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Parashara : A Great Mathematician
ॐ VEDIC ASTROLOGY : Obscure Passages of BPHS ( BrihatParaasharaHoraaShaastra )
Parashara : A Great Mathematician
Valorization of Auspicious and Inauspicious Planets
So far, we have listened about Sage Parashara as an exponent of predictive astrology, now let us discuss his mathematical prowess. There are proffs in BPHS suggesting him to be an exponent of exponents in mathematics, literally ! There are many obscure passages in BPHS which are very useful in predictive astrology (phalit jyotisha) but are out of use due to obscurity of meaning. One such passage is shloka 8 in chapter Ishtakashtaadhyaya, which gives numeric values for auspiciousness or inauspiciousness of planets depending upon their being in exaltation, moolatrikona, etc. ShubhaAshubhaGrihaanka . Shlokas 79 (स्वोच्चे मूलत्रिकोणे च स्वर्क्षेऽधि...)can be translated as follows :"If a planet is in a house of exaltation, moolatrikona, own rasi (sign), fast friend, friend, balance, enemy, bitter enemy or neech, then its auspicious number will be 60, 45, 30, 22, 15, 8, 4, 2, 0 respectively, and its inauspicous number will be obtained by substracting above numbers from 60. For other vargas (divisional charts like hora, navamaamsha, etc), half of the above numbers ought to be used."
If taken literally, these passages make no sense at all. For instance, if a planet is samgrihi (in balance) its auspicious valorization will be 8 and inauspicious valorization will be 60 minus 8, i.e., 52, which is unacceptable, because a planet in balance must have auspicious valorization exactly equal to inauspicious valorization. Again, a planet in its own sign has its auspicious valorization equal to its inauspicious valorization, both being 30, which is unaceptable. If a careful analysis is not carried out, such passages would appear to be interpolations by careless scribes. But following analysis shows that the sage Paraashara used a logarithmic scale with base 2 for this valorization.
Planet's condition  Value in BPHS  Revised value  Power of 2  Approx power of 2  60 minus app. power  Exact Scheme 
Exaltatation (uchcha)  60  60  5.907  6.0  0.0  60.0000 
Moolatrikona  45  42.43  5.407  5.5  0.5  42.6552 
Own Sign (svagrihi)  30  30  4.907  5.0  1.0  30.3244 
Fast friend  22  21.21  4.407  4.5  1.5  21.5582 
Friend  15  15  3.907  4.0  2.0  15.3262 
Balanced (samgrihi)  8  7.5  2.907  3.0  3.0  7.7460 
Enemy (shatrugrihi)  4  3.75  1.907  2.0  4.0  3.9149 
Bitter enemy  2  1.875  0.907  1.0  5.0  1.9786 
Debility (Neecha)  0  0.9375  0.093  0.0  6.0  0.0000 
The number 2 raised to the power 6 is equal to 64, and 2 raised to 5.907 is equal to 60. Fifth column in the above table (app. power of 2) shows the original scheme of Sage Paraashara on whose basis aforementioned stanzas were made. In this scheme, a samgrihi or balanced planet has a valorization of 23 = 8 ; instead of 8 we ought to take the power 3 as a significator of strength. Maximum value is 26 = 64 (approximated to 60 in the sexagesimal system), where the power is 6. Hence, a balanced planet has a 50% valorization ( 3 is half of 6), which is natural.
The fifth column (in red) should be used for determining auspicious valorization, and sixth column for inauspicious values.
If 1.9786 is used instead of the integer 2, we will get Sage Parashara's above series exactly, only for moolatrikona we get 43 instead of 45.
Now a great problem arises. Western "experts" say that decimals were not in use in those days. But had Sage Parasha used an integer 2 as base of the power series, he would have got : 2, 4, 8 ,16, 32, 64 ; last three being inaccurate because he gives 15, 30, 60 , ie, half of the series being wrong. Does it not imply that he actually used decimals as the base of a power series with powers 1, 2, 3, 4, 4.5, 5, 5.5, 6. Thus, we have to conclude that Sage Parashara used quatities like 1.98 raised to fractional powers like 4.5 and 5.5 !! Use of integer would have produced a series as 2, 4, 8 ,16, 23, 32, 45, 64 ; which has five out of eight terms wrong. Hence, Sage Parashara definitely used fractional number 1.98... as the base of a logarithmic series. This logarithmic series was not a power series exactly, because we have two fractional powers : 1.98 raised to the power 4.5 and 5.5 !! It could be possible only on a logarithmic scaling.
Now we come to a greater enigma. Using power series in aforementioned way is same as using logarithmic scale. We are told that John Napier discovered logarithm in 1614 AD, when there was a great reaction against it for many years. But the valorization series of Sage Parashara is clearly based upon logarithmic series !! Sage Parashara preceded John Napier.
Einstein proved that gravitational fields are pseudospherical in which space is curved, and even light has to traverse along curved paths. In a pseudospherical space, 3D curves along the surface make a logarithmic spiral if viewed from top or bottom, like a loxodrome on the surface of a spherical. Hence, in a gravitational field phenomena and events are better represented on a logarithmic scale, even outside the solar system. Even radiation and other forces follow logarithmic scale in their distribution. The rate of radioactive decay occurs along logarithmic scale. But the scale is natural (2.71828).
