अक्ष-हृदयम्
अथ नलोपाख्याने ऋतुपर्ण-नल-संवादे साङ्ख्य-शास्त्र-सम्मत-संभाव्यता-सिद्धान्तः।
In the Nala episode — in the dialogue between Ṛtuparṇa and Nala — the doctrine of probability (saṃbhāvyatā), set forth in harmony with sāṅkhya teaching.
॥ शारदूलविक्रीडितम् ॥
Verse 1
गण्यन्तेऽत्र न पल्लवानि सकलान्यप्रत्यक्षान्युत।
यद्वच्छास्त्र-विनिश्चितांश-कलनात् सर्वं विजानात्यसौ
तद्वज्ज्ञेय-समुच्चयेऽल्प-कणिका-ज्ञानेन सिद्धिर्भवेत् ॥ १ ॥
Translation:
Behold this great vibhītaka tree, a mass of branches and twigs: here one does not count every leaf, for many are beyond sight. Just as one who applies the śāstra-fixed rule for inferring parts from the whole understands everything, so in the sum of what is to be known, success comes even from grasping a small particle — do not be deluded.
Verse 2
व्यूहेऽस्मिन् गणितागतं हि नियमं पश्यस्व वै नैषध।
एकस्मिन् निमिषे यथात्र गणिताः पर्णाः मया कोटिशः
तथाऽक्ष-हृदयेऽपि संभव-कला ज्ञेया न मोहं व्रज ॥ २ ॥
Translation:
This does not run on fortune alone, nor is it sheer chance; O Naiṣadha, see the law inherent in this array. As in one blink I count leaves here in crores, so too the art of possible outcomes in the heart of dice must be understood — do not wander in confusion.
Verse 3
यादृच्छिक-भ्रमतः पृथक् कुरु सदा संवित्ति-शुद्धां मतिम्।
बहूनां हि फलानां मेलन-वशाद् यन्मध्यमं लभ्यते
तदेव हि सत्यं विद्धि नलं भो मा भ्रान्त्य-कूपे पत ॥ ३ ॥
Translation:
What arises by the kākatālīya maxim is surely false appearance; ever apart from random drift, keep perception clear. What mean arises from combining many outcomes — that alone is truth; know it, O Nala, and do not fall into the well of error.
Verse 4
तथा भीष्म-घटना जगति सततं बुद्धेः परा वर्तते।
मर्यादां प्रविभज्य कोश-निचयं दातव्य-मल्पं बुधैः
यथा लभ्यते लाभ-राशि-रधिको नाशं विना सर्वथा ॥ ४ ॥
Translation:
As the black swan rises unforeseen when delusion ends, so dread events in the world ever operate beyond (mere) wit. The wise apportion limits and stake a small share of their store, so gain may exceed the stake without ruin in every way.
॥ उपजातिः ॥
Verse 5
न तत्र शङ्का न च चापलं हि।
संभाव्यतायाः परमं रहस्यं
ज्ञात्वा जयस्व क्षणभङ्गुराक्षान् ॥ ५ ॥
Translation:
As fate’s own ordinance is fixed — there is neither doubt nor fickleness. Knowing the highest secret of probability, master the dice that last but a moment.
Verse 6
ते भाग्य-वन्तो न तु सत्य-वन्तः।
यः काल-तत्त्वं कलयेत् सुधीमान्
स एव मर्त्येषु भवेत् कुबेरः ॥ ६ ॥
Translation:
Those praised in endless worlds are lucky, not truthful. He who measures the nature of time — he alone among mortals becomes Kubera.
Verse 7
कोशस्य वृद्धौ निपुणः प्रदिष्टः।
तथैव धर्मेऽपि च संपदश्च
मर्याद-रक्षण-विधेः फलन्ति ॥ ७ ॥
Translation:
Just as the rule of play is taught as weighty and skilled for growing one’s purse, so in dharma and in wealth the precepts of guarding bounds bear fruit.
॥ अनुष्टुप् ॥
Verse 8
एकं वैयक्तिकं विद्धि सर्व-लोक-गतं परम् ॥ ८ ॥
Translation:
The probable is taught as twofold, by distinction of heaps in time: know one as individual, the other as spread through all the world.
Verse 9
ऋतं चानृत-मिश्रं हि जगदेतच्चराचरम् ॥ ९ ॥
Translation:
Whoever fails to know this distinction stumbles at every step; for this world, moving and still, mingles truth and untruth.
Verse 10
ततः परं प्रवक्ष्यामि कृष्ण-हंस-विनाशनम् ॥ १० ॥
Translation:
See the counting of vibhītaka leaves as it truly is; then I shall speak of the fall of the black swan (the illusion of the unseen).
