3.1 Sāmanta’s Plea to Other Astronomers

The concordance between prediction and observation is called dṛk-siddhi in Sanskrit. To achieve this, Sāmanta made extensive revisions to the parameters in his Siddhāntadarpaṇa, drawing upon his own observations, correlations, and empirical cross-verifications. Notwithstanding this, it is quite possible that the proposed revisions may simply be dismissed by the scholarly community as inconsequential or lacking merit. Hence, towards the end of the text, he appeals to the experts in the field not to dismiss his work as mere conjecture or worthless without first subjecting it to verification:⁹

सिद्धान्तानुदिता अपीह गदिता ये ये विशेषा मया

ते हेया नवकल्पना इति मतिर्मा भूत् प्रभूणां क्वचित् |

दृक्सिद्ध्यै किल लल्लभास्करशतानन्दार्यभट्टादिभिः

स्वग्रन्थेषु यदीरिता बहुमता ईदृग्विशेषा नवाः ‖

May all those new features which have been presented here by me, that have not been stated in the [earlier] siddhāntas, be not simply discarded by the authorities in the field (prabhu) as new inventions (navakalpanā) [worthy of consideration] because, after all, features of this kind – newly presented (Ä«rita) and held in high regard (bahumata) – were introduced by Lalla, Bhāskara, Śatānanda, Āryabhaá¹­á¹­a [sic],¹⁰ and others in their own works, for the attainment of dṛk-siddhi [the concordance between computation and observation].

Sāmanta makes this plea primarily because there is a general tendency among established scholars to underestimate the work of newcomers. Even when this is not the case, there often seems to be resistance to adopting new procedures in place of old ones. This is particularly true for almanacs, due to the misconception that siddhāntas and vākyas are inherently correct and require no revision. Sāmanta earnestly urges scholars to reconsider such views. He seeks their endorsement to adopt a new system that meets the criterion of dṛk-siddhi, citing earlier astronomers and the methods they employed. In this context, it may be worthwhile to recall the necessity of periodically revising parameters and procedures in astronomy, as laid down by earlier astronomers.

3.2 Need for Periodic Revision

NÄ«lakaṇṭha (c. 1500 CE) in his Āryabhaá¹­Ä«yabhāṣya, explaining the cause of variance in the values specified in different texts and also highlighting the importance of periodic revision of parameters, observes:¹¹

यत्पुनर्भगणादीनां क्वचित् केषाञ्चिदाचार्यैः नानाप्रतिपादनं तत् परिमाणानां सावयवत्वात्, अवयवानाञ्च आनन्त्यात्, कालदैर्घ्यात्, तदावृत्तौ तदवयवानां तावद्गुणितत्वात् | यद्वर्धमानं स्थौल्यं तदपि तन्मूलप्रमाणैः प्रत्यक्षादिभिरेव निराकार्यम् |

The differences in the revolution numbers provided by certain ācāryas are because these numbers are not [exact] integers (sāvayava, meaning they have fractional parts) and contain lengthy decimal parts (avayava means ‘part’ or ‘fraction’). Over long periods (kāladairghya referring to the extended timescales like the Mahāyuga of 4,320,000 years), these small discrepancies accumulate and multiply. These increasing inaccuracies (sthaulya, referring to compounded errors) must be corrected using reliable measures such as direct observation (pratyakṣa, which includes empirical verification) and other valid methods.

It is well known that planetary motion is not uniform over long timescales. Consequently, the mean rates – expressed through their revolution numbers – undergo minute variations that accumulate over extended periods. “The variation in the revolution numbers, etc., stated” (bhagaṇādīnāṃ nānāpratipādanam) is a natural and inevitable outcome of the revision made by astronomers based on long-term celestial observation. As observational accuracy improved – first by noticing discrepancies through careful naked-eye observations, and later through the systematic correlation of data across generations – astronomers continually refined these parameters to ensure closer agreement with observed phenomena.

Thus, successive ācāryas like Āryabhaṭa, Brahmagupta, Lalla, Bhāskara II, and Parameśvara each proposed and revised revolution counts, reflecting this ongoing process of correction of values based on empirical data and subsequent theoretical recalibration. This progressive refinement of constants underscores the Indian astronomical tradition’s awareness that revision was not a flaw but a scientific necessity. Table 2 below illustrates the differences in planetary revolution numbers as proposed by a few prominent ācāryas, highlighting the spirit of continual correction that Nīlakaṇṭha and Sāmanta allude to.

