In 2021, on Omar’s now traditionally accepted birthday, 18 May, Sandra Mason & Bill Martin featured a blog item (1) relating to Mohammad H. Tamdgidi’s claims that Omar was born on 10 June 1021 (2), not 18 May 1048 as calculated from the horoscope of Omar by Govinda Tirtha in his Nectar of Grace back in 1941. Having obtained a copy of Tamdgidi’s volume 2, I can throw some further light on Tamdgidi’s claim. First, let us remind ourselves of Tirtha’s source for the horoscope, Baihaqi:
His ascendant was the Gemini. The Sun and the Mercury were on the degree of the ascendant in the third degree of the Gemini. The Mercury was ‘Samimi’ and the Jupiter was aspecting (Nazar) both from triangulation (Tathlith). (p.XXXII)
Basically, Samimi means that Mercury was approaching the zone known as Samim, which is when its celestial / geocentric longitude (hereafter just “longitude”) comes within 16 minutes of arc (16’) of that of the Sun; Tathlith here means that Jupiter’s longitude differed from those of both the Sun and Mercury by 120° ± 9°; Nazar literally means “observing”, here rendered by Tirtha in astrological terms as “aspecting”.
Tirtha’s derivation of Omar’s date of birth comes in three parts.
In the first (p.XXXII–XXXIV) he uses the Indian Ephemeris “prepared from the beginning of the Kaliyuga (3101 BC) to 2000 AD by Dr Swami Kannu Pillai, on the basis of Arya Bhatta and Surya Siddhanta known to the Persians as Ibn–i Batuta and Sind Hind!” Using this, Tirtha shows that since Omar was born at Sunrise with the Sun in the third degree of Gemini, he must have been born on 18 May. Furthermore, in the period 1019 to 1054 AD, the only year that Mercury was also in the third degree of Gemini, and Jupiter satisfied the Tathlith condition for both Mercury and the Sun, was 1048. Thus Omar was born at Sunrise on 18 May 1048. (He does not mention whether or not the Samimi condition was met, perhaps because this was his first ‘stab’ at the problem, to be refined in his second.)
In his second part (p.XXXV–XXXVI), for which Fig.1 & Fig.2 may prove useful, Tirtha found it “necessary to verify the solution by direct calculation of the positions of the Sun, Mercury and Jupiter according to their motions known to the Persians in those times." (The emphasis is mine, and will be key later.) These calculations show that at Sunrise on 18 May 1048 the Sun’s longitude was 62° 23’, Mercury’s was 62° 46’, and Jupiter’s was 303° (Fig.1.) Longitude is measured eastwards from the point of the Vernal Equinox, and since Aries and Taurus both account for 30°, that means that the Sun was 2° 23’ inside Gemini, and Mercury 2° 46’ inside Gemini. Since the first degree of Gemini is 0° to 1°, the second degree 1° to 2°, and the third degree 2° to 3°, the Sun and Mercury were both in the third degree of Gemini (Fig.2.) Jupiter being 360° – 303° = 57 ° west of the Vernal Equinox and the Sun & Mercury being east of it, the Sun and Jupiter differed in longitude by 57° + 62° 23’ = 119° 23’ and Mercury and Jupiter by 57° + 62° 46’ = 119° 46’, both very close to the ideal 120° required for Tathlith (120° ± 9°) (Fig.1.) Finally, Mercury and the Sun were separated by 2° 46’ – 2° 23’ = 23’, some 7’ more than the Samim zone requirement of 16’, but with Mercury in retrograde, it was approaching that zone, hence the Samimi. (Mercury in retrograde means that it is moving backwards – i.e. westwards – towards the Sun (Fig.2.) The table on Tirtha’s p.XXXVII shows that Mercury is approaching the Sun at some 89’ (57’ + 32’) per day, so the 7’ gap for Samim would close, roughly, in just under 2 hours.) Thus everything is consistent with Baihaqi.