Verse 11
यत्र मोहः क्षयं याति सिद्धिर्भवति शाश्वती ॥ ११ ॥
Translation:
Knowledge of the heart of dice is reckoned the highest reckoning; where delusion wanes, success endures.
॥ शारदूलविक्रीडितम् ॥
Verse 12
यश्चाकस्मिक-दुर्विपाक-समये धीरो न कम्पेत वै।
तस्यैव हि संविदो विजयिनी सिद्धा सदा वर्तते
तस्मै गणितात्मने नृपतये तुभ्यं ददाम्येतद ॥ १२ ॥
Translation:
He who treats measured exit from play as equal in gain and loss, and in sudden ill outcome stands firm — for him alone winning awareness ever holds; to you, king of mathematical soul, I give this.
Verse 13
यथा पिङ्गल-सूत्रितेन विहितं छन्दो-विचित्त्यां पुरा।
शून्यं चैव तथा स्वरूप-कथनं द्वैतं च संमिश्रितं
तथा विश्वमिदं विभाति सकलं संभाव्यता-मण्डले ॥ १३ ॥
Translation:
By sāṅkhya’s expansion, divide into rows as Piṅgala once fixed for metre — void, twofold nature, duality mixed: so the whole world appears in the round of probability.
Verse 14
यो लक्षाधिपतिः क्वचित् क्वचन वा भिक्षुः पथि दृश्यते।
तस्यैतज्जननं न कर्म-कुशलं नैवापि वीर्यं खलु
केवल-यादृच्छिक-प्रवहणे कश्चित् समुत्तीर्यते ॥ १४ ॥
Translation:
Across myriad worlds, now a dentist is seen as lord of lakhs, now a beggar on the road — birth is not from deed-skill nor mere prowess; one is lifted only in the stream of chance.
Verse 15
केली-नियम-स्थितो भव सदा कोशांश-रक्षणे।
विभीतक-तरुः साक्षो गणित-पथ-प्रदर्शकः
अक्ष-हृदय-प्रदानेन कलि-बाधां व्यपोहय ॥ १५ ॥
Translation:
So never burn your all, O king, in ruin’s fire; stay within play’s rule, guarding a share of wealth. The vibhītaka is witness, pointing the path of reckoning; by this heart-of-dice teaching, cast off Kali’s trouble.
॥ अनुष्टुप् ॥
Verse 16
संभाव्यता-प्रवाहेऽस्मिन् ज्ञानं नौका-समं स्मृतम् ॥ १६ ॥
Translation:
In the void, things dissolve into voidness; in the real, truth stands firm. In this stream of probability, knowledge is likened to a boat.
Verse 17
केवल-प्रज्ञा-बलेन तु परिधिं निश्चिनोति वै ॥ १७ ॥
Translation:
No one knows the future as such; yet by intelligence alone one draws the boundary (of what can be said).
Verse 18
विभीतक-तरुं पश्य गणना-कौशलं कुरु ॥ १८ ॥
Translation:
Thus the hidden summit of reckoning is told. Gaze at the vibhītaka tree; train skill in counting.
॥ शारदूलविक्रीडितम् ॥
Verse 19
तथा ज्ञान-गभस्तिभिः कुरु रदं मोहस्य नाशं नृप।
अक्ष-क्रीडा-कलेय-मस्त-समये तर्केण शुद्धा सती
तव राज्यं तव कीर्ति-मव्यय-पदां दास्यत्यसंशयं खलु ॥ १९ ॥
Translation:
As dawn’s sun scatters night, O Nala, so with knowledge’s rays shatter delusion, O king. When dice and the mingled cup run high, clear reason will — without doubt — yield realm and fame that does not fade.
Verse 20
तावद् विश्व-विभूति-तुलन-विधिः प्रज्ञा-वतां गोचरः।
नलोऽपि ह्यभिवाद्य तं नृपवरं संप्राप्य विद्यां पराम्
तत्याज कलि-संभवं भ्रम-महो जातो गणित-कोविदः ॥ २० ॥
Translation:
While the śāstra-taught mesh of counting leaf-masses is seen, so long the wise may compare worldly fortune. Nala too, bowing to that best of kings, gained supreme learning, shed Kali-born delusion, and became adept in reckoning.
॥ अनुष्टुप् ॥
Verse 21
यत्र मुह्यन्ति विद्वांसो गणितागम-पारगाः ॥ २१ ॥
Translation:
Hear, king: I give an example of how time’s repetition divides cases — where even experts in reckoning lose their way.
