The following is an excerpt from Chapter 45 of Kṛṣṇa Book, in which Srila Prabhupada describes that after hearing only once from the teacher, Sandipani Muni, Kṛṣṇa and Balarāma learned all the arts and sciences.
…So Kṛṣṇa and Balarāma, the Supreme Personality of Godhead, are the source of all kinds of knowledge, but because They were playing like ordinary human boys, They set the example so that everyone would receive knowledge from the right source. Thus They agreed to take knowledge from a spiritual master.
After hearing only once from the teacher, Kṛṣṇa and Balarāma learned all the arts and sciences. In sixty-four days and sixty-four nights They learned all the necessary arts that are required in human society. During daytime They took lessons on a subject from the teacher, and by nightfall, after having heard from the teacher, They were expert in that department of knowledge.
Excerpt from; Kṛṣṇa, the Supreme Personality of Godhead
By His Divine Grace A. C. Bhaktivedanta Swami Prabhupāda
Chapter Forty-five
Kṛṣṇa Recovers the Son of His Teacher
…According to Vedic culture, every respectable person has an ācārya, or spiritual master. One is not considered to be a perfectly cultured man without being initiated and trained by an ācārya. It is said, therefore, that one who has approached an ācārya is actually in perfect knowledge. Lord Kṛṣṇa and Balarāma were the Supreme Personality of Godhead, the master of all education and knowledge. There was no need for Them to accept a spiritual master or ācārya, yet for the instruction of ordinary men, They also accepted a spiritual master for advancement in spiritual knowledge.
It is customary, after being initiated in the Gāyatrī mantra, for one to live away from home for some time under the care of the ācārya in order to be trained in spiritual life. During this period one has to work under the spiritual master as an ordinary menial servant. There are many rules and regulations for a brahmacārī living under the care of an ācārya, and both Lord Kṛṣṇa and Balarāma strictly followed those regulative principles while living under the instruction of their spiritual master, Sāndīpani Muni, in his place in northern India. According to scriptural injunctions, a spiritual master should be respected and be regarded on an equal level with the Supreme Personality of Godhead. Both Kṛṣṇa and Balarāma exactly followed those principles with great devotion and underwent the regulations of brahmacarya, and thus They satisfied Their spiritual master, who instructed Them in Vedic knowledge. Being very satisfied, Sāndīpani Muni instructed Them in all the intricacies of Vedic wisdom as well as in supplementary literatures such as the Upaniṣads. Because Kṛṣṇa and Balarāma happened to be kṣatriyas, They were specifically trained in military science, politics and mathematics. In politics there are six departments of knowledge–how to make peace, how to fight, how to pacify, how to divide and rule, how to give shelter, etc. All these items were fully explained and instructed to Kṛṣṇa and Balarāma.
The ocean is the source of water in a river. The cloud is created by the evaporation of ocean water, and the same water is distributed as rain all over the surface of the earth and then returns toward the ocean in rivers. So Kṛṣṇa and Balarāma, the Supreme Personality of Godhead, are the source of all kinds of knowledge, but because They were playing like ordinary human boys, They set the example so that everyone would receive knowledge from the right source. Thus They agreed to take knowledge from a spiritual master.
After hearing only once from the teacher, Kṛṣṇa and Balarāma learned all the arts and sciences. In sixty-four days and sixty-four nights They learned all the necessary arts and sciences that are required in human society. During daytime They took lessons on a subject from the teacher, and by nightfall, after having heard from the teacher, They were expert in that department of knowledge.
First of all They learned how to sing, how to compose songs and how to recognize the different tunes; They learned the favorable and unfavorable accents and meters, how to sing different kinds of rhythms and melodies, and how to follow them by beating different kinds of drums. They learned how to dance with rhythm, melody and different songs. They learned how to write dramas, and They learned the various types of paintings, beginning from different village arts up to the highest perfectional stage. They also learned how to paint tilaka on the face and make different kinds of dots on the forehead and cheeks. Then They learned the art of painting on the floor with liquid paste of rice and flour; such paintings are very popular at auspicious ceremonies performed at household affairs or in the temple. They learned how to make a resting place with flowers and how to decorate clothing and leaves with colorful paintings. They also learned how to set different valuable jewels in ornaments. They learned the art of ringing waterpots. Waterpots are filled with water to a certain measurement so that when one beats on the pots, different tunes are produced, and when the pots are beaten together they produce a melodious sound. They also learned how to throw water in the rivers or the lakes while taking a bath among friends. They also learned how to decorate with flowers. This art of decorating can still be seen in various temples of Vṛndāvana during the summer season. It is called phulabāḍi. The dais, the throne, the walls and the ceiling are all fully decorated, and a small, aromatic fountain of flowers is fixed in the center. Because of these floral decorations, the people, fatigued from the heat of the summer season, become refreshed.
