al-Mansur's behest, translations were made of many ancient treatises including Greek, Latin, Indian, and others.
      In 813 AD astronomical tables were prepared by Persian al-Khwarizmi using Hindu numerals,[30]
      and about 825 AD, he published a book synthesizing Greek and Hindu
      knowledge and also contained his own contribution to mathematics
      including an explanation of the use of zero.[31] This book was later translated into Latin in the 12th century under the title Algoritmi de numero Indorum.
      This title means "al-Khwarizmi on the Numerals of the Indians". The
      word "Algoritmi" was the translator's Latinization of Al-Khwarizmi's
      name, and the word "Algorithm" or "Algorism" started meaning any
      arithmetic based on decimals.[30]
      Muhammad ibn Ahmad al-Khwarizmi, in 976 AD, stated that if no number
      appears in the place of tens in a calculation, a little circle should be
      used "to keep the rows". This circle was called ṣifr.[32]

      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.[24]
      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."[24] The counting rod system is considered a positional notation system.[25]
      Zero was not treated as a number at that time, but as a "vacant
      position", unlike the Indian mathematicians who developed the numerical
      zero.[26] Ch'in Chu-shao's 1247 Mathematical Treatise in Nine Sections is the oldest surviving Chinese mathematical text using a round symbol for zero.[27] 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,[28] much earlier than the fifteenth century when they became well established in Europe.[27]

      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),[23]
      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:[23]
      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.


      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.[10]
      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.[11]
      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.
      Statue of Aryabhata
      The concept of zero as a number and not merely a symbol or an empty
      space 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.[12][13]
      The Indian scholar Pingala, of 2nd century BC or earlier, 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.[14] In his Chandah-sutras (prosody sutras), dated to 3rd or 2nd century BCE, Pingala used the Sanskrit word śūnya explicitly to refer to zero. This is so far the oldest known use of śūnya to mean zero in India.[15] The fourth Pingala sutra offers a way to accurately calculate large metric exponentiation, of the type (2)n, efficiently with less number of steps.[15]
      The earliest text to use a decimal place-value system, including a zero, is the Jain text from India entitled the Lokavibhāga, dated 458 AD, where śūnya ("void" or "empty") was employed for this purpose.[16] 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.[17][18] 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.[11]
      In 498 AD, Indian mathematician and astronomer Aryabhata stated that "sthānāt sthānaṁ daśaguṇaṁ syāt;"[19] i.e., "from place to place each is ten times the preceding,"[19][20] which is the origin of the modern decimal-based place value notation.[21][22]

      The word zero came via French zéro from Venetian zero, via Italian zefiro from ṣafira or ṣifr (Arabic صفر).[4] The word ṣifr, even in pre-Islamic time, had the meaning empty.[5] It got its meaning of word zero when it was used as a translation to mean śūnya (Sanskrit: शून्य) from India.[5] The first known English use was in 1598.[6]
      Italian zefiro already meant "west wind" from Latin and Greek zephyrus; this may have influenced the spelling when transcribing Arabic ṣifr.[7] 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 Arabic 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'."[7] 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.

      Another hypothesis by McCormac and Evans assumes that the Earth's field would disappear entirely during reversals.[42] They argue that the atmosphere of Mars may have been eroded away by the solar wind
      because it had no magnetic field to protect it. They predict that ions
      would be stripped away from Earth's atmosphere above 100 km. However,
      the evidence from paleointensity measurements is that the magnetic field
      does not disappear. Based on paleointensity data for the last 800,000
      years,[43] the magnetopause is still estimated to be at about 3 Earth radii during the Brunhes-Matuyama reversal.[36] Even if the magnetic field disappeared, the solar wind may induce a sufficient magnetic field in the Earth's ionosphere to shield the surface from energetic particles.[44]
      Hypotheses have also been advanced linking reversals to mass extinctions.[45]
      Many such arguments were based on an apparent periodicity in the rate
      of reversals; more careful analyses show that the reversal record is not
      It may be, however, that the ends of superchrons have caused vigorous
      convection leading to widespread volcanism, and that the subsequent
      airborne ash caused extinctions.[46]
      Tests of correlations between extinctions and reversals are difficult
      for a number of reasons. Larger animals are too scarce in the fossil
      record for good statistics, so paleontologists have analyzed microfossil
      extinctions. Even microfossil data can be unreliable if there are
      hiatuses in the fossil record. It can appear that the extinction occurs
      at the end of a polarity interval when the rest of that polarity
      interval was simply eroded away.[20] Statistical analysis shows no evidence for a correlation between reversals and extinctions.[47][36]

    As per Golwalkar, the North pole migrated thousands of km further to north in the arctic an idea sir ji!! This is saffron history...only myths and lies..

