Usually, initiation depends on the bona fide spiritual master, who directs the disciple. If he sees that a disciple has become competent and purified by the process of chanting, he offers the sacred thread to the disciple just so that he will be recognized as one-hundred-percent equal with a brāhmaṇa. This is also confirmed in the Hari-bhakti-vilāsa by Śrī Sanātana Gosvāmī: "As a base metal like bell metal can be changed into gold by a chemical process, any person can similarly be changed into a brāhmaṇa by dīkṣā-vidhāna, the initiation process".
(SRIMAD BHAGAVATAM-------3:33:6--------PURPORT).

The principle that only Indians and Hindus should be brought into the Vaiṣṇava cult is a mistaken idea. There should be propaganda to bring everyone to the Vaiṣṇava cult. The Kṛṣṇa consciousness movement is meant for this purpose. There is no bar to propagating the Kṛṣṇa consciousness movement even among people who are born in caṇḍāla, mleccha or yavana families. Even in India, this point has been enunciated by Śrīla Sanātana Gosvāmī in his book Hari-bhakti-vilāsa, which is smṛti and is the authorized Vedic guide for Vaiṣṇavas in their daily behavior. Sanātana Gosvāmī says that as bell metal can turn to gold when mixed with mercury in a chemical process, so, by the bona fide dīkṣā, or initiation method, anyone can become a Vaiṣṇava. One should take initiation from a bona fide spiritual master coming in the disciplic succession, who is authorized by his predecessor spiritual master. This is called dīkṣā-vidhāna. Lord Kṛṣṇa states in Bhagavad-gītā, vyapāśritya: one should accept a spiritual master. By this process the entire world can be converted to Kṛṣṇa consciousness.
(SRIMAD BHAGAVATAM-------4:8:54--------PURPORT).

Dhruva had a feeling of obligation to his mother, Sunīti. It was Sunīti who had given him the clue which had now enabled him to be personally carried to the Vaikuṇṭha planet by the associates of Lord Viṣṇu. He now remembered her and wanted to take her with him. Actually, Dhruva Mahārāja's mother, Sunīti, was his patha-pradarśaka-guru. Patha-pradarśaka-guru means "the guru, or the spiritual master, who shows the way." Such a guru is sometimes called śikṣā-guru. Although Nārada Muni was his dīkṣā-guru (initiating spiritual master), Sunīti, his mother, was the first who gave him instruction on how to achieve the favor of the Supreme Personality of Godhead. It is the duty of the śikṣā-guru or dīkṣā-guru to instruct the disciple in the right way, and it depends on the disciple to execute the process. According to śāstric injunctions, there is no difference between śikṣā-guru anddīkṣā-guru, and generally the śikṣā-guru later on becomes the dīkṣā-guru. Sunīti, however, being a woman, and specifically his mother, could not become Dhruva Mahārāja's dīkṣā-guru. Still, he was not less obliged to Sunīti. There was no question of carrying Nārada Muni to Vaikuṇṭhaloka, but Dhruva Mahārāja thought of his mother.
(SRIMAD BHAGAVATAM-------4:12:32--------PURPORT).

This incident proves that the śikṣā- or dīkṣā-guru who has a disciple who strongly executes devotional service like Dhruva Mahārāja can be carried by the disciple even though the instructor is not as advanced. Although Sunīti was an instructor to Dhruva Mahārāja, she could not go to the forest because she was a woman, nor could she execute austerities and penances as Dhruva Mahārāja did. Still, Dhruva Mahārāja was able to take his mother with him. Similarly, Prahlāda Mahārāja also delivered his atheistic father, Hiraṇyakaśipu. The conclusion is that a disciple or an offspring who is a very strong devotee can carry with him to Vaikuṇṭhaloka either his father, mother or śikṣā- or dīkṣā-guru. Śrīla Bhaktisiddhānta Sarasvatī Ṭhākura used to say, "If I could perfectly deliver even one soul back home, back to Godhead, I would think my mission—propagating Kṛṣṇa consciousness—to be successful." The Kṛṣṇa consciousness movement is spreading now all over the world, and sometimes I think that even though I am crippled in many ways, if one of my disciples becomes as strong as Dhruva Mahārāja, then he will be able to carry me with him to Vaikuṇṭhaloka.
(SRIMAD BHAGAVATAM-------4:12:33--------PURPORT).

