Котий-Любимова О. About unability of some high-ranking Soviet-Russian scientists to distinguish between place value & non-place-value systems when discussing the subject (on the example of illiterate statements made by mathenaticians for the people Doctor of Mathematics & Physical Science Academic A.T.Fomenko (Atf) & the Candidate of Physical and Mathematical Sciences G.V.Nosovskiy (Gvn) regarding Sumerian sexagesimal (base 60) positional numeral system &sumerian clay tablets). Part Ii
Аннотация: Could the Indian matematians invent zero struggling so much when it came to negatives & division into zero?
Guskova Olga Valentinovna
Moscow Institute of Linguistics,ovalg@mail.ru
ِ About unability of some high-ranking Soviet-Russian scientists to distinguish between place value & non-place-value systems when discussing the subject (on the example of illiterate statements made by mathenaticians for the people Doctor of Mathematics & Physical Science Academic A.T.Fomenko (ATF) & the Candidate of Physical and Mathematical Sciences G.V.Nosovskiy (GVN) regarding Sumerian sexagesimal (base 60) positional numeral
system &Sumerian clay tablets).
Part II.
Could the Indian matematians invent zero struggling so much when it came to negatives & division into zero?
Before answering this question let's remind those who read Part 1 of our publication that we began to discuss in it the alleged use of the Sumerian zero by Arabic ( Iraqi ) mathematician, astronomer and geographer Abu Muhammet Al-Horezmi (780-847). GVN & ATF do not mention this fact in regard to Sumerian positional numeral system. although it seems to be very important.
The reader probably knows Al-Horezmi for his introducing into the science the term "algebra" derived as we"d previously told from arabic الجبر al-ğabØru provided an exhaustive account of solving for the positive roots of polynomial equations up to the second degree. Abu Muhammet Al-Horezmi is also known as the aurhor of the book of the Hindu Art of Reckoning translated in the 12 th century A.D. into Latin under the name "Algoritmi de numero Indorum" where he characterized the Indian numeration system as a positive one having "zero". The information that the degits 0 1, 2, 3, 4, 5, 6, 7 , 8, 9 described by Al-Horezmi were Indian - that's what the partisans of the hypothesis of the Indian origin of the numerals say −is however doubtful not only because the original Arabic text isn"t available (it is said to be lost), but just only because the earliest reliable record of the Indian use of zero, which is agreed to be genuine, is an inscription of 867 A.D. in India [1}, Mathematitians date the inscription of the town of Gwalior differently although most of them indicate the date −876 A.D.{6] . Anyways it was made after Al-Horezmi"s death, not at his lifetime to consider his testimonies true & anyways the Indian symbols for zero borrowed by the Indians from the Arabs including Arabic dot etc. appeared much later than ''numeral zero'' (Ahmed Boucenna ) [4] known by the Sumerians (two wedges or small hooks)..
"We have an inscription on a stone tablet which contains a date which translates to 876 − write J J. O'Connor & E.F Robertson . − The inscription concerns the town of Gwalior, 400 km south of Delhi, where they planted a garden 187 by 270 hastas which would produce enough flowers to allow 50 garlands per day to be given to the local temple. Both of the numbers 270 and 50 are denoted almost as they appear today although the 0 is smaller and slightly raised. (Note that matematitians as a rule mention in connection with the town of Gwalior only one number - 270 -O.G)...There is evidence of an empty place holder in positional numbers from as early as 200 AD in India. - they continue telling − but some historians dismiss these as later forgeries" [3]. The number of such mathematicians in history must be added is really impressive.
We suppose it"s because of that the appearance of zero as a number has no relation to India & its mathematics history at all More than that. We even know for sure that the Indians didn"t devise zero and will announce the name of its real inventor in our further publications However now we"d" like to pay our reader"s attention to what had said J J. O'Connor & E.F Robertson about zero. It as they think is "not in any sense a natural candidate for a number. From early times numbers are words which refer to collections of objects. Certainly the idea of number became more and more abstract and this abstraction then makes possible the consideration of zero and negative numbers which do not arise as properties of collections of objects. Of course the problem which arises when one tries to consider zero and negatives as numbers is how they interact in regard to the operations of arithmetic, addition, subtraction, multiplication and division. In three important books the Indian mathematicians Brahmagupta, Mahavira and Bhaskara tried to answer these questions".[3] Let"s emphasize & underline these words which we ourselves understand as if the Indian mathematicians were searching for zero but unfortunately unsuccessfully, without finding it.