To emphasize the importance of experimentation and revision of parameters in the discipline of astronomy, Nīlakaṇṭha goes so far as to make the following emphatic declaration:

आर्यभटः परीक्षाप्रकारं तदुपयोगियुक्तिकलापं च प्रदर्शयितुमेव सिद्धान्तं चकार |

Āryabhaṭa composed his siddhānta only to demonstrate the methods of examining [the observational concordance] and the set of principles (yuktikalāpa) that would be useful toward that.

The discussion above, drawing on quotations from both Sāmanta and Nīlakaṇṭha, reflects not only their individual understanding of the dynamic nature of astronomical computations but also the broader tradition’s awareness of the same – as evidenced by the timeline of corrections and developments introduced by earlier astronomers. Āryabhaṭa (born in Kali year 3600 or 499 CE) introduced a system of planetary revolutions devoid of zero-corrections at the epoch of Kali. By zero-corrections, we mean that he did not specify any dhruva-corrections, which refer to the initial positions of the planets at the beginning of the epoch. Dhruva corrections are given by later astronomers. A detailed discussion of dhruva corrections, however, falls beyond the scope of this paper. Over time, observed celestial phenomena began to slightly deviate from the positions obtained by using Āryabhaṭa’s procedures. This prompted a need for revisiting and arriving at a precise system by way of revising parameters and introducing corrections.

4.1 A Unique Feature of the Text

Among the distinctive features of the Siddhāntadarpaṇa, one that stands out is Sāmanta’s extensive use of quotations from other standard works, such as the Siddhāntaśiromaṇi, SÅ«ryasiddhānta, and Brahmasiddhānta. While summarizing the text towards the end, Sāmanta provides a count of the verses he composed himself and those he quoted from other sources.¹²

श्लोका: स्वकॢप्ता इह वेदनागपक्षाक्षिसङ्ख्या अथ भूपपक्षाः |

ग्रन्थान्तरोत्थाः खखबाणपक्षाः सम्भूय भव्याय भवन्तु दक्षाः ‖

Here [in this text], the verses originally composed by me are 2284 in number; and the ones quoted from other works are 216; summing up to a total of 2500 verses. May these skilfully composed verses accomplish the auspicious end for which they were intended.

It may be noted that the numbers mentioned in the above verse use the bhūtasaṅkhyā system, which is employed throughout the text. For those unfamiliar with Indian tradition, deciphering these numbers can sometimes be quite challenging. Nevertheless, the system has its own charm and convenience, especially when composing meter-bound verses. This is why it has been the preferred choice among astronomers.

4.2 Division of the Text

As mentioned earlier, the text Siddhāntadarpaṇa consists of 24 chapters. All chapters, except the 23rd, address various astronomical problems. Chapter 23 is entirely dedicated to informing the reader about the glory of Lord Jagannātha, the author’s most beloved deity. This devotion to Jagannātha is not only evident from this chapter but also from the fact that Sāmanta concludes every chapter with tributes to Lord Jagannātha. The titles of the different chapters, which are related to the topics discussed, are presented in Table 3.

Among all the topics discussed in the text, Chapter 16 (praśnavarṇanam) stands out for its uniqueness and special significance. In this chapter, Sāmanta raises numerous important issues related to conventional assumptions and practices in Indian astronomy through a series of thought-provoking questions. These questions range in complexity, addressing topics such as the size and shape of the Earth, gravitational force, the constancy of planetary velocities, and the dimensions of manda and śīghra epicycles. Many of the revisions presented in his Siddhāntadarpaṇa are also questioned here. Only a detailed study would reveal whether all these questions are addressed later in the text.

4.3 Sāmanta’s Admiration for Bhāskarācārya

As mentioned earlier, Sāmanta frequently quoted verses from the two major works, Siddhāntaśiromaṇi and SÅ«ryasiddhānta. This clearly indicates the significant influence that these texts had on him. Notably, Sāmanta’s admiration for Bhāskarācārya and his work Siddhāntaśiromaṇi is profound. On numerous occasions, Sāmanta explicitly states that he follows Bhāskara’s style and has adopted the procedures he outlined. For instance, at the beginning of the chapter on spherics (golādhyāya), he notes:¹³

सिद्धान्तवाक्योद्धृतवाक्यचक्रसन्दर्भितात्मग्रथिताग्र्यपद्यैः |

गोलं ब्रुवे बालविबोधनाय वाचं पुरस्कृत्य च भास्करीयाम् ‖

By interspersing quotations from [other] Siddhānta texts, and integrating them [into a structural form] with my own reasoned discourse in the form of essential verses, I expound [the science of the] sphere (gola), guided by the words of Bhāskara, for the instruction of beginners (bāla-vibodhanāya).