      Get smart, boy. Golwalkar id dead. He can't help you.


      Further reading
      Behrendt, J.C., Finn, C., Morse, L., Blankenship, D.D. "One
      hundred negative magnetic anomalies over the West Antarctic Ice Sheet
      (WAIS), in particular Mt. Resnik, a subaerially erupted volcanic peak,
      indicate eruption through at least one field reversal"
      University of Colorado, U.S. Geological Survey, University of Texas.
      (U.S. Geological Survey and The National Academies); USGS OF-2007-1047,
      Extended Abstract 030. 2007.
      Okada, M., Niitsuma, N., "Detailed
      paleomagnetic records during the Brunhes-Matuyama geomagnetic reversal,
      and a direct determination of depth lag for magnetization in marine
      sediments" Physics of the Earth and Planetary Interiors, Volume 56, Issue 1-2, p. 133-150. 1989.
      External links
      How geomagnetic reversals are related to intensity
      "Look down, look up, look out!", The Economist, May 10 2007
      "Ships' logs give clues to Earth's magnetic decline", New Scientist, May 11 2006
      Simple explanation of geomagnetic reversal,, accessed Nov 2 2012

      Gaffin, S. (1989). "Analysis of scaling in the geomagnetic polarity reversal record". Physics of the Earth and Planetary Interiors 57: 284–289. Bibcode:1989PEPI...57..284G. doi:10.1016/0031-9201(89)90117-9.
      Coe, R. S.; Prévot, M.; Camps, P. (20 April 1995). "New evidence for extraordinarily rapid change of the geomagnetic field during a reversal". Nature 374 (6524): 687. Bibcode:1995Natur.374..687C. doi:10.1038/374687a0.
      Merrill, Ronald T. (2010). Our magnetic Earth : the science of geomagnetism. Chicago: The University of Chicago Press. ISBN 0-226-52050-1.
      M.; Mankinen, E.; Coe, R.; Grommé, C. (1985). "The Steens Mountain
      (Oregon) Geomagnetic Polarity Transition 2. Field Intensity Variations
      and Discussion of Reversal Models". J. Geophys. Res. 90 (B12): 10417–10448. Bibcode:1985JGR....9010417P. doi:10.1029/JB090iB12p10417.
      Edward A.; Prévot, Michel; Grommé, C. Sherman; Coe, Robert S. (1
      January 1985). "The Steens Mountain (Oregon) Geomagnetic Polarity
      Transition 1. Directional History, Duration of Episodes, and Rock
      Magnetism". Journal of Geophysical Research 90 (B12): 10393. Bibcode:1985JGR....9010393M. doi:10.1029/JB090iB12p10393.
      Nicholas A.; Coe, Robert S.; Glen, Jonathan M.G. (2011). "Evidence from
      lava flows for complex polarity transitions: the new composite Steens
      Mountain reversal record". Geophysical Journal International 186 (2): 580–602. Bibcode:2011GeoJI.186..580J. doi:10.1111/j.1365-246X.2011.05086.x.
      Edwards, Lin (6 September 2010). "Evidence of Second Fast North-South Pole Flip Found".


