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View of Garry KasparoveMat he m at ics o f t he Past by Garry Kasparo v Since my early childho o d, I have been inspired and excited by ancient and medieval histo ry. I also have a go o d memo ry, which allo ws me to remember histo rical events, dates, names, and related details. So , after reading many histo ry bo o ks, I analysed and co mpared the info rmatio n and, little by little, I began to feel that there was so mething wro ng with the dates o f antiquity. There were to o many discrepancies and co ntradictio ns that co uld no t be explained within the framewo rk o f traditio nal chro no lo gy. Fo r example, let's examine what we kno w o f ancient Ro me.

Global Revision of Hist oryPreface View of Garry Kasparov Investigation of the Historical Dating Egyptian Horoscopes Civiliz ing Events Open- Ended Time Discovery of Dante Falsification of the Classical Texts Recommended books

Resources" Empire of the Israelites" " Book of civiliz ation" " Mysteries of Egyptian Z odiacs" " Investigation of English history" Le ave yo ur o p inio n he re B uy o ur b o o ks

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The mo numental wo rk The Decline and Fall o f the Ro man Empire, written by English histo rian and scho lar Edward Gibbo n (1737-179 4), is a great so urce o f detailed info rmatio n o n the histo ry o f the Ro man Empire. Befo re co mmenting o n this bo o k, let me remark that I canno t imagine ho w - with their vast territo ries - the Ro mans did no t use geo graphical maps, ho w they co nducted trade witho ut a banking system, and ho w the Ro man army, o n which the Empire rested, was unable to impro ve its weapo ns and military tactics during nine centuries o f wars. With the use o f simple mathematics, it is po ssible to disco ver in ancient histo ry several such dramatic co ntradictio ns, which histo rians do n't seem to co nsider. Let us analyse so me numbers. E. Gibbo n gives a very precise descriptio n o f a Ro manPDFmyURL.com