The phrase ‘guided by the words of Bhāskara’ (bhāskarīyām vācaṃ puraskṛtya) in the verse above clearly indicates the deep veneration Sāmanta holds for Bhāskara’s scholarship. The phrase “siddhānta-vākya” used in the first half of the verse is more generic in nature and hence can also mean other siddhāntas, thereby implying the efforts that have gone in scholarly synthesis. The rest of the verse points to Sāmanta’s personal effort in weaving these ideas into a coherent framework and presenting them accessibly for novices.

Sāmanta’s high regard for Bhāskarācārya is also evident from the homage and tributes he pays to him. In many instances, he explicitly refers to Bhāskara as his preceptor. For example, in the following verse, which appears at the beginning of Golādhyāya, Sāmanta uses the term guru:¹⁴

प्राक्सिद्धान्तचयं प्रमाय नयनानर्हं महार्हाक्षरं

यः सिद्धान्तशिरोमणिं प्रणिगदन्नप्रीणयत् प्राणिनः |

आत्मीयावसरप्रणीतभगणप्रत्यक्षितैः खेचरैः

आस्माकीनमहोपकारकृतिनं वन्दे गुरुं भास्करम् ‖

I offer my salutations to the revered preceptor Bhāskara – who, after thoroughly studying (pramāya)¹⁵ all the siddhāntas composed before his time [which had elements] not verifiable by sight (nayanānarham, or, inconsistent with observation), composed the Siddhāntaśiromaṇi and thereby pleased all living beings (aprīṇayat prāṇinaḥ) – each syllable being of great worth (mahārhāká¹£aram) – and who did us a great favour by making the celestial bodies (khecaraiḥ) perceptible (pratyaká¹£itaiḥ) through planetary revolutions (bhagaṇas) [determined by his own observations and] suited to his era.

This verse is fully suffused with guru-bhakti. Here, Sāmanta not only praises Bhāskara and his work, but also glorifies him as a great benefactor (mahopakārakṛtin) and guru for all times. The phrase ‘aprīṇayat prāṇinaḥ’ essentially means he brought great satisfaction to the practitioners of this science, namely astronomers who make pañcāṅga and, in turn, to all the people, so that they can perform all rituals and observe spiritual and religious practices at the right time. In short, through this verse, Sāmanta portrays Bhāskara not merely as a predecessor but as a luminary who has illumined and benefited society for all time.

5.2 Sāmanta’s Courage and Conviction

Conviction in one’s own work is indispensable for scientific pursuit. The following statement illustrates the depth of conviction that Sāmanta had in his work. Since he had great conviction in the precision of the computations he had achieved, he had built the necessary confidence to challenge the experts:²¹

ग्राह्या दक्षैर्ग्रहणभगणाद्यत्र संलक्ष्य साक्षात् |

Let the scholars accept the work [or discard it] by verifying the [occurrence of] eclipses, the revolution numbers, etc., [that are computed using this text].

This reminds us of the confidence and spirit often found in great scientists. Having accomplished a significant task, Sāmanta takes pride in his work. Such confidence, however, should not be mistaken for arrogance. This is evident from the concluding remarks in the Siddhāntadarpaṇa. In the penultimate verse of this monumental treatise, Sāmanta humbly submits his work to the scholarly community, requests them to scrutinize it and humbly asks that any necessary corrections be made:²²

भीमस्यापि पराजयो युधि भवेद् बुद्धिभ्रमः स्यान्मुनेः

कादाचित्कतयाऽप्यतोऽल्पविदुषामस्मादृशां का कथा |

तस्माद्यद्यदशुद्धमत्र गणितं यद्वा सहार्थं पदम्

तत् सर्वं परिशोधयन्तु कृतिनः कृत्वाऽनुकम्पां मयि ‖

At times, if Bhīma can be defeated in a war and if a sage can have a wandering intellect, what to speak of an ordinary individual like me, of scant learning? Therefore, whatever error there may be found in this work of mine – whether in calculation, or [in the use of] words and [their] meanings – may the learned, out of compassion for me, kindly correct those.