Now comes a more puzzling phenomenon. Arithmeticians prefer base 10 for the sake of simplicity, but natural logarithm with base 2.7182818 is more popular among mathematicians and scientists, because the functions of calculus are intrinsically dependent on it. But in 20th century information scientists have found that logarothm with base 2 is more appropriate for the formula correlating the probability of occurrence of an event with the amount of information present in a message. According to the little known theory of two worlds, physical universe is bhooloka which is described by modern physical astronomy, and is called Drikpaksha by traditional astronomers of India, such as Kamlakar or Ketakar. The second universe is bhuvaloka in which deities like Surya, Chandra, etc reside. This is nonmaterial world of consciousness, in which material forces like gravitation or mass does not exist and processes take place by means of information theory, in which logarithmic base of 2 is but natural. Hence, forces of planets are in proportions to logarithm with base 2, and not with base 2.71828 as one could expect in the material world. Scientists will laugh at such notions, but once they accept astrology as a true science, they will get interested in these things.
Whatever be the case, we cannot deny the fact that nonmathematical texts of predictive astrology contains proofs of complicated mathematical notions like power of fractional quantities, logarithmic scaling, and base 2 as in modern communication theory. Isn't it surprising?
Use of Sine function in Ayanabala : In the section spashtabalanirnayaadhikaara,Sage Parashara used sine function in computing the ayanabala, for which he starts from three khandakaas (sections) 45, 33, 12, which add up to make 90. He does not elaborate these khandakaas. These are values of sine functions for three equal divisions at intervals of 30 degrees in units of 90. 45 is equal to sine of 30 degrees multiplied with 90. Sine of 60 degrees multiplied with 90 gives 77.9423, or 78 roughly, and if first khandakaa of 45 is substracted then the value of second khandakaa is obtained 78  45 = 33. Similarly, sine of 90 degrees multiplied with 90 is 90, from which if 78 is substracted we are left with value of third khandakaa as 12. Sage Parashara gave an approximate method of computing sine function, which was suitable for the limited purpose in this context. Such instances show he had good idea of mathematical operations. But what is intriguing is that his BPHS is replete with things which defy explanation but prove true astrologically. For instance, the formula for computing ayanabala is different for different planets, for which we have no reason.
Let us return to divisionals. For other divisional charts (shodash vargas), half the above values should be used. In other words, the strengths of planets in a hora or a navamaamsha chart is nearly half of those in the rasichart or basic horoscope. It is only an approximation. For actual computations of strengths in divisional charts, we ought to use vimshopaka as stated by Sage Paraashara, which are different in four sets of divisional charts as shown below.
Planet's condition  Shad varga  Sapta varga  Dash varga  Shodash varga 
1. Rasi (Lagna)  6  5  3  3.5 
9. Navaamsha  5  4.5  1.5  3 
3. Dreskaan  4  3  1.5  1 
7. Saptaamsha  2.5  1.5  0.5  
2. Hora  2  2  1.5  1 
12. Dvaadashaamsha  2  2  1.5  0.5 
4. Chaturthaamsha  0.5  
10. Dashamaamsha  1.5  0.5  
16. Shodashaamsha  1.5  2  
20. Vimshaamsha  0.5  
24. Chaturvimshaamsha  0.5  
27. Saptavimshaamsha  0.5  
30. Trinshaamsha  1  1  1.5  1 
40. Khavedaamsha  0.5  
45. Akshavedaamsha  0.5  
60. Shashtyaamsha  5  4  
TOTAL  20  20  20  20 
A comparison of this table of valorisation with the previous one makes it clear why the Sage Paraashara says strengths of planets in other vargas should be half of those in the Rasichart. This rule is applicable to the D10 set (dashavarga), in which valorization (vimshopakabala) of planets in all vargas are just half of that in the Rasi varga (varga means a divisional chart), shashtyamshavarga is the only exception which has an unexpectedly high value of 5.
Hence, shloka 9 is an approximation based on valorisation of D10 charts (dashavargas) in which values of any other varga is half of that of Rasivarga, shashtyamshavarga being an exception. Shashtyamshavarga is generally neglected by astrologers because it requires a precise determination of birth time as well as a precise method of computation. If Shashtyamshavarga is accurately made, horoscopic differences between twins can be ascertained.
Significance of Shashtyamshavarga
Shashtyamshavarga is accorded highest value among all divisions by Sage Paraashara as shown in the table above. Moreover, Sage Paraashara accords some definite subjects to other vargas, but shashtyamshavarga is important for all (akhilam) subjects. Hence, shashtyamshavarga summarises everything about past karmas of a natal ; and all other vargas, including the Rasichart, are various manifestations of various aspects of shashtyamshavarga.In actual practice, valorisation of planets in divisional charts (vargas) should not be always half of that of Rasivarga, but should be based upon the second table above. Whether one should use shadvarga, saptavarga, dashavarga or shodashvarga depends upon the purpose. For instance, when shadvarga is to be used, valorization of a planet in Rasichakra is 30% of total valorization of that particular planet in all six vargas (6 / 20 = 30%). But when dashavarga is used, valorization of Rasichart decreases to a mere 15% (3 / 20), and is only 17.5% in shodashavarga, while those of shashtyamsha are 25% and 20% respectively.
These valorizations are maximum possible values, applicable when a planet is in the middle of a house. If a planet is near the end of a house (in sandhi) its valorization will get drastically reduced. Precise computation of all vargas, esp. the shashtyamshavarga, is essential for reliable valorization of planets in Vedic astrology.
 By Vinay Jha
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