In Tirtha’s third part (p.XXXVII), Mr. S.R. Subrahmania Shastry “who is well–versed in the ancient as well as modern astronomy recalculated according to the Modern Elements (again, emphasis mine), the accurate positions of all the planets for Sunrise on 18 May 1048 at Naishapur.” The Sun was at longitude 62° 20’ (2° 20’ inside Gemini); Mercury at longitude 66° 25’ (6° 25’ inside Gemini) and Jupiter at longitude 307°. Thus the Sun & Jupiter are separated by 62° 20’ + (360° – 307°) = 115° 20’and Mercury & Jupiter by 66° 25’ + (360° – 307°) = 119° 25’ – both within the 120° ± 9° range required for Tathlith. Though the Sun is indeed in the third degree of Gemini, and close to the position calculated in Tirtha’s second part, Mercury is in the seventh degree of Gemini, not the third, and Jupiter’s longitude is 307° not the 303° of the second part. Clearly, then, and not surprisingly, these calculations using modern orbital elements yield somewhat different results to those obtained using the methods known in medieval Persia. Mercury, in particular, has always been a maverick planet which never seemed to be quite where astronomers thought it should be. In 1859, this led Le Verrier to postulate the intra–Mercurial planet Vulcan as being responsible for pulling Mercury off–course. Unfortunately, Vulcan too was never quite where astronomers thought it should be, and indeed, no–one ever actually saw it. It was left to Einstein in 1915 to show that there was a fault in the Newtonian Mechanics on which earlier methods were based, and to explain the maverick nature of Mercury in terms of his Theory of Relativity (the so–called Precession of the Perihelion of Mercury.) Jupiter, too, posed its own problems, and it wasn’t until the likes of Laplace in the 18th century and Le Verrier and G.W. Hill in the 19th, that what Jupiter did, and what it was predicted to do, became more fully understood, and hence predictable.
By way of emphasis, Tirtha’s second part uses medieval Persian methods and his third part, more sophisticated modern methods. It is important to remember this in what follows.
Now, where did Baihaqi get Omar’s horoscope from ? Clearly, there was no–one present at Omar’s birth actually measuring up the positions of the planets at the time, so the horoscope must have been done by someone (Omar?) within, perhaps, 50 years of Omar’s birth, when he was famous enough to merit such astrological attention. It would have used the methods of retro–calculations available at that time: that is, using the methods of 11th century Persia, which would give different results to the methods available today. As good an astronomer as Omar was, he, or the compiler of his horoscope, could not possibly have known anything about the likes of the Relativistic perturbations of Mercury. Nevertheless, calculating backwards over a period of some 50 years, and given the broad “third degree of Gemini” and the leeway available for the Tathlith (120° ± 9°) condition, then the horoscope quoted by Baihiqi is probably as good as we are going to get. One naturally does wonder about the accuracy of the retro–calculations done in Tirtha’s second part, for, though done using the same methods of 11th century Persia, they are working back over a period of nearly 900 years, much longer than the 50 or so years for Omar’s horoscope. Over such an extended period of time one might expect that errors in prediction would increase, but since Tirtha’s second part fits Baihaqi so well perhaps the problem is less than one might expect.
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Turning to Tamdgidi, now, it is important to reiterate here that in measuring longitude angles from the beginning of Gemini, the constellation’s first degree is 0° to 1°, its second degree is 1° to 2°, its third degree is 2° to 3°, and so on. Thus, in Tirtha’s second part, quoted above, the Sun at 2° 23’ and Mercury at 2° 46’ inside Gemini are both in the third degree of that constellation, exactly as Tirtha states (see Fig.2.) However, in his vol.2, p.51, Tamdgidi erroneously says that Tirtha’s positions for the Sun and Mercury are in the second degree, not the third. Tamdgidi’s error is somewhat like claiming that the year 250 AD was in the second century because 250 begins with a 2, whereas, of course, it was in the third century. On the basis of this bad mistake, Tamdgidi claims that Tirtha is wrong and therefore his calculations do not match Baihaqi’s text. In addition, he wrongly faults Tirtha by saying that the 23’ gap between the Sun and Mercury does not fulfil the Samimi requirement (p.51–2), whereas it does because Samimi means approaching the 16’ limit of Samim, which is exactly what Mercury is doing (again, see Fig.2.) In fact, Tirtha is right on all counts, and, as a result, Tamdgidi heads off on a false trail of his own making!
Before following him on that trail, there is one further point. Tirtha’s third part does not invalidate his first two parts as Tamdgidi thinks (p.53) – it simply demonstrates the difference between the results of medieval and modern retro–calculations, as indicated above, which are only to be expected given the progress made in predicting the movements of the planets in the light of a thousand years of detailed study.