      Merrill, Ronald T.; McElhinny, Michael W.; McFadden, Phillip L. (1998). The magnetic field of the earth: paleomagnetism, the core, and the deep mantle. Academic Press. ISBN 978-0-12-491246-5.
      Courtillot, Vincent (1999). Evolutionary Catastrophes: the Science of Mass Extinctions. Cambridge: Cambridge University Press. pp. 110–11. ISBN 978-0-521-58392-3. Translated from the French by Joe McClinton.
      Pavlov, V.; Gallet, Y. "A third superchron during the Early Paleozoic". Episodes (International Union of Geological Sciences) 28 (2): 78–84.
      McElhinny, Michael W.; McFadden, Phillip L. (2000). Paleomagnetism: Continents and Oceans. Academic Press. ISBN 0-12-483355-1.
      Phillips, J. D.; Cox, A. (1976). "Spectral analysis of geomagnetic reversal time scales". Geophysical Journal of the Royal Astronomical Society 45: 19–33. Bibcode:1976GeoJI..45...19P. doi:10.1111/j.1365-246X.1976.tb00311.x.
      e.g., Raup, D. M. (1985). "Magnetic reversals and mass extinctions". Nature 314: 341–343. Bibcode:1985Natur.314..341R. doi:10.1038/314341a0.
      Lutz, T. M. (1985). "The magnetic reversal record is not periodic". Nature 317: 404–407. Bibcode:1985Natur.317..404L. doi:10.1038/317404a0.
      Dumé, Belle (March 21, 2006). "Geomagnetic flip may not be random after all". Retrieved December 27, 2009.
      V.; Sorriso-Valvo, L.; Vecchio, A.; Lepreti, F.; Veltri, P.;
      Harabaglia, P.; Guerra, I. "Clustering of Polarity Reversals of the
      Geomagnetic Field". Physical Review Letters 96 (12): 128501. arXiv:physics/0603086. Bibcode:2006PhRvL..96l8501C. doi:10.1103/PhysRevLett.96.128501.


      age polarity reversal was global event: Extremely brief reversal of
      geomagnetic field, climate variability, and super volcano. Sciencedailydotcom (2012-10-16). Retrieved on 2013-07-28.
      Cox, Allan (1973). Plate tectonics and geomagnetic reversal. San Francisco, California: W. H. Freeman. pp. 138–145, 222–228. ISBN 0-7167-0258-4.
      Glen, William (1982). The Road to Jaramillo: Critical Years of the Revolution in Earth Science. Stanford University Press. ISBN 0-8047-1119-4.
      Vine, Frederick J.; Drummond H. Matthews (1963). "Magnetic Anomalies over Oceanic Ridges". Nature 199 (4897): 947–949. Bibcode:1963Natur.199..947V. doi:10.1038/199947a0.
      Morley, Lawrence W.; A. Larochelle (1964). "Paleomagnetism as a means of dating geological events". Geochronology in Canada. Special (Royal Society of Canada). Publication 8: 39–50.
      S. C.; Kent, D. V. (1995). "Revised calibration of the geomagnetic
      polarity timescale for the late Cretaceous and Cenozoic". Journal of Geophysical Research 100: 6093–6095. Bibcode:1995JGR...100.6093C. doi:10.1029/94JB03098.
      "Geomagnetic Polarity Timescale". Ocean Bottom Magnetometry Laboratory. Woods Hole Oceanographic Institution. Retrieved March 23, 2011.
      Banerjee, Subir K. (2001-03-02). "When the Compass Stopped Reversing Its Poles". Science (American Association for the Advancement of Science) 291 (5509): 1714–1715. doi:10.1126/science.291.5509.1714.

      Effects on biosphere
      Not long after the first geomagnetic polarity time scales were
      produced, scientists began exploring the possibility that reversals
      could be linked to extinctions. Most such proposals rest on the
      assumption that the Earth's magnetic field would be much weaker during
      reversals. Possibly the first such hypothesis was that high energy
      particles trapped in the Van Allen radiation belt could be liberated and bombard the Earth.[36][37]
      Detailed calculations confirm that, if the Earth's dipole field
      disappeared entirely (leaving the quadrupole and higher components),
      most of the atmosphere would become accessible to high energy particles,
      but would act as a barrier to them, and cosmic ray collisions would
      produce secondary radiation of beryllium-10 or chlorine-36.
      An increase of beryllium-10 was noted in a 2012 German study showing a
      peak of beryllium-10 in Greenland ice cores during a brief complete
      reversal 41,000 years ago which led to the magnetic field strength
      dropping to an estimated 5% of normal during the reversal.[1] There is evidence that this occurs both during secular variation[38][39] and during reversals.[40][41]

      Hypothesized triggers
      Some scientists, such as Richard A. Muller,
      believe that geomagnetic reversals are not spontaneous processes but
      rather are triggered by external events that directly disrupt the flow
      in the Earth's core. Proposals include impact events[32][33] or internal events such as the arrival of continental slabs carried down into the mantle by the action of plate tectonics at subduction zones or the initiation of new mantle plumes from the core-mantle boundary.[34]
      Supporters of this theory hold that any of these events could lead to a
      large scale disruption of the dynamo, effectively turning off the
      geomagnetic field. Because the magnetic field is stable in either the
      present North-South orientation or a reversed orientation, they propose
      that when the field recovers from such a disruption it spontaneously
      chooses one state or the other, such that half the recoveries become
      reversals. However, the proposed mechanism does not appear to work in a
      quantitative model, and the evidence from stratigraphy
      for a correlation between reversals and impact events is weak. Most
      strikingly, there is no evidence for a reversal connected with the
      impact event that caused the Cretaceous–Paleogene extinction event.[35]