Verse 22
षण्णवत्यास्तु साफल्यं समूहे तत्र दृश्यते ॥ २२ ॥
Translation:
Among a hundred separate casts (each player once), ninety-six successes appear in that whole cohort — the ensemble looks favorable even when individuals lose.
Verse 23
तस्य नाशः सुनिश्चितो काल-चक्र-प्रवर्तनात् ॥ २३ ॥
Translation:
But if one man here casts a hundred times, his ruin is sure — from time’s wheel turning.
Verse 24
एतद्विज्ञान-हीनो यः स वै द्यूते प्रणश्यति ॥ २४ ॥
Translation:
Ensemble reckoning differs from reckoning by the count of trials in time’s flow; whoever lacks this knowledge perishes at dice.
Verse 25
अक्ष-हृदय-तत्त्वज्ञो न कदाचिद् विपद्यते ॥ २५ ॥
Translation:
Reflecting on what must be for all beings, one who knows the heart of dice never comes to grief.
॥ उपजातिः ॥
Verse 26
मा सर्व-स्वं दाव-पदे निधेहि।
यथाऽनुपातेन विवर्धते श्रीः
तथैव खेदः क्षय-काल-जातः ॥ २६ ॥
Translation:
If you want your purse to grow, do not stake everything on ruin’s ground; as splendor swells by proportion, so sorrow swells from the season of loss.
Verse 27
स्व-मूल-धनेन समं प्रकुर्यात्।
यथा लघुर्घात-पथेन संख्या
वर्धेत तद्वत् कुरु भाग-धेयम् ॥ २७ ॥
Translation:
Split the gain-fraction, steady soul, and match stake to principal; as numbers grow by least steps, so apportion your shares.
Verse 28
जीवेद् यदा तर्हि फलं प्रलप्स्ये।
तस्माद् विरक्षेदति-सावधानः
स्व-मूल-कोशं व्यसनैर्विहीनः ॥ २८ ॥
Translation:
Ever shy of the ruin-point, while you live you will harvest fruit; so the vigilant guard core wealth, free of calamity.
Verse 29
उपदेशं ददाति प्रगल्भ-वाचा।
तस्योपदेशो न हि सत्य-मूलः
इति प्रविद्धि गणितस्य नीतिम् ॥ २९ ॥
Translation:
Who teaches without staking his own hide — his counsel is not truth-rooted; know this as reckoning’s ethic.
Verse 30
स्व-रक्त-मांसेन न तं शृणु त्वम्।
कदापि न स्यात् फल-भागिताऽस्य
विना विपत्त्या निज-प्राण-संस्थे ॥ ३० ॥
Translation:
Who plays house yet pays no forfeit of flesh and blood — heed him not; without disaster touching his own life-stake, he never truly shares the fruit.
॥ वसन्ततिलका ॥
Verse 31
कश्चिज्जनो विभव-शिखरं प्रयाति।
सामर्थ्य-हीन-मतिरपि च भाग्य-योगात्
तं प्राज्ञ-वर्ग-सहितं मनुते जनौघः ॥ ३१ ॥
Translation:
On chance’s open stage, someone reaches fortune’s peak; though weak in judgment, the crowd, by luck’s bond, counts him among the wise.
Verse 32
यत् साफल्यं स्व-कृत-कर्म-फलं ब्रवीति।
हानेस्तु दोष-मखिलं विधि-शासनाय
दत्त्वा स्वयं निरपराध-पदे स्थितः स्यात् ॥ ३२ ॥
Translation:
This is human nature’s folly — calling success the fruit of one’s own act, while charging every loss to fate, and standing blameless oneself.
Verse 33
तस्मिन्न् अतीव-विपुलो हि विनाश-योगः।
तस्मात् प्रमाण-पथ-वर्जित-दृश्य-जाते
मा संकुरुष्व गणितं गत-काल-मानैः ॥ ३३ ॥
Translation:
Where the black swan’s fall was never seen before, ruin’s odds are vast; so do not reckon by past clocks on sights that leave evidence’s road.
Verse 34
तत्रापि शून्य-निपतस्तु सदा प्रसुप्तः।
यो जाग्रति स्व-धन-रक्षण-बुद्धि-युक्तः
स एव पार-मुपयाति भवाम्बु-राशेः ॥ ३४ ॥
Translation:
Even in long-tail spread, the null fall ever sleeps; whoever wakes guarding wealth — he alone reaches the far shore of becoming’s sea.