legio n, which " ... was divided into 10 co ho rts ... The first co ho rt, ... was fo rmed o f 1 10 5 so ldiers ... The remaining 9 co ho rts co nsisted each o f 555 so ldiers, ... The who le bo dy o f legio nary infantry amo unted to 6 10 0 men." He also writes, "The cavalry, witho ut which the fo rce o f the legio n wo uld have remained imperfect, was divided into 10 tro o ps o r squadro ns; the first, as the co mpanio n o f the first co ho rt, co nsisted o f a 132 men; while each o f the o ther 9 amo unted o nly to 6 6 . The entire establishment fo rmed a regiment ... o f 726 ho rses, naturally co nnected with its respected legio n ..." Finally, he gives an exact estimate o f a Ro man legio n: "We may co mpute, ho wever, that the legio n, which was itself a bo dy o f 6 8 31 Ro mans, might, with its attendant auxiliaries, amo unt to abo ut 12 50 0 men. The peace establishment o f Hadrian and his successo rs was co mpo sed o f no less than 30 o f these fo rmidable brigades; and mo st pro bably fo rmed a standing fo rce o f 375 0 0 0 ." This eno rmo us military fo rce o f 3750 0 0 men, maintained during a time o f peace, was larger than the Napo leo nic army in the 18 0 0 s. Let me po int o ut that acco rding to the Encyclo pedia Britannica,6 "Battles o n the Co ntinent in the mid-18 th century typically invo lved armies o f abo ut 6 0 0 0 0 to 70 0 0 0 tro o ps." Of co urse, an army needed weapo ns, equipment, supplies, etc. Again, E. Gibbo n gives us a lo t o f details: "Besides their arms, which the legio naries scarcely co nsidered as an encumbrance, they were laden with their kitchen furniture, the instruments o f fo rtificatio ns, and the pro visio ns o f many days. Under this weight, which wo uld o ppress the delicacy o f a mo dern so ldier, they were trained by a regular step to advance, in abo ut six ho urs, nearly twenty miles. On the appearance o f an enemy, they threw aside their baggage, and by easy and rapid evo lutio ns co nverted the co lumn o f march into an o rder o f battle." This descriptio n o f the physical fitness o f an average Ro man so ldier is extrao rdinary. It brings us to the very strange co nclusio n that, at so me po int, the human race retro gressed in its ability to co pe with physical pro blems. Is it po ssible that there was a gradual decline o f the human race, with hundreds o f tho usands o f Schwarzenegger-like athletes o f Ro man times evo lving into medieval knights with relatively weak bo dies (like to day's teenage bo ys), who se little suits o f armuo r are to day pro udly displayed in museums? Is there a reaso nable bio lo gical o r genetic explanatio n to this dramatic change affecting the human race o ver such a sho rt perio d o f time? In o rder to supply such an army with weapo ns, a who le industry wo uld have been needed. In his wo rk, E. Gibbo n explicitly mentio ns iro n (o r even steel) weapo ns: "Besides a lighter spear, the legio nary so ldier grasped in his right hand the fo rmidable pilum ..., who se utmo st length was abo ut six feet, and which was terminated by a massy triangular po int o f steel o f eighteen inches." In ano ther place, he indicates "The use o f lances and o f iro n maces ..." It is believed that the extractio n o f iro n fro m o res was very co mmo n in the Ro man Empire. Ho wever, to smelt pure iro n, a temperature o f 1 539 o C is required, which co uldn't be achieved by burning wo o d o r co al witho ut the blo wing o r the blast furnaces invented mo re than a 1 0 0 0 years later. Even in the 15th century, the iro n pro duced was o f quite po o r quality because large amo unts o f carbo n had to be abso rbed to lo wer the melting temperature to 1 150 o C. There is also the questio n o f sufficient reso urces - the blast furnaces used in the mid-16 th century required large amo unts o f wo o d to pro duce charco al, an expensive and unclean pro cess that led to the eventual defo restatio n o f Euro pe. Ho w co uld ancient Ro me have sustained a pro ductio n o f quality iro n o n the scale necessary to supply tho usands o f to nnes o f arms and equipment to its vast army? Just by estimating the size o f the army, we can co nclude that the po pulatio n o f the Eastern and Western Ro man Empire in the seco nd century AD was at least 20 millio n peo ple, but it co uld have been as high as 40 o r even 50 millio n. Acco rding to E.Gibbo n, "Ancient Italy ... co ntained eleven hundred and ninety seven cities." The city o f Ro me had mo re After 18 0 0 , Napo leo n ro utinely maneuvered armies o f 250 0 0 0 . See Encyclo pdia Britannica. Encyclo pdia Britannica o nline at ht t p ://www.b rit annica.co m/ than a half-millio n inhabitants, and there were o ther great cities in the Empire. All o f these cities were co nnected by a netwo rk o f paved public highways, their co mbined lengths mo re than 4 0 0 0 miles! This co uld o nly be po ssible in a techno lo gically advanced so ciety. Acco rding to J.C. Russell, in the 4th century, the po pulatio n o f Western Ro man Empire was 22 millio n (including 750 0 0 0 peo ple in England and five millio n in France), while the po pulatio n o f the Eastern Ro man Empire was 34 millio n. It is no t hard to determine that there is a serio us pro blem with these numbers. In England, a po pulatio n o f fo ur millio n in the 15th century grew to 6 2 millio n in the 20 th century. Similarly, in France, a po pulatio n o f abo ut 20 millio n in the 17th century (during the reign o f Lo uis XIV), grew to 6 0 millio n in the 20 th century ... and this gro wth o ccurred despite lo sses due to several atro cio usPDFmyURL.com

reign o f Lo uis XIV), grew to 6 0 millio n in the 20 th century ... and this gro wth o ccurred despite lo sses due to several atro cio us wars. We kno w fro m histo rical reco rds that during the Napo leo nic wars alo ne, abo ut three millio n peo ple perished, mo st o f them yo ung men. But there was also the French Revo lutio n, the wars o f the 18 th century in which France suffered heavy lo sses, and the slaughter o f Wo rld War I. By assuming a co nstant po pulatio n gro wth rate, it is easy to estimate that the po pulatio n o f England do ubled every 120 years, while the po pulatio n o f France do ubled every 19 0 years. Figure 1