What did we mean by citing all the above? Only that someone strugglimg so much when it comes to at least to division into zero like the Indian mathematitions did cannot in our opinion invent it (zero). The first mathematitian officially proclaimed to state correspondingly the first set of rules for dealing with negative numbers is Brahmagupta (598 - 670), who used for negatives about 620 A.C. the idea of 'debts' denoted by two polysemous ( multi-valued ) words-synonimes: क्षय kSaya & ऋण RiNa, having except common meaning of "negative quantity" additional meanings of: decay (m), sickness in general (m), wane (m), abode(m), waning(m), end(m), abode in yama's dominion (m), annihilation (m), destruction of the universe (m), diminution (m), dwelling-place (m), ruin(m), termination )m), family (m), decline (m), house of yama (m), removal (m), wasting or wearing away(m), seat (m, loss (m), consumption (m), race (m), minus (m), fall (m), house (m), destruction (m) as well as dwelling (adj), residing (adj) −the first one ( क्षय kSaya). As for रीण RINa it"s used only for adhectives: melted, vanished, dissolved [5].
By that time as it is also stated a system based on place-value was established in India with zero being used in the Indian number system. In spite of all it probably isn"t surprising that in 1758 the British mathematician Francis Maseres was claiming that negative numbers "... darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple" [7]. It"s curious enough by the way that in the 9th century in Baghdad Al - Horezmi presented six standard forms for linear or quadratic equations ax2 + c = bx, ax 2 = c, s = s, ax2 bx + c =, ax2 + bx = c, bx + c = ax2 . & and produced their solutions using algebraic methods and geometrical diagrams. The members of each of all Al - Horezmi"s six types of equations are added not subtracted. Those of equations which don"t have positive solutions are not taken into account by him. . There appeared even before 3 types of his linear & quadratic equations although without algebraic formalization & Diofant .rhetorical algorithm such as: х2 +10x = 39, x2 + 21 = 10x, 3x + 4 = x2. It was first in Al -Horezmi"s book "المختصر في حساب الجبر والمقابلة,الكتاب" AlØki′tāb alØmuhØ′taṣaru ′fī ḥi′sābi alØ′ğabØri wa"alØmuqā′balati (Arabic: الكتاب المختصر في حساب الجبر والمقابلة,). which is known under a Latin name "The Compendious Book on Calculation by Completion and Balancing". These equations needed to be considered separately because they admitted only positive coefficients. They frequently occur afterwards in other Al - Horezmii"s texts, especially х2 +10x = 39.
Al - Horezmi acknowledged that he derived ideas from the work of Brahmagupta by not liking negatives to deal with as the noted mathematition didn"t like them. & so other Indian mathematians. As for example Bhaskara II ( 1114-. 1185), also called Bhāskarācārya, or Bhaskara The Learned, the lineal successor of Brahmagupta as head of an astronomical observatory at Ujjain, the leading mathematical centre of ancient India. In dealing with numbers Bhaskaracharya was sound (skilful) in addition, subtraction and multiplication involving zero but he realised that there were problems with Brahmagupta's ideas of dividing by zero. Bhaskara II didn"t entirely refuse from negative roots of equations, but expressed scepticism about their admissibility generally when finding for example the solution x = 50 and x = −5 for the equation x2 45x = 250. Involving negative roots in his decimal number system is considered to be corresponding more to the older practice established by the influence of Sumerian astronomy. Perhaps the work of Sumerian mathematicians persuaded Bhaskara a bit that negative results were meaningless.