      NASA computer simulation using the model of Glatzmaier and Roberts.[28] The tubes represent magnetic field lines,
      blue when the field points towards the center and yellow when away. The
      rotation axis of the Earth is centered and vertical. The dense clusters
      of lines are within the Earth's core.[27]
      The magnetic field of the Earth, and of other planets that have magnetic fields, are generated by dynamo action
      in which convection of molten iron in the planetary core generates
      electric currents which in turn give rise to magnetic fields.[9] In simulations
      of planetary dynamos, reversals often emerge spontaneously from the
      underlying dynamics. For example, Gary Glatzmaier and collaborator Paul
      Roberts of UCLA
      ran a numerical model of the coupling between electromagnetism and
      fluid dynamics in the Earth's interior. Their simulation reproduced key
      features of the magnetic field over more than 40,000 years of simulated
      time and the computer-generated field reversed itself.[28][29] Global field reversals at irregular intervals have also been observed in the laboratory liquid metal experiment VKS2.[30]
      In some simulations, this leads to an instability in which the
      magnetic field spontaneously flips over into the opposite orientation.
      This scenario is supported by observations of the solar magnetic field, which undergoes spontaneous reversals
      every 9–12 years. However, with the Sun it is observed that the solar
      magnetic intensity greatly increases during a reversal, whereas
      reversals on Earth seem to occur during periods of low field strength.[31]

      Character of transitions
      Most estimates for the duration of a polarity transition are between 1,000 and 10,000 years.[9] However, studies of 15 million year old lava flows on Steens Mountain, Oregon, indicate that the Earth's magnetic field is capable of shifting at a rate of up to 6 degrees per day.[19]
      This was initially met with skepticism from paleomagnetists. Even if
      changes occur that quickly in the core, the mantle, which is a semiconductor, is thought to act as a low-pass filter, removing variations with periods less than a few months. A variety of possible rock magnetic mechanisms were proposed that would lead to a false signal.[20]
      However, paleomagnetic studies of other sections from the same region
      (the Oregon Plateau flood basalts) give consistent results.[21][22] It appears that the reversed-to-normal polarity transition that marks the end of Chron C5Cr (16.7 million years ago) contains a series of reversals and excursions.[23]
      In addition, geologists Scott Bogue of Occidental College and Jonathan
      Glen of the US Geological Survey, sampling lava flows in Battle Mountain, Nevada,
      found evidence for a brief, several year long interval during a
      reversal when the field direction changed by over 50°. The reversal was
      dated to approximately 15 million years ago.[24][25]
      Magnetic field
      The magnetic field will not vanish completely, but many poles might
      form chaotically in different places during reversal, until it
      stabilizes again.[26][27]

      Statistical properties of reversals
      Several studies have analyzed the statistical properties of reversals
      in the hope of learning something about their underlying mechanism. The
      discriminating power of statistical tests is limited by the small
      number of polarity intervals. Nevertheless, some general features are
      well established. In particular, the pattern of reversals is random.
      There is no correlation between the lengths of polarity intervals.[13]
      There is no preference for either normal or reversed polarity, and no
      statistical difference between the distributions of these polarities.
      This lack of bias is also a robust prediction of dynamo theory.[9] Finally, as mentioned above, the rate of reversals changes over time.
      The randomness of the reversals is inconsistent with periodicity, but several authors have claimed to find periodicity.[14] However, these results are probably artifacts of an analysis using sliding windows to determine reversal rates.[15]
      Most statistical models of reversals have analyzed them in terms of a Poisson process or other kinds of renewal process.
      A Poisson process would have, on average, a constant reversal rate, so
      it is common to use a non-stationary Poisson process. However, compared
      to a Poisson process, there is a reduced probability of reversal for
      tens of thousands of years after a reversal. This could be due to an
      inhibition in the underlying mechanism, or it could just mean that some
      shorter polarity intervals have been missed.[9] A random reversal pattern with inhibition can be represented by a gamma process. In 2006, a team of physicists at the University of Calabria found that the reversals also conform to a Lévy distribution, which describes stochastic processes with long-ranging correlations between events in time.[16][17] The data are also consistent with a deterministic, but chaotic, process.[18]