C lick He re t o Enlarg e

Graphs sho wing the hypo thetical gro wth o f these two functio ns are pro vided in Figure 1. Acco rding to this mo del, in the 4th and 5th centuries, at the breakdo wn o f the Ro man Empire, the (hypo thetical) po pulatio n o f England wo uld have been 10 0 0 0 to 15 0 0 0 , while the po pulatio n o f France wo uld have been 170 0 0 0 to 250 0 0 0 . Ho wever, acco rding to estimates based o n histo rical do cuments, these numbers sho uld be in the millio ns. It seems that starting with the 5th century, there were perio ds during which the po pulatio n o f Euro pe stagnated o r decreased. Attempts at lo gical explanatio ns, such as po o r hygiene, epidemics, and sho rt lifespan, can hardly withstand criticism. In fact, fro m the 5th century until the 18 th century, there was no significant impro vement in sanitary co nditio ns in Western Euro pe, there were many epidemics, and hygiene was po o r. Also , the intro ductio n o f .rearms in the 15th century resulted in mo re war casualties. Acco rding to UNESCO demo graphic reso urces, an increase o f 0 .2 per cent per annum is required to assure the sustainable gro wth o f a human po pulatio n, while an increase o f 0 .0 2 per cent per annum is described as a demo graphical disaster. There is no evidence that such a disaster has ever happened to the human race. Therefo re, there is no reaso n to assume that the gro wth rate in ancient times differed significantly fro m the gro wth rate in later epo chs. These discrepancies lead me to suspect that there is a gap between the histo rical dates attributed to the Ro man Empire and tho se suggested by the abo ve co mputatio ns. But there are mo re inco nsistencies in the histo rical reco rd o f humankind. As I have already no ted, there are similar gaps o f several centuries in techno lo gical and scientific develo pment. No tice that kno wledge and techno lo gy traditio nally asso ciated with the ancient wo rld presumably disappears during the Dark Ages, o nly to resurface in the 15th century during the early Renaissance. The histo ry o f mathematics pro vides o ne such example. By chro no lo gically and lo gically o rdering majo r mathematical achievements, beginning with arithmetic and Greek geo metry and finishing with the inventio n o f calculus by I. Newto n (16 43-1727) and G.W. Leibnitz (16 46 -1716 ), we see a tho usand-year gap separating antiquity fro m the new era. Is this o nly a co incidence? But what abo ut astro no my, chemistry (alchemy), medicine, bio lo gy, and physics? There are to o many inco nsistencies and unexplained riddles in ancient histo ry. To day, we are unable to build simple o bjectsPDFmyURL.com

made in ancient times in the way they were o riginally created -this in a time when techno lo gy has pro duced the space shuttle and science is o n the brink o f clo ning the human bo dy! It is prepo stero us to blame all o f the lo st secrets o f the past o n the .re that destro yed the Library o f Alexandria, as so me have suggested. It is unfo rtunate that each time a parado x o f histo ry unfo lds, we are left witho ut satisfacto ry answers and are persuaded to believe that we have lo st the ancient kno wledge. Instead o f disregarding the facts that disagree with the traditio nal interpretatio n, we sho uld accept them and put the theo ry under rigo ro us scientific scrutiny. Explanatio ns o f these parado xes and co ntradictio ns sho uld no t be left o nly to histo rians. These are scientific and multidisciplinary pro blems and, in my o pinio n, histo ry - as a single natural science - is unable to so lve them alo ne. I think that the chro no lo gy o f techno lo gical and scientific develo pment sho uld be carefully investigated. The to o numero us claims o f techno lo gical wo nders in antiquity turn histo ry into science frictio n (e.g., the pro ductio n o f mo no lithic sto ne blo cks in Egypt, the precise astro no mical calculatio ns o btained witho ut mechanical clo cks, the glass o bjects and mirro rs made 5 0 0 0 years ago , and so o n). It is unfo rtunate that histo rians reject scientific incursio n into their do main. Fo r instance, the mo st reaso nable explanatio n o f Egyptian pyramidbuilding techno lo gy, presented by French chemist Jo seph Davido vits (the creato r o f the geo po lymer techno lo gy), was rejected by Egypto lo gists, who refused to pro vide him with samples o f pyramid material. Abo ut five years ago , I came acro ss several bo o ks written by two mathematicians fro m Mo sco w State University: academician A.T. Fo menko and G.V. No so vskij. The bo o ks described the wo rk o f a gro up o f pro fessio nal mathematicians, led by Fo menko , who had co nsidered the issues o f ancient and medieval chro no lo gy fo r mo re than 20 years with fascinating results. Using mo dern mathematical and statistical metho ds, as well as precise astro no mical co mputatio ns, they disco vered that ancient histo ry was artificially extended by mo re than 1 0 0 0 years. Fo r reaso ns beyo nd my understanding, histo rians are still igno ring their wo rk.


