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24 1 The Problems <strong>of</strong> Historical Chronology<br />

sis <strong>of</strong> numerical functions associated with historical data provided<br />

a very effective tool to identify multiple duplicates in<br />

history.<br />

First Period <strong>of</strong> the<br />

Roman Episcopate in<br />

141-314 A.D.<br />

St. Pius (16)<br />

(141-157)<br />

St. Anicetus (11)<br />

(157-168)<br />

¤<br />

¤<br />

St. Soter (168-177) (9)<br />

(168-177)<br />

St. Eleutherius (15)<br />

(177-192)<br />

St. Victor (9)<br />

(192-201)<br />

Zephyrinus (18)<br />

(201-219)<br />

¤<br />

¤<br />

¤<br />

¤<br />

¤<br />

¤<br />

Calixtus (5)<br />

(219-224)<br />

Urban I (7)<br />

(224-321)<br />

Pontianus (5)<br />

(231-236)<br />

Fabian (15)<br />

(236-251)<br />

Confusion (8)<br />

(251-259)<br />

¤<br />

Dionysius (12)<br />

(259-271)<br />

Eutychianus (?)<br />

Felix I (9) ¤<br />

(275-284)<br />

Felix I (?)<br />

Eutychianus (4)<br />

(271-275)<br />

Gaius (13)<br />

(283-296)<br />

Marcellinus (8)<br />

(296-304)<br />

¤<br />

Marcellus (5)<br />

(304-309)<br />

Eusebius (3)<br />

(309-312)<br />

Meltiades (3)<br />

(311-314)<br />

¤<br />

¤<br />

¤<br />

¤<br />

¤<br />

¤<br />

¤<br />

¤<br />

Second Period <strong>of</strong> the Roman<br />

Episcopate in 314-532 A.D.<br />

¤<br />

¤<br />

¤<br />

¥ ¤<br />

¤<br />

¤<br />

¤<br />

¤<br />

¤<br />

¤<br />

¤<br />

¤<br />

¤<br />

¤<br />

(22) Silvester<br />

(314-336)<br />

(17) Julius I<br />

(336-353)<br />

(15) Liberius<br />

(352-367)<br />

(18) Damasus<br />

(367-385)<br />

(13) Siricius<br />

(385-398)<br />

¤<br />

(19/14) Anastasius<br />

and Innocent<br />

(398-412-417)<br />

¥ ¤<br />

¥<br />

(5) Boniface I<br />

(418-423)<br />

(9) Celestine<br />

(423-432)<br />

(8) Sixtus<br />

(432-440)<br />

¤ (21) St. Leo<br />

Confusion<br />

Leo I<br />

(440-461)<br />

(8) Hilarius<br />

(461-467)<br />

¤<br />

(16) Simplicius<br />

(467-483)<br />

(9) Felix II<br />

(483-492)<br />

(4) Gelasius<br />

(492-496)<br />

(16) Symmachus<br />

(498-514)<br />

(9) Hormisdas<br />

(514-523)<br />

(3) John I<br />

(523-526)<br />

(4) Felix III<br />

(526-530)<br />

(2) Boniface III<br />

(530-532)<br />

Figure 1.27: Parallel between first and second periods <strong>of</strong> the<br />

Roman Episcopate<br />

In order to give to “similarity” a more precise meaning,<br />

Fomenko’s introduced a routine for distinguishing functions<br />

referring to different dynasties and defined a certain measure<br />

<strong>of</strong> distinctiveness between them (or rather a probability measure<br />

for distinctiveness). In simple words, he found a way to<br />

measure a ‘distance’ between the above numerical functions<br />

(like for example dynasty functions) as we measure a distance<br />

between two different locations. Mathematicians say that in<br />

such a case that they are dealing with a metric space. The<br />

geometry <strong>of</strong> a metric spaces is definitely different from the<br />

geometry we learn in school, but the usual properties related<br />

to the measurement <strong>of</strong> distances are still valid there. Now we<br />

can apply the idea, that if a distance, let’s say, between two<br />

towns A and B is less than few hundreds meters, then we are<br />

justified to think that in fact A and B represent practically<br />

the same town. Similarly, if a distance between two dynasty<br />

functions is sufficiently small we may think that indeed they<br />

¤<br />

represent the same dynasty. These methods were extensively<br />

tested on the data referring to well documented epochs. It<br />

was proved that if two dynasty functions (for 15 rulers) or<br />

volume functions were not related, the measure <strong>of</strong> distinctiveness<br />

between numerical functions associated with these<br />

dynasties was between 1 and 10 −4 . However, in the case <strong>of</strong><br />

related events from the same epoch, the measure <strong>of</strong> distinctiveness<br />

was never larger than 10 −8 .<br />

60<br />

50<br />

40<br />

30<br />

20<br />

10<br />

<br />

<br />

<br />

<br />

<br />

Jet A<br />

Jet B<br />

<br />

¦§¦¨¦§¦¨¦§¦§¦©¦§¦¨¦©¦©¦§¦©¦§¦<br />

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15<br />

<br />

<br />

<br />

<br />

<br />

© ©<br />

Figure 1.28: Parallel between the Holy Roman Empire in the<br />

10-13th cc. A.D. and the Second Roman Empire in the 1st<br />

c. B.C.-3rd c. A.D. Two graphs combined. Rigid 1053-year<br />

shift.<br />

It is difficult to imagine that two different dynasties could<br />

have identical or almost identical dynasty functions. The<br />

probability <strong>of</strong> such a coincidence is extremely small already<br />

for dynasties composed <strong>of</strong> 10 rulers. Nevertheless, the number<br />

<strong>of</strong> such coincidences, for even longer dynasties <strong>of</strong> 15 rulers,<br />

turns out to be unexpectedly large. N.A. Morozov, who noticed<br />

the coincidence between the ancient Rome and the ancient<br />

Jewish state, discovered the first examples <strong>of</strong> surprisingly<br />

identical pairs <strong>of</strong> dynasty graphs. A formal method to<br />

study such similarities was introduced by A.T. Fomenko.<br />

60<br />

50<br />

40<br />

30<br />

20<br />

10<br />

<br />

<br />

<br />

<br />

<br />

<br />

Jet A<br />

Jet B<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17<br />

Jet A: the Holy Roman Empire in the 10-13th cc. A.D.<br />

Jet B: the Roman Empire in the 4-6th cc. A.D. Two graphs combined.<br />

Figure 1.29: Parallel between the Holy Roman Empire in the<br />

10-13th cc. A.D. and the Roman Empire in the 4-6th cc. A.D.<br />

Two graphs combined.

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