Now to the trail:
Having ‘demolished’ Tirtha, as he sees it, Tamdgidi erroneously drops Tirtha’s third degree of Gemini as ‘not working’, and turns to the possibility that Tirtha may have misread an 8 as a 3 (hence his "third"), which is feasible since their abjad characters (ie letters used as numbers) differ only by a dot (p.65f) – see Fig.3. As Tamdgidi himself says, though, dots do come and go (p.79, p.113), and indeed in some manuscript copies of Baihaqi (Tirtha cites three on his p.XXXII), a 3 does feature (Tamdgidi p.79). But when Tamdgidi tried to make things fit with an 8 instead of a 3, he found they wouldn’t fit. In fact, it is possible that Tirtha saw an 8 in a manuscript of Baihaqi which he certainly used (Berlin 10055 M. O. 21, of which he gives a rather poor photographic reproduction), realised that 8 didn’t work, and turned instead to the easily mistaken 3, which did work; or he may actually have seen a 3 in one of the other manuscripts he mentions. Either way, he doesn’t explain, presumably because he felt it unnecessary with the 3 working so well. (Had he known Tamdgidi was waiting in the wings, he might have thought differently!)
Having turned Tirtha’s 3 into an 8 and found both wanting (the former erroneously, remember!), Tamdgidi next turns an 8 into an 18 via a hypothetical scribal error (p.112–3.) This involves the word “in” being a scribal error for an abjad number 10 (see Fig.4), and 10 + 8 = 18. He then re–words Baihaqi thus (p.128):
His ascendant was the Gemini, and the Sun and the Mercury were on the degree of the ascendant 18 of Gemini, and the Mercury was Samimi and the Jupiter from Taslees observing them both.
Tamdgidi then finds that things work wonderfully – at least as he sees it – but in 1021 not the 1048 of Tirtha (p.93, p.102, p.129): Tamdgidi assures us that Omar was born at Naishapur, at Sunrise, during the four minute period from 4.43.56am to 4.47.55am (Naishapur time), on 10 June 1021. Thus, for example, at the beginning of that four minute period, the Sun was 18° 7’ 44” inside Gemini and Mercury was 18° 15’ inside Gemini (though he erroneously claims that these figures satisfy the Samimi condition, whereas they actually satisfy the stricter condition of Samim, the difference being only some 8’); plus, Jupiter, at 113° away from both, also satisfies the Tathlith (= Taslees) condition. It all seems hunky dory – or mostly so – but is it? One should not be blinded by Tamdgidi's computer–generated levels of accuracy: an incorrect answer to a calculation can run to ten decimal places, but it is still an incorrect answer for all that.
Firstly, Tamdgidi’s re–working of Baihaqi says “on the degree ... 18”, which is ill–defined in that it could mean “the eighteenth degree” (17° to 18°) or, as Tamdgidi takes it, the interval 18° to 19°, which is “the nineteenth degree”. Tirtha wisely avoided this vagueness by specifying “the third degree.” But Tamdgidi can’t use “the eighteenth degree” because it doesn’t work, and he can’t use “the nineteenth degree” because his re–working of Baihaqi necessarily requires that abjad 18, and “the nineteenth degree” would require an abjad 19. And all this is on top of turning Tirtha's 3 into an 8, then that 8 into an 18.
Finally, Tamdgidi uses modern retro–calculations, so, as we saw with Tirtha’s third part, these cannot be expected to agree with retro–calculations done using the methods of medieval Persia, which methods were, of course, used by whoever compiled Omar’s horoscope. In effect, modern retro–calculations show where the planets actually were and the medieval retro–calculations show where the Persians thought they were – two different things.
Tirtha was certainly wrongly dismissed by Tamdgidi’s bad misunderstanding of “the third degree of Gemini.” He should have investigated what he would call “degree 2” – his equivalent of Tirtha’s third degree – but didn’t, and even had he done so, using modern methods he would have found the equivalent of Tirtha’s third part, not his more realistic second part – as, in fact, he inadvertently notes on his p.76, in the entry for 1048, May 18, where yet again he says that 2° 19’ is not in the third degree of Gemini!
Though I have some reservations about Tirtha’s claimed precision, I do think he was probably not far off the mark, if at all. In short, I personally would still cautiously run with “18 May 1048.” As for the 10 June 1021 horoscope derived by Tamdgidi, I’m not sure whose horoscope it is, but I do not think it is Omar’s.
Note 1: http://omarkhayyamrubaiyat.wordpress.com/2021/05/18/omar-khayyams-birthday/
Note 2: Tamdgidi is in the process of publishing a projected 12 volume series under the umbrella title Omar Khayyam’s Secret: Hermeneutics of the Robaiyat in Quantum Sociological Imagination. Volume 2 is subtitled “Khayyami Millennium – Reporting the Discovery and the Reconfirmation of the True Dates of Birth and Passing of Omar Khayyam (AD 1021–1123).” For further details of the series, see https://www.okcir.com/.
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