      A superchron is a polarity interval lasting at least 10 million
      years. There are two well-established superchrons, the Cretaceous
      Normal and the Kiaman. A third candidate, the Moyero, is more
      controversial. The Jurassic Quiet Zone in ocean magnetic anomalies was
      once thought to represent a superchron, but is now attributed to other
      The Cretaceous Normal (also called the Cretaceous Superchron or C34) lasted for almost 40 million years, from about 120 to 83 million years ago, including stages of the Cretaceous period from the Aptian through the Santonian.
      The frequency of magnetic reversals steadily decreased prior to the
      period, reaching its low point (no reversals) during the period. Between
      the Cretaceous Normal and the present, the frequency has generally
      increased slowly.[9]
      The Kiaman Reverse Superchron lasted from approximately the late Carboniferous to the late Permian, or for more than 50 million years, from around 312 to 262 million years ago.[9] The magnetic field had reversed polarity. The name "Kiaman" derives from the Australian village of Kiama, where some of the first geological evidence of the superchron was found in 1925.[10]
      The Ordovician is suspected to host another superchron, called the Moyero Reverse Superchron, lasting more than 20 million years (485 to 463 million
      years ago) . But until now this possible superchron has only been found
      in the Moyero river section north of the polar circle in Siberia.[11] Moreover, the best data from elsewhere in the world do not show evidence for this superchron.[12]
      Certain regions of ocean floor, older than 160 Ma,
      have low-amplitude magnetic anomalies that are hard to interpret. They
      are found off the east coast of North America, the northwest coast of
      Africa, and the western Pacific. They were once thought to represent a
      superchron called the Jurassic Quiet Zone, but magnetic anomalies
      are found on land during this period. The geomagnetic field is known to
      have low intensity between about 130 Ma and 170 Ma, and these sections of ocean floor are especially deep, so the signal is attenuated between the floor and the surface.[12]

      Geomagnetic polarity time scale
      Further information: Magnetostratigraphy
      Through analysis of seafloor magnetic anomalies and dating of
      reversal sequences on land, paleomagnetists have been developing a Geomagnetic Polarity Time Scale (GPTS). The current time scale contains 184 polarity intervals in the last 83 million years.[6][7]
      Changing frequency over time
      The rate of reversals in the Earth's magnetic field has varied widely over time. 72 million years ago (Ma), the field reversed 5 times in a million years. In a 4-million-year period centered on 54 Ma, there were 10 reversals; at around 42 Ma, 17 reversals took place in the span of 3 million years. In a period of 3 million years centering on 24 Ma, 13 reversals occurred. No fewer than 51 reversals occurred in a 12-million-year period, centering on 15 million years ago.
      Two reversals occurred during a span of 50,000 years. These eras of
      frequent reversals have been counterbalanced by a few "superchrons" –
      long periods when no reversals took place.[8]

      Observing past fields
      Geomagnetic polarity since the middle Jurassic.
      Dark areas denote periods where the polarity matches today's polarity,
      light areas denote periods where that polarity is reversed.
      Past field reversals can be and have been recorded in the "frozen" ferromagnetic (or more accurately, ferrimagnetic) minerals of consolidated sedimentary deposits or cooled volcanic flows on land.
      The past record of geomagnetic reversals was first noticed by observing the magnetic stripe "anomalies" on the ocean floor. Lawrence W. Morley, Frederick John Vine and Drummond Hoyle Matthews made the connection to seafloor spreading in the Morley-Vine-Matthews hypothesis[4][5] which soon led to the development of the theory of plate tectonics. The relatively constant rate at which the sea floor
      spreads results in substrate "stripes" from which past magnetic field
      polarity can be inferred from data gathered from towing a magnetometer along the sea floor.
      Because no existing unsubducted sea floor (or sea floor thrust onto continental plates) is more than about 180 million years (Ma) old, other methods are necessary for detecting older reversals. Most sedimentary rocks incorporate tiny amounts of iron rich minerals,
      whose orientation is influenced by the ambient magnetic field at the
      time at which they formed. These rocks can preserve a record of the
      field if it is not later erased by chemical, physical or biological change.
      Because the magnetic field is global, similar patterns of magnetic
      variations at different sites may be used to correlate age in different
      locations. In the past four decades much paleomagnetic data about
      seafloor ages (up to ~250 Ma)
      has been collected and is useful in estimating the age of geologic
      sections. Not an independent dating method, it depends on "absolute" age
      dating methods like radioisotopic systems to derive numeric ages. It
      has become especially useful to metamorphic and igneous geologists where
      index fossils are seldom available.