Mais revenons avec John Joseph O'Connor & Edward Frederic Robertson à nos "moutons". That is to Brahmagupta who attempted to give the rules for arithmetic involving zero & negative numbers in the seventh century. "He explained that given a number then if you subtract it from itself you obtain zero. He gave the following rules for addition which involve zero: The sum of zero and a negative number is negative, the sum of a positive number and zero is positive, the sum of zero and zero is zero. Subtraction is a little harder. A negative number subtracted from zero is positive, a positive number subtracted from zero is negative, zero subtracted from a negative number is negative, zero subtracted from a positive number is positive, zero subtracted from zero is zero. Brahmagupta says that any number when multiplied by zero is zero but struggles when it comes to division: A positive or negative number when divided by zero is a fraction with the zero as denominato. 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. Really Brahmagupta is saying very little when he suggests that n divided by zero is n/0. Clearly he is struggling here. He is certainly wrong when he then claims that zero divided by zero is zero" [3]. .
No value after all above-mentioned have J J. O'Connor"s & E.F Robertson"s naming Brahmagupta"s exercices de zero et nombres negatives (exercisies with zero & negatives ) "brilliant attempt from the first person who tried to extend arithmetic to negative numbers and zero" [3]. His attempt for doing this isn"t seem to be brilliant at all, showing only the "intuitive character" of Brahmagupta"s zero, which was exactly defined as it seems to us by Ahmed Boucenna (Laboratoire DAC, Department of Physics, Faculty of Sciences, Ferhat Abbas University 19000 Sétif, Algeria) in his "Origin of the numerals. Zero Concept" . So he writes: The '' intuitive zero '' is roughly equivalent to '' nothing '', '' rien '' and '' lashay ''. It is known and show only that since the oldest times by all societies as primitive either such. If a peasant had 7 bags of wheat initially and that after 10 months he would have consumed 7 bags of it, he knows that he remains to him ''zero'' bag, that means ''nothing''. The '' intuitive zero '' was known by the Egyptians, the Greeks, the Romans, ... This '' intuitive zero '' meaning '' nothing '' multiplied or divided by any number gives effectively '' nothing ''. Even the operation '' nothing '' divided by '' nothing '' gives '' nothing '', since '' nothing '' divided by 1000 gives '' nothing '', '' nothing '' divided by 100 gives '' nothing ''; '' nothing '' divided by 10 gives '' nothing ''; '' nothing '' divided by 1 gives '' nothing '' and there is not any reason so that '' nothing '' divided by '' nothing '' would not give, by a simple intuitive reasoning, '' nothing ''. It is this '' intuitive zero '' that is he '' Sunya '' of Brahmagupta as his reasoning and his result prove concerning the division of '' Sunya '' by '' Sunya '' that gives '' Sunya ''. It is the division by the '' mathematical zero '', unknown by Brahmagupta, which is empty of sense (impossible). It is not necessary conclude to make to tell Brahmagupta what he didn't say and to assign him the knowledge that he didn't have". Let"s only add that it is not necessary conclude to assign other Indian mathematitians the knowledge that they didn't have".as well.
To be continued.
References.
1)Cajori Florian The controversy on the origin of our Numerals, The scientific Monthly, Vol. 9, No. 5, 1919 , pp. 458-464.
2)McQuillin, Kristen/ A Brief History of Zero. July 1997 (revised January 2000. http://www.mediatinker.com/blog/archives/008821.html
3)O'Connor J J, Robertson E.F. A history of Zero MacTutor History of Mathematic http://www-history.mcs.st-andrews.ac.uk/HistTopics/Zero.html]
4)Origin of the numerals Zero Concept - arXiv.org arxiv.org/pdf/0707.357http://arxiv.org/ftp/arxiv/papers/0707/070.3579.pdf
5) Sanskrit Dictionary for Spoken Sanskrit http://spokensanskrit.de/
6)Struik, D.J. A concise history of mathematics, fourth revised edition (Dover Publications, New York, 1987). ISBN 0-486-60255-9, ISBN 978-0-486-60255-4 -280p.
7)The History of Negative Numbers: nrich.maths.org Stage: 3, 4 and 5 Article by Leo Rogers: nrich.maths.org/5961