7.1 Graceful Display of śabdālaṅkāra

Sāmanta’s style of composition is marked by grace, precision, and lucidity. His verses flow effortlessly, making even complex astronomical ideas remarkably clear and accessible. Throughout the Siddhāntadarpaṇa, one observes his aesthetic sensibility manifest in alliteration, elegant diction, and vivid figures of speech wherever possible. The invocatory verse that opens the text stands as a fine example of his refined poetic craftsmanship:²⁷

श्रीभूमाधवचक्रचक्र्यवनिभृद्भद्राभिरभ्युज्ज्वलम्

श्रीकण्ठप्रमुखाखिलामरशिखाजुष्टाङ्घ्रिपीठोपलम् |

श्रीनीलाचलमौलिमण्डनमहानीलायमानं महः

श्रीभूमाधरितस्मरं भवतु नः प्रत्यूहहत्युद्यतम् ‖

May that effulgence [i.e, Lord Jagannātha] radiant with Śrīdevī, Bhūdevī, Mādhava, Sudarśana (cakra), Viṣṇu (cakrin), Balabhadra (avanibhṛt, the upholder of the Earth), and Subhadrā, whose foot-pedestal [studded with precious] stones are graced and sought by the diadems of all the gods commencing with Lord Śiva (Śrīkaṇṭha); which shines like a great Indrānīla jewel adorning the crest of the sacred Nīlācala hill – may that divinity, who subdues the lord of love (smara) with the abundance (bhūman) of his wealth (śrī) [of beauty], be ever active in removing all obstacles for us.

The opening compound (śrī–bhū-mādhava–cakra–cakri–avanibhṛt–bhadrābhiḥ abhyujjvalam) is best read as an indirect/implicit description of the ratna–siṃhāsana (also called ratna–vedī), the shrine of the Jagannātha temple at Puri, since all the seven entities listed are supposed to be residing on it. The image is therefore liturgical, not geographic, and the entire stanza functions as a maṅgalācaraṇa evoking the Lord of the antar-vedī, the inner altar where he resides.

One of the beauties of the Sanskrit language is its natural ability to facilitate the poet to construct verses rich in alliteration and with great felicity. The felicity arises due to a variety of factors that include:

1. the availability of vast lexical resources,

2. the power of compounding (samāsa formation) in Sanskrit, and

3. even the systematized phonetic structure (as evident from the varṇamālā).

When readers encounter such alliteration, they often experience a sense of delight, even without fully understanding why. It is a common experience that alliteration entices readers to revisit verses, not necessarily for their meanings, but for their rhythmic charm. We can see that a specific śabdālaṅkāra, called vṛtti-anuprāsa, is at work in the verse above. Vṛtti-anuprāsa is a type of alliteration where a particular consonant or a sequence of them is repeatedly employed within a phrase to create rhythmic resonance. In the first quarter of the verse, one can observe the repetition of “bh” as well as the sequence “ca + k + r”:

श्रीभूमाधवचक्रचक्र्यवनिभृद्भद्राभिरभ्युज्ज्वलम्

It may be noted that “bh” appears five times and the sequence twice. Similarly, the consonants “kh” and “r” are used three and four times, respectively in the second quarter:

श्रीकण्ठप्रमुखाखिलामरशिखाजुष्टाङ्घ्रिपीठोपलम्

Repetition of the sounds “l” and “m” may be noted in the third quarter as well, producing a pleasing euphonic cadence. This use of vṛtti-anuprāsa appears in many verses throughout the Siddhāntadarpaṇa, attesting to Sāmanta’s natural mastery of sound and rhythm. The verse cited above in particular is a beautiful invocation to Lord Jagannātha, where Sāmanta blends devotional fervor with poetic brilliance. The same stylistic device appears again in the second verse as well.

7.2 Seamless Integration of Powerful Messages

We would like to cite one more illustrative example from the first chapter that not only exemplifies Sāmanta’s poetic elegance but also conveys certain other important aspects of jyotiśśāstra:²⁸

श्रेष्ठं सर्वश्रुतानां श्रुतमिति कृतिभिर्ज्योतिषं तत्र सारः

सिद्धान्तस्तत्र गोलस्तदवगतिकृती वर्तते यत्र मर्त्यः |

विद्वत्पूज्यः स देशः सकलकलुषहृद्धर्मशर्माश्रयः स्यात्

यत्रास्ते नैष तस्मिन् पशुचरितपरे पापजापत्प्रतापः ‖

The wise perceive that jyotiṣa is the most excellent among all branches of knowledge (sarvaśrutānām); the essence of jyotiṣa is siddhānta, and gola is the very essence of siddhānta. The place where dwells a man versed in this knowledge becomes revered [even] by the learned. It is a place that is devoid of sins and is also an abode of righteousness and happiness (śarma). But where such a scholar [of jyotiṣa] is absent, such a place will be full of scorching afflictions born of sin, dominated by [those of] animal-like conduct.