Kṛṣṇa and Balarāma learned the art of dressing hair in various styles and fixing a helmet in different positions on the head. They also learned how to perform on a theatrical stage, how to decorate dramatic actors with flower ornaments over the ear, and how to sprinkle sandalwood pulp and water to produce a nice fragrance. They also learned the art of performing magical feats. Within the magical field there is an art called bahurūpī by which a person dresses himself in such a way that when he approaches a friend he cannot be recognized. They also learned how to make beverages which are required at various times, and they studied syrups and tastes and the effects of intoxication. They learned how to manipulate thin threads for dancing puppets, and They learned how to string wires on musical instruments, such as the vīṇā, sitar and tampura, to produce melodious sound. Then They learned puzzles and how to set and solve them. They learned the art of reading books from which even a foolish student can very quickly learn to read the alphabet and comprehend writing. Then They learned how to rehearse and act out a drama. They also studied the art of solving crossword puzzles, filling up the missing space and making complete words.
They also learned how to draw pictographic literature. In some countries in the world, pictographic literature is still current. A story is represented by pictures; for instance, a man and a house are pictured to represent a man going home. Kṛṣṇa and Balarāma also learned the art of architecture–how to construct residential buildings. They learned to recognize valuable jewels by studying the luster and the quality of their colors. Then They learned the art of setting jewels with gold and silver. They also learned how to study soil to find minerals. This study of soil is now a greatly specialized science, but formerly it was common knowledge even for the ordinary man. They learned to study herbs and plants and to extract medicine from the elements. By studying the different species of plants, They learned how to crossbreed plants and get different types of fruits. They learned how to train and engage lambs and cocks in fighting for sporting purposes. They then learned how to teach parrots to speak and answer the questions of human beings.
They learned practical psychology–how to influence another’s mind and thus induce another to act according to one’s own desire. Sometimes this is called hypnotism. They learned how to wash hair, dye it in different colors and curl it in different ways. They learned the art of telling what is written in someone’s book without actually seeing it. They learned to tell what is contained in another’s fist. Sometimes children imitate this art, although not very accurately. One child keeps something within his fist and asks his friend, “Can you tell what is within?” and the friend gives some suggestion, although He actually cannot tell. But there is an art by which one can understand and actually tell what is held within the fist.
Kṛṣṇa and Balarāma learned how to speak and understand the languages of various countries. They learned not only the languages of human beings. Kṛṣṇa could also speak even with animals and birds. Evidence of this is found in Vaiṣṇava literature compiled by the Gosvāmīs. Then They learned how to make carriages and airplanes from flowers. It is said in the Ramāyāṇa that after defeating Rāvaṇa, Rāmacandra was carried from Laṅkā to Bhāratavarṣa on a plane of flowers called puṣpa-ratha. Kṛṣṇa then learned the art of foretelling events by seeing signs. In a book called Khanār vacana, the various types of signs and omens are described. If, when one is going out, one sees someone with a bucket full of water, that is a very good sign. But if one sees someone with an empty bucket, it is not a very good sign. Similarly, if one sees cow’s milk along with a calf, it is a good sign. The result of understanding these signs is that one can foretell events, and Kṛṣṇa learned the science. Kṛṣṇa also learned the art of composing mātṛkā. A mātṛkā is a crossword section with three letters in a line; counting any three from any side, it will count nine. The mātṛkās are of different kinds and are for different purposes.
Kṛṣṇa learned the art of cutting valuable stones such as diamonds, and He learned the art of questioning and answering by immediately composing poetry within His mind. He learned the science of the action and reaction of physical combinations and permutations. He learned the art of a psychiatrist, who can understand the psychic movements of another person. He learned how to satisfy one’s desires. Desires are very difficult to fulfill; but if one desires something which is unreasonable and can never be fulfilled, the desire can be subdued and satisfied, and that is an art. By this art one can also subdue sex impulses when they are aroused, as they are even in brahmacārī life. By this art one can make even an enemy his friend or transfer the direct action of a physical element to other things.
Lord Kṛṣṇa and Balarāma, the reservoir of all knowledge of arts and sciences, exhibited Their perfect understanding when They offered to serve Their teacher by awarding him anything he desired. This offering by the student to the teacher or spiritual master is called guru-dakṣiṇā. It is essential that a student satisfy the teacher in return for any learning received, either material or spiritual….
The Hare Krishna Movement 