Verse 35
गच्छस्व राज्य-विभवं पुनरेव भोक्तुम्।
नैवास्ति तत्र कलिरुग्र-विनाश-कारी
यत्रास्ति साङ्ख्य-नियमेन जिता च बुद्धिः ॥ ३५ ॥
Translation:
Knowing thus the heart of dice, O Nala, quit sorrow; return to enjoy your realm. Fierce ruinous Kali is not there where intellect bows to sāṅkhya’s rule.
॥ अनुष्टुप् ॥
Verse 36
ददौ विद्यां तदा तस्मै अक्ष-हृदय-संज्ञिताम् ॥ ३६ ॥
Translation:
So spoke Ṛtuparṇa and gave Nala, true in valor, the science named heart of dice.
Verse 37
गणितस्य प्रतापेन द्यूत-मोहं व्यपोहत ॥ ३७ ॥
Translation:
Receiving it, King Nala, freed of Kali’s taint, by reckoning’s power cast off dice-delusion.
Verse 38
संभाव्यता-परिज्ञानात् सर्वं करतली-कृतम् ॥ ३८ ॥
Translation:
Knowledge is the highest eye, knowledge the highest strength; by full grasp of probability, all is held in the palm.
Verse 39
गणित-तत्त्व-संयुक्तं स जयेत् सर्व-संकटान् ॥ ३९ ॥
Translation:
Whoever hears daily this dialogue of the two kings, rich in mathematical truth — overcomes every strait.
Verse 40
अक्ष-विद्यां समाश्रित्य जहि शत्रून् स्व-कर्मणा ॥ ४० ॥
Translation:
Thus, best of kings, I have told sāṅkhya’s secret; by dice-science strike foes through your own deed.
॥ शार्दूलविक्रीडितम् ॥
Verse 41
तस्यैवापि हि मापनं गणित-गैः संचिन्त्यते सर्वदा।
यावत् सत्य-मिदं भवेत् तदधिकं शून्यत्व-माया-वृतं
सूचना-प्रभवं हि तत्त्व-मखिलं ज्ञानस्य बीजं स्मृतम् ॥ ४१ ॥
Translation:
When doubt rises in mind from endless things, reckoning minds still measure it. Truth has its bound; beyond lies void veiled as illusion — all indicated being is knowledge’s seed.
Verse 42
सैवाद्य प्रकृतौ समस्त-कलन-प्राण-स्वरूपा स्थिता।
एकं चैव च शून्य-मक्षर-युगं सर्वस्व-निर्माण-कृत्
तस्माद् द्यूत-विधिक्रमोऽपि तदन्तर्गतः संस्थितः ॥ ४२ ॥
Translation:
The dual alternative-web the Pingalas showed — that same form is nature’s breath in all calculus; one, void, and the letter-pair build the whole; so gaming’s order dwells within it too.
॥ अनुष्टुप् ॥
Verse 43
अदृश्योऽपि स विदुषां प्रत्यक्षी-भवति क्षणात् ॥ ४३ ॥
Translation:
In this random stream a firm law runs; though unseen, to the learned it flashes clear in an instant.
Verse 44
विद्ययाऽनया सु-सम्पन्नः कुरु राज्यं अकण्टकम् ॥ ४४ ॥
Translation:
Therefore rise, king; drop vain grief; armed with this learning, rule without thorn.
Verse 45
न हि तस्य बलं किञ्चित् संभाव्यता-विदोऽग्रतः ॥ ४५ ॥
Translation:
Strike Puṣkara in war, skilled at dice; before one who knows probability his strength is nothing.
Verse 46
न तं कलिः प्रबाधेत न च द्यूत-पराजयः ॥ ४६ ॥
Translation:
Who holds this dice-thread inwardly — neither Kali harms him nor gambling’s defeat.
Verse 47
मननेन निदिध्यासात् साक्षात्-कुरु नराधिप ॥ ४७ ॥
Translation:
This whole essence I have sung; by thought and steady meditation realize it, lord of men.
Verse 48
तदेव तव जीवस्य मूलाधारं भविष्यति ॥ ४८ ॥
Translation:
The knowledge won beneath the vibhītaka — that will be your life’s foundation.
Verse 49
नमः प्रज्ञा-स्वरूपाय संभाव्यता-विदे नमः ॥ ४९ ॥
Translation:
Homage to reckoning wherein the world rests; homage to wisdom’s form, to knowing probability.
Verse 50
कुरुष्व यन्मनो-भीष्टं अक्ष-विद्या-बलाश्रितः ॥ ५० ॥
Translation:
Thus the highest secret is told; do as your heart wills, upheld by dice-science’s strength.