But let us return to mathematics and to ancient Ro me. The Ro man numeral system disco uraged serio us calculatio ns. Ho w co uld the ancient Ro mans build elabo rate structures such as temples, bridges, and aqueducts witho ut precise and elabo rate calculatio ns? The mo st impo rtant deficiency o f Ro man numerals is that they are co mpletely unsuitable even fo r perfo rming a simple o peratio n like additio n, no t to mentio n multiplicatio n, which presents substantial difficulties (see Figure 2). In early Euro pean universities, algo rithms fo r multiplicatio n and divisio n using Ro man numerals were do cto ral research to pics. It is abso lutely impo ssible to use clumsy Ro man numbers in multi-stage calculatio ns. The Ro man system had no numeral "zero ." Even the simplest decimal o peratio ns with numbers canno t be expressed in Ro man numerals. N.P. Just try to add Ro man numerals: MCDXXV + MCMLXV22 o r m ult iply : DCLIII CXCIX23 Try to write a multiplicatio n table in Ro man numerals. What abo ut fractio ns and o peratio ns with fractio ns?

Despite all these deficiencies, Ro man numerals suppo sedly remained the predo minant representatio n o f numbers in Euro pean culture until the 14th century. Ho w did the ancient Ro mans succeed in their calculatio ns and co mplicated astro no mical co mputatio ns? It is believed that in the 3rd century, the Greek mathematician Dio phantus was able to find po sitive and ratio nal so lutio ns to the fo llo wing system o f equatio ns, called Dio phantic to day x 31 + x 2 = y 3 x1 + x 2 = y. Acco rding to histo rians, at the time o f Dio phantus, o nly o ne symbo l was used fo r an unkno wn, a symbo l fo r "plus" did no t exist, neither was there a symbo l fo r "zero ." Ho w co uld Dio phantic equatio ns be so lved using Greek letters o r Ro man numerals (see Figure 2)? Can these so lutio ns be repro duced? Are we dealing here with ano ther secret o f ancient histo ry that we are no t suppo sed to questio n? Let us po int o ut that even Leo nardo da Vinci, at the beginning o f the 16 th century, had tro ubles withPDFmyURL.com

fractio nal po wers. It is also interesting that in all o f da Vinci's wo rks, there is no trace o f "zero " and that he was using 22/7 as the appro ximatio n o f p - pro bably it was the best appro ximatio n o f p available at that time. It is also interesting to lo o k at the inventio n o f the lo garithm. The lo garithm o f a number x (to the base 10 ) expresses simply the number o f digits in the decimal representatio n o f x, so it is clearly co nnected to the idea o f the po sitio nal numbering system. Obvio usly, Ro man numerals co uld no t have led to the inventio n o f lo garithms. Kno wledge o f o ur histo ry timeline is impo rtant, and no t o nly fo r histo rians. If indeed the dates o f antiquity are inco rrect, there co uld be pro fo und implicatio ns fo r o ur beliefs abo ut the past, and also fo r science. Histo rical kno wledge is impo rtant to better understand o ur present situatio n and the changes that take place aro und us. Impo rtant issues such as glo bal warming and enviro nmental changes depend o n available histo rical data. Astro no mical reco rds co uld have a co mpletely different meaning if the described events to o k place at times o ther than tho se pro vided by traditio nal chro no lo gy. I trust that the yo unger generatio n will have no fear o f "unto uchable" histo rical do gma and will use co ntempo rary kno wledge to challenge questio nable theo ries. Fo r sure, it is an exciting o ppo rtunity to reverse the subo rdinate ro le science plays to histo ry, and to create co mpletely new areas o f scientific research. REFERENCES : 1 E. Gibbo n. The Decline and Fall o f the Ro man Empire. Peter Fenelo n Co llier & So n, vo l. 1, New Yo rk, 18 9 9 . This bo o k is also available o nline at:ht t p ://www.cce l.o rg /g /g ib b o n/d e cline / .