A few points brought out here by Sāmanta that are noteworthy are:

1. He extols astronomy (jyotiṣa) as the most excellent among all branches of knowledge (sarvaśrutānām śreṣṭham) of all the Vedas.

2. The siddhānta (mathematical astronomy) is its purest distillation (sāra).

3. The gola section of siddhānta is considered most important among the various topics.²⁹

4. The verse also conveys a moral ideal – that true wisdom flourishes only in a land free from moral corruption. This is a very powerful thought that has been seamlessly integrated.

Here, again, in the second quarter, one finds the consonant “t” appearing ten times, and in the final quarter, the consonants “t” and “p” appear six and seven times respectively – pāpajāpatpratāpaḥ – is particularly aesthetically striking, further exemplifying vṛtti-anuprāsa.

Alongside this, one can also observe cheka-anuprāsa, where a group of two or more consonants is repeated in proximity. For instance, in the first quarter, the pair “ś + r” recurs. Particularly, in the phrase –

श्रेष्ठं सर्वश्रुतानां श्रुतम्

while in the third quarter, the consonant cluster “ka + l” appears in sakalakaluṣahṛt and the group “arma” is repeated in dharmaśarmāśrayaḥ. Such alliterative artistry occurs consistently in Sāmanta’s poetry, wherever the theme and meter allow. The rhythmic alliterations, coupled with the profound philosophical import, exemplify the harmonious fusion of science, poetry, and ethics that characterizes Sāmanta’s genius.

7.3 Skillful Use of Alliteration

We provide a few more examples to demonstrate how Sāmanta has seamlessly incorporated alliterations. The following verse appears as the opening verse in Chapter 17, where Sāmanta addresses some of the questions he posed in the previous chapter:³⁰

सच्छास्त्रगुच्छात् कतिचिद्विशेषान् सच्छात्रपृच्छाछलतः प्रदर्श्य |

तत्सारभूतोत्तरमार्यवाचा यच्छामि वत्सावहितः सकृत् स्याः ‖

Having introduced some salient features from the corpus in the form of noble science [astronomy], I have presented them as though they were queries posed by a good student. I shall now give their condensed/precise answers to those questions in noble [Sanskrit] diction. O son! Take heed for a moment.

It is noteworthy that the cluster “cchā” appears four times, besides the consonant “ch” appearing one more time (in the word chalataḥ) in the first half of the verse. In another instance, we find the long vowel appearing ten times, which is absolutely pleasing:³¹

किमाकारा किमाधारा सा धरा कतिसागरा |

What is the shape of the Earth? Upon what does she rest, and how many oceans does she possess?

Sāmanta’s verses thus reveal a poet who is as much a master of sound as he is of sense. His use of alliteration creates an aural texture that enhances the thematic force of each verse. These devices do not appear as ornamental excesses; rather, they reinforce meaning through musicality. This harmonious interplay of beauty and rigor prepares the ground for understanding another distinctive feature of his writing – his ability to balance precision, clarity, and aesthetic elegance. It is to this synthesis that we now turn.

7.4 Blending Brevity with Clarity

It is often the case that precision and clarity are sacrificed in the pursuit of brevity or bringing in musicality. However, Sāmanta has skilfully navigated this challenge. We provide an example that demonstrates his ability to be concise, precise, and yet clear:³²

भूगोलः सौम्यशुक्रावनितनयसुराचार्यसूर्यात्मजानां

कक्षावृत्तैर्वृतस्यास्फुटदिवसकृतः कक्षया वेष्टितोऽयम् |

मध्ये दूरेऽन्तिके च स्फुटरविभगणर्क्षेशकक्षापरीतः

तिष्ठत्यण्डस्य मध्ये नभसि किल सदाधारशून्यः स्वशक्त्या ‖

The Earth is circumscribed by the deferent circle of the mean Sun, which in turn is circumscribed by the deferent circles of the planets Mercury, Venus, Mars, Jupiter and Saturn. The Earth always stands at the centre of the space by its own strength without any external support, [and is] surrounded by the orbits of the true Sun and the Moon which are far and near respectively.

It is noteworthy that in a single verse, Sāmanta manages to describe the Earth’s situation graphically, integrating it with his ‘heliocentric’ planetary model. This model, which aligns with the one proposed by NÄ«lakaṇṭha³³ and, over a century later, by Tycho Brahe, depicts all five planets – Mercury, Venus, Mars, Jupiter, and Saturn – orbiting the Sun, while the Sun orbits the Earth.