According to the pāñcarātrika system, however, even though everyone is a śūdra due to the absence of the garbhādhāna-saṁskāra, if a person has but a little tendency to become Kṛṣṇa conscious, he should be given the chance to elevate himself to the transcendental platform of devotional service. Our Kṛṣṇa consciousness movement adopts this pāñcarātrika-vidhi, as advised by Śrīla Sanātana Gosvāmī, who says:
yathā kāñcanatāṁ yāti
kāṁsyaṁ rasa-vidhānataḥ
tathā dīkṣā-vidhānena
dvijatvaṁ jāyate nṛṇām
"As bell metal, when mixed with mercury, is transformed to gold, a person, even though not golden pure, can be transformed into a brāhmaṇa, or dvija, simply by the initiation process." (Hari-bhakti-vilāsa 2.12) Thus if one is initiated by a proper person, he can be accepted as twice-born immediately. In our Kṛṣṇa consciousness movement, we therefore offer the student his first initiation and allow him to chant the Hare Kṛṣṇa mahā-mantra.

(SRIMAD BHAGAVATAM-------4:31:10--------PURPORT).

Śrīla Bhaktisiddhānta Sarasvatī Ṭhākura also states that although one is situated as a brāhmaṇa, kṣatriya, vaiśya, śūdra, brahmacārī, vānaprastha, gṛhastha or sannyāsī, if he is conversant in the science of Kṛṣṇa he can become a spiritual master as vartma-pradarśaka-guru, dīkṣā-guru or śikṣā-guru. The spiritual master who first gives information about spiritual life is called the vartma-pradarśaka-guru, the spiritual master who initiates according to the regulations of the śāstras is called the dīkṣā-guru, and the spiritual master who gives instructions for elevation is called the śikṣā-guru. Factually the qualifications of a spiritual master depend on his knowledge of the science of Kṛṣṇa. It does not matter whether he is a brāhmaṇa, kṣatriya, sannyāsī or śūdra. This injunction given by Śrī Caitanya Mahāprabhu is not at all against the injunctions of the śāstras.

(SRI CAITANYA CARITAMRTA------2:8:128-------PURPORT).

Śrīla Jīva Gosvāmī explains dīkṣā in his Bhakti-sandarbha (283):
divyaṁ jñānaṁ yato dadyāt kuryāt pāpasya saṅkṣayam
tasmāt dīkṣeti sā proktā deśikais tattva-kovidaiḥ
"Dīkṣā is the process by which one can awaken his transcendental knowledge and vanquish all reactions caused by sinful activity. A person expert in the study of the revealed scriptures knows this process as dīkṣā." The regulative principles of dīkṣā are explained in the Hari-bhakti-vilāsa (2.3–4) and the Bhakti-sandarbha (283). As stated:

dvijānām anupetānāṁ svakarmādhyayanādiṣu
yathādhikāro nāstīha syāc copanayanād anu
tathātrādīkṣitānāṁ tu mantra-devārcanādiṣu
nādhikāro ‘sty ataḥ kuryād ātmānaṁ śiva-saṁstutam
"Even though born in a brāhmaṇa family, one cannot engage in Vedic rituals without being initiated and having a sacred thread. Although born in a brāhmaṇa family, one becomes a brāhmaṇa only after initiation and the sacred thread ceremony. Unless one is initiated as a brāhmaṇa, one cannot worship the holy name properly."

(SRI CAITANYA CARITAMRTA------2:15:108-------PURPORT).

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