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I. Davidenko and Y. Kesler. Bo o k o f Civilizatio n, (with preface by Garry Kasparo v). Eko Press-20 0 0 , Mo sco w, 20 0 1. J. Davido vits and M. Mo rris. The Pyramids: An Enigma So lved. New Yo rk: Hippo crene Bo o ks, 19 8 8 (4th printing). Later by Do rset Press, New Yo rk, 19 8 9 , 19 9 0 . A. T. Fo menko . Empirico -Statistical Analysis o f Narrative Material and its Applicatio ns to Histo rical Dating. Vo lume 1: The Develo pment o f the Statistical To o ls, and Vo lume 2: The Analysis o f Ancient and Medieval Reco rds. Kluwer Academic Publishers, 19 9 4, The Netherlands. A. T. Fo menko , V.V. Kalashniko v and G.V. No so vskij. Geo metrical and Statistical Metho ds o f Analysis o f Star Co nfiguratio ns: Dating Pto lemy's Almagest. CRC Press, 19 9 3, USA. J. C. Russell. Late Ancient and Medieval Po pulatio n. American Philo so phical So ciety. 152 p., (Transactio ns o f the American Philo so phical So ciety 48 pt. 3), Philadelphia, 19 58 . J.E. Dayto n. Minerals, Metals, Glazing and Man. Harrap, Lo ndo n, 19 78 . ISBN: 0 245528 0 75. The No tebo o ks o f Leo nardo da Vinci, 2nd ed., 2 vo l. (19 55, reissued 19 77); and Jean Paul Richter (co mpiler and ed.). Original kept at Institut de France, Paris. Leo nardo da Vinci. Co dex Atlanticus. Kept in Biblio teca Ambro siana in Milan, Italy.

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Garry Kasparo v has been the chess wo rld champio n since 19 8 5, when he wo n the title at the age o f 22. In 19 9 7, during a histo rical chess challenge that made headlines all o ver the wo rld, he defeated IBM's Deep Blue superco mputer. There are many web sides devo ted to Garry, but we reco mmend :ht t p ://www.kasp aro vche ss.co m/ .

A bio graphy can be fo und atPDFmyURL.com

ht t p ://www.che nnaiwe b .co m/sp /che ss/b io /g aryk/ .

We invite all co mments and o ther po ints o f view. Co rrespo ndence can be sent directly to p in the Sky by email at inf o @ ne wt rad it io n.o rg , o r by snail mail. All letters will be fo rwarded to Garry Kasparo v.

The math pro fesso r's six-year-o ld so n kno cks at the do o r o f his father's study. "Daddy," he says. "I need help with a math pro blem I co uldn't do at scho o l." "Sure," the father says and smiles. "Just tell me what's bo thering yo u." "Well, it's a really hard pro blem: There are fo ur ducks swimming in a po nd, when two mo re ducks co me and jo in them. Ho w many ducks are no w swimming in the po nd?" The pro fesso r stares at his so n in disbelief. "Yo u co uldn't do that?! All yo u need to kno w is that 4 + 2 = 6 !" "Do yo u think, I'm stupid?! Of co urse I kno w that 4 + 2 = 6 . But what do es this have to do with ducks!?"

A visito r to the Ro yal Tyrell museum asks a museum emplo yee: "Ho w o ld is the skeleto n o f that T-Rex?" "Precisely 6 0 millio n and three years, two mo nths, and 12 days." "Ho w can yo u kno w that with such precisio n?" "That's easy. When I started wo rking here, a sign said that the skeleto n was 6 0 millio n years o ld. And that was three years, two mo nths, and 12 days ago ..." "What is p?" A mathematician: "p is the ratio o f the circumference o f a circle to its diameter." A co mputer pro grammer: "p is 3.14159 26 5358 9 in do uble precisio n." A physicist: "p is 3.14159 plus o r minus 0 .0 0 0 0 0 5." An engineer: "p is abo ut 22/7."PDFmyURL.com

A nutritio nist: "Pie is a healthy and delicio us dessert!"Le ave yo ur o p inio n he re



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