      During the 1950s and 1960s information about variations in the
      Earth's magnetic field was gathered largely by means of research
      vessels. But the complex routes of ocean cruises rendered the
      association of navigational data with magnetometer
      readings difficult. Only when data were plotted on a map did it become
      apparent that remarkably regular and continuous magnetic stripes
      appeared on the ocean floors.[2][3]
      In 1963 Frederick Vine and Drummond Matthews provided a simple explanation by combining the seafloor spreading theory of Harry Hess
      with the known time scale of reversals: if new sea floor is magnetized
      in the direction of the field, then it will change its polarity when the
      field reverses. Thus, sea floor spreading from a central ridge will
      produce magnetic stripes parallel to the ridge.[4] Canadian L. W. Morley independently proposed a similar explanation in January 1963, but his work was rejected by the scientific journals Nature and Journal of Geophysical Research, and remained unpublished until 1967, when it appeared in the literary magazine Saturday Review.[2] The Morley–Vine–Matthews hypothesis was the first key scientific test of the seafloor spreading theory of continental drift.[3]
      Beginning in 1966, Lamont–Doherty Geological Observatory scientists found that the magnetic profiles across the Pacific-Antarctic Ridge were symmetrical and matched the pattern in the north Atlantic's Reykjanes
      ridges. The same magnetic anomalies were found over most of the world's
      oceans, which permitted estimates for when most of the oceanic crust
      had developed.[2][3]

      In the early 20th century geologists first noticed that some volcanic
      rocks were magnetized opposite to the direction of the local Earth's
      field. The first estimate of the timing of magnetic reversals was made
      in the 1920s by Motonori Matuyama, who observed that rocks with reversed fields were all of early Pleistocene age or older. At the time, the Earth's polarity was poorly understood and the possibility of reversal aroused little interest.[2][3]
      Three decades later, when Earth's magnetic field was better
      understood, theories were advanced suggesting that the Earth's field
      might have reversed in the remote past. Most paleomagnetic research in
      the late 1950s included an examination of the wandering of the poles and
      continental drift.
      Although it was discovered that some rocks would reverse their magnetic
      field while cooling, it became apparent that most magnetized volcanic
      rocks preserved traces of the Earth's magnetic field at the time the
      rocks had cooled. In the absence of reliable methods for obtaining
      absolute ages for rocks, it was thought that reversals occurred
      approximately every million years.[2][3]
      The next major advance in understanding reversals came when techniques for radiometric dating were developed in the 1950s. Allan Cox and Richard Doell, at the United States Geological Survey, wanted to know whether reversals occurred at regular intervals, and invited the geochronologist Brent Dalrymple
      to join their group. They produced the first magnetic-polarity time
      scale in 1959. As they accumulated data, they continued to refine this
      scale in competition with Don Tarling and Ian McDougall at the Australian National University. A group led by Neil Opdyke at the Lamont-Doherty Geological Observatory showed that the same pattern of reversals was recorded in sediments from deep-sea cores.[3]

      A geomagnetic reversal is a change in a planet's magnetic field such that the positions of magnetic north and magnetic south are interchanged. The Earth's field has alternated between periods of normal polarity, in which the direction of the field was the same as the present direction, and reverse polarity, in which the field was the opposite. These periods are called chrons. The time spans of chrons are randomly distributed with most being between 0.1 and 1 million years[citation needed] with an average of 450,000 years. Most reversals are estimated to take between 1,000 and 10,000 years. The latest one, the Brunhes–Matuyama reversal, occurred 780,000 years ago. A brief complete reversal, known as the Laschamp event, occurred only 41,000 years ago during the last glacial period.
      That reversal lasted only about 440 years with the actual change of
      polarity lasting around 250 years. During this change the strength of
      the magnetic field dropped to 5% of its present strength.[1] Brief disruptions that do not result in reversal are called geomagnetic excursions.

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